Yahoo Tuning Groups Ultimate Backup tuning meantone as an ET

While it is quite possible to take any meantone and examine what ET it might apply, It makes assumptions that are possibly ungrounded.
While ET is not tunable by ear, to place this as the a priori of a scale seems misplaced in regard to that which is.
Also it is arbitrary. One could just as easily say that meantone was based on a recurrent sequence, or various forms of generators.
While it is quite possible that composers and culture at large might hear a particular matrix of pitch steps, there is absolutely nothing that implies that this matrix might not be flexible.
in fact the way in which what we call 12 ET is just such a case, where one has a set of variable 12.
While i am sure there are part of Mahler that might fit into 31 ET i can assure you as someone who has immersed myself in it , that he would be screaming for a good 9/8, especially in his brass melodies.
And if one listens to the 4th movement of the 3rd symphony, this cannot exist with out a really good 9/8.
Also there is no reason to assume that a composer would hear the same tuning throughout an entire piece. In fact as the material and focus changed, one would expect the intonation to change.
This is already the case as string players in a string quartet will change their intonation do to context
-- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Afmmjr@aol.com

Kraig's post prompt me to share some thoughts on the relationship between
meantone and ET. In many ways the two can appear to be the same thing.

When a "mean" tone was invented for keyboard modulatory reasons, it was as an
intentional equal temperament bisecting of the major third interval. The
results accomplished in any meantone tuning was much more of an equalness in
music than listeners of earlier periods of music had ever heard before. And it
was noticieable. Each of the keys of any variant of meantone tuning has more of
a sequence sounding follow up that one can associate with equalness.

ET is, in fact, eleventh comma meantone. It exists for the same reason that
all meantones exist, but it is less expensive in the number of notes needed
for it to comply to created music.

Likewise (to it being a legitimate meantone tuning variant), ET is a tempered
Pythagorean tuning. The 2-cent difference in the "perfect fifths" points to
this fact.

The changing of a composer's manuscript notation is insidious. The result,
however, is no different than mistreating a composer's intonation so that if
fits into a modern ideology. The performer's credo is to perform a composer's
music with the best of the composer's intentions. The care given to a
composer's intonation has a bearing on tempo, phrasing, ornatmentation, vibrato,
accents, mood, sentiments.

Unequalness makes for more interest in music because of what it stirs up. It
is a better metaphor for the overtone series, which is also unequal.
Unequalness makes instruments ring more, especially harpsichords and organs. And yet
meantone is the necessary step to ET.

ET is descended directly from meantone, while well temperament was an off
shoot of meantone that went into a different direction. ET, once the theory that
no one could hear right, has gained such hegemony that well temperament now
appears most inscrutable. The shoe is merely on the other foot.

all best, Johnny Reinhard

🔗monz <monz@tonalsoft.com>

hi Kraig,

--- In tuning@yahoogroups.com,
Kraig Grady <kraiggrady@a...>
wrote:

> While i am sure there are
> part of Mahler that might
> fit into 31 ET i can assure
> you as someone who has
> immersed myself in it ,
> that he would be screaming
> for a good 9/8, especially
> in his brass melodies.
> And if one listens to the
> 4th movement of the 3rd
> symphony, this cannot exist
> with out a really good 9/8.

yes, i'm sure Mahler relished the sound of a good 9/8 as much
as any other listener. but Mahler himself said this:

"The loss of ... distinctive key coloration, which
transforms the fixed pitch music of this [earlier] period
with subtle coloristic distinctions impossible to imagine
until one has heard them, is the great loss we have
suffered in changing from meantone to the equal intervals
and indistinguishable keys of equal temperament.

[Peter Yates 1964, "An Amateur at the Keyboard", p 60;
quoted by Douglas Leedy in _Interval_ vol. 4 #1, winter 1982-83]

and since Mahler indicates that he himself had heard
meantone, it was most likely Josef Petzval's lectures
and demonstrations of 31-edo at the Vienna University.

