Full thread (32 messages)
From: stephenszpak (2005-12-24)
Subject: different major 3rds and 5ths
Thought about posting this idea (but I won't knowing me).
I was wondering if the list members could tell the difference
between these major 3rds with their perfect 5ths. (Or what one is
most pleasing to the ear.)They are almost
the same on paper.
One is the major 3rd of 12 EDO (15 EDO also) and another is
the major 3rd of Porcupine [15] in 7-limit minimax tuning
(which I tried to find in Scala without luck). Then there is
the JI major 3rd for completness sake. Fifths are different
in the below chords too.
12 EDO (15 EDO) 0-400 -700
Porcupine [15] 7-l-mM 0-386.3 -711.8
JI 0-386.3 -702
What I would like to do (probably won't) is to have the three
notes play simultaneously as a chord in piano sound. The first
chord would be A then B then C (as one or multiple files). The
order *MUST* be random and unknown to the rest of the group. Only
the poster would know what chord is what.
It's a busy time and a so-so idea so I won't expect much here.
Regards,
Stephen Szpak
From: Carl Lumma (2005-12-24)
Subject: Re: [MMM] different major 3rds and 5ths
>Thought about posting this idea (but I won't knowing me).
>
>I was wondering if the list members could tell the difference
>between these major 3rds with their perfect 5ths. (Or what one is
>most pleasing to the ear.)They are almost
>the same on paper.
>
>One is the major 3rd of 12 EDO (15 EDO also) and another is
>the major 3rd of Porcupine [15] in 7-limit minimax tuning
>(which I tried to find in Scala without luck). Then there is
>the JI major 3rd for completness sake. Fifths are different
>in the below chords too.
>
>12 EDO (15 EDO) 0-400 -700
>Porcupine [15] 7-l-mM 0-386.3 -711.8
>JI 0-386.3 -702
>
>What I would like to do (probably won't) is to have the three
>notes play simultaneously as a chord in piano sound. The first
>chord would be A then B then C (as one or multiple files). The
>order *MUST* be random and unknown to the rest of the group. Only
>the poster would know what chord is what.
>
>It's a busy time and a so-so idea so I won't expect much here.
>
> Regards,
>
> Stephen Szpak
Hiya Stephen,
Lots of comparisons like this have been done on the Tuning list.
The archives of these lists are notoriously hard to search,
though, and I'm not sure this exact one has ever been performed.
These three tunings can probably be found on Herman Miller's
Warped Canon page -- have you seen it?
The easiest way I've found to do comparisons like these is with
Scala .seq files. You can write them by hand. The Scala docs
have more info, and you can view the included .seq files (in
the Scala program directory) in a text editor like Notepad to
see examples. In this case, what you want probably looks
something like this...
!
0 text "12/15/Porcupine triad test."
0 outfile B.mid
0 exclude 10
0 tempo 65 pm
!
0 track 1
0 program 1
0 timesig 4/4
0 division 1
0 velocity 100
!
0 key 0
0 note 0 4
0 note 1 4
0 note 2 4
!
...Then you just create three .scl files, one for each tuning,
with only 3 notes each. Like this...
! B.scl
!
Porcupine triad
3
!
386.30000
711.80000
2/1
...Load one of them, then choose "Transform sequence to MIDI file"
from the Tools menu. Change the "outfile" line in your .seq file,
load the next .scl file, and do it again. When you have all three
MIDI files, you can play them in an ordinary MIDI player (like
Windows Media Player) and record that in Audacity (if your sound
card supports recording from an output like this). Or, you can
render the MIDI file directly to WAV with a tool like Audio Compositor.
Then you post to the list, have people download the files and listen,
and reveal the answer in a few weeks.
It's best to set up a free web account somewhere to host the
files, as Jon said.
Cheers!
-Carl
From: stephenszpak (2005-12-24)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
Carl
Thanks for putting far more into this than I expect I will.
What interests me is if there is any real difference in the
0-386-712 and the 0-400-700, because I might be doing something in
some form of 15 in 2006.
Hope to make a modest effort in the above two chords for
my own sake.
Stephen Szpak
> >Thought about posting this idea (but I won't knowing me).
> >
> >I was wondering if the list members could tell the difference
> >between these major 3rds with their perfect 5ths. (Or what one is
> >most pleasing to the ear.)They are almost
> >the same on paper.
> >
> >One is the major 3rd of 12 EDO (15 EDO also) and another is
> >the major 3rd of Porcupine [15] in 7-limit minimax tuning
> >(which I tried to find in Scala without luck). Then there is
> >the JI major 3rd for completness sake. Fifths are different
> >in the below chords too.
