Correct tuning for correct period/composer?

Hi mates,

I'm sure you have been asked this personally or as a group for several
times before but Yahoo's search is virtually unusable and I'm not in
the mood of ferreting. :P

The point is, I want to retune my MIDI and NWC collection. For MIDI we
have Scala and other stuff (the most foremost, IMHO, being Fred
Nachbaur's kit). For NWC 2, Andrew Purdam is working on a tuning "User
Tool", whose lucky alpha tester is yours truly.

My collection spans the widest possible period; I have Troubadour
stuff, Leoninus and Perotinus, Gothics, Rennaissances, Baroques and so
on. (A detailed list can be supplied if necessary.) For which period
which tuning should I use? If there are composers prefering different
tunings than their periods' standard, which ones should be used for them?

Honestly, I can no more stand hearing Josquin and others in 12EDO, so
your assistance will be much appreciated. As always, although I'll try
to catch up with this particular thread, a CC: to ertugrulinanc at
superonline dot com would be great.

Best,
Ertugrul

Hello Ertugrul,

This is a life long quest for me, the search for the right match between
composer and their preferred tuning. It started with a Master's thesis called
Bach's Tuning. At the time of Columbia University, it seemed likely that
Werckmeister III was the most likely tuning. 25 years later, I feel it a certaintly
(current wiggles excepted).

Some information has come to me from this List. It seem quite comfortable to
say the following:

Troubadors through Middle Ages, use Pythagorean tuning

Early Renaissance introduceds the pure major third into the Mediterranean.
Different tunings are employed: fretted tunings, irregular tunings (John
Dowland), a cappella tunigns, etc. Pythagorean models of tuning linger on in
different forms, mostly influencing the fretted tunings.

The Baroque coincides with the prominence of the keyboard. For well
temperament in Thuringia and its environs (Pachelbell, the Bachs, Krebs) Werckmeister
III makes the most sense for keyboard and instrumental. Werckmeister,
himself, was the area's major promoter of mixing instruments with the organ in the
church.

Telemann was into extended sixth-comma meantone, as did Frederick the Great
in Potsdam. Mozart followed suit. The story of how sixth-comma meantone took
over Europe is still to be told...but it happened. The Dutch remained
stauchly quarter-comma meantone. England, perhaps the homeland of the just third,
produced some independent tuning thinkers (Newton, Thompson, Bosanquet), came up
with lots of irregular system. Through Thomas Young there was a mirror of
Valotti tuning, only starting on a different keynote.

The other night (March 26, 2005), the AFMM presented four works in Kirnberger
tuning (II). In my mind, it was near impossible to know what these pieces
would sound like. The audience was super excited about the music: C.P. Bach,
Ludwig van Beethoven, Felix Mendelssohn, Robert Schumann. I played bassoon in
the Bach and the Mendelssohn. The tuning came easily. People "couldn't tell
the difference." Thing is, all well temperaments sound more similar to each
other than either one would to equal temperament.

The Romantic period continues extended sixth comma meantone and gradually
eases it into an equal temperament theory. Brahms and Mahler would benefit from
extended sixth comma meantone. Schoenberg makes for equal temperament because
it is backed up in Schoenberg's theory (although he recognizes the harmonic
bases of notes in practice). Ives idealized an extended Pythagorean tuning.

I hope this helps. Certainly there is the wild Vicentino with the few extant
examples of his extra-chromatic technique. Ah, Beethoven, deaf.

all best, Johnny Reinhard

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

> The point is, I want to retune my MIDI and NWC collection. For MIDI we
> have Scala and other stuff (the most foremost, IMHO, being Fred
> Nachbaur's kit). For NWC 2, Andrew Purdam is working on a tuning "User
> Tool", whose lucky alpha tester is yours truly.

I've had a lot of retuning experience; why not ask some specific
questions about it.

I just put up another retuned web page today, of music by modern
conservatives tuned to 31 equal:

http://66.98.148.43/~xenharmo/mmm.htm

This kind of meantone retuning is often possible.