> Also there is no reason to assume that a composer would
> hear the same tuning throughout an entire piece. In fact
> as the material and focus changed, one would expect the
> intonation to change.

yes, i agree completely. for Mahler, i've always been
careful to say that he intended meantone "part of the time".
certainly, the fact that he wrote *all* of his major works
for orchestra, and nothing at all for piano excepting the
accompaniment of his songs, indicates that he had an interest
in flexible intonation ... or perhaps it specifically
indicates his *distinterest* in fixed tuning.

-monz

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
...
> Mahler himself said this:
>
> "The loss of ... distinctive key coloration, which
> transforms the fixed pitch music of this [earlier] period
> with subtle coloristic distinctions impossible to imagine
> until one has heard them, is the great loss we have
> suffered in changing from meantone to the equal intervals
> and indistinguishable keys of equal temperament.
>
> [Peter Yates 1964, "An Amateur at the Keyboard", p 60;
> quoted by Douglas Leedy in _Interval_ vol. 4 #1, winter 1982-83]
>
>
> and since Mahler indicates that he himself had heard
> meantone, it was most likely Josef Petzval's lectures
> and demonstrations of 31-edo at the Vienna University.

Then Mahler must have been very confused about meantone. Perhaps he
was confusing it with well-temperament. Or perhaps the meantone he
heard was badly tuned.

As alluded to by Johnny, earlier in this thread, no "subtle
colouristic distinctions" between keys are possible in a typical
properly-tuned meantone.

It should be obvious that in 31 equal, all diatonic keys have exactly
the same size intervals.

But even in a meantone where the chain of tempered fifths does not
close on itself, all keys that are contiguous on the open chain will
have exactly the same intervals - i.e. the central 6 major and 3 minor
keys for a 12-note-per-octave meantone.

And far from the gently undulating landscape of a well-temperament,
when one departs from those central 6 majors and 3 minors in a typical
meantone-12, one falls off a cliff.

Of course if the meantone happened to be not typical, but close to
1/11th-comma i.e. 12 equal, then the wolf might be quite tame and then
one might speak of "subtle colouristic distinctions" between at least
the more remote keys. But the central 6 majors and 3 minors would
still be identical in all intervals.

-- Dave Keenan

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> And far from the gently undulating landscape of a well-temperament,
> when one departs from those central 6 majors and 3 minors in a typical
> meantone-12, one falls off a cliff.

It's not really a cliff until you hit the wolf fifth, since the
diminished fourth in the place of a major third sort of works, and an
augmented second in place of a minor third is really pretty nice. We
get just 7/6s for those with the (112/3)^(1/9) fifth, which is pretty
close to 31 and quite close to 81; in other words, in an optimal
meantone region near 1/4 comma.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > And far from the gently undulating landscape of a well-temperament,
> > when one departs from those central 6 majors and 3 minors in a typical
> > meantone-12, one falls off a cliff.
>
> It's not really a cliff until you hit the wolf fifth, since the
> diminished fourth in the place of a major third sort of works, and an
> augmented second in place of a minor third is really pretty nice. We
> get just 7/6s for those with the (112/3)^(1/9) fifth, which is pretty
> close to 31 and quite close to 81; in other words, in an optimal
> meantone region near 1/4 comma.

Maybe so. But the point is, no-one in their right mind would call it a
"subtle coloristic distinction" (between diatonic keys) when a
consonant interval jumps in size by nearly 40 cents!

-- Dave Keenan

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Afmmjr@aol.com

In a message dated 4/25/2005 2:20:58 AM Eastern Standard Time,
kraiggrady@anaphoria.com writes:
I appreciate your perspective on this Johnny , but i am not sure how
comfortable you are with the idea of meantones being something that is
embedded in large number ETs, even if you do find them related.
possibly lower number ones are not so much a problem, but what about
larger ones. just curious
Hi Kraig,

It is not a matter of comfort, but of generalizations. 55 is a number that
gives a good first round of sixth comma meantone. However, many of the 55-et
pitches are as foreign to sixth comma meantone practice as can be. The larger
numbers are good for grouping meantone variants, as has been done since at
least Saveur (who listed 31, 43, and 55). But they seem misleading as to
performance practice, which is my primary focus.