> >
> >12 EDO (15 EDO) 0-400 -700
> >Porcupine [15] 7-l-mM 0-386.3 -711.8
> >JI 0-386.3 -702
> >
> >What I would like to do (probably won't) is to have the three
> >notes play simultaneously as a chord in piano sound. The first
> >chord would be A then B then C (as one or multiple files). The
> >order *MUST* be random and unknown to the rest of the group. Only
> >the poster would know what chord is what.
> >
> >It's a busy time and a so-so idea so I won't expect much here.
> >
> > Regards,
> >
> > Stephen Szpak
>
> Hiya Stephen,
>
> Lots of comparisons like this have been done on the Tuning list.
> The archives of these lists are notoriously hard to search,
> though, and I'm not sure this exact one has ever been performed.
> These three tunings can probably be found on Herman Miller's
> Warped Canon page -- have you seen it?
>
> The easiest way I've found to do comparisons like these is with
> Scala .seq files. You can write them by hand. The Scala docs
> have more info, and you can view the included .seq files (in
> the Scala program directory) in a text editor like Notepad to
> see examples. In this case, what you want probably looks
> something like this...
>
> !
> 0 text "12/15/Porcupine triad test."
> 0 outfile B.mid
> 0 exclude 10
> 0 tempo 65 pm
> !
> 0 track 1
> 0 program 1
> 0 timesig 4/4
> 0 division 1
> 0 velocity 100
> !
> 0 key 0
> 0 note 0 4
> 0 note 1 4
> 0 note 2 4
> !
>
> ...Then you just create three .scl files, one for each tuning,
> with only 3 notes each. Like this...
>
> ! B.scl
> !
> Porcupine triad
> 3
> !
> 386.30000
> 711.80000
> 2/1
>
> ...Load one of them, then choose "Transform sequence to MIDI file"
> from the Tools menu. Change the "outfile" line in your .seq file,
> load the next .scl file, and do it again. When you have all three
> MIDI files, you can play them in an ordinary MIDI player (like
> Windows Media Player) and record that in Audacity (if your sound
> card supports recording from an output like this). Or, you can
> render the MIDI file directly to WAV with a tool like Audio
Compositor.
> Then you post to the list, have people download the files and
listen,
> and reveal the answer in a few weeks.
>
> It's best to set up a free web account somewhere to host the
> files, as Jon said.
>
> Cheers!
>
> -Carl
>
From: Carl Lumma (2005-12-24)
Subject: Re: [MMM] different major 3rds and 5ths
I certainly hear a difference, but I suspect the experience
is unique for each person. And it will depend greatly on
musical context, so if you don't get around to making these
single-chord files don't regret it too much.
-Carl
> Thanks for putting far more into this than I expect I will.
> What interests me is if there is any real difference in the
> 0-386-712 and the 0-400-700, because I might be doing something in
> some form of 15 in 2006.
>
> Hope to make a modest effort in the above two chords for
> my own sake.
>
> Stephen Szpak
>
>
>> >Thought about posting this idea (but I won't knowing me).
>> >
>> >I was wondering if the list members could tell the difference
>> >between these major 3rds with their perfect 5ths. (Or what one is
>> >most pleasing to the ear.)They are almost
>> >the same on paper.
>> >
>> >One is the major 3rd of 12 EDO (15 EDO also) and another is
>> >the major 3rd of Porcupine [15] in 7-limit minimax tuning
>> >(which I tried to find in Scala without luck). Then there is
>> >the JI major 3rd for completness sake. Fifths are different
>> >in the below chords too.
>> >
>> >12 EDO (15 EDO) 0-400 -700
>> >Porcupine [15] 7-l-mM 0-386.3 -711.8
>> >JI 0-386.3 -702
>> >
>> >What I would like to do (probably won't) is to have the three
>> >notes play simultaneously as a chord in piano sound. The first
>> >chord would be A then B then C (as one or multiple files). The
>> >order *MUST* be random and unknown to the rest of the group. Only
>> >the poster would know what chord is what.
>> >
>> >It's a busy time and a so-so idea so I won't expect much here.
>> >
>> > Regards,
>> >
>> > Stephen Szpak
>>
>> Hiya Stephen,
>>
>> Lots of comparisons like this have been done on the Tuning list.
>> The archives of these lists are notoriously hard to search,
>> though, and I'm not sure this exact one has ever been performed.
>> These three tunings can probably be found on Herman Miller's
>> Warped Canon page -- have you seen it?