> My collection spans the widest possible period; I have Troubadour
> stuff, Leoninus and Perotinus, Gothics, Rennaissances, Baroques and so
> on. (A detailed list can be supplied if necessary.) For which period
> which tuning should I use?

For Medieval, Pythagorean works pretty well most of the time, but not
for things like Sumer is Ichumen In. For Renaissance though the early
18th century, use meantone. 31 equal is easy to retune to, and is
quite acceptable as a meantone tuning. For later in the 18th century
and some 19 century music, you can use a circulating temperament or
extended meantone (which requires a little more effort, but which can
produce some very nice results.) If you use meantone, check for wolf
fifths.

If there are composers prefering different
> tunings than their periods' standard, which ones should be used for
them?
>
> Honestly, I can no more stand hearing Josquin and others in 12EDO, so
> your assistance will be much appreciated. As always, although I'll try
> to catch up with this particular thread, a CC: to ertugrulinanc at
> superonline dot com would be great.
>
> Best,
> Ertugrul

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Telemann was into extended sixth-comma meantone, as did Frederick
the Great
> in Potsdam. Mozart followed suit. The story of how sixth-comma
meantone took
> over Europe is still to be told...but it happened.

I imagine it was because the diminished fourths make for better
approximations to 5/4 thirds than 1/4 comma gives. 1/6 comma gives
diminished fourths that are 26.7 cents sharper than 5/4, whereas 1/4
comma gives 41.1 cents sharper, a big difference.

> The other night (March 26, 2005), the AFMM presented four works in
Kirnberger
> tuning (II). In my mind, it was near impossible to know what these
pieces
> would sound like. The audience was super excited about the music:
C.P. Bach,
> Ludwig van Beethoven, Felix Mendelssohn, Robert Schumann. I played
bassoon in
> the Bach and the Mendelssohn.

Not only is Bach an excellent candidate for non-12-equal, so is
Mendelssohn; he really should not be played in equal temperament IMHO.

> The Romantic period continues extended sixth comma meantone and
gradually
> eases it into an equal temperament theory. Brahms and Mahler would
benefit from
> extended sixth comma meantone.

It's interesting you should say this because I've been wondering if I
should try to put some Brahms into extended meantone. I don't see
complelling reason to use 1/6 comma for extended meantone, however,
since most of the time you are not using the diminished fourth,
because it is *extended* meantone. Of course it crops up a lot anyway,
in things like the augmented triad, which is two major thirds and a
diminished fourth, but my inclination would be to be bold and use
something closer to 5/17 comma meantone, making the diminished fourth
into a 9/7. Of course that could be regarded as inauthentic, but what
the heck, so might any meantone version. I've found Manuel's new P31
notation makes 31 easy to retune to, so I'd suggest using that for the
most part, unless Manuel wants to also give us P55, P50, and P43,
which wouldn't be a bad idea.

__________________________________________

>Honestly, I can no more stand hearing Josquin and others in 12EDO,

Where do you find Josquin in 12EDO? No unaccompanied choral work is going
to be in 12EDO..... maybe I am misreading what you meant

hi Gene and Johnny,

--- In tuning@yahoogroups.com,
"Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com,
> Afmmjr@a... wrote:
>
> > The Romantic period continues
> > extended sixth comma meantone
> > and gradually eases it into an
> > equal temperament theory.
> > Brahms and Mahler would benefit
> > from extended sixth comma
> > meantone.
>
> It's interesting you should say this because I've been
> wondering if I should try to put some Brahms into extended
> meantone. I don't see complelling reason to use 1/6 comma
> for extended meantone, however, since most of the time
> you are not using the diminished fourth, because it is
> *extended* meantone. Of course it crops up a lot anyway,
> in things like the augmented triad, which is two major
> thirds and a diminished fourth, but my inclination would
> be to be bold and use something closer to 5/17 comma meantone,
> making the diminished fourth into a 9/7. Of course that
> could be regarded as inauthentic, but what the heck, so
> might any meantone version. I've found Manuel's new P31
> notation makes 31 easy to retune to, so I'd suggest using
> that for the most part, unless Manuel wants to also give
> us P55, P50, and P43, which wouldn't be a bad idea.

