Topic: The Holy Grail temperament

1 scales

Thread (21 messages)

From: Gene Ward Smith (2003-06-02)
Subject: The Holy Grail temperament

I've been spending some time trying to find a temperament which I
named to myself a "holy grail" type of temperament. This is one
designed for retuning midi files, and I wanted the following attributes:

(1) Near the key center, it functions as an honest meantone, with
major thirds not too far off pure

(2) All fifths must be usable; no wolf fifths are allowed

(3) All thirds in all keys must be functional

I finally found such a temperament, named below "grail.scl". The key
idea was to have two pure 14/11 major thirds and one pure 9/7 major
third in the remote keys. By giving them a precise just value, even if
that value is not 5/4, I got something which didn't sound bad. For the
minor thirds, I was happy to get two fine 7/6 subminors and settled
for a couple of 13/11 intermediate minor thirds.

Here are the fifths, major thirds, and minor thirds above each scale
degree:

0 695.623009 391.246018 304.376991
1 708.753982 417.507964 304.376991
2 700.000000 382.457951 308.753982
3 708.788065 391.246018 273.703969
4 695.623008 404.376991 304.376991
5 695.623009 391.246018 291.246018
6 708.788067 435.084096 317.542049
7 700.000000 391.246017 317.542047
8 708.753982 404.376991 291.246017
9 695.623009 391.246018 304.376991
10 691.211935 382.457953 273.703971
11 691.211934 417.507965 308.753983

The major thirds on degree 1 and 11 are exact 14/11's, and on degree 6
we have the 9/7. On degree 3 and 10 we get minor thirds of 273.7
cents, which are good subminor thirds (to my mind, this is very
acceptable.) On degrees 5 and 8 we have 291 cent minor thirds, which
is pretty close to a 13/11 at 289 cents. All the other minor thirds
improve on those of 12-equal. We have three sharp fifths a tad flatter
than the 22-et fifth, which is quite acceptable, two of 12-et's
excellent fifths, three 5/17-comma meantone fifths and two 1/2-comma
meantone fifths; the last (over degrees 10 and 11) are the only fifths
which are any kind of problem, being "flattone" fifths a cent flatter
than the 26-equal fifth.

Here are some retuning examples. I also retuned a movement from the
Emperor concerto, sequenced by some guy named G. Breed, but as
sometimes happens Scala munged it, despite not giving the error
message about not enough midi channels. I also retuned Mendelssohn's
Italian, which worked except for adding a lot of weird percussion.
Even if you disable channel 10, this still happens with complex
retunings at the limit of what Scala capable of.

http://groups.yahoo.com/group/tuning_files/files/grail/steppes.mid

http://groups.yahoo.com/group/tuning_files/files/grail/mv1.mid

http://groups.yahoo.com/group/tuning_files/files/grail/mv3.mid

http://groups.yahoo.com/group/tuning_files/files/grail/op6n9m4.mid


Here is the Scala scl file:

! grail.scl

Holy Grail circulating temperament with two 14/11 and one 9/7 major third

12

!

86.869027

195.623009

304.376991

391.246018

504.376991

578.080960

695.623009

795.623009

895.623009

1013.165056

1086.869026

1200.000000

From: Gene Ward Smith (2003-06-03)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Here is the Scala scl file:

I also have a version where I simply took my 36 target intervals and
did an rms optimization. Instead of having two flat fifths, 1/2 comma
flat, it has two sharp fifths, 1/2 comma sharp, which is sharper even
than the 27-et fifth, though still almost a cent flatter than the
37-et fifth. Here's this tuning of the grail:

! grailrms.scl
RMS optimized Holy Grail
12
!
84.048251
196.735887
309.423522
393.471773
506.897045
580.913009
699.794113
796.735887
893.677661
1012.558765
1086.574729
1200.000000

From: Jon Szanto (2003-06-03)
Subject: Re: The Holy Grail temperament

Gene,

I appreciate the passion with which you are approaching your 'quest', so take the following in that light.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I've been spending some time trying to find a temperament which I
> named to myself a "holy grail" type of temperament. This is one
> designed for retuning midi files, and I wanted the following attributes:
> 
> (1) Near the key center, it functions as an honest meantone, with
> major thirds not too far off pure
> 
> (2) All fifths must be usable; no wolf fifths are allowed
> 
> (3) All thirds in all keys must be functional
> 
> I finally found such a temperament, named below "grail.scl".