>>
>> The easiest way I've found to do comparisons like these is with
>> Scala .seq files. You can write them by hand. The Scala docs
>> have more info, and you can view the included .seq files (in
>> the Scala program directory) in a text editor like Notepad to
>> see examples. In this case, what you want probably looks
>> something like this...
>>
>> !
>> 0 text "12/15/Porcupine triad test."
>> 0 outfile B.mid
>> 0 exclude 10
>> 0 tempo 65 pm
>> !
>> 0 track 1
>> 0 program 1
>> 0 timesig 4/4
>> 0 division 1
>> 0 velocity 100
>> !
>> 0 key 0
>> 0 note 0 4
>> 0 note 1 4
>> 0 note 2 4
>> !
>>
>> ...Then you just create three .scl files, one for each tuning,
>> with only 3 notes each. Like this...
>>
>> ! B.scl
>> !
>> Porcupine triad
>> 3
>> !
>> 386.30000
>> 711.80000
>> 2/1
>>
>> ...Load one of them, then choose "Transform sequence to MIDI file"
>> from the Tools menu. Change the "outfile" line in your .seq file,
>> load the next .scl file, and do it again. When you have all three
>> MIDI files, you can play them in an ordinary MIDI player (like
>> Windows Media Player) and record that in Audacity (if your sound
>> card supports recording from an output like this). Or, you can
>> render the MIDI file directly to WAV with a tool like Audio
>Compositor.
>> Then you post to the list, have people download the files and
>listen,
>> and reveal the answer in a few weeks.
>>
>> It's best to set up a free web account somewhere to host the
>> files, as Jon said.
>>
>> Cheers!
>>
>> -Carl
>>
>
>
>
>
>
>
>
>
>Yahoo! Groups Links
>
>
>
>
From: stephenszpak (2005-12-24)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Carl
I figure these two are much the same, to my ears anyway:
0-386-712 and the 0-400-700
Half-heartedly tried to do what you said in Scala. Twice.
I did find: Herman Miller's
Warped Canon page here:
http://www.io.com/~hmiller/music/warped-canon.html
Didn't see anything as yet about the above.
Thanks,
Stephen Szpak
___________________________________________________________
> I certainly hear a difference, but I suspect the experience
> is unique for each person. And it will depend greatly on
> musical context, so if you don't get around to making these
> single-chord files don't regret it too much.
>
> -Carl
> ___________________________________________________________
> >
From: Carl Lumma (2005-12-24)
Subject: Re: [MMM] different major 3rds and 5ths
> I figure these two are much the same, to my ears anyway:
>
> 0-386-712 and the 0-400-700
>
> Half-heartedly tried to do what you said in Scala. Twice.
That should equal 1 heart. :)
> I did find: Herman Miller's Warped Canon page here:
>
> http://www.io.com/~hmiller/music/warped-canon.html
>
> Didn't see anything as yet about the above.
http://www.io.com/~hmiller/midi/canon12.mid (400-700)
http://www.io.com/~hmiller/midi/canon59.mid (386.4-711.9)
-Carl
From: stephenszpak (2005-12-24)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
Carl
Thanks again. I did download some of the .mid
files there. WinAmp usually (like 98%) plays
the original one. Even if another title is in the
box (on the WinAmp screen).
I even used the URL box to put the different addresses
in, and that didn't work either. Just tried the two
files in this e-mail, and they sound the same. I think
WinAmp is playing the canon12.mid as usual.
Stephen
_________________________________________________________________
> > I figure these two are much the same, to my ears anyway:
> >
> > 0-386-712 and the 0-400-700
> >
> > Half-heartedly tried to do what you said in Scala. Twice.
>
> That should equal 1 heart. :) ++++Guess I should take heart.
>
> > I did find: Herman Miller's Warped Canon page here:
> >
> > http://www.io.com/~hmiller/music/warped-canon.html
> >
> > Didn't see anything as yet about the above.
>
> http://www.io.com/~hmiller/midi/canon12.mid (400-700)
>
> http://www.io.com/~hmiller/midi/canon59.mid (386.4-711.9)
>
> -Carl
>
From: stephenszpak (2005-12-24)
Subject: Re: [MMM] different major 3rds and 5ths
> >
> Carl
I have both files on my Desktop screen. They both say
4:55 (on the WinAmp screen,playing time I guess) yet the file
sizes are 40.0 and 24.0. Apparently WinAmp won't accept a new file
to play for some reason.