actually, for Mahler, i am convinced that he had meantone
in mind for his own symphonies at least some of the time,
and according to my speculations, the meantone he would
have known would be 31-edo. i'm hoping someday to retune
my MIDI version of the 1st movement of his 7th Symphony
into 31-edo ... i've already done a small part of it using
my own software (Tonalsoft Musica), and it's a revelation.

as for 1/6-comma meantone ... Johnny and i have talked
about this, and based on what both of us know about Telemann,
Mozart, and recordings from the 1920s, there does indeed
seem to have been a strong tradition of orchestral players
playing in a ~20-tone subset of 55-edo / 1/6-comma meantone
from the 1700s to the advent of electronic recording c.1923.

-monz

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

> unless Manuel wants to also give us P55, P50, and P43,
> which wouldn't be a bad idea.

I've implemented those now and you can download it.
Also I made an ennealimmal 441 of some sort: EL441 which is
not exactly what you specified, but I'm still open to
suggestions. In any case it's similar to EL72 and EL99.

Manuel

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Early Renaissance introduceds the pure major third into the
Mediterranean.
> Different tunings are employed: fretted tunings, irregular tunings
(John
> Dowland), a cappella tunigns, etc. Pythagorean models of tuning
linger on in
> different forms, mostly influencing the fretted tunings.

I'm not sure what 'fretted tuning' is here. Meantone seems indicated
for Renaissance and early Baroque keyboards and stringed instruments.

> The other night (March 26, 2005), the AFMM

Who? Academy For Modern Music? Where?

> presented four works in Kirnberger tuning (II). (...) C.P. Bach,
> Ludwig van Beethoven, Felix Mendelssohn, Robert Schumann. I played
bassoon in
> the Bach and the Mendelssohn. The tuning came easily.
People "couldn't tell
> the difference." Thing is, all well temperaments sound more
similar to each
> other than either one would to equal temperament.

?? Bassoons do not play equal temperament, or any fixed tuning. How
did the orchestra (both wind and strings) ensure that they had the
correct tuning?

> The Romantic period continues extended sixth comma meantone and
gradually
> eases it into an equal temperament theory. Brahms and Mahler would
benefit from
> extended sixth comma meantone.