To a modern it may not be necessry to conform to a sixth comma variant of
mentone, although it may be the historically appropriate variant. They can opt
for their own preferred aesthetic and not that of a long dead composer. They
might also make use in a modern composition of pitches from the larger set of
meantone extension. My work in presenting live performances of early music
makes me more prudent.

all best, Johnny Reinhard

🔗monz <monz@tonalsoft.com>

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

>
> --- In tuning@yahoogroups.com,
> "Dave Keenan" <d.keenan@b...>
> wrote:
>
> > And far from the gently
> > undulating landscape of a
> > well-temperament, when one
> > departs from those central
> > 6 majors and 3 minors in a
> > typical meantone-12, one
> > falls off a cliff.
>
> It's not really a cliff until
> you hit the wolf fifth, since
> the diminished fourth in the
> place of a major third sort
> of works, and an augmented
> second in place of a minor
> third is really pretty nice.
> We get just 7/6s for those
> with the (112/3)^(1/9) fifth,
> which is pretty close to 31
> and quite close to 81; in
> other words, in an optimal
> meantone region near 1/4 comma.

thank you both for your thoughts on this. it always bothered
me that Mahler specifically cites meantone, but that his
emphasis was on distinctive key coloration, which i have
known all along implies a well-temperament.

however, a quick perusal of his symphonic scores shows him
using both notes of an enharmonic pair in a relatively
short time frame. if he really was thinking in terms of
a 12-note tuning, whether well-tempered or meantone, he
probably wouldn't have written it that way. so apparently
he was thinking of real meantone, and one that extended
beyond 12 notes. how far beyond, is a question that can
only be answered by a close examination of not only his
published scores, but also his manuscripts and sketches.

as i write on the "Vienna" webpage, it's easy to find
double-sharps in Mahler's manuscripts which have been
"naturalized" by his editors in the Critical Edition.
given his favorable statement about meantone, i think
a performance of such a passage should take his original
notation into account and play the double-sharp at a
lower pitch than the enharmonically equivalent natural.

Mahler's harmonic vocabulary was post-Wagnerian, and
was certainly sophisticated enough to contain both
diminished-4ths and augmented-2nds -- but one
interesting point to note is that despite this
sophistication, and as he himself admitted, the
basis of his harmony was simple diatonicism, which
again, i think, argues in favor of meantone.

perhaps Mahler knew the sound of 31-edo from Petzval's
lectures, but was working with only a 19-tone subset
of it, a la Mozart with 55-edo.

finally, perhaps Mahler got his history muddled.
it's a possibility. but he did speak of "subtle
coloristic distinctions impossible to imagine until
one has heard them", and i'm sure he had a very fine
ear for intonation.

also, i don't think he would have been so concerned
with the sound of individual intervals, but rather
the overall sound of a key or set of chords.

-monz
http://tonalsoft.com
microtonal music software

🔗Afmmjr@aol.com

In a message dated 4/25/2005 11:32:33 AM Eastern Standard Time,
monz@tonalsoft.com writes:
also, i don't think he would have been so concerned
with the sound of individual intervals, but rather
the overall sound of a key or set of chords.
Hi Monz,

Since Mahler is post-Wagner (who Joel Mandelbaum marks as ET), any move
toward meantone would travel through sixth comma meantone notes in the direction
toward quarter comma notes. In this sense, Mahler can mean both! Since he was
speaking in the ideal, any meantone would give more color than equal
temperament.

The Wagner-ET combo is based on a study on the Tristan chord. It was found
that only ET worked to give the Tristan chord a unique, recognizeable quality.
Joel and I spoke of this about 10 years ago.

all best, Johnny Reinhard

🔗Gene Ward Smith <gwsmith@svpal.org>

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

> The Wagner-ET combo is based on a study on the Tristan chord. It
was found
> that only ET worked to give the Tristan chord a unique,
recognizeable quality.
> Joel and I spoke of this about 10 years ago.

The intervals of the Tristan chord are an augmented fourth, a major
third and a perfect fourth, and in standard septimal meantone an
augmented fourth approximates 7/5. Hence a JI version of it could go
1-7/5-7/4-7/3, which is simply a utonal tetrad and by no means
requires 12-et or any other tempering. Why traditional music theory
has found the Tristan chord to be so mysterious I cannot say. It does
not strike me as in any way a move towards atonality or any of the
usual blather theorists spout about it. We can, however, equate it to
other JI chords; if we think of it as 1-7/5-9/5-7/3 then in order to
get the 35/27 interval from 9/5 to 7/3 to be a fourth we need to
temper out 36/35, and this is strongly associated to 12-et.

