Question for the Group

Do you consider quarter comma meantone to have identical sounding keys, only
at different pitch heights?

In other words, with the use of flexible pitch instruments to extend pitch
vocabulary, and in theory, isn't meantone a kind of equal temperament in that
each key is tuned identically only starting at different pitch frequencies?

Johnny

************************************** See what's new at http://www.aol.com

Afmmjr@aol.com wrote:
> Do you consider quarter comma meantone to have identical sounding keys, only > at different pitch heights? Yes.

> In other words, with the use of flexible pitch instruments to extend pitch > vocabulary, and in theory, isn't meantone a kind of equal temperament in that > each key is tuned identically only starting at different pitch frequencies?

The term is "regular temperament".

Graham

--- In tuning@yahoogroups.com, Afmmjr@... wrote:
>
> Do you consider quarter comma meantone to have identical
> sounding keys, only at different pitch heights?
>
> In other words, with the use of flexible pitch instruments
> to extend pitch vocabulary, and in theory, isn't meantone
> a kind of equal temperament in that each key is tuned
> identically only starting at different pitch frequencies?
>
> Johnny

Yes, I think 1/4-comma meantone does have identical
sounding keys, if allowed to stretch off to infinity.
Exact 1/4-comma meantone never closes into an equal
temperament (though 31-ET is very close), so there will
be two different sizes of step, not one as in a true
equal temperament. It is thus a "linear temperament".

-Carl

I agree with Carl's characterization, and will add two comments, the first is that, given the ubiquity of meantone, "key characters" in the meantone era, within the typical major tonality (key) range (Bb-D, plus either Eb or A) were probably due to a complex of reasons and associations (tessitura, in general; keys favored by particular instruments due either to technique or tradition), of which the specific intonation of a key was probably least important, with one exception. The exception is the intonation in minor, which due to minor's use of pitches extracted from a longer sequence of fifths, more quickly forces the use of enharmonic equivalents when one is limited to 12 pitch classes. The ramifications of this may be fairly significant -- the tonal plan of a work like the Messiah seems to me to be closely connected to the limits on minor tonalities, and even Mozart's Symphonies -- the mature ones without continuo -- stick to to the good meantone major keys, plus g minor, arguably the best of the meantone minor keys in intonation.

djw

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@...> wrote:
>
> I agree with Carl's characterization, and will add two comments,
> the first is that, given the ubiquity of meantone, "key
> characters" in the meantone era, within the typical major
> tonality (key) range (Bb-D, plus either Eb or A) were probably
> due to a complex of reasons and associations (tessitura, in
> general; keys favored by particular instruments due either to
> technique or tradition), of which the specific intonation of a
> key was probably least important, with one exception.

Thank you, Daniel. I tried to argue this here about key
characters of the well temperament era, and had a hard time
convincing anyone. I can't remember if I remembered to argue
that they predate well temperament.

> The exception is the intonation in minor, which due to minor's
> use of pitches extracted from a longer sequence of fifths, more
> quickly forces the use of enharmonic equivalents when one is
> limited to 12 pitch classes. The ramifications of this may be
> fairly significant -- the tonal plan of a work like the Messiah
> seems to me to be closely connected to the limits on minor
> tonalities, and even Mozart's Symphonies -- the mature ones
> without continuo -- stick to to the good meantone major keys,
> plus g minor, arguably the best of the meantone minor keys in
> intonation.
>
> djw

Orchestral instruments of Mozart's day were not all capable
of playing in all keys (certainly not brass, and I don't think
woodwinds either). Traditions of symphonic writing in general
surely played a part, too.

-Carl

Hi Daniel,

--- In tuning@yahoogroups.com, Daniel Wolf <djwolf@...> wrote:

> The exception is the intonation in minor, which due to
> minor's use of pitches extracted from a longer sequence
> of fifths, more quickly forces the use of enharmonic
> equivalents when one is limited to 12 pitch classes.

That is absolutely true and correct. However ...

> The ramifications of this may be fairly significant
> -- the tonal plan of a work like the Messiah seems to
> me to be closely connected to the limits on minor
> tonalities, and even Mozart's Symphonies -- the mature
> ones without continuo -- stick to to the good meantone
> major keys, plus g minor, arguably the best of the
> meantone minor keys in intonation.

I haven't studied Handel too deeply, but i know for sure
that Mozart explicitly taught his student Thomas Attwood
music-theory in terms of a 21-tone chain-of-5ths meantone
from Ebb ... A#:

http://tonalsoft.com/monzo/55edo/55edo.aspx

(a little more than halfway down the page begins my
quote of Attwood's actual notebooks.)

Thus, while discussion of his keyboard works should
be limited to 12-tone meantone (if not a well-temperament),
for Mozart's orchestral and vocal music one should
certainly assume that he would think of meantone as
being extended as far as he needed, in order to keep
chord-members closely related.

It's interesting that Mozart wrote only 2 of his
symphonies (out of 41) in a minor key, and both of
them were in G-minor (#25 and #40).

In addition, G-minor is the key of his great string
quintet K.516, which has the crazy use of enharmonic
pairs of notes (separated by a couple of octaves)
between the violins and cellos. There was a disussion
of this on one of these lists not too long ago (within
the last year or two), and i even made a MIDI-file of
that part of it, but i can't find it in a search now.

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

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

> for Mozart's orchestral and vocal music one should
> certainly assume that he would think of meantone as
> being extended as far as he needed, in order to keep
> chord-members closely related.

I wanted to add that i have analyzed the *timing* of
the occurence of each new accidental in the 1st movement
of the 40th Symphony (which i never published ... i
wanted to finish doing it for the whole symphony).