I think Jorgensen goes into great detail about what tunings were used
in the 19th century - things like a mixture of 7 fifths tuned to 1/7
Pythagorean comma and 5 just fifths, or 8 x 1/8 comma and 4 just.
CPE Bach and Haydn could have used something similar for their
keyboards.

~~~Thomas~~~

--- In tuning@yahoogroups.com, pgreenhaw@n... wrote:
> __________________________________________
>
>
>
> >Honestly, I can no more stand hearing Josquin and others in 12EDO,
>
>
> Where do you find Josquin in 12EDO? No unaccompanied choral work is
going
> to be in 12EDO..... maybe I am misreading what you meant

I'm afraid you can easily find midi files with Josquin in 12EDO.

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> as for 1/6-comma meantone ... Johnny and i have talked
> about this, and based on what both of us know about Telemann,
> Mozart, and recordings from the 1920s, there does indeed
> seem to have been a strong tradition of orchestral players
> playing in a ~20-tone subset of 55-edo / 1/6-comma meantone
> from the 1700s to the advent of electronic recording c.1923.

Mozart did indeed teach 1/6 comma, and it is interesting to learn this
might still have been a living tradition so much later. My point about
extended meantone was a general one. Of course, 1/6 comma gives you a
fifth which is a little nearer just, and that has its effect on melody
as well as harmony; it has slightly less of the gentle quality of
flatter versions of meantone, and conveys more briskness. It also, of
course, has a diminished fourth which is closer to a third, which
might be thought desireable.

Do you have a theory why, in *extended* meantone, 55-et would be
preferred over 31-et? I think it does need to have its own
"Pythagorean" notation system in Scala, certainly. We have 12, 19, and
now 31. Adding 55, 43, 50 would fill in the gaps better, and 69
wouldn't be a bad deal either.

Hi Thomas,

I'm warming up a bassoon reed right now, just before heading out for the
evening. But I wanted to get right back to you.

In a message dated 4/22/2005 12:51:25 PM Eastern Standard Time, tdent@auth.gr
writes:
--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Early Renaissance introduceds the pure major third into the
Mediterranean.
> Different tunings are employed: fretted tunings, irregular tunings
(John
> Dowland), a cappella tunigns, etc. Pythagorean models of tuning
linger on in
> different forms, mostly influencing the fretted tunings.

I'm not sure what 'fretted tuning' is here. Meantone seems indicated
for Renaissance and early Baroque keyboards and stringed instruments.

JR: Actually, equal temperament can be read here. And variants thereof.
Galileo's father had introduced a 99-cent equal tempered semitone by using the
17th harmonic.

> The other night (March 26, 2005), the AFMM

Who? Academy For Modern Music? Where?

JR: American Festival of Microtonal Music in New York City at Faust Harrison
Pianos (205 West 58th Street).
> presented four works in Kirnberger tuning (II). (...) C.P. Bach,
> Ludwig van Beethoven, Felix Mendelssohn, Robert Schumann. I played
bassoon in
> the Bach and the Mendelssohn. The tuning came easily.
People "couldn't tell
> the difference." Thing is, all well temperaments sound more
similar to each
> other than either one would to equal temperament.

?? Bassoons do not play equal temperament, or any fixed tuning. How
did the orchestra (both wind and strings) ensure that they had the
correct tuning?

JR: It has been my priviledge to work in tuning instruments into different
tunings systems since 1981, as a bassoonist. Once the bassoonist hear's in his
inner ear a particular interval, it is emanently playable on the axe.

> The Romantic period continues extended sixth comma meantone and
gradually
> eases it into an equal temperament theory. Brahms and Mahler would
benefit from
> extended sixth comma meantone.

I think Jorgensen goes into great detail about what tunings were used
in the 19th century - things like a mixture of 7 fifths tuned to 1/7
Pythagorean comma and 5 just fifths, or 8 x 1/8 comma and 4 just.
CPE Bach and Haydn could have used something similar for their
keyboards.

~~~Thomas~~~

JR: Yes, I have read and reread Jorgensen. I am ever fascinated by the
Handel well temperament he offered, published just after Handel's death by
England's royalty.

all best,

Johnny Reinhard, Director
American Festival of Microtonal Music, Inc.
PITCH CDs
318 East 70th Street, #5-FW, New York 10021 USA
(212) 517-3550

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > unless Manuel wants to also give us P55, P50, and P43,
> > which wouldn't be a bad idea.
>
> I've implemented those now and you can download it.
> Also I made an ennealimmal 441 of some sort: EL441 which is
> not exactly what you specified, but I'm still open to
> suggestions. In any case it's similar to EL72 and EL99.

Thanks! It is important that all equal divisions notated using the same
temperament use the same notation, so that a MOS is spelled exactly
like an equal division. This should accomplish that, anyway. My
notation plan was based on the idea that this can best be accomplished
by notations that define themselves in terms of period and generator.

Note that Manuel has now made it easier not only to retune midi files
to meantone (where I am discovering the note names are a big help
compared to the numbers I used to have to use), but we now have
coverage of the major *kinds* of meantone tunings. We've got 55, a la
Telemann and Mozart. We have 31, close to the classic Pietro Aron 1/4
comma meantone. We have 50, close to 2/7 comma, and near the optimal
meantones of Robert Smith and Wesley Woolhouse (not to mention Paul
Erlich!) We have 43, also a good choice between 55 and 31, and almost
precisely 1/5-comma meantone, a tuning which has recieved some attention.