A version of Tristan in meantone would be interesting to hear;
something close to an optimal septimal meantone such as 31, 50 or even
81 would be a good choice.

🔗monz <monz@tonalsoft.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > A version of Tristan in meantone would be interesting to hear;
> > something close to an optimal septimal meantone such as 31, 50 or
even
> > 81 would be a good choice.
>
> Tristan was finished in 1859, 18 years before Brahms wrote his first
> symphony. Could it be people have been puzzling over the harmony of
it
> because we've been playing it out of tune for the last 100 years?

maybe!

keep in mind that Brahms was a neo-classicist, and prefered
things like natural horns (with their JI pitches) ... and
probably ~1/6-comma meantone for orchestral performance too.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

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

> keep in mind that Brahms was a neo-classicist, and prefered
> things like natural horns (with their JI pitches) ... and
> probably ~1/6-comma meantone for orchestral performance too.

The question of course is what Wagner preferred; also, what would work
for his music of course.

The Tristan chord is a minor triad in first inversion lying over an
augmented fourth. How closely it approximates to a utonal tetrad
depends in good measure on how close the augmented fourth is to a 7/5,
since presumably the minor triad part will be heard as such. We have
the following table:

1/6 comma 7.7 cents sharp
1/5 comma 3.4 cents sharp
2/9 comma 0.5 cents sharp
1/4 comma 3 cents flat

The 7/5 will be exact if the fifth is exactly (56/5)^(1/6), or 697.085
cents, the Aaron Johnson meantone fifth; but clearly 1/5 comma, or
even 1/6 comma, will give a strong sense of utonal tetrad to the
Tristan chord.

🔗Tom Dent <tdent@auth.gr>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> (...)
> > > And far from the gently undulating landscape of a well-
temperament,
> > > when one departs from those central 6 majors and 3 minors in a
typical
> > > meantone-12, one falls off a cliff.
> >
> > It's not really a cliff until you hit the wolf fifth, since the
> > diminished fourth in the place of a major third sort of works,
and an
> > augmented second in place of a minor third is really pretty nice.
We
> > get just 7/6s for those with the (112/3)^(1/9) fifth, which is
pretty
> > close to 31 and quite close to 81; in other words, in an optimal
> > meantone region near 1/4 comma.
>
> Maybe so. But the point is, no-one in their right mind would call
it a
> "subtle coloristic distinction" (between diatonic keys) when a
> consonant interval jumps in size by nearly 40 cents!
>
> -- Dave Keenan

I thought this discussion was about orchestral practice where there
may be no wolf at all - since most orchestral instruments can produce
continuous variation of pitch with a little effort on the part of the
players. Only keyboard players 'fall off a cliff' in meantone.

The question would be if Mahler *notated* a wolf - for example,
notated a chord E - A flat - B ... or just like Mozart, used
accidentals in such a way as to avoid wolves, for example if he
notated D sharp - F double sharp - A sharp, that is a standard major
chord, which becomes a 'wolf' chord if the editors change the F
double sharp to a G.

Of course if he also used enharmonic modulation, there would be no
choice but to have a wolf somewhere, but even then he might have
carefully arranged it not to be glaringly obvious.