Stephen
________________________________________________________________-
>
> Thanks again. I did download some of the .mid
> files there. WinAmp usually (like 98%) plays
> the original one.
From: stephenszpak (2005-12-25)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
>
> > >
> > Carl
>
> The sizes of the major 3rd and perfect 5th may not
matter in the end anyway. Not sure. What came to me
quite some time ago was 15 UDF.
15 UDF (15 notes per octave in a Universal Dynamic
Framework)
I don't know if I posted
here about it recently or not.
Basically, what I have in
mind is knowing what one wants to do ahead of time regarding
a melody, etc. So what one would do is choose the root notes
to be whatever is desired,for three or four chords
(maybe, keep minor 3rds 300,
major 3rds 400, and perfect fifths 700, maybe). With 15 notes
available for a octave, one could have 3 or 4 chords that could
not exist in virtually any form of 15 (at least that
is my guess about it). So one would play in these 3 or 4 chords
for a given composition. That is 9 or 12 notes, maybe more
if one wanted even more complexity. Although there is a mental
limit on this.
The other notes of the octave would
not be in use, so they could result in roots that had terrible
3rds and fifths. It wouldn't matter.
All the above is for actually playing on a keyboard in 15.
I'm not refering to composing with a computer.
P.S.
(some aspects of 15 UDF not stated here, and may even be
discarded in the future)
Stephen Szpak
From: Carl Lumma (2005-12-25)
Subject: Re: [MMM] different major 3rds and 5ths
>> http://www.io.com/~hmiller/midi/canon12.mid (400-700)
>>
>> http://www.io.com/~hmiller/midi/canon59.mid (386.4-711.9)
> Thanks again. I did download some of the .mid
> files there. WinAmp usually (like 98%) plays
> the original one. Even if another title is in the
> box (on the WinAmp screen).
>
> I even used the URL box to put the different addresses
> in, and that didn't work either. Just tried the two
> files in this e-mail, and they sound the same. I think
> WinAmp is playing the canon12.mid as usual.
I'm afraid I don't follow you. Have you tried pasting
these urls into your browser?
It's quite possible that whatever MIDI synth Winamp is
using isn't playing back the pitch bends -- making all
the files on Herman's page sound the same. You could
try some of the more seriously 'warped' ones to see if
that's the case.
-Carl
From: stephenszpak (2005-12-25)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
I don't get it either. I know it worked once. I forgot
what file it was now. Now matter what I put into the
browser and click on 'OPEN' WinAmp plays the same
thing, canon12.mid I guess.
Don't worry about it.
Stephen Szpak
>
> >> http://www.io.com/~hmiller/midi/canon12.mid (400-700)
> >>
> >> http://www.io.com/~hmiller/midi/canon59.mid (386.4-711.9)
>
> >
>
> I'm afraid I don't follow you. Have you tried pasting
> these urls into your browser?
>
> It's quite possible that whatever MIDI synth Winamp is
> using isn't playing back the pitch bends -- making all
> the files on Herman's page sound the same. You could
> try some of the more seriously 'warped' ones to see if
> that's the case.
>
> -Carl
>
From: Gene Ward Smith (2005-12-27)
Subject: Re: different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
>
> Thought about posting this idea (but I won't knowing me).
>
> I was wondering if the list members could tell the difference
> between these major 3rds with their perfect 5ths. (Or what one is
> most pleasing to the ear.)They are almost
> the same on paper.
Your porcupine major third looks exactly the same as JI; that is, in
fact, the 5- and 7-limit minimax tuning. However, other porcupine
tunings, such as 22-et, are possible.
From: Gene Ward Smith (2005-12-27)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
> Carl
>
> Thanks for putting far more into this than I expect I will.
> What interests me is if there is any real difference in the
> 0-386-712 and the 0-400-700, because I might be doing something in
> some form of 15 in 2006.
There is a big difference between the two, but I don't see why you are
mentioning 15 in this connect; 15 gives 0-400-720. More to the point
would be 59-et, giving 0-386.4-711.9, or even 22-et, giving 0-381.8-709.1.
From: Gene Ward Smith (2005-12-27)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
> I even used the URL box to put the different addresses
> in, and that didn't work either. Just tried the two
> files in this e-mail, and they sound the same. I think
> WinAmp is playing the canon12.mid as usual.
I wonder if your soundcard is fixed to 12-edo? What happens if you
render the file using Audacity (or Timidity, for that matter?)
From: Gene Ward Smith (2005-12-27)
Subject: Re: different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> I wonder if your soundcard is fixed to 12-edo? What happens if you
> render the file using Audacity (or Timidity, for that matter?)