Jorgensen quotes John Robinson to the effect that a tuning in this
range was "in great repute" and "generally practiced"; this is the one
following Keller's tuning rules which Jorgensen apparently (he doesn't
give the formula, but I extracted this) interprets as giving the
positive real root of f^4+2*x-8=0. This is quite close to 74-et
meantone. Also, 69-et is close to the Wilson meantone. Since Lucy is
unlikely to accept 88 as a replacement for Lucy Tuning, these are the
most plausible tunings to add. I've used 81, since it is optimal or
nearly optimal for some definitions, but probably 50 will do for that.

__________________________________________

>>>Honestly, I can no more stand hearing Josquin and others in 12EDO,

>> Where do you find Josquin in 12EDO? No unaccompanied choral work is
>>going
>> to be in 12EDO..... maybe I am misreading what you meant

>I'm afraid you can easily find midi files with Josquin in 12EDO.

That is scary

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--- In tuning@yahoogroups.com,
pgreenhaw@n... wrote:
> ____________________________
>
>
> >>> Honestly, I can no more
> >>> stand hearing Josquin
> >>> and others in 12EDO,
>
>
> >> Where do you find Josquin
> >> in 12EDO? No unaccompanied
> >> choral work is going to be
> >> in 12EDO..... maybe I am
> >> misreading what you meant
>
> > I'm afraid you can easily
> > find midi files with Josquin
> > in 12EDO.
>
> That is scary

what's so scary about it? MIDI was created back in 1983 with
12-edo as its tuning basis, and most people who create MIDIs
don't bother to retune them out of 12-edo, so there are
literally thousands (maybe even millions?) of MIDI-files
out there of music which was composed or originally performed
in a non-12-edo tuning, but which MIDI-files *are* in 12-edo.

PS -- [shameless plug] Tonalsoft Musica (version 1.0 coming
summer 2005) will help remedy this situation: Musica's own
native file format stores a whole lot of extra informative
data along with what MIDI needs (so that you can see the music
in real-time on the lattice diagram, etc.), but it will also
be able to convert its output to a properly tuned MIDI-file
as well.

-monz

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, pgreenhaw@n... wrote:
> > __________________________________________
> >
> >
> >
> > >Honestly, I can no more stand hearing Josquin and others in 12EDO,
> >
> >
> > Where do you find Josquin in 12EDO? No unaccompanied choral work is
> going
> > to be in 12EDO..... maybe I am misreading what you meant
>
> I'm afraid you can easily find midi files with Josquin in 12EDO.

Exactly. MIDI is, well, MIDI :) and NWC files store notation + MIDI data.

hi Gene,

--- In tuning@yahoogroups.com,
"Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning@yahoogroups.com,
"monz" <monz@t...> wrote:
>
> > as for 1/6-comma meantone
> > ... Johnny and i have talked
> > about this, and based on what
> > both of us know about Telemann,
> > Mozart, and recordings from
> > the 1920s, there does indeed
> > seem to have been a strong
> > tradition of orchestral players
> > playing in a ~20-tone subset
> > of 55-edo / 1/6-comma meantone
> > from the 1700s to the advent
> > of electronic recording c.1923.
>
> Mozart did indeed teach 1/6 comma, and it is interesting
> to learn this might still have been a living tradition so
> much later.

when i first created the 55-edo MIDI file that's on
my webpage, i was *astonished* to hear that it sounded
just like what i remember of an old recording of the
G-minor Symphony, which was the first electrical
recording ever made of a complete symphony. when i
told Johnny Reinhard about this, he confirmed that
according to his knowledge, players in Europe were
still playing in ~1/6-comma meantone into the 20th century.