The .scl file is listed below, with elements such as:

> 0 695.623009 391.246018 304.376991

I include the following from John Loffinks microtonal-synthesis website:

"Most synthesizers are limited in resolution to 1 to 2 cents for pitch. This resolution is not necessarily constant over the entire range of the synthesizer. Most synthesizers and samplers also have an absolute pitch resolution in Hertz that limits the bass frequency resolution. [snip] Many synthesizers use cents as the retuning measurement, while others use proprietary increments that match the tuning capability of the instrument. Most synthesizers that "appear" to have 1 cent resolution actually have an internal resolution, often 768 steps per octave, that the user programmable tuning table is mapped to. Unfortunately, this can cause tuning errors worse than you might program otherwise."

So, how is it that you are devising scales that take tunings out to 6 decimal places when in all probability you won't get anywhere near that close in accuracy or resolution with pitch bends and midi files? It seems that if you seriously want to get music to conform to these tunings, in order to judge their musical qualities, you're going to need to find another way to implement them. Possibly the arduous task of converting, in some way, to Csound. It certainly doesn't appear that Timidity, WaveMaker, or AudioCompositor could reliably and demonstrably give you your desired accuracy.

Have you taken any testbed tuning files, as implemented with midi pitch bends, and measured the accuracy of the resulting files? (Not that there are any tuners out there with 6 decimal place measurements...)

My God, the "Italian" as a midi file.

Cheers,
Jon

From: Carl Lumma (2003-06-03)
Subject: Re: [tuning] Re: The Holy Grail temperament

>So, how is it that you are devising scales that take tunings out to 6 
>decimal places

The extra accuracy doesn't hurt anything.  Gene didn't say one needed
all of it to get the benefit of the tunings.  But if in the future...

>Have you taken any testbed tuning files, as implemented with midi pitch 
>bends, and measured the accuracy of the resulting files? (Not that there
>are any tuners out there with 6 decimal place measurements...)

Unforch, there really isn't any good way to measure the exact tuning of
polyphonic music from a sound file.

-Carl

From: Gene Ward Smith (2003-06-03)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> "Most synthesizers are limited in resolution to 1 to 2 cents for
pitch. This resolution is not necessarily constant over the entire
range of the synthesizer. 

If that's the sort of thing people want to use, fine. I don't. In any
event, what's wrong with using the grail given this pitch resolution?
In other words, what's your point?

> So, how is it that you are devising scales that take tunings out to
6 decimal places when in all probability you won't get anywhere near
that close in accuracy or resolution with pitch bends and midi files?

This seems like a perverse sort of question. I got that many decimal
places because I didn't reset Maple to give me fewer; I can see no
point in doing that. I also didn't set it to give me more, for the
same reason.

> My God, the "Italian" as a midi file.

You'd have your work cut out for you if they used this version for a
real performance. All that weird & wacky percussion!

> Cheers,
> Jon

From: Jon Szanto (2003-06-03)
Subject: Re: The Holy Grail temperament

C,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> The extra accuracy doesn't hurt anything.

No, of course not. But it is, in a sense, misleading, if not only will one not hear those pitches reproduced but possibly seriously mis-reproduced.

> But if in the future...

Yeah, I know: the grass is always greener in the future.

> Unforch, there really isn't any good way to measure the exact 
> tuning of polyphonic music from a sound file.

That wasn't my point. One could easily devise a simple scale containing some very explicit and exacting pitches, make a midi file holding some of those notes, try it out on a variety of hardware and software, and measure the individual notes. Otherwise, how in the world can someone lay a claim, extoll a virtue of a given tuning when they don't even know if it is being produced correctly?

