Topic: New Generalized Keyboard

1 scales

Thread (56 messages)

From: Bill Sethares (2005-12-31)
Subject: New Generalized Keyboard

I'm not sure if it's been discussed here - but there
is a new hexagonal keyboard that looks very promising... it's called
the "Thummer." Here is the website:

http://www.thummer.com/

You can see it's bright red, has a split keyboard (one for
each hand) with about 70 hex keys under each hand, as well
as assorted controllers (I guess the little knobby joystick 
forf the thumb is where it gets its name).

There's a video of it in operation 

http://www.thummer.com/demo.asp

and, while the demos are all in 12-tet, the keyboard is 
not restricted to this -- in fact, it is connected (through
a USB cable) to a computer which either generates the sounds or
relays the signals to an external synth. 

Amazingly, they say it will cost about $500 Australian
(which is about $360 US) and should be available 
"in the second half of 2006."

This is looking to be an exciting year for 
alternative controllers!

--Bill Sethares

From: Herman Miller (2006-01-01)
Subject: Re: [tuning] New Generalized Keyboard

Bill Sethares wrote:
> I'm not sure if it's been discussed here - but there
> is a new hexagonal keyboard that looks very promising... it's called
> the "Thummer." Here is the website:
> 
> http://www.thummer.com/
> 
> You can see it's bright red, has a split keyboard (one for
> each hand) with about 70 hex keys under each hand, as well
> as assorted controllers (I guess the little knobby joystick 
> forf the thumb is where it gets its name).

Interesting. It looks like it's ideal for 19-note meantone scales, but 
could also be adapted for other kinds of scale structures. Sort of like 
an extended concertina keyboard.

...Gb..Ab..Bb..C...D...E...F#..G#..A#...
.Cb..Db..Eb..F...G...A...B...C#..D#..E#.
...Gb..Ab..Bb..C...D...E...F#..G#..A#...
.Cb..Db..Eb..F...G...A...B...C#..D#..E#.
...Gb..Ab..Bb..C...D...E...F#..G#..A#...
.Cb..Db..Eb..F...G...A...B...C#..D#..E#.

One way to implement lemba temperament on this keyboard might be like 
this (where the horizontal axis represents a series of notes separated 
by a lemba generator, around 5 steps of 26-ET, and the note "O" 
represents the G#/Ab halfway between the two D's):

...N#..P...J...D...T...N...Pb..Jb..Db...
.I#..R#..L...U...O...I...R...Lb..Ub..Ob.
...T#..N#..P...J...D...T...N...Pb..Jb...
.O#..I#..R#..L...U...O...I...R...Lb..Ub.
...D#..T#..N#..P...J...D...T...N...Pb...
.U#..O#..I#..R#..L...U...O...I...R...Lb.

But it might make more sense to run the lemba generators diagonally 
downward to the left and line up the half-octave periods vertically, 
which would allow for all 26 notes of lemba[26] (and then some):

...Pbb.Ib..Jb..R...D...L...T#..U#..Nx...
.Jbb.Rb..Db..Lb..T...U...N#..O#..P#..Ix.
...Lbb.Tb..Ub..N...O...P...I#..J#..Rx...
.Ubb.Nb..Ob..Pb..I...J...R#..D#..L#..Tx.
...Pbb.Ib..Jb..R...D...L...T#..U#..Nx...
.Jbb.Rb..Db..Lb..T...U...N#..O#..P#..Ix.

This looks nice; the basic lemba[10] scale is right in the middle of the 
keyboard, with "sharps" and "flats" on each side. Here's how that would 
work out in 26-ET:

...14..17..20..23...0...3...6...9..12...
.19..22..25...2...5...8..11..14..17..20.
....1...4...7..10..13..16..19..22..25...
..6...9..12..15..18..21..24...1...4...7.
...14..17..20..23...0...3...6...9..12...
.19..22..25...2...5...8..11..14..17..20.

It could be tricky to finger more than 2 notes at once on the same hand, 
though. A meantone 7-limit tetrad would end up like this:

.C.......E...........A#.
...G....................

which might be okay if you can use the same finger on C and G... The 
corresponding tetrads on the lemba key arrangements would look like this:

...D...........Pb.
.U................
...J..............

or

.......D...
.........U.
...........
.Pb......J.

These look a little tricky, but it's hard to say without trying it out 
on the actual keyboard. Still, being able to play anything at all on a 
keyboard like this might end up being better than trying to learn a 
bunch of arbitrary patterns on a standard keyboard.

From: pkroser@netzero.net (2006-01-02)
Subject: Re: [tuning] New Generalized Keyboard

Herman,

You might have explained this somewhere else, but could you go over the (to me) unfamiliar letter assignments you're using for Lemba below?

Regards,
Paul
-------
"Dreaming permits each and every one of us to be quietly and safely insane every night of our lives."    -Charles Fisher

---------------------------------
Date: Sun, 01 Jan 2006 13:10:54 -0600
From: Herman Miller <hmiller@IO.COM>
Subject: Re: New Generalized Keyboard

Bill Sethares wrote:
> I'm not sure if it's been discussed here - but there
> is a new hexagonal keyboard that looks very promising... it's called
> the "Thummer." Here is the website:
> 
> http://www.thummer.com/
> 
> You can see it's bright red, has a split keyboard (one for
> each hand) with about 70 hex keys under each hand, as well
> as assorted controllers (I guess the little knobby joystick 
> forf the thumb is where it gets its name).

Interesting. It looks like it's ideal for 19-note meantone scales, but 
could also be adapted for other kinds of scale structures. Sort of like 
an extended concertina keyboard.

...Gb..Ab..Bb..C...D...E...F#..G#..A#...
.Cb..Db..Eb..F...G...A...B...C#..D#..E#.
...Gb..Ab..Bb..C...D...E...F#..G#..A#...
.Cb..Db..Eb..F...G...A...B...C#..D#..E#.
...Gb..Ab..Bb..C...D...E...F#..G#..A#...
.Cb..Db..Eb..F...G...A...B...C#..D#..E#.

One way to implement lemba temperament on this keyboard might be like 
this (where the horizontal axis represents a series of notes separated 
by a lemba generator, around 5 steps of 26-ET, and the note "O" 
represents the G#/Ab halfway between the two D's):

...N#..P...J...D...T...N...Pb..Jb..Db...
.I#..R#..L...U...O...I...R...Lb..Ub..Ob.
...T#..N#..P...J...D...T...N...Pb..Jb...
.O#..I#..R#..L...U...O...I...R...Lb..Ub.
...D#..T#..N#..P...J...D...T...N...Pb...
.U#..O#..I#..R#..L...U...O...I...R...Lb.

But it might make more sense to run the lemba generators diagonally 
downward to the left and line up the half-octave periods vertically, 
which would allow for all 26 notes of lemba[26] (and then some):

...Pbb.Ib..Jb..R...D...L...T#..U#..Nx...
.Jbb.Rb..Db..Lb..T...U...N#..O#..P#..Ix.
...Lbb.Tb..Ub..N...O...P...I#..J#..Rx...
.Ubb.Nb..Ob..Pb..I...J...R#..D#..L#..Tx.
...Pbb.Ib..Jb..R...D...L...T#..U#..Nx...
.Jbb.Rb..Db..Lb..T...U...N#..O#..P#..Ix.

This looks nice; the basic lemba[10] scale is right in the middle of the 
keyboard, with "sharps" and "flats" on each side. Here's how that would 
work out in 26-ET:

...14..17..20..23...0...3...6...9..12...
.19..22..25...2...5...8..11..14..17..20.
....1...4...7..10..13..16..19..22..25...
..6...9..12..15..18..21..24...1...4...7.
...14..17..20..23...0...3...6...9..12...
.19..22..25...2...5...8..11..14..17..20.

It could be tricky to finger more than 2 notes at once on the same hand, 
though. A meantone 7-limit tetrad would end up like this:

.C.......E...........A#.
...G....................

which might be okay if you can use the same finger on C and G... The 
corresponding tetrads on the lemba key arrangements would look like this:

...D...........Pb.
.U................
...J..............

or

.......D...
.........U.
...........
.Pb......J.

These look a little tricky, but it's hard to say without trying it out 
on the actual keyboard. Still, being able to play anything at all on a 
keyboard like this might end up being better than trying to learn a 
bunch of arbitrary patterns on a standard keyboard.

From: Herman Miller (2006-01-02)
Subject: Re: [tuning] New Generalized Keyboard

pkroser@netzero.net wrote:
> Herman,
> 
> You might have explained this somewhere else, but could you go over the (to me) unfamiliar letter assignments you're using for Lemba below?
> 
> Regards,
> Paul

The generator of lemba temperament divides the fifth into three equal 
parts. One step above D is a note slightly sharper than E, which could 
be labeled "E^"; the next step could be labeled "Gv", then "A". I find 
it useful to have a single letter to represent these notes, so for the 
"slightly flatter" notes I use the letters H to N, the letter "O" for 
the note a half octave between the D's (the G# or Ab on a 12-note 
keyboard), and the letters P to V for the "slightly sharper" notes.

|---P---Q-R---S---T-U---V-|
|O-A---B-C---D---E-F---G-O|
|-H---I-J---K---L-M---N---|

Since lemba temperament has 6-note and 10-note basic scales (that is, DE 
or distributionally even scales, ones with only two different sizes of 
steps), I could have used 6 letters to notate lemba, but since I'd like 
to be able to easily notate all 26 notes of lemba[26], I decided to go 
with the 10-note basic scale, centered around D. Two generators above 
and below D are notated P-J-D-T-N, and around the half-octave O (G#/Ab) 
it ends up as L-U-O-I-R.

From: harold_fortuin (2006-01-03)
Subject: Re: New Generalized Keyboard

Keep in mind that any generalized keyboard with a sufficient number 
of keys can be used to map a wide variety of tunings and temperaments 
in a consistent manner.

A study of relevant papers from the Wilson archives can reveal this.

More specifically, look up the papers like "Multi Keyboard Grid 
Iron", "Farey Series", "Scale Tree", "Diophantine Triplets":

http://www.anaphoria.com/wilson.html

I could provide more specifics, but Erv likes people to study the 
material first for themselves.

Note that the software for the Starr Labs keyboards was developed 
making use of these principles.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
> pkroser@n... wrote:
> > Herman,
> > 
> > You might have explained this somewhere else, but could you go 
over the (to me) unfamiliar letter assignments you're using for Lemba 
below?
> > 
> > Regards,
> > Paul
> 
> The generator of lemba temperament divides the fifth into three 
equal 
> parts. One step above D is a note slightly sharper than E, which 
could 
> be labeled "E^"; the next step could be labeled "Gv", then "A". I 
find 
> it useful to have a single letter to represent these notes, so for 
the 
> "slightly flatter" notes I use the letters H to N, the letter "O" 
for 
> the note a half octave between the D's (the G# or Ab on a 12-note 
> keyboard), and the letters P to V for the "slightly sharper" notes.
> 
> |---P---Q-R---S---T-U---V-|
> |O-A---B-C---D---E-F---G-O|
> |-H---I-J---K---L-M---N---|
> 
> Since lemba temperament has 6-note and 10-note basic scales (that 
is, DE 
> or distributionally even scales, ones with only two different sizes 
of 
> steps), I could have used 6 letters to notate lemba, but since I'd 
like 
> to be able to easily notate all 26 notes of lemba[26], I decided to 
go 
> with the 10-note basic scale, centered around D. Two generators 
above 
> and below D are notated P-J-D-T-N, and around the half-octave O 
(G#/Ab) 
> it ends up as L-U-O-I-R.
>

From: wallyesterpaulrus (2006-01-03)
Subject: Re: New Generalized Keyboard

I've sent them an e-mail to find out more (and to correct some 
misstatements about meantone on their website) . . . looks like an 
expressive, affordable instrument with a lot of potential, but I'm 
not even sure how the diatonic scale is mapped to it yet!


--- In tuning@yahoogroups.com, "Bill Sethares" <sethares@e...> wrote:
>
> I'm not sure if it's been discussed here - but there
> is a new hexagonal keyboard that looks very promising... it's called
> the "Thummer." Here is the website:
> 
> http://www.thummer.com/
> 
> You can see it's bright red, has a split keyboard (one for
> each hand) with about 70 hex keys under each hand, as well
> as assorted controllers (I guess the little knobby joystick 
> forf the thumb is where it gets its name).
> 
> There's a video of it in operation 
> 
> http://www.thummer.com/demo.asp
> 
> and, while the demos are all in 12-tet, the keyboard is 
> not restricted to this -- in fact, it is connected (through
> a USB cable) to a computer which either generates the sounds or
> relays the signals to an external synth. 
> 
> Amazingly, they say it will cost about $500 Australian
> (which is about $360 US) and should be available 
> "in the second half of 2006."
> 
> This is looking to be an exciting year for 
> alternative controllers!
> 
> --Bill Sethares
>

From: Ozan Yarman (2006-01-03)
Subject: Re: [tuning] Re: New Generalized Keyboard

You play whole-tones diagonally I think.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 03 Ocak 2006 Sal\ufffd 23:07
Subject: [tuning] Re: New Generalized Keyboard


> I've sent them an e-mail to find out more (and to correct some
> misstatements about meantone on their website) . . . looks like an
> expressive, affordable instrument with a lot of potential, but I'm
> not even sure how the diatonic scale is mapped to it yet!
>
>

From: wallyesterpaulrus (2006-01-03)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "harold_fortuin" <harold_fortuin@y...> 
wrote:
>
> Keep in mind that any generalized keyboard with a sufficient number 
> of keys can be used to map a wide variety of tunings and temperaments 
> in a consistent manner.
> 
> A study of relevant papers from the Wilson archives can reveal this.

After discussing this at length with George Secor, it seems that Wilson 
missed out on an important set of temperaments, as my "Middle Path" 
paper hopefully makes clear (let me know if you need a copy). For 
example, the "Srutal" temperament where 2048:2025 is tempered out. 
Lemba would be another example. These are temperaments of JI where a 
basis cannot be found such that the octave is a member of the basis 
(instead, one can express the octave as a multiple of one of the basis 
intervals in these systems). Some of the keyboard designs associated 
with these temperaments have been posted over on the MakeMicroMusic 
list.