> Do you have a theory why, in *extended* meantone,
> 55-et would be preferred over 31-et?

i don't really have much to substantiate what i think
... but most likely there are two reasons for the
preference of 55-edo:

1)
by the 1700s, well-temperaments had become prevalent
on keyboards, and this to my mind began a slow shift
of the tuning paradigm away from extended open-ended
meantones and towards closed 12-tone systems, which
seems to have had an effect even on orchestral playing
based on extended (i.e., 19 or 20-tone) meantones.
the well-temperaments also feature pythagorean intervals,
and as you point out, 55-edo or 1/6-comma have intervals
which are audibly closer to the pythagorean ones than
those of the other "softer" meantones.

2)
beginning with the rediscovery of ancient Greek
music-theory texts, shortly after the Crusades, European
theorists often expressed a strong desire to relate
contemporary European theory and practice to that
described by the ancient Greeks. the earliest Greek
theorist whose work survives, Philolaus, described
a division of the pythagorean whole-tone (9/8 ratio)
into 4 "diaschismas" of ~45 cents each plus a
pythagorean comma of ~23.5 cents.

see:
http://tonalsoft.com/enc/philolaus.htm

Philolaus's diaschisma is thus almost exactly double
the size of the comma, thus encouraging one to think
of the whole-tone as divided into 9 commas ... which
in fact is exactly what medieval theorists did.
(IIRC, Margo Schulter cited Johannes de Garlandia as
the first medieval theorist to do so.)

assuming a closed tuning, this division into 9 commas
produces either 53-edo or 55-edo, depending on which
of the two different semitones (chromatic and diatonic)
is the larger one. making the chromatic semitone larger
(thus, a pythagorean system) gives 53-edo, and making
the diatonic larger (thus, a meantone) gives 55:

.......................... 53-edo ........... 55-edo

t = tone .................... 9 ................ 9
s = diatonic semitone ....... 4 ................ 5
octave = 5t + 2s ..... (5*9)+(2*4)=53 ... (5*9)+(2*5)=55

-monz

In a message dated 4/22/2005 7:14:12 PM Eastern Standard Time,
monz@tonalsoft.com writes:
> Do you have a theory why, in *extended* meantone,
> 55-et would be preferred over 31-et?
Please allow me to point out that extended sixth comma meantone was not
thought of by musicians as 55-et. In 1700 Saveur spoke of it as the general tuning
of musicians. Sixth comma meantone was merely extended as needed to fulfill
harmonic obligations. Once the keyboard had been surpassed by a note it did
not contain, the note was picked up by a more flexible instrument.

The issue for me is how it became that Silbermann and Telemann were using
sixth comma meantone when this particualr variant seems to have been skipped over
by all the theorists. It seems more as an outgrowth of contemporary
chromaticism as it was known in the Baroque. Sixth comma meantone is a better
counterpart to Werckmeister's chromatic.

But where is the historical record of this move to sixth comma in the early
1700s?

Johnny Reinhard

hi Johnny,

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Please allow me to point out that extended sixth comma
> meantone was not thought of by musicians as 55-et.
> In 1700 Saveur spoke of it as the general tuning
> of musicians. Sixth comma meantone was merely extended
> as needed to fulfill harmonic obligations. Once the
> keyboard had been surpassed by a note it did not contain,
> the note was picked up by a more flexible instrument.

right, and good of you to point that out. Mozart himself
taught a 20-tone subset of 55-edo, or 1/6-comma meantone
if you prefer -- if the entire 55-tone set isn't being
employed, then it really makes no difference which moniker
you apply to the tuning.

but the fact that the Mozarts (Leopold and Wolfgang) taught
that "whole-tone = 9 commas, diatonic semitone = 5 commas,
chromatic semitone = 4 commas" and assumed octave equivalence,
indicates 55-edo as the superset, at least conceptually.

as i just wrote in another post, if the octave is 5 tones
+ 2 diatonic semitones, then the algebra of Mozart commas
is (5*9) + (2*5) = 45+10 = 55.

-monz

Johnny replied to Ertugrul,
________________________________________________________________________
Date: Thu, 21 Apr 2005 19:49:41 EDT
From: Afmmjr@...
Subject: Re: Correct tuning for correct period/composer?