What is a subtle distinction is the difference between a chromatic
and a diatonic semitone (as someone has already mentioned). The
tunings where one gets the most coloristic distinctions are of course
not meantone at all.

~~~Thomas~~~

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 4/25/2005 11:32:33 AM Eastern Standard Time,
> monz@t... writes:
> also, i don't think he would have been so concerned
> with the sound of individual intervals, but rather
> the overall sound of a key or set of chords.

If two keys have all the same intervals then they also have the same
overall sound and the same chords. Keys in meantone differ only by a
constant shift in pitch to all the notes (until one falls off the end
of the chain and hits the wolf, which is far from subtle in any
characteristic meantone, i.e. 1/6 to 1/3 comma).

> Hi Monz,
>
> Since Mahler is post-Wagner (who Joel Mandelbaum marks as ET), any move
> toward meantone would travel through sixth comma meantone notes in
the direction
> toward quarter comma notes. In this sense, Mahler can mean both!
Since he was
> speaking in the ideal, any meantone would give more color than equal
> temperament.

Yes. Color is available in any meantone, but only by using enharmonics
outside the key signature. Monz quotes Mahler as referring to "subtle
distinctions between keys".

The set of available enharmonic shifts is different in the different
keys so I suppose that that could account for the "distinctions
between keys" part.

But I feel it is impossible to make sense of the "subtle" part unless
he had in mind an uncharacteristic meantone of less than 1/6-comma. At
1/6-comma an enharmonic shift is still 20 cents. When we get down to
1/8-comma we start to blur the line between meantones and
well-temperaments, with an enharmonic shift of 9 cents.

See Margo Schulter's
http://www.medieval.org/emfaq/harmony/pyth5.html#6.2

-- Dave Keenan

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Jon Szanto <JSZANTO@ADNC.COM>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
>
> I thought this discussion was about orchestral practice where there
> may be no wolf at all - since most orchestral instruments can produce
> continuous variation of pitch with a little effort on the part of the
> players. Only keyboard players 'fall off a cliff' in meantone.

Good point, but it doesn't alter mine.

> The question would be if Mahler *notated* a wolf - for example,
> notated a chord E - A flat - B ... or just like Mozart, used
> accidentals in such a way as to avoid wolves, for example if he
> notated D sharp - F double sharp - A sharp, that is a standard major
> chord, which becomes a 'wolf' chord if the editors change the F
> double sharp to a G.

Yes. A good question.

> Of course if he also used enharmonic modulation, there would be no
> choice but to have a wolf somewhere, but even then he might have
> carefully arranged it not to be glaringly obvious.
>
> What is a subtle distinction is the difference between a chromatic
> and a diatonic semitone (as someone has already mentioned).

If a syntonic comma difference can be considered subtle then I suppose
I can accept that Mahler may have had in mind 1/6-comma meantone, but
certainly nothing like the 1/4-comma or 31-ET that Monz and Gene were
suggesting.

> The tunings where one gets the most coloristic distinctions are of
> course not meantone at all.

Agreed. But I'm trying to make sense of that Mahler quote that Monz
posted:

The only way I can make sense of this is if he was thinking of
meantones between about 1/6 and 1/9 comma.

And even then any "distinctive key coloration" could only come from
using enharmonics outside the standard notes of the key, as opposed to
well-temperaments where "distinctive key coloration", albeit _very_
subtle, is available without departing from the standard notes of the key.

-- Dave Keenan

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> "The loss of ... distinctive key coloration, which
> transforms the fixed pitch music of this [earlier] period
> with subtle coloristic distinctions impossible to imagine
> until one has heard them, is the great loss we have
> suffered in changing from meantone to the equal intervals
> and indistinguishable keys of equal temperament."
>
> The only way I can make sense of this is if he was thinking of
> meantones between about 1/6 and 1/9 comma.

Or he is talking about the circulating temperaments which have a patch
of meantone and then some sharper fifths.

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > "The loss of ... distinctive key coloration, which
> > transforms the fixed pitch music of this [earlier] period
> > with subtle coloristic distinctions impossible to imagine
> > until one has heard them, is the great loss we have
> > suffered in changing from meantone to the equal intervals
> > and indistinguishable keys of equal temperament."
> >
> > The only way I can make sense of this is if he was thinking of
> > meantones between about 1/6 and 1/9 comma.
>