I meant SynthFont or Timidity, sorry.
From: Rick McGowan (2005-12-27)
Subject: Re: [MMM] different major 3rds and 5ths
> I was wondering if the list members could tell the difference
> between these major 3rds with their perfect 5ths. (Or what one is
> most pleasing to the ear.)
"Pleasing" will be a very relative notion. The 5ths 702 and 712 are
noticeably different, and 386 is noticeably different from 400 for the
3rds...
Rick
From: Paul Erlich (2005-12-27)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
> <stephen_szpak@h...> wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...>
wrote:
> > >
> > Carl
> >
> > Thanks for putting far more into this than I expect I will.
> > What interests me is if there is any real difference in the
> > 0-386-712 and the 0-400-700, because I might be doing something
in
> > some form of 15 in 2006.
>
> There is a big difference between the two, but I don't see why you
are
> mentioning 15 in this connect;
Gene,
Stephen is mentioning 15 because he wants to use a scale with 15
notes in it, for example the 15-note Porcupine scale with a good
number of 0-386-712 triads that we discussed with him some time ago.
Not 22 notes, not 59 notes, but 15 notes.
> 15 gives 0-400-720.
You're mentally inserting the words "equal temperament" where Stephen
neither said nor implied any such thing.
> More to the point
> would be 59-et, giving 0-386.4-711.9, or even 22-et, giving 0-381.8-
> 709.1.
Utterly besides the point as regards Stephen's clearly stated
concerns.
From: Paul Erlich (2005-12-27)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, Rick McGowan <rick@u...> wrote:
>
> > I was wondering if the list members could tell the difference
> > between these major 3rds with their perfect 5ths. (Or what one is
> > most pleasing to the ear.)
>
> "Pleasing" will be a very relative notion. The 5ths 702 and 712 are
> noticeably different, and 386 is noticeably different from 400 for
the
> 3rds...
And even more blatantly, the *minor* third (the interval found
*between* the major third and the fifth) audibly differentiates these
two chords -- 326 cents vs. 300 cents!
From: stephenszpak (2005-12-27)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith" <> >
Gene
I'm very slowly getting into 15 (in some form or another).
In 15 EDO we have: 0-400-720
which results in a perfect fifth that is significantly sharp.
I can't find my post right now that listed the
Porcupine [15] in 7-limit minimax tuning. (sorry)
In that tuning we have: 0-386.3-711.8.
Maybe, since different people have different tastes, maybe we
should ask which tuning is mathematically more correct
( only for the major chords of course , not the entire tuning )
386.3 gives a major 3 closer than 12 ED0 (15EDO) yet
the perfect 5th at 711.8 is farther away from the 700 mark.
Also,
I'm trying to stick to 15 notes here, from the playing standpoint.
58-et is not going to happen. 22-et also cuts back
on playability.
Stephen Szpak
>
From: Paul Erlich (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith" <> >
>
> Gene
>
> I'm very slowly getting into 15 (in some form or another).
>
> In 15 EDO we have: 0-400-720
And you have 15 instances of this chord per octave.
> which results in a perfect fifth that is significantly sharp.
>
> I can't find my post right now that listed the
> Porcupine [15] in 7-limit minimax tuning. (sorry)
>
> In that tuning we have: 0-386.3-711.8.
But in this tuning, you don't have this chord at 15 different spots
in the octave -- only 10, I believe.
> Maybe, since different people have different tastes, maybe we
> should ask which tuning is mathematically more correct
> ( only for the major chords of course , not the entire tuning )
What does that mean? How do you trade off purity of the chord vs. the
number of times it appears in the tuning?
> 386.3 gives a major 3 closer than 12 ED0 (15EDO)
What does that mean? 3 closer? The pure major third is 386.31 cents.
> yet
> the perfect 5th at 711.8 is farther away from the 700 mark.
The pure perfect fifth is 701.96 cents.
From: stephenszpak (2005-12-28)
Subject: Re: different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
>
Gene
I don't have SynthFont or Timidity.
Just tried Deck the Halls and Star-Spangled Banner and they
work! Maybe all the canons just sound the same to my ears.
Not worth pursuing. The only reason it came up was that I wanted
to hear:
0-400-700 simultaneously as a piano chord
AND
0-386.3-711.8 simultaneously as a piano chord
Carl even wrote the program for me:
http://launch.groups.yahoo.com/group/MakeMicroMusic/message/11540
Stephen
________________________________________________________
> > I wonder if your soundcard is fixed to 12-edo? What happens if
you
> > render the file using Audacity (or Timidity, for that matter?)