From: wallyesterpaulrus (2006-01-03)
Subject: Re: New Generalized Keyboard

Herman seems to be claiming otherwise -- he puts the whole-tones 
horizontally:

http://launch.groups.yahoo.com/group/tuning/message/63267


--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> You play whole-tones diagonally I think.
> 
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> To: <tuning@yahoogroups.com>
> Sent: 03 Ocak 2006 Salý 23:07
> Subject: [tuning] Re: New Generalized Keyboard
> 
> 
> > I've sent them an e-mail to find out more (and to correct some
> > misstatements about meantone on their website) . . . looks like an
> > expressive, affordable instrument with a lot of potential, but I'm
> > not even sure how the diatonic scale is mapped to it yet!
> >
> >
>

From: Ozan Yarman (2006-01-03)
Subject: Re: [tuning] Re: New Generalized Keyboard

Oh right. Yet, it would have been an idea to skew the whole thing up by 45
degrees from the right corner.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 03 Ocak 2006 Sal\ufffd 23:53
Subject: [tuning] Re: New Generalized Keyboard


Herman seems to be claiming otherwise -- he puts the whole-tones
horizontally:

http://launch.groups.yahoo.com/group/tuning/message/63267

From: Jon Szanto (2006-01-04)
Subject: Re: New Generalized Keyboard

With the exception possibly of Herman, it doesn't appear anyone looked
at the video demo of the product. It shows a diagram of the keyboard
with note names - 3 octaves of diatonics in the middle, 3 of flats on
the left, 3 of sharps on the right. I can't tell from the info on the
site how configurable any or all of this is, but if you want a look I
did a screen cap of the video. It isn't real clear, but you can
certainly see how it defaults:

http://www.microtonal.org/hold/thummer_kbd.jpg

Cheers,
Jon

From: wallyesterpaulrus (2006-01-04)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:
>
> With the exception possibly of Herman, it doesn't appear anyone looked
> at the video demo of the product. It shows a diagram of the keyboard
> with note names - 3 octaves of diatonics in the middle, 3 of flats on
> the left, 3 of sharps on the right. I can't tell from the info on the
> site how configurable any or all of this is, but if you want a look I
> did a screen cap of the video. It isn't real clear, but you can
> certainly see how it defaults:
> 
> http://www.microtonal.org/hold/thummer_kbd.jpg
> 
> Cheers,
> Jon

Thanks, Jon -- I watched a video but didn't see this moment.

From: paolovalladolid (2006-01-05)
Subject: Re: New Generalized Keyboard

The "Expand Your Horizons" video discusses microtuning with the
Thummer Jammer and can be found here:

http://www.thummer.com/demo.asp

I'd be interested in reading your takes on it.

From: Yahya Abdal-Aziz (2006-01-07)
Subject: Re: New Generalized Keyboard

On Thu, 05 Jan 2006 "paolovalladolid" wrote: 
> 
> The "Expand Your Horizons" video discusses microtuning with the
> Thummer Jammer and can be found here:
> 
> http://www.thummer.com/demo.asp
> 
> I'd be interested in reading your takes on it. 


Hi Paolo,

I've spent quite a bit of time reading the material
available on the website.  My conclusions are these:

1.  There are a few minor technical inaccuracies eg 
the claim that Arabic music is a 17-note meantone.

2.  The design of the MIDI Controller ("jammer")
seems capable of doing what they claim, with respect
to:
a) retunings to any 12-tone meantone and up to
19-EDO;
b) preserving the same fingering for all such tunings;
c) allowing easy transposion, preserving fingering
patterns;
d) playing a wider span of notes from the same
harmonic series (up to 3 octaves per hand);
e) providing two thumb controllers for continuous
signals, requiring interpretation by the attached 
computer, for realisation as pitch bend, modulation
depth, volume, retuning or whatever;
f) playing two notes a fifth apart simultaneously
with each finger.

3.  The controller seems well priced (AUD$500) for 
what it offers; a key virtue will be portability.

4.  The biggest drawback that I see is that it bundles
no sound chip.  At this price point, one has to ask
"Whyever not?"

5.  There is no onboard retuning - that must be done 
by software on a computer the jammer plugs into.

6.  They provide no details of how this connects to
other equipment.  It requires a minimum of MIDI Out
to function as a MIDI controller.

7.  The associated invention (not obligatory) of a new
notation system with 7 lines is interesting in itself.

8.  Will it be the next big thing?  The marketing 
expertise of the company's CEO (ex-Microsoft)
should tell.  I think they have a chance.  I'm sure it 
would be better if they widened their market by 
including a sound chip & speakers for realising the
sounds intended by the player of the MIDI 
controller.  The thumb controls could, by default, be 
used as mod wheels and volume pedals (that would 
require onboard logic at least, maybe extra samples 
on the sound chip).  Any user wanting more could 
attach a PC with software to interpret the thumb 
controls differently.

Regards,
Yahya

-- 
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.14.15/223 - Release Date: 6/1/06

From: paolovalladolid (2006-01-09)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

Hi Yahya,

> I've spent quite a bit of time reading the material
> available on the website.  My conclusions are these:
> 
> 1.  There are a few minor technical inaccuracies eg 
> the claim that Arabic music is a 17-note meantone.

I'd be curious to hear how the Thummer team responds to corrections
regarding Arabic music theory and other theoretical explanations that
may be "off".

> 2.  The design of the MIDI Controller ("jammer")
> seems capable of doing what they claim, with respect
> to:
> a) retunings to any 12-tone meantone and up to
> 19-EDO;
> b) preserving the same fingering for all such tunings;
> c) allowing easy transposion, preserving fingering
> patterns;
> d) playing a wider span of notes from the same
> harmonic series (up to 3 octaves per hand);
> e) providing two thumb controllers for continuous
> signals, requiring interpretation by the attached 
> computer, for realisation as pitch bend, modulation
> depth, volume, retuning or whatever;
> f) playing two notes a fifth apart simultaneously
> with each finger.

These interest me, as well as support for polyphonic aftertouch, which
is very rare on MIDI keyboards.

> 5.  There is no onboard retuning - that must be done 
> by software on a computer the jammer plugs into.

I thought the video claimed that this could be done?  I only watched
the vid once, though.

> 6.  They provide no details of how this connects to
> other equipment.  It requires a minimum of MIDI Out
> to function as a MIDI controller.

I thought I saw USB mentioned elsewhere on the website.  Apparently,
the Jammer is designed primarily as a softsynth controller (hence no
built in synth), via USB.  They also plan to support OSC (Open Sound
Control), a network-based protocol that allows far more resolution and
bandwidth than MIDI which is supported in a few commercial products
such as Max/MSP, Reaktor, and Bidule.

I'm definitely interested in the Jammer as a potential entry-level
generalized-layout controller.

Paolo

From: Ozan Yarman (2006-01-09)
Subject: Re: [tuning] Re: New Generalized Keyboard

----- Original Message -----
From: "paolovalladolid" <phv40@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 09 Ocak 2006 Pazartesi 21:45
Subject: [tuning] Re: New Generalized Keyboard


> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> Hi Yahya,
>
> > I've spent quite a bit of time reading the material
> > available on the website.  My conclusions are these:
> >
> > 1.  There are a few minor technical inaccuracies eg
> > the claim that Arabic music is a 17-note meantone.
>
> I'd be curious to hear how the Thummer team responds to corrections
> regarding Arabic music theory and other theoretical explanations that
> may be "off".



Aren't you a least bit interested in Turkish Music theory then? Really, we
should all consider the traditional genres from this region (encompassed by
the term `Middle East`) as `Maqam Music` of diverse ethnic flavors to which
Arabs and Turks inter alia are but more partial.

SNIP

Oz.

From: paolovalladolid (2006-01-10)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> 
> ----- Original Message -----
> From: "paolovalladolid" <phv40@h...>
> To: <tuning@yahoogroups.com>
> Sent: 09 Ocak 2006 Pazartesi 21:45
> Subject: [tuning] Re: New Generalized Keyboard
> 
> 
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
> >
> > Hi Yahya,
> >
> > > I've spent quite a bit of time reading the material
> > > available on the website.  My conclusions are these:
> > >
> > > 1.  There are a few minor technical inaccuracies eg
> > > the claim that Arabic music is a 17-note meantone.
> >
> > I'd be curious to hear how the Thummer team responds to corrections
> > regarding Arabic music theory and other theoretical explanations that
> > may be "off".
> 
> 
> 
> Aren't you a least bit interested in Turkish Music theory then? 

Sure I am.  Why do you ask?

Really, we
> should all consider the traditional genres from this region
(encompassed by
> the term `Middle East`) as `Maqam Music` of diverse ethnic flavors
to which
> Arabs and Turks inter alia are but more partial.

I think you are confusing me with the Thummer team.  You should direct
this feedback to them.

Paolo

From: Ozan Yarman (2006-01-10)
Subject: Re: [tuning] Re: New Generalized Keyboard

My apologies for the confusion. I'm rather sensitive on this matter. Still,
I wish not to carry this argument further. Please feel free to act in my
place if you so desire or deem yourself responsible.

Cordially,
Ozan

----- Original Message -----
From: "paolovalladolid" <phv40@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 10 Ocak 2006 Sal\ufffd 6:29
Subject: [tuning] Re: New Generalized Keyboard


SNIP

> >
> > Aren't you a least bit interested in Turkish Music theory then?
>
> Sure I am.  Why do you ask?
>
> Really, we
> > should all consider the traditional genres from this region
> (encompassed by
> > the term `Middle East`) as `Maqam Music` of diverse ethnic flavors
> to which
> > Arabs and Turks inter alia are but more partial.
>
> I think you are confusing me with the Thummer team.  You should direct
> this feedback to them.
>
> Paolo
>
>
>
>

From: wallyesterpaulrus (2006-01-10)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> 
> On Thu, 05 Jan 2006 "paolovalladolid" wrote: 
> > 
> > The "Expand Your Horizons" video discusses microtuning with the
> > Thummer Jammer and can be found here:
> > 
> > http://www.thummer.com/demo.asp
> > 
> > I'd be interested in reading your takes on it. 
> 
> 
> Hi Paolo,
> 
> I've spent quite a bit of time reading the material
> available on the website.  My conclusions are these:
> 
> 1.  There are a few minor technical inaccuracies eg 
> the claim that Arabic music is a 17-note meantone.

Separate from the question of how Arabic music is actually tuned, I'm 
currently addressing with these folks their claim that any chain-of-
fifths tuning where the fifth is between 4/7 and 3/5 octave 
is "meantone". So far, I think it's just plain wrong, but perhaps 
they're tying timbre to tuning in a very specific way, so I'm 
reserving judgment for now.

> 4.  The biggest drawback that I see is that it bundles
> no sound chip.  At this price point, one has to ask
> "Whyever not?"

Hmm . . . if that's so, then I have serious doubts that they could be 
tying timbre to tuning in such a way that makes this "meantone" 
business correct.

From: Gene Ward Smith (2006-01-10)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> Separate from the question of how Arabic music is actually tuned, I'm 
> currently addressing with these folks their claim that any chain-of-
> fifths tuning where the fifth is between 4/7 and 3/5 octave 
> is "meantone". 

That means schismatic/helmholtz is the same as meantone?

From: wallyesterpaulrus (2006-01-10)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "paolovalladolid" <phv40@h...> wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> 
wrote:
> 
> Hi Yahya,
> 
> > I've spent quite a bit of time reading the material
> > available on the website.  My conclusions are these:
> > 
> > 1.  There are a few minor technical inaccuracies eg 
> > the claim that Arabic music is a 17-note meantone.
> 
> I'd be curious to hear how the Thummer team responds to corrections
> regarding Arabic music theory and other theoretical explanations 
that
> may be "off".

Well, despite the fact that they say "meantone", what they mean is a 
long way from meantone tunings -- what they mean here is 17-equal!

> I'm definitely interested in the Jammer as a potential entry-level
> generalized-layout controller.

Me too!

From: wallyesterpaulrus (2006-01-10)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> 
> > Separate from the question of how Arabic music is actually tuned, 
I'm 
> > currently addressing with these folks their claim that any chain-of-
> > fifths tuning where the fifth is between 4/7 and 3/5 octave 
> > is "meantone". 
> 
> That means schismatic/helmholtz is the same as meantone?

This was my reaction exactly. Their reply, I think, was that this would 
require a different mapping to the keyboard. My reply was that it 
wouldn't; the chain of fifths would still be mapped in exactly the same 
way. So there's no reason I can see why they're calling all 
these "meantone" and not "schismatic", "helmholtz", 
or "superpythagorean", etc. Of course, any of these options would be 
wrong. They should say "chain-of-fifths diatonic tuning" or something 
like that, and drop the "meantone" language entirely. Don't you agree?

From: Gene Ward Smith (2006-01-10)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> Of course, any of these options would be 
> wrong. They should say "chain-of-fifths diatonic tuning" or something 
> like that, and drop the "meantone" language entirely. Don't you agree?

That would certainly make sense, but I think it would also make sense
to use 12-et as the boundry between meantone and schismic, and 7-et as
the boundry between meantone and mavila, so that "meantone"
encompasses the range from 685.7 cents to 700 cents, but not up to 720
cents.

From: Keenan Pepper (2006-01-11)
Subject: Re: [tuning] Re: New Generalized Keyboard

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> 
> 
>>Of course, any of these options would be 
>>wrong. They should say "chain-of-fifths diatonic tuning" or something 
>>like that, and drop the "meantone" language entirely. Don't you agree?
> 
> 
> That would certainly make sense, but I think it would also make sense
> to use 12-et as the boundry between meantone and schismic, and 7-et as
> the boundry between meantone and mavila, so that "meantone"
> encompasses the range from 685.7 cents to 700 cents, but not up to 720
> cents.

Wow, I was just looking at the diagram of all the linear temperaments in "A 
Middle Path" and thinking about this, and suddenly I saw this zigzag path of 
fifth-generated temperaments. It goes from mavila to 7 to meantone to 12 to 
helmholtz to 17 to superpyth and then it goes off the page again. Neat!

Keenan

From: Yahya Abdal-Aziz (2006-01-12)
Subject: Re: New Generalized Keyboard

Hi Paolo,

On Mon, 09 Jan 2006 "paolovalladolid" wrote: 
> > I've spent quite a bit of time reading the material
> > available on the website.  My conclusions are these:
> > 
> > 1.  There are a few minor technical inaccuracies eg 
> > the claim that Arabic music is a 17-note meantone.
> 
> I'd be curious to hear how the Thummer team responds to corrections
> regarding Arabic music theory and other theoretical explanations that
> may be "off".

My main concern with the Thummer is "will it help
me make the music I want to?"  That surely doesn't
depend on its makers having a degree in any
particular tuning theory!  Which is why I wrote
"minor technical inaccuracies".  Still ...