Cheers,
Jon

P.S. I see Gene has something to say as well, further down the list...

From: Jon Szanto (2003-06-03)
Subject: Re: The Holy Grail temperament

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> 
> > "Most synthesizers are limited in resolution to 1 to 2 cents for
> pitch. This resolution is not necessarily constant over the entire
> range of the synthesizer. 
> 
> If that's the sort of thing people want to use, fine. I don't.

What do you mean "I don't"? I'll try to be succinct: the means that you are using to produce examples do not, with any certainty, represent your scales and tunings accurately. How can one make any assertions or observations about a particular tuning, with any certainty, when it doesn't appear that the tunings are being accurately reproduced?

> This seems like a perverse sort of question.

Not at all. Many around here might wonder: "If these boxes and beasts only come to within a cent or two of a given pitch bend, what is it with this guy and all his precision?" I'm *assumed* that the data representation was as you received it in your calculations, but how much rounding off could these tunings survive? If you put every note of a .scl file in a whole number, would the properties you are looking for still be present?

> All that weird & wacky percussion!

I think that may be just one of the reasons I would prefer listening to a piece like that in the original instrumentation: no percussion!

Cheers,
Jon

From: Gene Ward Smith (2003-06-03)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> That wasn't my point. One could easily devise a simple scale
containing some very explicit and exacting pitches, make a midi file
holding some of those notes, try it out on a variety of hardware and
software, and measure the individual notes. Otherwise, how in the
world can someone lay a claim, extoll a virtue of a given tuning when
they don't even know if it is being produced correctly?

You are being utterly inconsistent. One month you are roasting me for
considering microtemperaments as a way of getting effective JI, and
the next you are saying forget about anything less than a difference
of a cent or two. I used three nonoctave JI intervals, in order to get
the "locked in" JI effect in the remote keys in lieu of something
which was a decent 5/4--and, in fact, it works. How close you need to
come to get  the locked in aspect is another argument, which we've had
before.

If Scala scales were defined in terms of cawapus, I would have
computed precise integer values of cawapus and used them. Since it
uses floats, I computed using floats. Do you have any experience
computing? Your whole argument seems to come out of far right field.

From: Gene Ward Smith (2003-06-03)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> > > "Most synthesizers are limited in resolution to 1 to 2 cents for
> > pitch. This resolution is not necessarily constant over the entire
> > range of the synthesizer. 
> > 
> > If that's the sort of thing people want to use, fine. I don't.
> 
> What do you mean "I don't"? 

I mean I don't use "most synthesizers". I use Scala, Timidity and Csound.

I'll try to be succinct: the means that you are using to produce
examples do not, with any certainty, represent your scales and tunings
accurately.

Evidence?

From: David Beardsley (2003-06-03)
Subject: Re: [tuning] Re: The Holy Grail temperament

----- Original Message -----
From: "Gene Ward Smith" <gwsmith@svpal.org>

> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> > That wasn't my point. One could easily devise a simple scale
> containing some very explicit and exacting pitches, make a midi file
> holding some of those notes, try it out on a variety of hardware and
> software, and measure the individual notes. Otherwise, how in the
> world can someone lay a claim, extoll a virtue of a given tuning when
> they don't even know if it is being produced correctly?
>
> You are being utterly inconsistent. One month you are roasting me for
> considering microtemperaments as a way of getting effective JI, and
> the next you are saying forget about anything less than a difference
> of a cent or two. I used three nonoctave JI intervals, in order to get
> the "locked in" JI effect in the remote keys in lieu of something
> which was a decent 5/4--and, in fact, it works. How close you need to
> come to get  the locked in aspect is another argument, which we've had
> before.
>
> If Scala scales were defined in terms of cawapus, I would have
> computed precise integer values of cawapus and used them. Since it
> uses floats, I computed using floats. Do you have any experience
> computing? Your whole argument seems to come out of far right field.

Forgive him, for he uses 12tet at work all day and his judgement is
unbalanced as a result.