>
> I meant SynthFont or Timidity, sorry.
>
From: stephenszpak (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
> >
> > Gene
> >
> > I'm very slowly getting into 15 (in some form or another).
> >
> > In 15 EDO we have: 0-400-720
>
> And you have 15 instances of this chord per octave.
>
> > which results in a perfect fifth that is significantly sharp.
> >
> > I can't find my post right now that listed the
> > Porcupine [15] in 7-limit minimax tuning. (sorry)
> >
> > In that tuning we have: 0-386.3-711.8.
>
> But in this tuning, you don't have this chord at 15 different
spots
> in the octave -- only 10, I believe.
+++++++++++++++Yes, I wrote down 10 way back. You are right.
>
> > Maybe, since different people have different tastes, maybe we
> > should ask which tuning is mathematically more correct
> > ( only for the major chords of course , not the entire tuning )
>
> What does that mean? How do you trade off purity of the chord vs.
the
> number of times it appears in the tuning?
+++++++++++++++++Just forget there are 10 I guess? One would not
necessarily use all 15 notes in a 15 note per
octave piece anyway.
>
> > 386.3 gives a major 3 closer than 12 ED0 (15EDO)
>
> What does that mean? 3 closer? The pure major third is 386.31
cents.
>
> > yet
> > the perfect 5th at 711.8 is farther away from the 700 mark.
>
> The pure perfect fifth is 701.96 cents.
+++++++++++++++Yes, sorry should have said, 702. The 3rd is
closer to where JI is. The perfect 5th is
farther away.
Stephen Szpak
>
From: Paul Erlich (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
>
>
> > >
> > > Gene
> > >
> > > I'm very slowly getting into 15 (in some form or another).
> > >
> > > In 15 EDO we have: 0-400-720
> >
> > And you have 15 instances of this chord per octave.
> >
> > > which results in a perfect fifth that is significantly sharp.
> > >
> > > I can't find my post right now that listed the
> > > Porcupine [15] in 7-limit minimax tuning. (sorry)
> > >
> > > In that tuning we have: 0-386.3-711.8.
> >
> > But in this tuning, you don't have this chord at 15 different
> spots
> > in the octave -- only 10, I believe.
>
> +++++++++++++++Yes, I wrote down 10 way back. You are right.
> >
> > > Maybe, since different people have different tastes, maybe we
> > > should ask which tuning is mathematically more correct
> > > ( only for the major chords of course , not the entire
tuning )
> >
> > What does that mean? How do you trade off purity of the chord vs.
> the
> > number of times it appears in the tuning?
>
> +++++++++++++++++Just forget there are 10 I guess? One would not
> necessarily use all 15 notes in a 15 note per
> octave piece anyway.
Well, one can take this to its logical extreme and look at 15 note JI
scales. The chord will be perfectly pure, but can only be constructed
on about half the notes of the scale. Perhaps this would be of even
more interest to you?
> > > 386.3 gives a major 3 closer than 12 ED0 (15EDO)
> >
> > What does that mean? 3 closer? The pure major third is 386.31
> cents.
> >
> > > yet
> > > the perfect 5th at 711.8 is farther away from the 700 mark.
> >
> > The pure perfect fifth is 701.96 cents.
>
> +++++++++++++++Yes, sorry should have said, 702. The 3rd is
> closer to where JI is. The perfect 5th is
> farther away.
And the minor third (the interval between the two upper notes in the
chord) is important too I feel.
From: stephenszpak (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...>
wrote:
>
> > >
> > > >
> > +++++++++++++++++Just forget there are 10 I guess? One would not
> > necessarily use all 15 notes in a 15 note per
> > octave piece anyway.
>
> Well, one can take this to its logical extreme and look at 15 note
JI
> scales. The chord will be perfectly pure, but can only be
constructed
> on about half the notes of the scale. Perhaps this would be of
even
> more interest to you?
+++++++++++++++++This is interesting. I have never heard of this.
Do you have a link?????
>
> > > > 386.3 gives a major 3 closer than 12 ED0 (15EDO)
> > >
> > > What does that mean? 3 closer? The pure major third is 386.31
> > cents.
> > >
> > > > yet
> > > > the perfect 5th at 711.8 is farther away from the 700 mark.
> > >
> > > The pure perfect fifth is 701.96 cents.
> >
> > +++++++++++++++Yes, sorry should have said, 702. The 3rd is
> > closer to where JI is. The perfect 5th is
> > farther away.