I've had some feedback from Jim Plamondon, CEO
of Thummer, to the message I posted here.  I think
he intended it for general consumption on this list, 
even tho it seemed to be addressed only to myself.

Jim, if you're reading this, please reply to the list
as you did to me!   I'd much rather the Thummer 
people spoke for themselves.  In his message to me,
Jim sounded eager to have corrections from 
subject-matter experts, and to learn more about 
the actual tuning practices of various times and
cultures.  That couldn't hurt, could it?

I'm no expert on Arab tuning!  I can only relate
what I find in published sources, of which the 
classic work by Helmholtz still seems to be the 
most thorough exposition readily available to 
readers of English.  The following is a summary of
that material, as I understand it, but I welcome 
any corrections:

------------------------------------------------------------ 
While it's true that the mediaeval Arabic lute gamut
was formed from a series of 17 perfect fourths (ref.
Helmholtz trans. Ellis 'On the Sensations of Tone',
p 281), the impression gained and promulgated by 
Villoteau was that the Arabs intended to divide the 
octave into equal steps of about a third of a tone
(1200/17 = 70.588 cents), or possibly even to divide
equal-tempered tones of 200 cents into exact thirds
of 66.667 cents.  In fact, the gamut of 17 tones per
octave had the following step intervals:

  L L C L L C L L L C L L C L L L C

Here L = Pyth. Limma = 256/243 ~= 90 c
and C = Pyth. Comma = 531441/524288 ~= 24 c.

These are very unequal steps, not at all close to 
either kind of third-tone Villoteau envisaged.  

[There is, however, some evidence from Michael 
Meshaqah (cited by Eli Smith according to Ellis)
that "modern Greeks" (in the 19th Century) divided
the octave into 4 X 17 = 68 equal parts, forming a 
scale with steps:

12 9 7 12 9 7 12 of these (octave/68) divisions.

Ellis comments that if the steps of 9 and 7 parts
were instead both of 8 parts, the scale would
consist of:

3 2 2 3 2 2 3 of these (octave/17) divisions,
"the precise scale of Villoteau" (op. cit. p 556).]

Each _scale_ (maqam) that the mediaeval Arab 
lutists (players on al-`ud) formed from this gamut 
contained either seven or eight tones per octave
(tho individual notes might be inflected by way of 
ornament, much as modern guitarists bend notes).

This gamut of 17 tones was clearly tuned by exact 
ratios and was a 3-limit system, consisting of a
single chain of pure fourths upwards (or fifths 
downwards where necessary to stay in the playing
range of a couple of octaves).  It was not a 
meantone system.


_Modern_ Arabic theory - as given "by the Syrian, 
Michael Meshaqah" in 1847 (op. cit p. 264) uses 
equal quartertones - an exact 24-fold division of 
the octave.  The basic theoretical scale has steps:

 200 150 150 200 150 150 200 (cents)
or
  4 3 3 4 3 3 4 (quartertones).

Interestingly, the three-quartertone interval was 
introduced by the lutist Zalzal some 1100 years ago.
It was the ratio 12/11 = 151 cents (op. cit. p.264).
This note disappeared from the lutist's gamut in 
mediaeval times.
 
Helmholtz / Ellis also contains at least three distinct
explanations of the maqamat - it's quite entertaining
reading in places.  Ellis' interpretation seems to me 
to hold water best.

------------------------------------------------------------

> > 2.  The design of the MIDI Controller ("jammer")
> > seems capable of doing what they claim, with respect
> > to:
> > a) retunings to any 12-tone meantone and up to
> > 19-EDO;
> > b) preserving the same fingering for all such tunings;
> > c) allowing easy transposion, preserving fingering
> > patterns;
> > d) playing a wider span of notes from the same
> > harmonic series (up to 3 octaves per hand);
> > e) providing two thumb controllers for continuous
> > signals, requiring interpretation by the attached 
> > computer, for realisation as pitch bend, modulation
> > depth, volume, retuning or whatever;
> > f) playing two notes a fifth apart simultaneously
> > with each finger.
> 
> These interest me, as well as support for polyphonic aftertouch, which
> is very rare on MIDI keyboards.

Not to mention expensive!  Yes, that will be 
a selling point for musos who want to control
the expression of their playing (me too).


> > 5.  There is no onboard retuning - that must be done 
> > by software on a computer the jammer plugs into.
> 
> I thought the video claimed that this could be done?  I only watched
> the vid once, though.

You can waggle the thumb controls to change
the tuning - but only if you've set up the 
software that way.  I should have been more 
precise, and said "You can't switch from one
tuning to another by pressing a button, nor 
can you set up the tuning you want to play in,
without using software."


> > 6.  They provide no details of how this connects to
> > other equipment.  It requires a minimum of MIDI Out
> > to function as a MIDI controller.
> 
> I thought I saw USB mentioned elsewhere on the website.  Apparently,
> the Jammer is designed primarily as a softsynth controller (hence no
> built in synth), via USB. ...

You're right; my bad.  Jim pointed out the USB 
to me; I must have missed it.  And of course the 
USB is bidirectional and uses a smaller & cheaper
connector than the pair of DIN plugs & sockets 
required by older MIDI implementations.


> ...  They also plan to support OSC (Open Sound
> Control), a network-based protocol that allows far more resolution and
> bandwidth than MIDI which is supported in a few commercial products
> such as Max/MSP, Reaktor, and Bidule.

Yes, that is interesting.  Jim's also talking of
making the controller software ("Thummer 
Setup") open source.


> I'm definitely interested in the Jammer as a potential entry-level
> generalized-layout controller.
> 
> Paolo

Ditto.  I hope Jim speaks up for himself here to 
answer any further questions.  I note he has a 
slew of beta-testers who've been busy testing
Thummer controllers out for over a year - Darn!
I was going to ask if he needed a volunteer!  But
I will ask him how soon he can give a demo to the
Melbourne PC User Group - I'm sure many of our
members will be interested.

Regards,
Yahya

------------------------------------------------
      Yahya Abdal-Aziz
      Melbourne PC User Group
      Convener, Music Interest Group
------------------------------------------------


-- 
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.14.17/226 - Release Date: 10/1/06

From: paolovalladolid (2006-01-12)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> 
> Hi Paolo,
> 
> On Mon, 09 Jan 2006 "paolovalladolid" wrote: 
> > > I've spent quite a bit of time reading the material
> > > available on the website.  My conclusions are these:
> > > 
> > > 1.  There are a few minor technical inaccuracies eg 
> > > the claim that Arabic music is a 17-note meantone.
> > 
> > I'd be curious to hear how the Thummer team responds to corrections
> > regarding Arabic music theory and other theoretical explanations that
> > may be "off".
> 
> My main concern with the Thummer is "will it help
> me make the music I want to?"  That surely doesn't
> depend on its makers having a degree in any
> particular tuning theory!  Which is why I wrote
> "minor technical inaccuracies".  Still ...

I agree that tuning theory isn't necessary to build the instrument
itself.  However one of the stated purposes of the instrument is music
education, shouldn't their educational materials present tuning theory
accurately?  I thought that was a concern of yours and apparently
mistunderstood.

> Jim, if you're reading this, please reply to the list
> as you did to me!   I'd much rather the Thummer 
> people spoke for themselves.  In his message to me,
> Jim sounded eager to have corrections from 
> subject-matter experts, and to learn more about 
> the actual tuning practices of various times and
> cultures.  That couldn't hurt, could it?

Sounds great!  I'm glad to hear you and Paul have already been in
contact with Jim and his folks.

> Ditto.  I hope Jim speaks up for himself here to 
> answer any further questions.  I note he has a 
> slew of beta-testers who've been busy testing
> Thummer controllers out for over a year - Darn!

I signed up for the Head Start program (to work with a prototype) but
did not get any response.  I can let that slide, though, if I keep
hearing positive reports about their customer service.

Thanks for the followup, Yahya!

Paolo

From: Ozan Yarman (2006-01-12)
Subject: Re: [tuning] Re: New Generalized Keyboard

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 12 Ocak 2006 Per\ufffdembe 14:48
Subject: [tuning] Re: New Generalized Keyboard


SNIP

>
> I'm no expert on Arab tuning!  I can only relate
> what I find in published sources, of which the
> classic work by Helmholtz still seems to be the
> most thorough exposition readily available to
> readers of English.  The following is a summary of
> that material, as I understand it, but I welcome
> any corrections:
>
> ------------------------------------------------------------
> While it's true that the mediaeval Arabic lute gamut
> was formed from a series of 17 perfect fourths (ref.
> Helmholtz trans. Ellis 'On the Sensations of Tone',
> p 281),


If the reference here is to Safi Al-Din's theory of 17 Pythagorean ratios
per octave preserved by Meragi himself, then this definition is wrong. 17
pure fourths from a reference tone gives all the correct pitches except
81/64. Actually, one needs 4 pure fifths up, 12 fifths down.

Besides, Baghdad was a cosmopolitan centre, hardly making it Arabic during
the conquest by Mongols. The following Levantine treatises are written
during the Ottoman Era, making them more Turkish than Arabic.


the impression gained and promulgated by
> Villoteau was that the Arabs intended to divide the
> octave into equal steps of about a third of a tone
> (1200/17 = 70.588 cents), or possibly even to divide
> equal-tempered tones of 200 cents into exact thirds
> of 66.667 cents.


That impression could only be justied during the time of Kantemir, with
possible 1/3rd tones here and there.


In fact, the gamut of 17 tones per
> octave had the following step intervals:
>
>   L L C L L C L L L C L L C L L L C
>
> Here L = Pyth. Limma = 256/243 ~= 90 c
> and C = Pyth. Comma = 531441/524288 ~= 24 c.
>


Correct.


> These are very unequal steps, not at all close to
> either kind of third-tone Villoteau envisaged.
>


They are uniquely Pythagorean ratios.


> [There is, however, some evidence from Michael
> Meshaqah (cited by Eli Smith according to Ellis)
> that "modern Greeks" (in the 19th Century) divided
> the octave into 4 X 17 = 68 equal parts, forming a
> scale with steps:
>
> 12 9 7 12 9 7 12 of these (octave/68) divisions.
>


Preposterous suggestion.


> Ellis comments that if the steps of 9 and 7 parts
> were instead both of 8 parts, the scale would
> consist of:
>
> 3 2 2 3 2 2 3 of these (octave/17) divisions,
> "the precise scale of Villoteau" (op. cit. p 556).]
>


Certainly not. 17-eq is never assumed by anyone except my colleague Kemal
Karaosmanoglu who supports Yalcin Tura when it comes to equalizing the 17
traditional pitches per octave.


> Each _scale_ (maqam) that the mediaeval Arab
> lutists (players on al-`ud) formed from this gamut
> contained either seven or eight tones per octave
> (tho individual notes might be inflected by way of
> ornament, much as modern guitarists bend notes).
>

Right.

> This gamut of 17 tones was clearly tuned by exact
> ratios and was a 3-limit system, consisting of a
> single chain of pure fourths upwards (or fifths
> downwards where necessary to stay in the playing
> range of a couple of octaves).  It was not a
> meantone system.


The exact ratios are (according to Urmevi and Meragi):

  0:          1/1               0.000 unison, perfect prime
  1:        256/243            90.225 limma, Pythagorean minor second
  2:      65536/59049         180.450 Pythagorean diminished third
  3:          9/8             203.910 major whole tone
  4:         32/27            294.135 Pythagorean minor third
  5:       8192/6561          384.360 Pythagorean diminished fourth
  6:         81/64            407.820 Pythagorean major third
  7:          4/3             498.045 perfect fourth
  8:       1024/729           588.270 Pythagorean diminished fifth
  9:     262144/177147        678.495 Pythagorean diminished sixth
 10:          3/2             701.955 perfect fifth
 11:        128/81            792.180 Pythagorean minor sixth
 12:      32768/19683         882.405 Pythagorean diminished seventh
 13:         27/16            905.865 Pythagorean major sixth
 14:         16/9             996.090 Pythagorean minor seventh
 15:       4096/2187         1086.315 Pythagorean diminished octave
 16:    1048576/531441       1176.540 Pythagorean diminished ninth
 17:          2/1            1200.000 octave

>
>
> _Modern_ Arabic theory - as given "by the Syrian,
> Michael Meshaqah" in 1847 (op. cit p. 264) uses
> equal quartertones - an exact 24-fold division of
> the octave.  The basic theoretical scale has steps:
>
>  200 150 150 200 150 150 200 (cents)
> or
>   4 3 3 4 3 3 4 (quartertones).
>


Certainly not. Meshaqah's system is quasi-quartertonal based on high prime
ratios:

from d'Erlanger vol.5, p.34, after Mih.a'il Mu^saqah, 1899, a Lebanese
scholar
|
  0:          1/1           C          unison, perfect prime
  1:       3456/3361        C|   Db;
  2:        864/817         C#   Db
  3:        384/353         C#|  D;
  4:        216/193         D
  5:       3456/3011        D|   Eb;
  6:         32/27          D#   Eb    Pythagorean minor third
  7:       3456/2833        D#|  E;
  8:         54/43          E
  9:        128/99          E|   F;
 10:        864/649         F
 11:       3456/2521        F|   Gb;
 12:         24/17          F#   Gb    1st septendecimal tritone
 13:       3456/2377        F#|  G;
 14:        864/577         G
 15:        128/83          G|   Ab;
 16:         27/17          G#   Ab    septendecimal minor sixth
 17:       3456/2113        G#|  A;
 18:         32/19          A          19th subharmonic
 19:       3456/1993        A|   Bb;
 20:        216/121         A#   Bb
 21:        384/209         A#|  B;
 22:        864/457         B
 23:       3456/1777        B|   C;
 24:          2/1           C          octave


> Interestingly, the three-quartertone interval was
> introduced by the lutist Zalzal some 1100 years ago.
> It was the ratio 12/11 = 151 cents (op. cit. p.264).
> This note disappeared from the lutist's gamut in
> mediaeval times.


It did not dissapear, but was dismissed by theory alone. An excessive zeal
and reverence for Pythagoras may be the culprit for this trend. Notice the
introduction of octave equivalance by Safi Al-Din.


>
> Helmholtz / Ellis also contains at least three distinct
> explanations of the maqamat - it's quite entertaining
> reading in places.  Ellis' interpretation seems to me
> to hold water best.
>

And what might that be?