* David Beardsley
* microtonal guitar
* http://biink.com/db

From: Kurt Bigler (2003-06-04)
Subject: Re: [tuning] Re: The Holy Grail temperament

on 6/3/03 4:46 AM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> 
>> "Most synthesizers are limited in resolution to 1 to 2 cents for
> pitch. This resolution is not necessarily constant over the entire
> range of the synthesizer.
> 
> If that's the sort of thing people want to use, fine. I don't. In any
> event, what's wrong with using the grail given this pitch resolution?
> In other words, what's your point?
> 
>> So, how is it that you are devising scales that take tunings out to
> 6 decimal places when in all probability you won't get anywhere near
> that close in accuracy or resolution with pitch bends and midi files?
> 
> This seems like a perverse sort of question. I got that many decimal
> places because I didn't reset Maple to give me fewer; I can see no
> point in doing that. I also didn't set it to give me more, for the
> same reason.

I just want to support Gene in doing things the way he is doing it.  I
personally was able to use his data, directly entering it into software I
wrote myself to do synthesis.  My software won't be as accurate as his
number, but I also didn't bother to edit out any of the extra precision.

The numbers he gave may have excess precision for some purposes, but I agree
it doesn't hurt anything.  In fact the values he calculated ARE proably that
exact.  The community will have to fight with the issue of lacking a way to
reproduce scales accurately.  Reducing the presented accuracy certainly
won't help anything.  Giving numbers only as much precision as typical
synthesisizers can render would render the scale information useless,
instead of being of limited use, which is better than no use at all.

Numbers in decimal cents can be recognized by software as representing exact
integral ratios using fairly simple algorithms.  The more digits presented,
the less ambiguity there is in the intended integer ratio (when applicable).

So it seems to me Gene's data is useful to some, less useful to others.
Perhaps it is of limited use to the majority of people, but that is a
problem that needs to be worked on.  Keep in mind that whenever anyone
presents scales using exact integer ratios or equal-temperament steps rather
than cents, they are actually giving INFINITE accuracy, which is much more
than 6 digits after the decimal point.  In other words, the integer 1 is a
shorthand for 1.0000000000000000000000000000... (etc.), and we don't want to
stop using integers because of their extraneous precision.

This is just DATA being presented, and it is being presented in the
"universal language" of numbers, and can be interpreted across many cultures
and used on many kinds of instruments by a large variety of possible
mechanisms.  People can find ways to tune any instrument using these
numbers, and can throw away any extra precision that they can't use.  Any
new software written now can be written to interpret the .scl file format,
and the contents can be read by hand and used to manually calculate pitches
in Hz for any instrument.  So the data as presented seems to me very
appropriate for a public forum.

Independent of this, people need to be educated regarding this current
difficulting in rendering pitches accurately, so that they can be aware when
they might not really be hearing the intended scale.  But this is not Gene's
problem.

-Kurt Bigler

From: Jon Szanto (2003-06-04)
Subject: Re: The Holy Grail temperament

Gene,

Answering online (instead of when I get the digest) has to be msg-by-msg, so I hope it isn't too inconvenient.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> You are being utterly inconsistent.

I don't think so. Either I haven't made clear my questions, or you are misunderstanding me based on past events.

> One month you are roasting me for
> considering microtemperaments as a way of getting effective JI

No, I just like - philosophically - for the use of ratios and ratio structures for JI, not a temperament. If *you* want to do it, that's fine, if you are using it for your music. I realize that for you it won't matter either way.

> and the next you are saying forget about anything less than a 
> difference of a cent or two.

Not at all! In fact, the opposite: if your calculations lead you to pitches that are using discrete measurements less than a cent, I simply was asking (and pointing out) whether or not you felt you had a medium of reproduction that was as accurate as the scales you've crafted. I *never* implied 'forgetting' about innaccuracies of less than 2 cents. There are others around here that can and will debate how small these differences can be and be measureable, musically and otherwise.

> If Scala scales were defined in terms of cawapus, I would have
> computed precise integer values of cawapus and used them.

Also noting that cawapu is a term that even only a few denizens of this list would know about; I'll have to look and see if the current line of Cakewalk products still uses the term/structure referred to.