>
> And the minor third (the interval between the two upper notes in
the
> chord) is important too I feel.
++++++++++++++++++Yes, of course. Maybe Kleismic-15? But that's
another story.
Thanks Paul,
Stephen Szpak
>
From: Paul Erlich (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...>
> wrote:
> >
> > > >
> > > > >
> > > +++++++++++++++++Just forget there are 10 I guess? One would not
> > > necessarily use all 15 notes in a 15 note per
> > > octave piece anyway.
> >
> > Well, one can take this to its logical extreme and look at 15
note
> JI
> > scales. The chord will be perfectly pure, but can only be
> constructed
> > on about half the notes of the scale. Perhaps this would be of
> even
> > more interest to you?
>
>
> +++++++++++++++++This is interesting. I have never heard of this.
> Do you have a link?????
Here are five different 15-note JI scales (all five are 5-limit, and
they're all Constant Structures):
cents ratio
0 1 / 1
70.672 25 / 24
182.4 10 / 9
203.91 9 / 8
315.64 6 / 5
386.31 5 / 4
498.04 4 / 3
568.72 25 / 18
631.28 36 / 25
701.96 3 / 2
813.69 8 / 5
884.36 5 / 3
996.09 16 / 9
1017.6 9 / 5
1129.3 48 / 25
cents ratio
0 1 / 1
111.73 16 / 15
182.4 10 / 9
203.91 9 / 8
315.64 6 / 5
386.31 5 / 4
498.04 4 / 3
590.22 45 / 32
609.78 64 / 45
701.96 3 / 2
813.69 8 / 5
884.36 5 / 3
996.09 16 / 9
1017.6 9 / 5
1088.3 15 / 8
cents ratio
0 1 / 1
21.506 81 / 80
182.4 10 / 9
203.91 9 / 8
315.64 6 / 5
386.31 5 / 4
498.04 4 / 3
519.55 27 / 20
680.45 40 / 27
701.96 3 / 2
813.69 8 / 5
884.36 5 / 3
996.09 16 / 9
1017.6 9 / 5
1178.5 160 / 81
cents ratio
0 1 / 1
70.672 25 / 24
182.4 10 / 9
244.97 144 / 125
315.64 6 / 5
386.31 5 / 4
498.04 4 / 3
568.72 25 / 18
631.28 36 / 25
701.96 3 / 2
813.69 8 / 5
884.36 5 / 3
955.03 125 / 72
1017.6 9 / 5
1129.3 48 / 25
cents ratio
0 1 / 1
70.672 25 / 24
182.4 10 / 9
253.08 125 / 108
315.64 6 / 5
386.31 5 / 4
498.04 4 / 3
568.72 25 / 18
631.28 36 / 25
701.96 3 / 2
813.69 8 / 5
884.36 5 / 3
946.92 216 / 125
1017.6 9 / 5
1129.3 48 / 25
A good number of 15-note JI scales have been posted to the tuning
list and the tuning-math list. Since this isn't the place for it, I
suggest posting to one of those lists, where I'm sure you'll receive
many helpful replies.
> ++++++++++++++++++Yes, of course. Maybe Kleismic-15?
Otherwise known as Hanson-15.
> But that's another story.
Yes, Hanson-15 would be much closer to one of the 15-note JI scales.
The difference would be that a small minority of the good chords in
the Hanson scale would have errors of a kleisma (8.1 cents) in the JI
scale, making them worse, while the rest of them would be slightly
improved. Anyway, let's continue this on another list.
From: stephenszpak (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
Thanks Paul. I'm saving this message number for my records.
Stephen Szpak
_____________________________________________________________
From: Gene Ward Smith (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
> Maybe, since different people have different tastes, maybe we
> should ask which tuning is mathematically more correct
> ( only for the major chords of course , not the entire tuning )
Because different people have different tastes, this is a question
with no answer, I think. The minimax tuning for porcupine has a
stronger theoretical claim, but I think porcupine actually sounds
better in 22-et.
> I'm trying to stick to 15 notes here, from the playing standpoint.
> 58-et is not going to happen. 22-et also cuts back
> on playability.
However, 22 gives an excellent tuning for porcupine, and allows the
15-note MOS to modulate freely.
From: Gene Ward Smith (2005-12-28)
Subject: Re: different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "stephenszpak"
<stephen_szpak@h...> wrote:
> I don't have SynthFont or Timidity.
They are freeware programs, so you can have them if you want them. I
recommend doing that.
> Just tried Deck the Halls and Star-Spangled Banner and they
> work! Maybe all the canons just sound the same to my ears.