SNIP

Cordially,
Ozan

From: wallyesterpaulrus (2006-01-13)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> 
> > Of course, any of these options would be 
> > wrong. They should say "chain-of-fifths diatonic tuning" or 
something 
> > like that, and drop the "meantone" language entirely. Don't you 
agree?
> 
> That would certainly make sense, but I think it would also make sense
> to use 12-et as the boundry between meantone and schismic, and 7-et as
> the boundry between meantone and mavila, so that "meantone"
> encompasses the range from 685.7 cents to 700 cents, but not up to 720
> cents.

I'm not into these mutually exclusive boundaries. You'd have to put 
some pretty stringent conditions of what temperament classes are 
allowed before such boundaries could even have a chance of making 
sense; otherwise, overlaps will be inevitable.

From: wallyesterpaulrus (2006-01-14)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...> 
wrote:
>
> Gene Ward Smith wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> > 
> > 
> >>Of course, any of these options would be 
> >>wrong. They should say "chain-of-fifths diatonic tuning" or 
something 
> >>like that, and drop the "meantone" language entirely. Don't you 
agree?
> > 
> > 
> > That would certainly make sense, but I think it would also make 
sense
> > to use 12-et as the boundry between meantone and schismic, and 7-
et as
> > the boundry between meantone and mavila, so that "meantone"
> > encompasses the range from 685.7 cents to 700 cents, but not up 
to 720
> > cents.
> 
> Wow, I was just looking at the diagram of all the linear 
>temperaments

Some of them aren't linear temperaments, of course . . .

> in "A 
> Middle Path" and thinking about this, and suddenly I saw this 
zigzag path of 
> fifth-generated temperaments. It goes from mavila to 7 to meantone 
to 12 to 
> helmholtz to 17 to superpyth and then it goes off the page again. 

Where it hits 5 and then the bonus temperament "father" (not marked 
with a line) takes you back through the 13 on the upper left, and 
beyond . . .

> Neat!

The diagram Keenan is referring to looks like this:

http://groups.yahoo.com/group/tuning-math/files/hex2.gif

> Keenan

It's just luck that no other 5-limit 2D temperaments with period ~= 
2:1 and generator ~= 3:2 made it into the "main sequence" criteria of 
my paper. My earlier diagram for Monz's page:

http://tonalsoft.com/enc/e/equal-temperament.aspx

shows, for example, "counterschismic" (mouse over "zoom: 100" to see 
it), which also has a period ~= 2:1 and generator ~= 3:2. That seems 
to ruin the nice zig-zag pattern, and also the idea 
of "boundaries" . . .

From: wallyesterpaulrus (2006-01-14)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> While it's true that the mediaeval Arabic lute gamut
> was formed from a series of 17 perfect fourths (ref.
> Helmholtz trans. Ellis 'On the Sensations of Tone',
> p 281), the impression gained and promulgated by 
> Villoteau was that the Arabs intended to divide the 
> octave into equal steps of about a third of a tone
> (1200/17 = 70.588 cents), or possibly even to divide
> equal-tempered tones of 200 cents into exact thirds
> of 66.667 cents.  In fact, the gamut of 17 tones per
> octave had the following step intervals:
> 
>   L L C L L C L L L C L L C L L L C
> 
> Here L = Pyth. Limma = 256/243 ~= 90 c
> and C = Pyth. Comma = 531441/524288 ~= 24 c.
> 
> These are very unequal steps, not at all close to 
> either kind of third-tone Villoteau envisaged.  

But identical to the series of 16 perfect fourths (17 notes) that you 
started with above.

> [There is, however, some evidence from Michael 
> Meshaqah (cited by Eli Smith according to Ellis)
> that "modern Greeks" (in the 19th Century) divided
> the octave into 4 X 17 = 68 equal parts, forming a 
> scale with steps:
> 
> 12 9 7 12 9 7 12 of these (octave/68) divisions.
> 
> Ellis comments that if the steps of 9 and 7 parts
> were instead both of 8 parts, the scale would
> consist of:
> 
> 3 2 2 3 2 2 3 of these (octave/17) divisions,
> "the precise scale of Villoteau" (op. cit. p 556).]
> 
> Each _scale_ (maqam) that the mediaeval Arab 
> lutists (players on al-`ud) formed from this gamut 
> contained either seven or eight tones per octave
> (tho individual notes might be inflected by way of 
> ornament, much as modern guitarists bend notes).
> 
> This gamut of 17 tones was clearly tuned by exact 
> ratios and was a 3-limit system,

Unless Villoteau was right or even partially right, or Helmholtz at 
least partially wrong. At least Ozan has claimed that the supposed 3-
limit system is a purely theoretical creation with little or no 
relationship with practice.

> consisting of a
> single chain of pure fourths upwards (or fifths 
> downwards where necessary to stay in the playing
> range of a couple of octaves).  It was not a 
> meantone system.

It would be even *less* of a meantone system if Villoteau was even 
partially right, since that would involve even *wider* fifths.

> 
> _Modern_ Arabic theory - as given "by the Syrian, 
> Michael Meshaqah" in 1847 (op. cit p. 264) uses 
> equal quartertones - an exact 24-fold division of 
> the octave.  The basic theoretical scale has steps:
> 
>  200 150 150 200 150 150 200 (cents)
> or
>   4 3 3 4 3 3 4 (quartertones).

Notice how close this is to Villoteau's spec.

From: wallyesterpaulrus (2006-01-14)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> 
> ----- Original Message -----
> From: "Yahya Abdal-Aziz" <yahya@m...>
> To: <tuning@yahoogroups.com>
> Sent: 12 Ocak 2006 Perþembe 14:48
> Subject: [tuning] Re: New Generalized Keyboard
> 
> 
> SNIP
> 
> >
> > I'm no expert on Arab tuning!  I can only relate
> > what I find in published sources, of which the
> > classic work by Helmholtz still seems to be the
> > most thorough exposition readily available to
> > readers of English.  The following is a summary of
> > that material, as I understand it, but I welcome
> > any corrections:
> >
> > ------------------------------------------------------------
> > While it's true that the mediaeval Arabic lute gamut
> > was formed from a series of 17 perfect fourths (ref.
> > Helmholtz trans. Ellis 'On the Sensations of Tone',
> > p 281),
> 
> 
> If the reference here is to Safi Al-Din's theory of 17 Pythagorean 
ratios
> per octave preserved by Meragi himself, then this definition is 
wrong. 17
> pure fourths from a reference tone gives all the correct pitches 
except
> 81/64. Actually, one needs 4 pure fifths up, 12 fifths down.

I would consider the two alternatives exactly the same -- all you 
have to do is change the reference tone and the two are identical. 
Unless there was a clear choice of reference tone such as an ever-
present drone, I think "wrong" is too strong a word here. Tuning 4 
pure fifths up and 12 fifths down from a reference note *does* result 
in a set of 17 notes forming a single series of perfect fourths (or 
fifths), including that reference note.

From: Gene Ward Smith (2006-01-14)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> > 12 9 7 12 9 7 12 of these (octave/68) divisions.
> > 
> > Ellis comments that if the steps of 9 and 7 parts
> > were instead both of 8 parts, the scale would
> > consist of:

You can also replace 12 with 9/8, 9 with 10/9, and 7 with 16/15. The
scale will now be a 5-limit Fokker block, synmav3 in my catalog. It is
also a rotated form of various scales, including al-farabi_g1, about
which the Scala scl says "Al-Farabi's Greek genus conjunctum medium,
Land". If now you temper out 99/98 and 225/224, you get something
quite a lot closer to the above scale, with a considerable quantity of 
11-limit harmony worked in.

Here it is in the rms tuning of {99/98,225/224}-planar, for which I've
proposed the name "apollo" in case anyone really wants to name such
things. Apollo is a pretty good temperament.

! apol.scl
synmav3 in apollo {100/99, 225/224} temperament
7
!
207.252202
381.116799
496.373899
703.626101
877.490697
992.747798
1200.000000

From: Ozan Yarman (2006-01-14)
Subject: Re: [tuning] Re: New Generalized Keyboard

SNIP

>
>
> If the reference here is to Safi Al-Din's theory of 17 Pythagorean
ratios
> per octave preserved by Meragi himself, then this definition is
wrong. 17
> pure fourths from a reference tone gives all the correct pitches
except
> 81/64. Actually, one needs 4 pure fifths up, 12 fifths down.

I would consider the two alternatives exactly the same -- all you
have to do is change the reference tone and the two are identical.
Unless there was a clear choice of reference tone such as an ever-
present drone, I think "wrong" is too strong a word here. Tuning 4
pure fifths up and 12 fifths down from a reference note *does* result
in a set of 17 notes forming a single series of perfect fourths (or
fifths), including that reference note.


---------------------


You cannot change the reference tone, because the relative frequency of the
reference tone is always 1, and hence, your definition is incomplete.

Nevertheless, I concur that it IS a chain of 17 fourths or fifths. One needs
only to start the cycle up by fourths or down by fifths from E (81/64)
instead of C (1/1). However, my definition above is more exact.

From: Yahya Abdal-Aziz (2006-01-14)
Subject: Re: New Generalized Keyboard

Hi Ozan,

Thank you for your elucidations, my friend.
One could hardly expect Helmholtz and Ellis
to be better informed about maqam music
more than a century ago than you; besides,
their information was mostly second-hand.

On 12 Jan 2006, Ozan Yarman wrote:
[SNIP]
> > ....  The following is a summary of
> > that material, as I understand it, but I welcome
> > any corrections:
> >
> > ------------------------------------------------------------
> > While it's true that the mediaeval Arabic lute gamut
> > was formed from a series of 17 perfect fourths (ref.
> > Helmholtz trans. Ellis 'On the Sensations of Tone',
> > p 281),
>
> If the reference here is to Safi Al-Din's theory of 17 Pythagorean ratios
> per octave preserved by Meragi himself, then this definition is wrong. ...

My source refers neither to Safi-ud-din nor to
Meragi.


> ... 17
> pure fourths from a reference tone gives all the correct pitches except
> 81/64. Actually, one needs 4 pure fifths up, 12 fifths down.

17 pure fourths up from the ratio 18/64, adjusted
to remain within the octave, gives a cycle of 17
notes, which is of course a  cycle of fifths read in
the reverse order.  This is the procedure Ellis shows
(loc. cit.), giving familiar European names to (and
cents measures for) the 17 tones, thus:

1 E 408
2 A 906
3 D 204
4 G 702
5 C 0
6 F 498
7 Bb 996
8 Eb 294
9 Ab 792
10 Db 90
11 Gb 588
12 Cb 1086
13 Fb 384
14 Bbb 882
15 Ebb 180
16 Abb 678
17 Dbb 1176

The only theorists mentioned by Ellis in this passage
are al-Farabi, Zalzal and Abdul-Qadir.  Helmholtz
writes of:
"the directions for the division of the monochord
given by Abdul Kadir, a celebrated Persian theorist
of the fourteenth century of our era, that lived at
the courts of Timur and Bajazet.  ... These directions
also agree in essentials with those of the much older
Farabi, (who died in AD 950), and of his own
contemporary, Mahmud Shirazi, (who died in 1315),
for dividing the fingerboard of lutes.  According to
the directions of Abdul Kadir all the tonal degrees
of the Arabic scale are obtained by a series of 16
Fifths ...."


> Besides, Baghdad was a cosmopolitan centre, hardly making it Arabic during
> the conquest by Mongols. The following Levantine treatises are written
> during the Ottoman Era, making them more Turkish than Arabic.

I won't argue questions of race with anyone.
I am very proud of my race - human!


> the impression gained and promulgated by
> > Villoteau was that the Arabs intended to divide the
> > octave into equal steps of about a third of a tone
> > (1200/17 = 70.588 cents), or possibly even to divide
> > equal-tempered tones of 200 cents into exact thirds
> > of 66.667 cents.
>
> That impression could only be justied during the time of Kantemir, with
> possible 1/3rd tones here and there.

Didn't know that!  What was his motivation?


> In fact, the gamut of 17 tones per
> > octave had the following step intervals:
> >
> >   L L C L L C L L L C L L C L L L C
> >
> > Here L = Pyth. Limma = 256/243 ~= 90 c
> > and C = Pyth. Comma = 531441/524288 ~= 24 c.
>
> Correct.

Good!


> > These are very unequal steps, not at all close to
> > either kind of third-tone Villoteau envisaged.
>
> They are uniquely Pythagorean ratios.

Exactly so.


> > [There is, however, some evidence from Michael
> > Meshaqah (cited by Eli Smith according to Ellis)
> > that "modern Greeks" (in the 19th Century) divided
> > the octave into 4 X 17 = 68 equal parts, forming a
> > scale with steps:
> >
> > 12 9 7 12 9 7 12 of these (octave/68) divisions.
>
> Preposterous suggestion.

Why preposterous?

I presume that Smith had reason to believe
this, and so too Michael Meshaqah.  Is it
likely that the latter would have invented
such a specifically detailed tuning out of
nothing, then attributed it to the Greeks?
Is it not MORE likely that he observed
Greek instruments with fingerboards so
divided, or conversed with Greek musicians
and simply repeated what they told him?


> > Ellis comments that if the steps of 9 and 7 parts
> > were instead both of 8 parts, the scale would
> > consist of:
> >
> > 3 2 2 3 2 2 3 of these (octave/17) divisions,
> > "the precise scale of Villoteau" (op. cit. p 556).]
>
> Certainly not. 17-eq is never assumed by anyone except my colleague Kemal
> Karaosmanoglu who supports Yalcin Tura when it comes to equalizing the 17
> traditional pitches per octave.

I'm sorry, I don't see the relevance of modern
"assumptions" when judging the accuracy of an
historical report made around 1850!

And is your collegue "assuming" 17-EDO or
rather advocating it?


> > Each _scale_ (maqam) that the mediaeval Arab
> > lutists (players on al-`ud) formed from this gamut
> > contained either seven or eight tones per octave
> > (tho individual notes might be inflected by way of
> > ornament, much as modern guitarists bend notes).
>
> Right.

Good again.