> Or he is talking about the circulating temperaments which have a patch
> of meantone and then some sharper fifths.

I suppose it's possible, but even then it would have to be a very weak
meantone, nothing like 1/4-comma. And it couldn't really still be
called meantone unless it had at least 10 contiguous meantone fifths.

But the other thing against that is that Monz tells us that Mahler
uses enharmonics, including some double-sharp, very close together in
time, which strongly suggests he did not have in mind any kind of
circulating temperament (at least not a 12-tone one).

-- Dave Keenan

🔗monz <monz@tonalsoft.com>

hi Dave (and Johnny),

--- In tuning@yahoogroups.com,
"Dave Keenan" <d.keenan@b...>
wrote:

> Yes. Color is available in
> any meantone, but only by
> using enharmonics outside
> the key signature. Monz
> quotes Mahler as referring
> to "subtle distinctions
> between keys".
>
> The set of available
> enharmonic shifts is
> different in the different
> keys so I suppose that that
> could account for the
> "distinctions between keys"
> part.

yes, i think that's exactly what Mahler was talking about.

> But I feel it is impossible to make sense of the "subtle"
> part unless he had in mind an uncharacteristic meantone
> of less than 1/6-comma. At 1/6-comma an enharmonic shift
> is still 20 cents. When we get down to 1/8-comma we start
> to blur the line between meantones and well-temperaments,
> with an enharmonic shift of 9 cents.

well, the whole line of reasoning here depends on exactly
what Mahler meant by "subtle". even to my ears, accustomed
as they are to microtonal intonational distinctions,
20 cents still seems quite subtle.

the big question for me is: did Mahler think that the
~39-cent enharmonic distinctions of 31-edo were subtle?
my guess would be that he did. by the time he made these
comments to Schoenberg, it was already pretty clear that
there was an intonational trend in Europe towards 12-edo.
39 cents is far more subtle than the 100 that you get
as the smallest distinction in 12-edo, and even more
subtle than the 0 (zero) cents which 12-edo gives you
for enharmonics.

but Dave's point does lend weight to the idea that the
form of meantone Mahler had in mind may have been more
like 1/6-comma ... particularly if it really was an
established orchestral practice in Mahler's time to
play in that tuning, and might well have been the case.

-monz
http://tonalsoft.com
microtonal music software

🔗Gene Ward Smith <gwsmith@svpal.org>

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

> I'm not sure Mahler would agree, though. Anyway, there was this screwy
> system of 1/5 comma meantone and two semi-wolves, though that was from
> an earlier period.

"Semiwolves" is really too strong: the two fifths are 711.73 cents,
which is pretty sharp but still usable. You get some major thirds
which are really pretty much 14/11s in this way. My inclination, of
course, would be to say let's make the meantone fifths exactly
(176/7)^(1/8), about 5/26 comma, and then they really are 14/11s. The
dog fifths (not wolves, of course) are now 710.9 cents. It's intesting
to see that something not too different from one of my screwy
circulating temperament ideas was actualy used in practice.

🔗Kraig Grady <kraiggrady@anaphoria.com>

But we will soon get into the Petrushka chord. I should have used the term subharmonic. Considering the range of subharmonic flutes and auloi in Europe (well Greece has more to do with Aisa that Europe) such a sonority is not that unusual Message: 8 Date: Tue, 26 Apr 2005 03:11:38 -0000 From: "Jon Szanto" <JSZANTO@ADNC.COM> Subject: Re: The Tristan chord in 7-limit JI --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

>> I believe the untonality 4-5-6-7 ...
> >

And Kraig, you have to admit that is a pretty funny typo:
"untonality". I'm sure all my ugliest works contained a lot of
untonalities.

My last in a series of drive-by postings,
Jon

>.
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
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🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Dave Keenan wrote:

Gene replied:
> Or he is talking about the circulating temperaments which
> have a patch of meantone and then some sharper fifths.

[Yahya]
Now *this* makes sense.

I also had the vague impression, from readings long ago,
that this was the commonest way to use meantone in the
first half of the 19th Century and possibly later.

Regards,
Yahya

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🔗Carl Lumma <ekin@lumma.org>

>Yes. Color is available in any meantone, but only by using enharmonics
>outside the key signature. Monz quotes Mahler as referring to "subtle
>distinctions between keys".
>
>The set of available enharmonic shifts is different in the different
>keys so I suppose that that could account for the "distinctions
>between keys" part.
>
>But I feel it is impossible to make sense of the "subtle" part unless
>he had in mind an uncharacteristic meantone of less than 1/6-comma.

What about absolute-pitch effects?

-Carl