Good! However, I think if you can't tell something is strange about,
for instance, the 8-edo warped canon something still must be wrong
with your sound equipment.
One thing the warped canon page should do make clear why 12-et is such
an obvious choice. If you want to do 5-limit music, it's the first
equal division which works, in the sense of actually sounding like
5-limit music. As you go up through 5, 6, 7, 8, 9, 10, 11 you will
find interesting versions of the canon, but not any which sound close
to being right. Then you hit 12, and bingo! It works. If you keep on
going, the next one which works is 19, and after that, 22. After a
while everything starts to work, which is another thing to bear in mind.
From: Gene Ward Smith (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> Because different people have different tastes, this is a question
> with no answer, I think. The minimax tuning for porcupine has a
> stronger theoretical claim, but I think porcupine actually sounds
> better in 22-et.
Which may just mean theory needs adjustment. While we haven't made as
much use of it, there is NOT tuning, which is like TOP tuning, only
with pure octaves. The NOT 7 or 11 limit porcupine is almost exactly
22-et, and the 5-limit NOT is much better represented by 22 than by
the minimax tuning, which is completely different. NOT meantone is
better represeted by 55 or 43, which many people prefer to flatter
fifths. Hence, I would not make too much of a deal out of the minimax
tuning.
From: stephenszpak (2005-12-28)
Subject: Re: different major 3rds and 5ths
Gene
I don't have SynthFont or Timidity.
>
> They are freeware programs, so you can have them if you want them.
I
> recommend doing that.
++++++++++++++++++I like free stuff. Maybe I'll have time to
check these out.
>
> > Just tried Deck the Halls and Star-Spangled Banner and they
> > work! Maybe all the canons just sound the same to my ears.
>
> Good! However, I think if you can't tell something is strange
about,
> for instance, the 8-edo warped canon something still must be wrong
> with your sound equipment.
++++++++++++++8-edo is *definitly+ different. Guess my ears
are the problem here.
++++++++++Stephen
From: Paul Erlich (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> <gwsmith@s...> wrote:
>
> > Because different people have different tastes, this is a question
> > with no answer, I think. The minimax tuning for porcupine has a
> > stronger theoretical claim, but I think porcupine actually sounds
> > better in 22-et.
>
> Which may just mean theory needs adjustment. While we haven't made
as
> much use of it, there is NOT tuning, which is like TOP tuning, only
> with pure octaves.
Graham and I have a different interpretation of what "like TOP
tuning, only with pure octaves." But we've discussed that on the
tuning-math list, where all this stuff belongs.
> Hence, I would not make too much of a deal out of the minimax
> tuning.
Minimax vs. RMS vs. Sum-abs is another dimension along which one can
vary the definition of "optimal", in addition to the dimension I was
referring to above, and others. So one example is not enough to
determine what exactly it is about our "optimality" criteria that we
wish to change. Anyway, let's continue on tuning-math or tuning.
From: stephenszpak (2005-12-28)
Subject: Re: [MMM] different major 3rds and 5ths
--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...>
wrote:
Paul
I've added #11606,#11608 and #11617 to my notes. When I
actually start playing 15 then I'll have to make some decisions
on a tuning(s). The way I'm getting into 15 now is the way I got
into 24. I have my old keyboard off, while I go over and over
the chords. (Each note of 15 has a color assigned to it in my
system. A strip of poster board across the keyboard shows me
where each note is.) A few minutes a day for many months has
allowed some real progress in 15.
I'm unfamiliar with NOT,TOP,Sum-abs and even Mini-Max, other
than the word "Mini-Max".
Maybe it will indeed be UDF for me. The reason I like it, is
because it can be almost anything. The tuning is dynamic,
changable for the melody, etc. one needs for the composition.
Off course there are limits on it, know that.
The more notes in a scale the greater the difficulty in
physically playing it. Not to mention that yet another scale
has to be learned. For me we are talking a few minutes a day
for a couple years, with mandatory review time each week.
I've found that not going over the semi-augmented 4ths in
24 lately has resulted in me forgetting where they are.
Yet I've been playing in 24 the same amount of time per week
as usual. Just not this ratio.
As far as playing on a keyboard goes, I think we're talking
12EDO ,15 whatever,24 whatever (Szpak Scale or some variation) .
There is so much in these.
Don't think I need to go to tuning-math or tuning right now.
I appreciate you letting me know about NOT,TOP,Sum-abs. That is,
that there are other tunings out there I could check out when
the time is right.
Thanks for the invitation Paul,
Stephen Szpak
>