> > This gamut of 17 tones was clearly tuned by exact
> > ratios and was a 3-limit system, consisting of a
> > single chain of pure fourths upwards (or fifths
> > downwards where necessary to stay in the playing
> > range of a couple of octaves).  It was not a
> > meantone system.
>
> The exact ratios are (according to Urmevi and Meragi):
>
>   0:          1/1               0.000 unison, perfect prime
>   1:        256/243            90.225 limma, Pythagorean minor second
>   2:      65536/59049         180.450 Pythagorean diminished third
>   3:          9/8             203.910 major whole tone
>   4:         32/27            294.135 Pythagorean minor third
>   5:       8192/6561          384.360 Pythagorean diminished fourth
>   6:         81/64            407.820 Pythagorean major third
>   7:          4/3             498.045 perfect fourth
>   8:       1024/729           588.270 Pythagorean diminished fifth
>   9:     262144/177147        678.495 Pythagorean diminished sixth
>  10:          3/2             701.955 perfect fifth
>  11:        128/81            792.180 Pythagorean minor sixth
>  12:      32768/19683         882.405 Pythagorean diminished seventh
>  13:         27/16            905.865 Pythagorean major sixth
>  14:         16/9             996.090 Pythagorean minor seventh
>  15:       4096/2187         1086.315 Pythagorean diminished octave
>  16:    1048576/531441       1176.540 Pythagorean diminished ninth
>  17:          2/1            1200.000 octave

Not being able to recognise the higher powers
of 3 at a glance, I don't know whether this
disagrees with the genesis of the 17 tones as
a series of 16 fourths upwards from the ratio
81/64.  But I assume not.


> > _Modern_ Arabic theory - as given "by the Syrian,
> > Michael Meshaqah" in 1847 (op. cit p. 264) uses
> > equal quartertones - an exact 24-fold division of
> > the octave.  The basic theoretical scale has steps:
> >
> >  200 150 150 200 150 150 200 (cents)
> > or
> >   4 3 3 4 3 3 4 (quartertones).

A clarification: Helmholtz gives as reference for
this statement:
"Journal of the American Oriental Society,
vol. i. p. 173, 1847."

I don't have access to that journal, but  I do
wonder exactly what Meshaqah wrote there.


> Certainly not. Meshaqah's system is quasi-quartertonal based on high prime
> ratios:
>
> from d'Erlanger vol.5, p.34, after Mih.a'il Mu^saqah, 1899, a Lebanese
> scholar
> |
>   0:          1/1           C          unison, perfect prime
>   1:       3456/3361        C|   Db;
>   2:        864/817         C#   Db
>   3:        384/353         C#|  D;
>   4:        216/193         D
>   5:       3456/3011        D|   Eb;
>   6:         32/27          D#   Eb    Pythagorean minor third
>   7:       3456/2833        D#|  E;
>   8:         54/43          E
>   9:        128/99          E|   F;
>  10:        864/649         F
>  11:       3456/2521        F|   Gb;
>  12:         24/17          F#   Gb    1st septendecimal tritone
>  13:       3456/2377        F#|  G;
>  14:        864/577         G
>  15:        128/83          G|   Ab;
>  16:         27/17          G#   Ab    septendecimal minor sixth
>  17:       3456/2113        G#|  A;
>  18:         32/19          A          19th subharmonic
>  19:       3456/1993        A|   Bb;
>  20:        216/121         A#   Bb
>  21:        384/209         A#|  B;
>  22:        864/457         B
>  23:       3456/1777        B|   C;
>  24:          2/1           C          octave

Very interesting!  But there's a long time between
1847 and 1899 - time enough for a scholar to make
many a revision of his theories.  Assuming that "the
Syrian, Michael Mesha-qah" of 1847 is the same
person as the "Lebanese scholar Mih.a'il Mu^saqah"
of 1899.  Only the vagaries of transliteration
throws it into doubt, really.  (Lebanon used to be
part of Syria.)

Perhaps he learnt more as he got older?


> > Interestingly, the three-quartertone interval was
> > introduced by the lutist Zalzal some 1100 years ago.
> > It was the ratio 12/11 = 151 cents (op. cit. p.264).
> > This note disappeared from the lutist's gamut in
> > mediaeval times.
>
> It did not dissapear, but was dismissed by theory alone. An excessive zeal
> and reverence for Pythagoras may be the culprit for this trend. Notice the
> introduction of octave equivalance by Safi Al-Din.

When did this happen?  Can you tell me more
about this Safi-ud-Din?


> > Helmholtz / Ellis also contains at least three distinct
> > explanations of the maqamat - it's quite entertaining
> > reading in places.  Ellis' interpretation seems to me
> > to hold water best.
>
> And what might that be?

What, you don't have this book?  I'm amazed! :-)

In fact, it's long and tedious and I don't have
the energy to type it all up right now (I should
have been in bed hours ago), tho I will do so
later if you want me to.  In short, he gives exact
tunings for the 12 maqams:
(`Ushaq, Nawaa, Busilik, Raast, `Iraaq, Isfahaan,
Zirafkend, Buzurk, Zenkuleh, Raahawi, Husa\ufffdni,
Hijaazi).


Good night!
Yahya
--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.14.17/229 - Release Date: 13/1/06

From: Ozan Yarman (2006-01-15)
Subject: Re: [tuning] Re: New Generalized Keyboard

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 14 Ocak 2006 Cumartesi 18:28
Subject: [tuning] Re: New Generalized Keyboard


>
> Hi Ozan,
>
> Thank you for your elucidations, my friend.
> One could hardly expect Helmholtz and Ellis
> to be better informed about maqam music
> more than a century ago than you; besides,
> their information was mostly second-hand.
>


Truly, you are most gracious, but I do not deserve the compliment. I'm one
of the most ignorant people in the world.


>
> > ... 17
> > pure fourths from a reference tone gives all the correct pitches except
> > 81/64. Actually, one needs 4 pure fifths up, 12 fifths down.
>
> 17 pure fourths up from the ratio 18/64, adjusted
> to remain within the octave, gives a cycle of 17
> notes, which is of course a  cycle of fifths read in
> the reverse order.  This is the procedure Ellis shows
> (loc. cit.), giving familiar European names to (and
> cents measures for) the 17 tones, thus:
>
> 1 E 408
> 2 A 906
> 3 D 204
> 4 G 702
> 5 C 0
> 6 F 498
> 7 Bb 996
> 8 Eb 294
> 9 Ab 792
> 10 Db 90
> 11 Gb 588
> 12 Cb 1086
> 13 Fb 384
> 14 Bbb 882
> 15 Ebb 180
> 16 Abb 678
> 17 Dbb 1176
>


An agreeable procedure. You might want to check:

http://www.ozanyarman.com/files/Doktora%20Tezi%20Raporu%203.pdf

(p. 45-51) For a wholesome table of Ebjed notations based on this tuning
scheme.


> The only theorists mentioned by Ellis in this passage
> are al-Farabi, Zalzal and Abdul-Qadir.  Helmholtz
> writes of:
> "the directions for the division of the monochord
> given by Abdul Kadir, a celebrated Persian theorist
> of the fourteenth century of our era, that lived at
> the courts of Timur and Bajazet.  ... These directions
> also agree in essentials with those of the much older
> Farabi, (who died in AD 950), and of his own
> contemporary, Mahmud Shirazi, (who died in 1315),
> for dividing the fingerboard of lutes.  According to
> the directions of Abdul Kadir all the tonal degrees
> of the Arabic scale are obtained by a series of 16
> Fifths ...."
>


Abdulkadir's directions certainly do not agree with Al-Farabi! The tuning
scheme proposed by Al-Farabi is in the Scala archive (al-farabi_22.scl):

Al-Farabi 22 note ud scale
|
  0:          1/1               0.000 unison, perfect prime
  1:        256/243            90.225 limma, Pythagorean minor second
  2:         18/17             98.955 Arabic lute index finger
  3:         12/11            150.637 3/4-tone, undecimal neutral second
  4:          9/8             203.910 major whole tone
  5:         32/27            294.135 Pythagorean minor third
  6:         27/22            354.547 neutral third, Zalzal wosta of
al-Farabi
  7:       8192/6561          384.360 Pythagorean diminished fourth
  8:         81/64            407.820 Pythagorean major third
  9:          4/3             498.045 perfect fourth
 10:       1024/729           588.270 Pythagorean diminished fifth
 11:         24/17            597.000 1st septendecimal tritone
 12:         16/11            648.682 undecimal semi-diminished fifth
 13:          3/2             701.955 perfect fifth
 14:        128/81            792.180 Pythagorean minor sixth
 15:         18/11            852.592 undecimal neutral sixth
 16:      32768/19683         882.405 Pythagorean diminished seventh
 17:         27/16            905.865 Pythagorean major sixth
 18:         16/9             996.090 Pythagorean minor seventh
 19:       4096/2187         1086.315 Pythagorean diminished octave
 20:         32/17           1095.045 17th subharmonic
 21:         64/33           1146.727 33rd subharmonic
 22:          2/1            1200.000 octave


Notice that this scheme not only contains 22 notes per octave, but also is
17-limit, while Meragi adopts the 3-limit Pythagorean tradition as proposed
by Urmevi.

The revival of quarter-tones by Mushaqa requires the pre-eminence of
Al-Farabi and Zalzal over Urmevi and Meragi, which is the fundamental
difference between Turkish and Arabic Maqam Music theory.

>
> > Besides, Baghdad was a cosmopolitan centre, hardly making it Arabic
during
> > the conquest by Mongols. The following Levantine treatises are written
> > during the Ottoman Era, making them more Turkish than Arabic.
>
> I won't argue questions of race with anyone.
> I am very proud of my race - human!
>
>


That makes me an outworlder I suppose. ;)



> > the impression gained and promulgated by
> > > Villoteau was that the Arabs intended to divide the
> > > octave into equal steps of about a third of a tone
> > > (1200/17 = 70.588 cents), or possibly even to divide
> > > equal-tempered tones of 200 cents into exact thirds
> > > of 66.667 cents.
> >
> > That impression could only be justied during the time of Kantemir, with
> > possible 1/3rd tones here and there.
>
> Didn't know that!  What was his motivation?
>


He required to distinguish leading-tones from diatonical steps. His
instructions clearly indicate the necessity of 1/3rd tones.


> > > [There is, however, some evidence from Michael
> > > Meshaqah (cited by Eli Smith according to Ellis)
> > > that "modern Greeks" (in the 19th Century) divided
> > > the octave into 4 X 17 = 68 equal parts, forming a
> > > scale with steps:
> > >
> > > 12 9 7 12 9 7 12 of these (octave/68) divisions.
> >
> > Preposterous suggestion.
>
> Why preposterous?
>


68 equal is a division which hardly makes sense.


> I presume that Smith had reason to believe
> this, and so too Michael Meshaqah.


I dare someone to come forward and prove that Greeks indeed advocated such a
thing in history.


Is it
> likely that the latter would have invented
> such a specifically detailed tuning out of
> nothing, then attributed it to the Greeks?


Given the unreliability of myths and fairy tales as concocted by the human
mind, I would conclude so.


> Is it not MORE likely that he observed
> Greek instruments with fingerboards so
> divided, or conversed with Greek musicians
> and simply repeated what they told him?
>
>


It is a question whether he understood Greek in the first place.


> > > Ellis comments that if the steps of 9 and 7 parts
> > > were instead both of 8 parts, the scale would
> > > consist of:
> > >
> > > 3 2 2 3 2 2 3 of these (octave/17) divisions,
> > > "the precise scale of Villoteau" (op. cit. p 556).]
> >
> > Certainly not. 17-eq is never assumed by anyone except my colleague
Kemal
> > Karaosmanoglu who supports Yalcin Tura when it comes to equalizing the
17
> > traditional pitches per octave.
>
> I'm sorry, I don't see the relevance of modern
> "assumptions" when judging the accuracy of an
> historical report made around 1850!
>


This is the mode out of 17-eq:

  0:          1/1               0.000 unison, perfect prime
  1:        211.765 cents     211.765
  2:        352.941 cents     352.941
  3:        494.118 cents     494.118
  4:        705.882 cents     705.882
  5:        847.059 cents     847.059
  6:        988.235 cents     988.235
  7:          2/1            1200.000 octave


I dare say, it is a compelling scale with a distinct Maqam flavor. But I
would have rathered:

1
9/8
27/22
4/3
3/2
18/11
16/9
2


> And is your collegue "assuming" 17-EDO or
> rather advocating it?
>
>


Advocating it as an educational methodology. I beg to differ of course.


> > The exact ratios are (according to Urmevi and Meragi):
> >
> >   0:          1/1               0.000 unison, perfect prime
> >   1:        256/243            90.225 limma, Pythagorean minor second
> >   2:      65536/59049         180.450 Pythagorean diminished third
> >   3:          9/8             203.910 major whole tone
> >   4:         32/27            294.135 Pythagorean minor third
> >   5:       8192/6561          384.360 Pythagorean diminished fourth
> >   6:         81/64            407.820 Pythagorean major third
> >   7:          4/3             498.045 perfect fourth
> >   8:       1024/729           588.270 Pythagorean diminished fifth
> >   9:     262144/177147        678.495 Pythagorean diminished sixth
> >  10:          3/2             701.955 perfect fifth
> >  11:        128/81            792.180 Pythagorean minor sixth
> >  12:      32768/19683         882.405 Pythagorean diminished seventh
> >  13:         27/16            905.865 Pythagorean major sixth
> >  14:         16/9             996.090 Pythagorean minor seventh
> >  15:       4096/2187         1086.315 Pythagorean diminished octave
> >  16:    1048576/531441       1176.540 Pythagorean diminished ninth
> >  17:          2/1            1200.000 octave
>
> Not being able to recognise the higher powers
> of 3 at a glance, I don't know whether this
> disagrees with the genesis of the 17 tones as
> a series of 16 fourths upwards from the ratio
> 81/64.  But I assume not.
>
>

It agrees with it.


>
> A clarification: Helmholtz gives as reference for
> this statement:
> "Journal of the American Oriental Society,
> vol. i. p. 173, 1847."
>
> I don't have access to that journal, but  I do
> wonder exactly what Meshaqah wrote there.
>


I have his essay in Arabic and I can provide the JPG files if you can help
decipher them.


>
> Very interesting!  But there's a long time between
> 1847 and 1899 - time enough for a scholar to make
> many a revision of his theories.  Assuming that "the
> Syrian, Michael Mesha-qah" of 1847 is the same
> person as the "Lebanese scholar Mih.a'il Mu^saqah"
> of 1899.  Only the vagaries of transliteration
> throws it into doubt, really.  (Lebanon used to be
> part of Syria.)
>
> Perhaps he learnt more as he got older?
>


I wonder if that is so.


>
> > > Interestingly, the three-quartertone interval was
> > > introduced by the lutist Zalzal some 1100 years ago.
> > > It was the ratio 12/11 = 151 cents (op. cit. p.264).
> > > This note disappeared from the lutist's gamut in
> > > mediaeval times.
> >
> > It did not dissapear, but was dismissed by theory alone. An excessive
zeal
> > and reverence for Pythagoras may be the culprit for this trend. Notice
the
> > introduction of octave equivalance by Safi Al-Din.
>
> When did this happen?  Can you tell me more
> about this Safi-ud-Din?
>
>


This occured during the 13th century, just before the Mongol invasion. The
Abbasid Empire was in tethers, the caliph merely a puppet of the lords of
the land. Safi Al-Din was a musician from Urumiyah (hence the title,
Urmevi), and chief librarian to Al-Musta'sim.