Hello Ertugrul,

This is a life long quest for me, the search for the right match between
composer and their preferred tuning. It started with a Master's thesis called
Bach's Tuning. At the time of Columbia University, it seemed likely that
Werckmeister III was the most likely tuning. 25 years later, I feel it a certaintly
(current wiggles excepted).

Some information has come to me from this List. It seem quite comfortable to
say the following:

... [all the meat cut off the bone here] ...

all best, Johnny Reinhard
________________________________________________________________________

[YA] Johnny, this is excellent information!
Would you mind if I quoted you on the tuning wiki?

Regards,
Yahya

--
Internal Virus Database is out-of-date.
Checked by AVG Anti-Virus.
Version: 7.0.308 / Virus Database: 266.9.15 - Release Date: 16/4/05

Gene wrote, in reply to Johnny's answer to Ertugrul:
________________________________________________________________________
Date: Fri, 22 Apr 2005 02:57:46 -0000
From: "Gene Ward Smith" <gwsmith@...>
Subject: Re: Correct tuning for correct period/composer?

...
> The other night (March 26, 2005), the AFMM presented four works in
> Kirnberger tuning (II). In my mind, it was near impossible to know
> what these pieces would sound like. The audience was super excited
> about the music: C.P. Bach, Ludwig van Beethoven, Felix Mendelssohn,
> Robert Schumann. I played bassoon in the Bach and the Mendelssohn.

Not only is Bach an excellent candidate for non-12-equal, so is
Mendelssohn; he really should not be played in equal temperament IMHO.
________________________________________________________________________

[YA] Nor _sung_ in ET!

Regards,
Yahya

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__________________________________________

> >> Where do you find Josquin
> >> in 12EDO? No unaccompanied
> >> choral work is going to be
> >> in 12EDO..... maybe I am
> >> misreading what you meant
>
> > I'm afraid you can easily
> > find midi files with Josquin
> > in 12EDO.
>
>>>> That is scary

>what's so scary about it?...

I was referring to the listening experience of Josquin-MIDI

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Gene wrote:
>Note that Manuel has now made it easier not only to retune midi files
>to meantone (where I am discovering the note names are a big help
>compared to the numbers I used to have to use), but we now have
>coverage of the major *kinds* of meantone tunings. We've got 55, a la
>Telemann and Mozart. We have 31, close to the classic Pietro Aron 1/4
>comma meantone.

The notations P31, P55 etc that I've added didn't actually make
retuning to meantone possible now, that was already possible with
all the E<n> notations. Because the function that converts a note
name to a pitch recognises the apotome and 5-limit commas used in
any combination.
You can check this with for example
echo %noteval(Cx,E55)
echo %noteval(Cxxxx,E55)
No need to use P55 here.

Manuel

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> The notations P31, P55 etc that I've added didn't actually make
> retuning to meantone possible now, that was already possible with
> all the E<n> notations. Because the function that converts a note
> name to a pitch recognises the apotome and 5-limit commas used in
> any combination.
> You can check this with for example
> echo %noteval(Cx,E55)
> echo %noteval(Cxxxx,E55)
> No need to use P55 here.

So if I wanted to make a seq file that converts to a midi file in
Pythagorean, I could just put in a line "0 equal 53" and would not
need a line for notation?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> So if I wanted to make a seq file that converts to a midi file in
> Pythagorean, I could just put in a line "0 equal 53" and would not
> need a line for notation?

No, you need a line "0 notation E53", the notation and the tuning
are entirely independent. So using "0 equal 53" with E53 isn't
required either of course. The help file says about the "note" statement:

"...or a note name in the specified notation system. In the latter
case, the nearest scale pitch to the nominal value of the note name
will be taken (Except when the system is JI or JI2). So the notation
system should be suitable for the current or specified scale for
proper results."