> Since it  uses floats, I computed using floats.

Right, I get that. The reason I pointed out the information from Loffink was to say "great that you've measured so carefully, but when we pour out the ingredients were going to round up or down a fair - and semi-undetermined - amount; hope that's ok with you". And I was curious if, when you calculate these extremely precise scale constructs, that you get exactly what you've calculated in the end result - the music. Have you ever tested, with frequency counters or pitch analysis, if you indeed are getting the values you intend?

> Do you have any experience computing?

BS in Software Engineering, 1990. Came during a period when the orchestra was in (essentially) bankruptcy. David Beardsley would have liked me a whole lot better back then, I imagine. :)

> Your whole argument seems to come out of far right field.

Please, please! If anything, can't I come out of *left* field?

Cheers,
Jon

From: Jon Szanto (2003-06-04)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> Forgive him, for he uses 12tet at work all day and his judgement is
> unbalanced as a result.

But, just like the guys doing street repairs and construction, I always take a shower when I get home and wash off all the bad intonations. Then I feel much better!

Besides, I've always found it a positive thing to speak more than one language, and learning new ones needn't be done by the abandonment of others.

Cheers,
Jon

From: Jon Szanto (2003-06-04)
Subject: Re: The Holy Grail temperament

Kurt,

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> I just want to support Gene in doing things the way he is doing it.  

Oddly enough, so do I. I never asked Gene to consider reducing the precision of his calculations - that would be insanely wrong.

> Independent of this, people need to be educated regarding this current
> difficulting in rendering pitches accurately, so that they can be aware when
> they might not really be hearing the intended scale.

Which was EXACTLY what I was trying to point out.

> But this is not Gene's problem.

Quite possibly not. But his scale calculations point out one of the glaring problems in midi implementation of tuning, and it would be a helpful convergence if his tuning research led to a greater understanding of what is, and what is not, possible with our rendering tools at this point.

Cheers,
Jon

From: czhang23@aol.com (2003-06-04)
Subject: Re: [tuning] Re: The Holy Grail temperament

In a message dated 2003:06:03 08:36:02 PM, JSZANTO@ADNC.COM writes:

>--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
>
>> Forgive him, for he uses 12tet at work all day and his judgement is
>> unbalanced as a result.
>
>But, just like the guys doing street repairs and construction, I always
>take a shower when I get home and wash off all the bad intonations. Then
>I feel much better!

    *snarfle!*  Quench your thirst with Partch, fill your sweet tooth with 
pelog, curl up with something Xeno-Gothic...

>Besides, I've always found it a positive thing to speak more than one 
language,
>and learning new ones needn't be done by the abandonment of others.
    
    "The sum of human wisdom is not contained in any one language,
and no single language is capable of expressing all forms and degrees of 
human comprehension." - Ezra Pound

     Language[s] change[s]: vowels shift, phonologies crash-&-burn, grammars 
leak, morpho-syntactics implode, lexico-semantics mutate, lexicons explode, 
orthographies reform, typographies blip-&-beep, slang flashes, stylistics 
warp... linguistic (R)evolutions mark each-&-every quantum leap...

"Some Languages Are Crushed to Powder but Rise Again as New Ones" -
title of a chapter on pidgins and creoles, John McWhorter,
_The Power of Babel: A Natural History of Language_

    "One thing foreigners, computers, and poets have in common
is that they make unexpected linguistic associations." --- Jasia Reichardt

    "There is no reason for the poet to be limited to words, and in fact the 
poet is most poetic when inventing languages. Hence the concept of the poet as 
'language designer'."  --- O. B. Hardison, Jr.

"La poésie date d' aujour d'hui."   (Poetry dates from today)
"La poésie est en jeu."             (Poetry is in play)
                --- Blaise Cendrars

---
Hanuman Zhang (aka "Z")
WOG (Wiley Oriental Gentleman ;)  
Avatar of Sun WuKong, a.k.a _Ma-Lau_ ("Monkey")
a.k.a. "TricksterGod of the Glorious Anti-Imperialist Chinese Boxers";
¡¡¡  TricksterShapeShifterIncarnate  !!!
 