Here is an interesting discussion about him:

http://www.mikeouds.com/messageboard/viewthread.php?tid=2355


> > > Helmholtz / Ellis also contains at least three distinct
> > > explanations of the maqamat - it's quite entertaining
> > > reading in places.  Ellis' interpretation seems to me
> > > to hold water best.
> >
> > And what might that be?
>
> What, you don't have this book?  I'm amazed! :-)
>


You mean the Sensations On Tone? I have it right here, but I hardly could
look at it.


> In fact, it's long and tedious and I don't have
> the energy to type it all up right now (I should
> have been in bed hours ago), tho I will do so
> later if you want me to.  In short, he gives exact
> tunings for the 12 maqams:
> (`Ushaq, Nawaa, Busilik, Raast, `Iraaq, Isfahaan,
> Zirafkend, Buzurk, Zenkuleh, Raahawi, Husa\ufffdni,
> Hijaazi).
>


I'll examine these at my leisure.


>
> Good night!
> Yahya
> --

Night!
Oz.

From: Yahya Abdal-Aziz (2006-01-15)
Subject: Re: New Generalized Keyboard

On Sun, 15 Jan 2006 Ozan Yarman wrote:
> > Thank you for your elucidations, my friend.
> > One could hardly expect Helmholtz and Ellis
> > to be better informed about maqam music
> > more than a century ago than you; besides,
> > their information was mostly second-hand.
>
> Truly, you are most gracious, but I do not deserve the compliment. I'm one
> of the most ignorant people in the world.

Are you he of whom it is said:
"Your ignorance is exceeded only by your good looks!"


> > > ... 17
> > > pure fourths from a reference tone gives all the correct pitches
except
> > > 81/64. Actually, one needs 4 pure fifths up, 12 fifths down.
> >
> > 17 pure fourths up from the ratio 18/64, adjusted
> > to remain within the octave, gives a cycle of 17
> > notes, which is of course a  cycle of fifths read in
> > the reverse order.  This is the procedure Ellis shows
> > (loc. cit.), giving familiar European names to (and
> > cents measures for) the 17 tones, thus:
> >
> > 1 E 408
> > 2 A 906
> > 3 D 204
> > 4 G 702
> > 5 C 0
> > 6 F 498
> > 7 Bb 996
> > 8 Eb 294
> > 9 Ab 792
> > 10 Db 90
> > 11 Gb 588
> > 12 Cb 1086
> > 13 Fb 384
> > 14 Bbb 882
> > 15 Ebb 180
> > 16 Abb 678
> > 17 Dbb 1176
>
> An agreeable procedure. You might want to check:
>
> http://www.ozanyarman.com/files/Doktora%20Tezi%20Raporu%203.pdf
>
> (p. 45-51) For a wholesome table of Ebjed notations based on this tuning
> scheme.

Wish I could read the Turkish, too ... Well, that's
the next language on my list.


> > The only theorists mentioned by Ellis in this passage
> > are al-Farabi, Zalzal and Abdul-Qadir.  Helmholtz
> > writes of:
> > "the directions for the division of the monochord
> > given by Abdul Kadir, a celebrated Persian theorist
> > of the fourteenth century of our era, that lived at
> > the courts of Timur and Bajazet.  ... These directions
> > also agree in essentials with those of the much older
> > Farabi, (who died in AD 950), and of his own
> > contemporary, Mahmud Shirazi, (who died in 1315),
> > for dividing the fingerboard of lutes.  According to
> > the directions of Abdul Kadir all the tonal degrees
> > of the Arabic scale are obtained by a series of 16
> Fifths ...."
> >
>
>
> Abdulkadir's directions certainly do not agree with Al-Farabi! The tuning
> scheme proposed by Al-Farabi is in the Scala archive (al-farabi_22.scl):
>
> Al-Farabi 22 note ud scale
> |
>   0:          1/1               0.000 unison, perfect prime
>   1:        256/243            90.225 limma, Pythagorean minor second
>   2:         18/17             98.955 Arabic lute index finger
>   3:         12/11            150.637 3/4-tone, undecimal neutral second
>   4:          9/8             203.910 major whole tone
>   5:         32/27            294.135 Pythagorean minor third
>   6:         27/22            354.547 neutral third, Zalzal wosta of
> al-Farabi
>   7:       8192/6561          384.360 Pythagorean diminished fourth
>   8:         81/64            407.820 Pythagorean major third
>   9:          4/3             498.045 perfect fourth
>  10:       1024/729           588.270 Pythagorean diminished fifth
>  11:         24/17            597.000 1st septendecimal tritone
>  12:         16/11            648.682 undecimal semi-diminished fifth
>  13:          3/2             701.955 perfect fifth
>  14:        128/81            792.180 Pythagorean minor sixth
>  15:         18/11            852.592 undecimal neutral sixth
>  16:      32768/19683         882.405 Pythagorean diminished seventh
>  17:         27/16            905.865 Pythagorean major sixth
>  18:         16/9             996.090 Pythagorean minor seventh
>  19:       4096/2187         1086.315 Pythagorean diminished octave
>  20:         32/17           1095.045 17th subharmonic
>  21:         64/33           1146.727 33rd subharmonic
>  22:          2/1            1200.000 octave

Was this scheme based upon his transmission
of Greek tuning theory, or was there something
novel in it?


> Notice that this scheme not only contains 22 notes per octave, but also is
> 17-limit, while Meragi adopts the 3-limit Pythagorean tradition as
proposed
> by Urmevi.

Interesting coincidence, that the Indian classical
gamut (not scale! nor mode!) includes 22 s'ruti per
octave ...


> The revival of quarter-tones by Mushaqa requires the pre-eminence of
> Al-Farabi and Zalzal over Urmevi and Meragi, which is the fundamental
> difference between Turkish and Arabic Maqam Music theory.

You speak of a "revival" - who had used them
before Mushaqa?


> > > Besides, Baghdad was a cosmopolitan centre, hardly making it Arabic
> > > during the conquest by Mongols. The following Levantine treatises are
> > > written during the Ottoman Era, making them more Turkish than Arabic.
> >
> > I won't argue questions of race with anyone.
> > I am very proud of my race - human!
>
> That makes me an outworlder I suppose. ;)

Well, at times you DO seem a little ... alien?  ;-)


> > > the impression gained and promulgated by
> > > > Villoteau was that the Arabs intended to divide the
> > > > octave into equal steps of about a third of a tone
> > > > (1200/17 = 70.588 cents), or possibly even to divide
> > > > equal-tempered tones of 200 cents into exact thirds
> > > > of 66.667 cents.
> > >
> > > That impression could only be justied during the time of Kantemir,
with
> > > possible 1/3rd tones here and there.
> >
> > Didn't know that!  What was his motivation?
>
>
> He required to distinguish leading-tones from diatonical steps. His
> instructions clearly indicate the necessity of 1/3rd tones.
>
>
> > > > [There is, however, some evidence from Michael
> > > > Meshaqah (cited by Eli Smith according to Ellis)
> > > > that "modern Greeks" (in the 19th Century) divided
> > > > the octave into 4 X 17 = 68 equal parts, forming a
> > > > scale with steps:
> > > >
> > > > 12 9 7 12 9 7 12 of these (octave/68) divisions.
> > >
> > > Preposterous suggestion.
> >
> > Why preposterous?
>
>
> 68 equal is a division which hardly makes sense.

Unless it works ...!


> > I presume that Smith had reason to believe
> > this, and so too Michael Meshaqah.
>
> I dare someone to come forward and prove that Greeks indeed advocated such
a
> thing in history.

I hope "someone" takes your dare!


> > Is it likely that the latter would have invented
> > such a specifically detailed tuning out of
> > nothing, then attributed it to the Greeks?
>
> Given the unreliability of myths and fairy tales as concocted by the human
> mind, I would conclude so.

Ah, we all love a story ...


> > Is it not MORE likely that he observed
> > Greek instruments with fingerboards so
> > divided, or conversed with Greek musicians
> > and simply repeated what they told him?
>
> It is a question whether he understood Greek in the first place.

You have contrary evidence?


> > > > Ellis comments that if the steps of 9 and 7 parts
> > > > were instead both of 8 parts, the scale would
> > > > consist of:
> > > >
> > > > 3 2 2 3 2 2 3 of these (octave/17) divisions,
> > > > "the precise scale of Villoteau" (op. cit. p 556).]
> > >
> > > Certainly not. 17-eq is never assumed by anyone except my colleague
> > > Kemal Karaosmanoglu who supports Yalcin Tura when it comes to
> > > equalizing the 17 traditional pitches per octave.
> >
> > I'm sorry, I don't see the relevance of modern
> > "assumptions" when judging the accuracy of an
> > historical report made around 1850!
>
>
> This is the mode out of 17-eq:
>
>   0:          1/1               0.000 unison, perfect prime
>   1:        211.765 cents     211.765
>   2:        352.941 cents     352.941
>   3:        494.118 cents     494.118
>   4:        705.882 cents     705.882
>   5:        847.059 cents     847.059
>   6:        988.235 cents     988.235
>   7:          2/1            1200.000 octave
>
>
> I dare say, it is a compelling scale with a distinct Maqam flavor. But I
> would have rathered:
>
> 1
> 9/8
> 27/22
> 4/3
> 3/2
> 18/11
> 16/9
> 2

I think we were discussing history, rather than
personal preference.


> > And is your collegue "assuming" 17-EDO or
> > rather advocating it?
>
>
> Advocating it as an educational methodology. I beg to differ of course.

Of course!


> > > The exact ratios are (according to Urmevi and Meragi):
> > >
> > >   0:          1/1               0.000 unison, perfect prime
> > >   1:        256/243            90.225 limma, Pythagorean minor second
> > >   2:      65536/59049         180.450 Pythagorean diminished third
> > >   3:          9/8             203.910 major whole tone
> > >   4:         32/27            294.135 Pythagorean minor third
> > >   5:       8192/6561          384.360 Pythagorean diminished fourth
> > >   6:         81/64            407.820 Pythagorean major third
> > >   7:          4/3             498.045 perfect fourth
> > >   8:       1024/729           588.270 Pythagorean diminished fifth
> > >   9:     262144/177147        678.495 Pythagorean diminished sixth
> > >  10:          3/2             701.955 perfect fifth
> > >  11:        128/81            792.180 Pythagorean minor sixth
> > >  12:      32768/19683         882.405 Pythagorean diminished seventh
> > >  13:         27/16            905.865 Pythagorean major sixth
> > >  14:         16/9             996.090 Pythagorean minor seventh
> > >  15:       4096/2187         1086.315 Pythagorean diminished octave
> > >  16:    1048576/531441       1176.540 Pythagorean diminished ninth
> > >  17:          2/1            1200.000 octave
> >
> > Not being able to recognise the higher powers
> > of 3 at a glance, I don't know whether this
> > disagrees with the genesis of the 17 tones as
> > a series of 16 fourths upwards from the ratio
> > 81/64.  But I assume not.
>
> It agrees with it.

> >
> > A clarification: Helmholtz gives as reference for
> > this statement:
> > "Journal of the American Oriental Society,
> > vol. i. p. 173, 1847."
> >
> > I don't have access to that journal, but  I do
> > wonder exactly what Meshaqah wrote there.
>
> I have his essay in Arabic and I can provide the JPG files if you can help
> decipher them.

Sounds like a worthwhile project!  Please send me
a picture or two so I can ascertain whether or not
I will be able to help out.


> > Very interesting!  But there's a long time between
> > 1847 and 1899 - time enough for a scholar to make
> > many a revision of his theories.  Assuming that "the
> > Syrian, Michael Mesha-qah" of 1847 is the same
> > person as the "Lebanese scholar Mih.a'il Mu^saqah"
> > of 1899.  Only the vagaries of transliteration
> > throws it into doubt, really.  (Lebanon used to be
> > part of Syria.)
> >
> > Perhaps he learnt more as he got older?
>
> I wonder if that is so.
>
>
> > > > Interestingly, the three-quartertone interval was
> > > > introduced by the lutist Zalzal some 1100 years ago.
> > > > It was the ratio 12/11 = 151 cents (op. cit. p.264).
> > > > This note disappeared from the lutist's gamut in
> > > > mediaeval times.
> > >
> > > It did not dissapear, but was dismissed by theory alone. An excessive
> > > zeal and reverence for Pythagoras may be the culprit for this trend.
> > > Notice the introduction of octave equivalance by Safi Al-Din.
> >
> > When did this happen?  Can you tell me more
> > about this Safi-ud-Din?
>
> This occured during the 13th century, just before the Mongol invasion. The
> Abbasid Empire was in tethers, the caliph merely a puppet of the lords of
> the land. Safi Al-Din was a musician from Urumiyah (hence the title,
> Urmevi), and chief librarian to Al-Musta'sim.
>
> Here is an interesting discussion about him:
>
> http://www.mikeouds.com/messageboard/viewthread.php?tid=2355

Thanks.  I will try to read this tomorrow.


> > > > Helmholtz / Ellis also contains at least three distinct
> > > > explanations of the maqamat - it's quite entertaining
> > > > reading in places.  Ellis' interpretation seems to me
> > > > to hold water best.
> > >
> > > And what might that be?
> >
> > What, you don't have this book?  I'm amazed! :-)
>
> You mean the Sensations On Tone? I have it right here, but I hardly could
> look at it.
>
> > In fact, it's long and tedious and I don't have
> > the energy to type it all up right now (I should
> > have been in bed hours ago), tho I will do so
> > later if you want me to.  In short, he gives exact
> > tunings for the 12 maqams:
> > (`Ushaq, Nawaa, Busilik, Raast, `Iraaq, Isfahaan,
> > Zirafkend, Buzurk, Zenkuleh, Raahawi, Husa\ufffdni,
> > Hijaazi).
>
> I'll examine these at my leisure.

Leisure?  You have leisure?!

Good night, once more!  (Actually, it's almost time
for Fajr.)

Yahya

--
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From: Gene Ward Smith (2006-01-15)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:

> > > > 12 9 7 12 9 7 12 of these (octave/68) divisions.
> > >
> > > Preposterous suggestion.
> >
> > Why preposterous?

> 68 equal is a division which hardly makes sense.