Manuel

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> "...or a note name in the specified notation system. In the latter
> case, the nearest scale pitch to the nominal value of the note name
> will be taken (Except when the system is JI or JI2). So the notation
> system should be suitable for the current or specified scale for
> proper results."

I'm not at all clear what this means. Is it simply saying that in any
equal temperament notation system, if you take the best fifth, and the
corresponding apotome, any combination of seven nominals f-B plus
flats and sharps will be interpreted in terms of this fifth?

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> England, perhaps the homeland of the just third,
> produced some independent tuning thinkers (Newton, Thompson,
Bosanquet), came up
> with lots of irregular system.
like
http://www.societymusictheory.org/mto/issues/mto.93.0.3/mto.93.0.3.lindley7.gif

53=0: |__|solut|fa|--| 3^0=1
____: |__|__|__|__|__| 3^...
8___: |mi|la|re|__|__| 3^-10 ~ 10/9? an schisma 32805/32768 to sharp!
9___: |__|__|__|solut| 3^2=9/8
____: |__|__|__|__|__| 3^...
13__: |fa|__|__|__|__| 3^-3=32/27
____: |__|__|__|__|__| 3^...
17__: |__|__|mi|la|re| 3^-8 ~ 5/4 also schismatic sharp
____: |__|__|__|__|__| 3^...
22__: |solut|fa|--|__| 3^-1=4/3 an 4th
____: |__|__|__|__|__| 3^...
26__: |__|__|__|__|mi| 3^-6=1024/729
____: |__|__|__|__|__| 3^...
30__: |la|re|__|__|__| 3^-11 ~ 40/27? " " "
31__: |__|__|solut|fa| 3/2 an 5th
____: |__|__|__|__|__| 3^...
35__: |--|__|__|__|__| 3^-4=128/81
____: |__|__|__|__|__| 3^...
39__: |__|mi|la|re|__| 3^-9 ~ 5/3? " " "
40__: |__|__|__|__|sol 3^3=27/16
____: |__|__|__|__|__| 3^...
44__: |ut|fa|--|__|__| 3^-2=16/9
____: |__|__|__|__|__| 3^...
48__: |__|__|__|mi|la| 3^-7 ~ 15/8? " " "
____: |__|__|__|__|__| 3^...
52__: |re|__|__|__|__| 3^-12=2/PC ~ ?160/81=2/SC doubtful " " "!
53=0: |__|solut|fa|--| 3^0=1 modulo (any power of) 2

N.s master scale seems to come from a chain of 11 pure just 5ths

Ebb re
Bbb la
Fb mi
Cb --
Gb
Db
Ab
Eb
F fa
C ut
G sol

Choose an arbitrarily 12-tone subset scale out of above 53

C___0: 1/1____ ut or today "do"
d___8: 3^-10__ re_Newtonian
D___9: 9/8____ RE_Gothic
e__17: 3^-8___ mi_Newtonian
E__18: 81/64__ mi_Gothic
F__22: 4/3____ fa
G__31: 3/2____ sol
a__39: 3^-9___ la_Newtonian
A__40: 27/16__ LA_Gothic
Bb_44: 16/9___ |--|_Newtonian, in german the note:"B"
b__48: 3^-7___ (ti)_NeoGothic, the later german:"h"
B__49: 243/128 (TI)_NeoGothic, the later german:"H"
C'_53: 2/1____ ut'

Retune your own keyboard-instrument in that ratios
trying out yourself how well it sounds.
Here comes my preferred board-layout,
i'm reccomending to apply above dozen pitches.

----------------------
_8 key C middle ~264Hz
---------|9=key=C#=Db|
17 key D
---------|18=key=Eb=D#
22 key E
----------------------
31 key F
---------|39=key=F#=Gb|
40 key G
---------|44=key=G#=Ab| ~415Hz
48 key A ~440Hz
---------|49=key=Bb=A#|
53=0 key B
-----------------------
8 key C'
---------|key C# &ct.

but any other distribution or starting pitch frequency
may be chosen too, as you like.

Have a lot of fun playing in that!
A.S.