<=  thee prIs ov X.iztenz iz aetern'l warfaer 'N' kreativ playf'llnizz...  =>

    =>  om hung hanumatay rudratmakai hung phat  <=
    mantra to Hanuman the Hindu Monkey TricksterGod

>Finally a religious statement I can agree with:
>
>the Zoroastrian teaching that it is a sin for a person to be boring.

"Life is all a great joke, but only the brave ever get the point."
                                    - Kenneth Rexroth

googolgigglabyte
goegolgiechelbijt  - of - met een vette megagrijns
GoogolGekicherByte
googolrisibyte ===> el byte de la  risita de googol 
googolrisadinhabyte ===>  o byte de risadinha de googol
googolspassoctet
guugoIllolbijt
gugolhihibajt
gugolngisibayt
okukolkikikol   
egúgelegigalibaith
kiletstroknolyadgigabaiti
cimacimakekehapi
baitakhakhweifayatrauni
ufi'auayinisuguguluarkhar   
pokatra oemadroabhethetre
inarevuta yhiyhayhake nawyo
va'i utne tuktukt'ishushukuko`g tuk  go`go`o`gwgaga

From: Gene Ward Smith (2003-06-04)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> Not at all! In fact, the opposite: if your calculations lead you to
pitches that are using discrete measurements less than a cent, I
simply was asking (and pointing out) whether or not you felt you had a
medium of reproduction that was as accurate as the scales you've crafted. 

Scala does sometimes have problems, but it is possible to check on its
pitch bends. I don't know how to check Timidity except by ear, but it
seems very good. Real sticklers can use Csound if they like, in which
case your only problem will be when Paul busts into the room talking
about the classical uncertainty principle.

> > If Scala scales were defined in terms of cawapus, I would have
> > computed precise integer values of cawapus and used them.
> 
> Also noting that cawapu is a term that even only a few denizens of
this list would know about; I'll have to look and see if the current
line of Cakewalk products still uses the term/structure referred to.

Scala seems to tune to the nearest cawapu.

> > Since it  uses floats, I computed using floats.
> 
> Right, I get that. The reason I pointed out the information from
Loffink was to say "great that you've measured so carefully, but when
we pour out the ingredients were going to round up or down a fair -
and semi-undetermined - amount; hope that's ok with you". And I was
curious if, when you calculate these extremely precise scale
constructs, that you get exactly what you've calculated in the end
result - the music. Have you ever tested, with frequency counters or
pitch analysis, if you indeed are getting the values you intended?

No, and I don't plan to. I can check the midi files themselves and see
if the pitch bends are being done correctly, and in fact did check on
Scala in just that way.

> > Do you have any experience computing?
> 
> BS in Software Engineering, 1990. 

When you wrote a program, did you worry that Fortran or C was giving
you more precision in your floating point numbers than you actually
required, and if so, why?

From: Jon Szanto (2003-06-04)
Subject: Re: The Holy Grail temperament

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I don't know how to check Timidity except by ear, but it
> seems very good.

Well, that's all I was asking, wasn't it? Did you have any degree of certainty about whether your tunings were being accurately rendered! I installed Timidity last night but couldn't get any files rendered.

> ...when Paul busts into the room talking
> about the classical uncertainty principle.

Hey, people are uncertain about a lot of things, like whether he should be tuning pianos...

> No, and I don't plan to. I can check the midi files themselves 
> and see if the pitch bends are being done correctly, and in fact 
> did check on Scala in just that way.

So, between looking at pitch bend values and using your ear upon rendering with Timidity, you are satisfied with the accuracy of the implementation of your various tunings.

> When you wrote a program, did you worry that Fortran or C was 
> giving you more precision in your floating point numbers than you 
> actually required, and if so, why?

Worry? No. I used the values to effect the computations, but when displaying the data I rounded or truncated the values (as the case indicated) to values that would be appropriate and meaningful for the end user. In all the many months of your posting lists of temperaments and other tunings, it is not a stretch to see that one might get the idea that - for some of these tunings to *really* mean anything - one would need the precision that you displayed.