On the contrary, 68 equal is an excellent division which makes a lot
of sense. The trouble here, if any, is that this scale doesn't play to
its strengths; at least, I can't see it. I'd suggest that using 41-et
and 7 6 4 7 6 4 7 might be more interesting.

17 et has good fifths, 34 et has good thirds, and 68 et does quite
well in the 7-limit. It tempers out 245/243, 2048/2025, 2401/2400,
3136/3125, 6144/6125 and 15625/15552 among other intervals. It also
could be of interest to people who like the 88 cent generator
business, as 5 steps of 68 gives 88.235 cents, which seems to be doing
what the 88 cent people want done. This is actually the generator for
"octacot temperament", which uses eight steps to get to a fifth,
eleven steps to get to the "7/4", and eighteen steps to get to the
"5/2". Of course, if you want *exactly* 88 cents for your octacot
generator, you can use 11 steps of 150-et instead, which is a
reasonable choice. 

> I dare say, it is a compelling scale with a distinct Maqam flavor. But I
> would have rathered:
> 
> 1
> 9/8
> 27/22
> 4/3
> 3/2
> 18/11
> 16/9
> 2

Zalzal, according to Scala. In 41, it becomes 7 5 5 7 5 5 7, which is
more accurate than what 24 gives.

From: Gene Ward Smith (2006-01-15)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
 But I
> > would have rathered:
> > 
> > 1
> > 9/8
> > 27/22
> > 4/3
> > 3/2
> > 18/11
> > 16/9
> > 2
> 
> Zalzal, according to Scala. In 41, it becomes 7 5 5 7 5 5 7, which is
> more accurate than what 24 gives.

I was trying to pin an Arabic label on 243/242 a while back,
particularly in connection with a {2,3,11} temperament. If you temper
out both 243/242 and 896/891, you get a {2,3,7,11} temperament (or
else a planar temperament.) We get the same neutral third generator.
If we add 245/243 to the mix, we get a linear temperament, still
supported by 41-et, with neutral third generators. It would be
tempting to give an Arabic-inspired name to this. Would that be sensible?

Here are 7 and 17 note scales obtained by detempering neutral third
chain MOS from 41-equal. Possibly they will be of interest to someone.

seven notes: [160/147, 11/9, 4/3, 3/2, 18/11, 11/6, 2]

seventeen notes: [25/24, 160/147, 9/8, 25/21, 11/9, 14/11, 4/3, 
11/8, 16/11, 3/2, 11/7, 18/11, 27/16, 16/9, 11/6, 27/14, 2]

From: a_sparschuh (2006-01-16)
Subject: Al Farabis 12-limma & 5-PC Pyth. 17-tone scale: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
> In fact, the gamut of 17 tones per
  octave had the following step intervals:
>  
   Li Li pc Li Li pc Li Li Li pc Li Li pc Li Li Li pc
>  
> Li := Pyth. Limma = 256/243 ~= 90 cents
> pc := Pyth. Comma = 531441/524288 ~= 24 cents
> > 
> > These are very unequal steps, 
> But identical to the series of 16 perfect fourths (17 notes).> 
or with:
# := 3^7/2^11=2187/2048 'the apotome "sharp" symbol
b := 1/# 'reverse apatome "flat" symbol
then
Li=#/c=2^8/3^5=256/243
the 16-chain of 5ths (reverse 4ths) out of 53 becomes

...Gb Db Ab Eb Bb F. C. G. D. A. E. B. F# C# G# D# A#...
3^ -8 -7 -6 -5 -4 -3 -2 -1 +0 +1 +2 +3 +4 +5 +6 +7 +8

C. 3^-2 > Li 
Db 3^-7 > pc
C# 3^+5 > Li 
D. 3^+0 > Li
Eb 3^-5 > pc
D# 3^+7 > Li
E. 3^+2 > Li
F. 3^-3 > Li
Gb 3^+6 > pc
F# 3^+4 > Li
G. 3^-1 > Li
Ab 3^-6 > pc
G# 3^+6 > Li
A. 3^+1 > Li
Bb 3^-4 > pc
A# 3^+7 > Li
B. 3^+3 > Li
C' 3^-2

From: a_sparschuh (2006-01-17)
Subject: 243/242 as tuning step, was Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
. 
> I was trying to pin an Arabic label on 243/242 a while back,
Dear Gene
do the same game as with 225/224 or 100/99 last time

A 57,114,228,456 Hz
E 171
B 1,...,512/513 Erasthostens bridge 19=~=3
F# 3
C# 9
G# 27
Eb 81
Bb 121,242/243 bridge 11^2=~=3 here occures the ratio: 243/242
F 181,362/363
C 271,542/543
G 203,406,812/813
D 19,38,76,152,304,608/609
A 57
Division of the
PC=531441/528244=3^12/2^19=
(513/512)(243/242)(363/362)(543/542)(813/812)(608/609)
into 6 superparticular subfactors.

C: 1
C# 288/271
D: 304/271
Eb 322/271
E: 342/271
F: 362/271
F# 384/271
G: 406/271
G# 432/271
A: 456/271
Bb 484/271
B: 512/271
C' 2
sounds best @ middle C=271 Hz or A=456 Hz

From: wallyesterpaulrus (2006-01-19)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> 
> > > 12 9 7 12 9 7 12 of these (octave/68) divisions.
> > > 
> > > Ellis comments that if the steps of 9 and 7 parts
> > > were instead both of 8 parts, the scale would
> > > consist of:
> 
> You can also replace 12 with 9/8, 9 with 10/9, and 7 with 16/15. The
> scale will now be a 5-limit Fokker block, synmav3 in my catalog. It 
is
> also a rotated form of various scales, including al-farabi_g1, about
> which the Scala scl says "Al-Farabi's Greek genus conjunctum medium,
> Land". If now you temper out 99/98 and 225/224, you get something
> quite a lot closer to the above scale, with a considerable quantity 
of 
> 11-limit harmony worked in.
> 
> Here it is in the rms tuning of {99/98,225/224}-planar, for which 
I've
> proposed the name "apollo" in case anyone really wants to name such
> things. Apollo is a pretty good temperament.
> 
> ! apol.scl
> synmav3 in apollo {100/99, 225/224} temperament
> 7
> !
> 207.252202
> 381.116799
> 496.373899
> 703.626101
> 877.490697
> 992.747798
> 1200.000000

It looks like something went awry. Is it 99/98, or 100/99, that you 
really mean?

From: wallyesterpaulrus (2006-01-19)
Subject: Reference frequency (was: Re: New Generalized Keyboard)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> 
> SNIP
> 
> >
> >
> > If the reference here is to Safi Al-Din's theory of 17 Pythagorean
> ratios
> > per octave preserved by Meragi himself, then this definition is
> wrong. 17
> > pure fourths from a reference tone gives all the correct pitches
> except
> > 81/64. Actually, one needs 4 pure fifths up, 12 fifths down.
> 
> I would consider the two alternatives exactly the same -- all you
> have to do is change the reference tone and the two are identical.
> Unless there was a clear choice of reference tone such as an ever-
> present drone, I think "wrong" is too strong a word here. Tuning 4
> pure fifths up and 12 fifths down from a reference note *does* 
result
> in a set of 17 notes forming a single series of perfect fourths (or
> fifths), including that reference note.
> 
> 
> ---------------------
> 
> 
> You cannot change the reference tone, because the relative 
>frequency of the
> reference tone is always 1, and hence, your definition is 
>incomplete.

It's always 1 what? Surely you don't mean 1Hz, since that's an 
inaudible frequency.

From: Gene Ward Smith (2006-01-19)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> It looks like something went awry. Is it 99/98, or 100/99, that you 
> really mean?

Sorry, I meant 100/99. Actually, you can simply use 11-limit magic,
which is close in tuning.

From: Ozan Yarman (2006-01-24)
Subject: Re: [tuning] Re: New Generalized Keyboard

----- Original Message -----
From: "Gene Ward Smith" <gwsmith@svpal.org>
To: <tuning@yahoogroups.com>
Sent: 15 Ocak 2006 Pazar 22:45
Subject: [tuning] Re: New Generalized Keyboard


> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>  But I
> > > would have rathered:
> > >
> > > 1
> > > 9/8
> > > 27/22
> > > 4/3
> > > 3/2
> > > 18/11
> > > 16/9
> > > 2
> >
> > Zalzal, according to Scala. In 41, it becomes 7 5 5 7 5 5 7, which is
> > more accurate than what 24 gives.
>
> I was trying to pin an Arabic label on 243/242 a while back,
> particularly in connection with a {2,3,11} temperament. If you temper
> out both 243/242 and 896/891, you get a {2,3,7,11} temperament (or
> else a planar temperament.) We get the same neutral third generator.
> If we add 245/243 to the mix, we get a linear temperament, still
> supported by 41-et, with neutral third generators. It would be
> tempting to give an Arabic-inspired name to this. Would that be sensible?
>


Possibly. Thalith means third in Arabic. Halis means pure, cleansed,
unadulterated, Thalith Al-Halis would mean Neutral Third. The comma would be
Baqiyyah. Neutral third comma would be Baqiyyat'ul Thalith Al-Halis.

Or did you have something else in mind?


> Here are 7 and 17 note scales obtained by detempering neutral third
> chain MOS from 41-equal. Possibly they will be of interest to someone.
>
> seven notes: [160/147, 11/9, 4/3, 3/2, 18/11, 11/6, 2]
>
> seventeen notes: [25/24, 160/147, 9/8, 25/21, 11/9, 14/11, 4/3,
> 11/8, 16/11, 3/2, 11/7, 18/11, 27/16, 16/9, 11/6, 27/14, 2]
>
>
>

Maqam flavored, no doubt.

Oz.

From: Ozan Yarman (2006-01-24)
Subject: Re: [tuning] Re: New Generalized Keyboard

I'm back!

----- Original Message -----
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
To: <tuning@yahoogroups.com>
Sent: 15 Ocak 2006 Pazar 19:26
Subject: [tuning] Re: New Generalized Keyboard


> >
> > Truly, you are most gracious, but I do not deserve the compliment. I'm
one
> > of the most ignorant people in the world.
>
> Are you he of whom it is said:
> "Your ignorance is exceeded only by your good looks!"
>


I was the one who coined the term: "Ignorance is as ignorant does". I
support Averroes against Al-Gazali!

Here is another:

`Ignorance is only exceeded by incoherence.`

Somebody ought to revive the Mutezilah. ROFL


> >
> > http://www.ozanyarman.com/files/Doktora%20Tezi%20Raporu%203.pdf
> >
> > (p. 45-51) For a wholesome table of Ebjed notations based on this tuning
> > scheme.
>
> Wish I could read the Turkish, too ... Well, that's
> the next language on my list.
>
>


I shall aid you with anything you care to ask.


> >
> > Abdulkadir's directions certainly do not agree with Al-Farabi! The
tuning
> > scheme proposed by Al-Farabi is in the Scala archive (al-farabi_22.scl):
> >
> > Al-Farabi 22 note ud scale
> > |
> >   0:          1/1               0.000 unison, perfect prime
> >   1:        256/243            90.225 limma, Pythagorean minor second
> >   2:         18/17             98.955 Arabic lute index finger
> >   3:         12/11            150.637 3/4-tone, undecimal neutral second
> >   4:          9/8             203.910 major whole tone
> >   5:         32/27            294.135 Pythagorean minor third
> >   6:         27/22            354.547 neutral third, Zalzal wosta of
> > al-Farabi
> >   7:       8192/6561          384.360 Pythagorean diminished fourth
> >   8:         81/64            407.820 Pythagorean major third
> >   9:          4/3             498.045 perfect fourth
> >  10:       1024/729           588.270 Pythagorean diminished fifth
> >  11:         24/17            597.000 1st septendecimal tritone
> >  12:         16/11            648.682 undecimal semi-diminished fifth
> >  13:          3/2             701.955 perfect fifth
> >  14:        128/81            792.180 Pythagorean minor sixth
> >  15:         18/11            852.592 undecimal neutral sixth
> >  16:      32768/19683         882.405 Pythagorean diminished seventh
> >  17:         27/16            905.865 Pythagorean major sixth
> >  18:         16/9             996.090 Pythagorean minor seventh
> >  19:       4096/2187         1086.315 Pythagorean diminished octave
> >  20:         32/17           1095.045 17th subharmonic
> >  21:         64/33           1146.727 33rd subharmonic
> >  22:          2/1            1200.000 octave
>
> Was this scheme based upon his transmission
> of Greek tuning theory, or was there something
> novel in it?
>


Not having access to any translation of his book, even in Turkish, I only
can conjecture that he was improving on Greek theory. He was a neo-Platonist
you know. The Mutezilah Inquisition (Mihna) provided the grounds for the
Islamic Classicism until the advent of Al-Gazali, so I would safely surmise
that Al-Farabi was raised in a philosophical environment based on works from
Antiquity.


>
> > Notice that this scheme not only contains 22 notes per octave, but also
is
> > 17-limit, while Meragi adopts the 3-limit Pythagorean tradition as
> proposed
> > by Urmevi.
>
> Interesting coincidence, that the Indian classical
> gamut (not scale! nor mode!) includes 22 s'ruti per
> octave ...
>


Coincidence? Hardly. Hindustani Sangeet is nothing other than another
variant of Maqam Music. Notice that Rauf Yekta's first proposition also
suggests 22 perdes (or srutis, if you will) per octave.


>
> > The revival of quarter-tones by Mushaqa requires the pre-eminence of
> > Al-Farabi and Zalzal over Urmevi and Meragi, which is the fundamental
> > difference between Turkish and Arabic Maqam Music theory.
>
> You speak of a "revival" - who had used them
> before Mushaqa?
>
>


Al-Farabi, for starters.


> >
> > That makes me an outworlder I suppose. ;)
>
> Well, at times you DO seem a little ... alien?  ;-)
>
>


Tramontane my dear fellow.


> >
> > 68 equal is a division which hardly makes sense.
>
> Unless it works ...!
>
>


Gene seems to think so.


>
>
> > > Is it not MORE likely that he observed
> > > Greek instruments with fingerboards so
> > > divided, or conversed with Greek musicians
> > > and simply repeated what they told him?
> >
> > It is a question whether he understood Greek in the first place.
>
> You have contrary evidence?
>
>


I base my claims on hearsay.


> > > I don't have access to that journal, but  I do
> > > wonder exactly what Meshaqah wrote there.
> >
> > I have his essay in Arabic and I can provide the JPG files if you can
help
> > decipher them.
>
> Sounds like a worthwhile project!  Please send me
> a picture or two so I can ascertain whether or not
> I will be able to help out.
>
>


Right, I'll send it to you shortly.

> >
> > > In fact, it's long and tedious and I don't have
> > > the energy to type it all up right now (I should
> > > have been in bed hours ago), tho I will do so
> > > later if you want me to.  In short, he gives exact
> > > tunings for the 12 maqams:
> > > (`Ushaq, Nawaa, Busilik, Raast, `Iraaq, Isfahaan,
> > > Zirafkend, Buzurk, Zenkuleh, Raahawi, Husa\ufffdni,
> > > Hijaazi).
> >
> > I'll examine these at my leisure.
>
> Leisure?  You have leisure?!
>


Oh yes! After 15 years of racing like a warhorse, I do deserve the break. ;)


> Good night, once more!  (Actually, it's almost time
> for Fajr.)
>

Good afternoon! (time for the noon prayer)


> Yahya
>

Cordially,
Oz.

From: Ozan Yarman (2006-01-24)
Subject: Re: [tuning] Re: New Generalized Keyboard

Hi Gene,

----- Original Message -----
From: "Gene Ward Smith" <gwsmith@svpal.org>
To: <tuning@yahoogroups.com>
Sent: 15 Ocak 2006 Pazar 21:20
Subject: [tuning] Re: New Generalized Keyboard


> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> > > > > 12 9 7 12 9 7 12 of these (octave/68) divisions.
> > > >
> > > > Preposterous suggestion.
> > >
> > > Why preposterous?
>
> > 68 equal is a division which hardly makes sense.
>
> On the contrary, 68 equal is an excellent division which makes a lot
> of sense. The trouble here, if any, is that this scale doesn't play to
> its strengths; at least, I can't see it. I'd suggest that using 41-et
> and 7 6 4 7 6 4 7 might be more interesting.
>
> 17 et has good fifths, 34 et has good thirds, and 68 et does quite
> well in the 7-limit. It tempers out 245/243, 2048/2025, 2401/2400,
> 3136/3125, 6144/6125 and 15625/15552 among other intervals. It also
> could be of interest to people who like the 88 cent generator
> business, as 5 steps of 68 gives 88.235 cents, which seems to be doing
> what the 88 cent people want done. This is actually the generator for
> "octacot temperament", which uses eight steps to get to a fifth,
> eleven steps to get to the "7/4", and eighteen steps to get to the
> "5/2". Of course, if you want *exactly* 88 cents for your octacot
> generator, you can use 11 steps of 150-et instead, which is a
> reasonable choice.
>


Ok, the scale mentioned (mode 12 9 7 12 9 7 12 of 68-edo) was this:

  0:          1/1               C          unison, perfect prime
  1:        211.765 cents   D
  2:        370.588 cents   D#7  E[
  3:        494.118 cents   F
  4:        705.882 cents   G
  5:        864.706 cents   G#7  A[
  6:        988.235 cents   A//  Bb
  7:          2/1                C          octave

The ratios desired could be:

1
9/8
21/17
4/3
3/2
28/17
16/9
2


> > I dare say, it is a compelling scale with a distinct Maqam flavor. But I
> > would have rathered:
> >
> > 1
> > 9/8
> > 27/22
> > 4/3
> > 3/2
> > 18/11
> > 16/9
> > 2
>
> Zalzal, according to Scala. In 41, it becomes 7 5 5 7 5 5 7, which is
> more accurate than what 24 gives.
>
>
>

106 is comparatively accurate.

Oz.

From: Gene Ward Smith (2006-01-24)
Subject: Re: New Generalized Keyboard

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:

> Possibly. Thalith means third in Arabic. Halis means pure, cleansed,
> unadulterated, Thalith Al-Halis would mean Neutral Third. The comma
would be
> Baqiyyah. Neutral third comma would be Baqiyyat'ul Thalith Al-Halis.

How does "alhalis" strike you as the name of a temperament?

From: Ozan Yarman (2006-01-24)
Subject: [tuning] Reference frequency (was: Re: New Generalized Keyboard)

>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: 20 Ocak 2006 Cuma 1:36
> Subject: [tuning] Reference frequency (was: Re: New Generalized Keyboard)
> > >
> > >
> > > You cannot change the reference tone, because the relative
> > >frequency of the
> > > reference tone is always 1, and hence, your definition is
> > >incomplete.
> >
> > It's always 1 what? Surely you don't mean 1Hz, since that's an
> > inaudible frequency.
> >
>
1 hz cannot be a relative frequency, it is a frequency. 1/1 equals 0 cents,
hence the reference tone.

From: Ozan Yarman (2006-01-24)
Subject: Re: [tuning] Re: New Generalized Keyboard

Wicked, man!

----- Original Message -----
From: "Gene Ward Smith" <gwsmith@svpal.org>
To: <tuning@yahoogroups.com>
Sent: 24 Ocak 2006 Sal\ufffd 13:39
Subject: [tuning] Re: New Generalized Keyboard


> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> > Possibly. Thalith means third in Arabic. Halis means pure, cleansed,
> > unadulterated, Thalith Al-Halis would mean Neutral Third. The comma
> would be
> > Baqiyyah. Neutral third comma would be Baqiyyat'ul Thalith Al-Halis.
>
> How does "alhalis" strike you as the name of a temperament?
>
>

From: wallyesterpaulrus (2006-01-30)
Subject: Reference frequency (was: Re: New Generalized Keyboard)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> 
> >
> > ----- Original Message -----
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning@yahoogroups.com>
> > Sent: 20 Ocak 2006 Cuma 1:36
> > Subject: [tuning] Reference frequency (was: Re: New Generalized 
Keyboard)
> > > >
> > > >
> > > > You cannot change the reference tone, because the relative
> > > >frequency of the
> > > > reference tone is always 1, and hence, your definition is
> > > >incomplete.
> > >
> > > It's always 1 what? Surely you don't mean 1Hz, since that's an
> > > inaudible frequency.
> > >
> >
> 1 hz cannot be a relative frequency, it is a frequency. 1/1 equals 
0 cents,
> hence the reference tone.

So you can change it (the reference tone) however you like and 
its "relative frequency" as you put it will remain the same. Right or 
wrong?

From: Ozan Yarman (2006-01-30)
Subject: Re: [tuning] Reference frequency (was: Re: New Generalized Keyboard)

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 30 Ocak 2006 Pazartesi 23:58
Subject: [tuning] Reference frequency (was: Re: New Generalized Keyboard)


> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
> >
> >
> > >
> > > ----- Original Message -----
> > > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > > To: <tuning@yahoogroups.com>
> > > Sent: 20 Ocak 2006 Cuma 1:36
> > > Subject: [tuning] Reference frequency (was: Re: New Generalized
> Keyboard)
> > > > >
> > > > >
> > > > > You cannot change the reference tone, because the relative
> > > > >frequency of the
> > > > > reference tone is always 1, and hence, your definition is
> > > > >incomplete.
> > > >
> > > > It's always 1 what? Surely you don't mean 1Hz, since that's an
> > > > inaudible frequency.
> > > >
> > >
> > 1 hz cannot be a relative frequency, it is a frequency. 1/1 equals
> 0 cents,
> > hence the reference tone.
>
> So you can change it (the reference tone) however you like and
> its "relative frequency" as you put it will remain the same. Right or
> wrong?
>
>
>

Right. The relative frequeny of the reference tone is always the ratio 1/1,
or 0 cents. This applies to perde rast for all times, all circumstances in
Maqam Music.

From: wallyesterpaulrus (2006-01-31)
Subject: Reference frequency (was: Re: New Generalized Keyboard)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> wrote:
>
> 
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> To: <tuning@yahoogroups.com>
> Sent: 30 Ocak 2006 Pazartesi 23:58
> Subject: [tuning] Reference frequency (was: Re: New Generalized 
Keyboard)
> 
> 
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@o...> 
wrote:
> > >
> > >
> > > >
> > > > ----- Original Message -----
> > > > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > > > To: <tuning@yahoogroups.com>
> > > > Sent: 20 Ocak 2006 Cuma 1:36
> > > > Subject: [tuning] Reference frequency (was: Re: New 
Generalized
> > Keyboard)
> > > > > >
> > > > > >
> > > > > > You cannot change the reference tone, because the relative
> > > > > >frequency of the
> > > > > > reference tone is always 1, and hence, your definition is
> > > > > >incomplete.
> > > > >
> > > > > It's always 1 what? Surely you don't mean 1Hz, since that's 
an
> > > > > inaudible frequency.
> > > > >
> > > >
> > > 1 hz cannot be a relative frequency, it is a frequency. 1/1 
equals
> > 0 cents,
> > > hence the reference tone.
> >
> > So you can change it (the reference tone) however you like and
> > its "relative frequency" as you put it will remain the same. 
Right or
> > wrong?
> >
> >
> >
> 
> Right. The relative frequeny of the reference tone is always the 
ratio 1/1,
> or 0 cents.

Excellent. Then what I did above was indeed valid.

> This applies to perde rast for all times, all circumstances in
> Maqam Music.

Why?

From: Ozan Yarman (2006-01-31)
Subject: Re: [tuning] Reference frequency (was: Re: New Generalized Keyboard)

> > 
> > Right. The relative frequeny of the reference tone is always the 
> ratio 1/1,
> > or 0 cents.
> 
> Excellent. Then what I did above was indeed valid.
> 


Remind me what it was?


> > This applies to perde rast for all times, all circumstances in
> > Maqam Music.
> 
> Why?
> 
> 

Because perde rast (1/1) is the reference tone for all Ahenks (Keys?).

From: wallyesterpaulrus (2006-02-17)
Subject: Reference frequency (was: Re: New Generalized Keyboard)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> 
> > > 
> > > Right. The relative frequeny of the reference tone is always 
the 
> > ratio 1/1,
> > > or 0 cents.
> > 
> > Excellent. Then what I did above was indeed valid.
> > 
> 
> 
> Remind me what it was?

Show that two different chain-of-16-pure-fifths scales were identical 
in all physical respects, differing only in the arbitrary choice of 
which note to call the "reference tone", i.e., "1/1".

> > > This applies to perde rast for all times, all circumstances in
> > > Maqam Music.
> > 
> > Why?
> > 
> > 
> 
> Because perde rast (1/1) is the reference tone for all Ahenks >
(Keys?).

Can you elaborate?

From: Ozan Yarman (2006-02-19)
Subject: Re: [tuning] Reference frequency (was: Re: New Generalized Keyboard)

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 18 \ufffdubat 2006 Cumartesi 1:12
Subject: [tuning] Reference frequency (was: Re: New Generalized Keyboard)


> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> >
> > > >
> > > > Right. The relative frequeny of the reference tone is always
> the
> > > ratio 1/1,
> > > > or 0 cents.
> > >
> > > Excellent. Then what I did above was indeed valid.
> > >
> >
> >
> > Remind me what it was?
>
> Show that two different chain-of-16-pure-fifths scales were identical
> in all physical respects, differing only in the arbitrary choice of
> which note to call the "reference tone", i.e., "1/1".
>


You can only select on reference tone at a time.


> > > > This applies to perde rast for all times, all circumstances in
> > > > Maqam Music.
> > >
> > > Why?
> > >


Because roses are red and violets are blue, perde rast is considered a tone
so true!


> > >
> >
> > Because perde rast (1/1) is the reference tone for all Ahenks >
> (Keys?).
>
> Can you elaborate?
>
>


Ahenks are pitch level standards in Maqam Music. Kiz Ney gives a rast tone
at ~440 Hz. Mansur Ney gives a rast tone at ~391 Hz. Regardless, rast is
1/1, the reference tone, similar to the Key-transposing instruments in
Western common-practice music. Remember that all Neys are octave-transposing
as well as key-transposing.

If you consider that Sipurde Ahenk produces perde rast at C ~261 Hz, you can
say that A=440 Hz (which is perde huseyni in this Ahenk). Because one can
perform all natural tones in reference to Western Staff Notation in the
default scale of the principle Rast Maqam, I choose this Ahenk to be my
pitch standard.

perde rast for:

Sipurde is in C,
Mustahzen is in B,
Kiz is in A,
Mansur is in G,
Shah is in F,
Davud is in E,
Bolahenk is in D.

according to the Western pitch standard.

Cordially,
Ozan

From: wallyesterpaulrus (2006-02-21)
Subject: Reference frequency (was: Re: New Generalized Keyboard)

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> 
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@...>
> To: <tuning@yahoogroups.com>
> Sent: 18 Þubat 2006 Cumartesi 1:12
> Subject: [tuning] Reference frequency (was: Re: New Generalized Keyboard)
> 
> 
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > >
> > > > >
> > > > > Right. The relative frequeny of the reference tone is always
> > the
> > > > ratio 1/1,
> > > > > or 0 cents.
> > > >
> > > > Excellent. Then what I did above was indeed valid.
> > > >
> > >
> > >
> > > Remind me what it was?
> >
> > Show that two different chain-of-16-pure-fifths scales were identical
> > in all physical respects, differing only in the arbitrary choice of
> > which note to call the "reference tone", i.e., "1/1".
> >
> 
> 
> You can only select on reference tone at a time.

I am!

 
> > > > > This applies to perde rast for all times, all circumstances in
> > > > > Maqam Music.
> > > >
> > > > Why?
> > > >
> 
> 
> Because roses are red and violets are blue, perde rast is considered a tone
> so true!
> 
> 
> > > >
> > >
> > > Because perde rast (1/1) is the reference tone for all Ahenks >
> > (Keys?).
> >
> > Can you elaborate?
> >
> >
> 
> 
> Ahenks are pitch level standards in Maqam Music. Kiz Ney gives a rast tone
> at ~440 Hz. Mansur Ney gives a rast tone at ~391 Hz. Regardless, rast is
> 1/1, the reference tone, similar to the Key-transposing instruments in
> Western common-practice music. Remember that all Neys are octave-transposing
> as well as key-transposing.
> 
> If you consider that Sipurde Ahenk produces perde rast at C ~261 Hz, you can
> say that A=440 Hz (which is perde huseyni in this Ahenk). Because one can
> perform all natural tones in reference to Western Staff Notation in the
> default scale of the principle Rast Maqam, I choose this Ahenk to be my
> pitch standard.

OK but this sound like a personal choice on your part.


> perde rast for:
> 
> Sipurde is in C,
> Mustahzen is in B,
> Kiz is in A,
> Mansur is in G,
> Shah is in F,
> Davud is in E,
> Bolahenk is in D.
> 
> according to the Western pitch standard.
> 
> Cordially,
> Ozan
>