I guess we are at an end point. On to your spurious percussion...

Cheers,
Jon

From: Kurt Bigler (2003-06-04)
Subject: tuning accuracy [was: The Holy Grail temperament]

on 6/3/03 12:47 AM, Jon Szanto <JSZANTO@ADNC.COM> wrote:

> I include the following from John Loffinks microtonal-synthesis website:
> 
> "Most synthesizers are limited in resolution to 1 to 2 cents for pitch.

Regarding this issue, I seem to recall reading (but can not find the
reference) that 1 to 2 cents is considered about the best that is achievable
when tuning organs.  And an organ tuner who is here with me today says that
practical tunings may often be off by a few cents and still be considered
"in tune", that you would drive yourself crazy as a tuner truing to do
better.  This sheds a slightly different light on the limitations of
electronic instruments, making even crude synthesizer technology look pretty
good!

This would also seem to make some distinctions based on exact ratios
apprently irrelevant for organ tunings.  I have tenatively decided not to be
concerned with any fine distinctions in exact ratios, and go more by things
like RMS info instead, to help me make choices.  The choices will ultimately
be determined by listening anyway, and listening on a synthesised instrument
for simulation purposes is unlikely to reveal the actual _qualities_ that
the tuning will have on the real instrument, because of fine distinctions in
harmonic structure that will also vary note to note.

So I am feeling somewhat set back in my hopes to be able to wisely chose a
scale in advance of actually trying it in the real instrument in question
(organ in my case).  But I'll go back to my original thread to reply on that
issue.

-Kurt Bigler

From: Gene Ward Smith (2003-06-04)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Gene,
> 
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > I don't know how to check Timidity except by ear, but it
> > seems very good.
> 
> Well, that's all I was asking, wasn't it? Did you have any degree of
certainty about whether your tunings were being accurately rendered! I
installed Timidity last night but couldn't get any files rendered.

You can't render files without also getting a GUS patch set. The one
to get is eawpats, now up to version 12. It's 36.4 MB uncompressed.
You also need a timidity.cfg file to point to it and tell it what
patch, volume and panning to use for each GM instrument. You also
should use one of the presets instead of messing about with all of the
command line complexities. If you use Windows, I would suggest making
a bat file to run it.

> So, between looking at pitch bend values and using your ear upon
rendering with Timidity, you are satisfied with the accuracy of the
implementation of your various tunings.

That's it, but if I really need to be certain I can always use Csound.

>
In all the many months of your posting lists of temperaments and other
tunings, it is not a stretch to see that one might get the idea that -
for some of these tunings to *really* mean anything - one would need
the precision that you displayed.

I'm guessing most people on this list know a little about music and
tuning. Why would you assume otherwise?

From: Jon Szanto (2003-06-04)
Subject: Re: The Holy Grail temperament

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> You can't render files without also getting a GUS patch set.

Great. With all the sample sets and SoundFont files I have already... rats. The docs with Timidity were thin and poorly written, but I haven't searched the web for more info yet. If I can't use my own samples with it then I probably won't even reinstall it.

> It's 36.4 MB uncompressed.

I'll trust you on the quality recommendation. But then I'm also on a dial-up, so it sounds like a trip to a friends who has broadband and a CDR.

> That's it, but if I really need to be certain I can always use Csound.

Yep.

> I'm guessing most people on this list know a little about music and
> tuning. Why would you assume otherwise?

I don't. I assume most people on this list...same as you. And then I try to be explicit and clear in my explanations. All one need do is look at questions from people on the list to know that everyone is *not* on the same page.

Cheers,
Jon

From: Gene Ward Smith (2003-06-04)
Subject: Re: The Holy Grail temperament

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Gene,
> 
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > You can't render files without also getting a GUS patch set.
> 
> Great. With all the sample sets and SoundFont files I have
already... rats. 

They say you can use sf2 files. I've been meaning to see if I could
actually get it to work, so I'll give it a shot.