It's very interesting to see how carefully Mozart
brings in each new accidental, pretty much following
the chain-of-5ths as he adds in each new one, on
both sides of the original 9-note chain (Eb to F#,
skipping B), as the music modulates to new keys.

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

I think it is highly overoptimistic and misleading to attempt any
*quantitative* deduction about a particular meantone from the 18th
century evidence. Indeed, if we are not discussing keyboard
instruments, I see no reason at all to restrict ourselves to meantone
schemes... and if we are discussing them, 1/4-comma is the most likely
and widely described meantone apart from 12-et.

Neither Tosi nor Leopold Mozart tells us with any useful accuracy what
they mean by a comma. How can we tell they didn´t mean what we think
of as a diesis? Did they know or care about the difference between a
comma and a diesis?
The most we can deduce is that the difference between enharmonic
sharps and flats is, generally, not inaudibly small, but still rather
smaller than a semitone. Note that the difference between G# and Ab in
various prescriptions for JI is also some type of comma or diesis.

The 20th century discussions, and Monz´s webpage, proceed on the
assumption that these guys (along with Quantz and so on) were
mathematical tuning theorists who had exactly the same understanding
of regular temperaments and jargon as, say, Barbour did - whereas in
fact neither of them even DEFINED the comma in their writings. How
could a reader possibly know how large the enharmonic difference
should be, if is it merely called "a comma" but never given a clear
definition? The sources also say "Go look at a monochord", but they
never say what one should do with the monochord.

The relevant quote:

"it is true that the relative sizes of the two
different semitones it is not stated anywhere in this book."

- Nor is the size of "a comma" ever defined in Tosi or L.Mozart or
Quantz or ...

"we know that Mozart's father Leopold taught
that the flats were a comma higher than the sharps,
which indicates 55edo or another meantone similar to it."

- No, it doesn´t necessarily indicate any meantone at all, nor does it
tell us what was meant by "a comma" without further unwarranted
assumptions.

Besides, what right do we have to assume that the same (diatonic or
chromatic) semitone was always played the same size regardless of the
musical situation? Some semitones have mainly harmonic implications
(eg B-C supported by G7-C harmony), some mainly melodic (eg F#-E#-F#
over a static harmony of D major). Are we supposed to believe that one
size fitted all without exception? That is replacing musical judgement
with mathematical machinery.

The most we can tell is that Mozart´s theoretical paradigm of
intonation had enharmonic differences which are similar to those of
some kinds of meantone. (But also to those of 5-limit JI.) And that
the keyboards in later 18th century England, where presumably the
Attwood tutorial took place, were not tuned in equal temperament.

As for Tosi, please search back in the message archives at the Yahoo
groups webpage to see how that source has been misquoted and
selectively quoted over the years to make it seem much more certain
and qualitatively precise than it was. Tosi had NO theoretical idea of
what a "comma" was, and was confused as to whether it should be a
seventh part of a tone or a ninth part.

I can´t emphasize often enough how easily you produce bad history by
ignoring the primary sources and assuming that the secondary
literature is 100% correct - when it may actually be be 95% speculation.

~~~T~~~

I can´t emphasize often enough how easily you produce bad history by
ignoring the primary sources and assuming that the secondary
literature is 100% correct - when it may actually be be 95% speculation.

~~~T~~~

Thank you, Tom, for laying out my foremost criticism of music historians --
the non-translation of important writings such as Salinas's De Musica and
Werckmeister's Musicalische Temperatur, and the presumptious assumption that
regurgitations of such should be trusted. Now with Vicentino and Marchetto
translated we have new hope to get to the crux of the matter.

Johnny

************************************** See what's new at http://www.aol.com

Hi Tom,

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

> <snip>
>
> Neither Tosi nor Leopold Mozart tells us with any useful
> accuracy what they mean by a comma. How can we tell they
> didn´t mean what we think of as a diesis? Did they know
> or care about the difference between a comma and a diesis?
>
> <snip>
>
> As for Tosi, please search back in the message archives
> at the Yahoo groups webpage to see how that source has
> been misquoted and selectively quoted over the years to
> make it seem much more certain and qualitatively precise
> than it was. Tosi had NO theoretical idea of what a
> "comma" was, and was confused as to whether it should
> be a seventh part of a tone or a ninth part.
>
> I can´t emphasize often enough how easily you produce
> bad history by ignoring the primary sources and assuming
> that the secondary literature is 100% correct - when it
> may actually be be 95% speculation.

From my webpage, i have:

>> according to Tosi, the large diatonic half step is
>> theoretically equal to five ninths of a whole step,
>> and the small chromatic half step is theoretically
>> four-ninths of a whole step. Tosi thereby divides
>> the octave into fifty-five equal parts.

But i don't have the Chesnut article handy, and at this
point i don't know if it was Tosi, Chesnut, or Erlich
who pinpointed these measurements.

If you have Tosi available, can you please tell us
exactly what he said about this? For that matter, i'd
like to see more of Leopold Mozart's violin method
-- the only part quoted by Chesnut is the two exercises
which contrast naturals-and-flats with naturals-and-sharps.

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

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

> Thank you, Tom, for laying out my foremost criticism of music
historians --
> the non-translation of important writings such as Salinas's De
Musica and
> Werckmeister's Musicalische Temperatur, and the presumptious
assumption that
> regurgitations of such should be trusted. Now with Vicentino and
Marchetto
> translated we have new hope to get to the crux of the matter.

With all due respect, Johnny , there are a number of us around here
who are able to read these in the original languages. Why should a
translation --adding yet another level of distance from the original
text -- be any more trustworthy?

djw

Dear Daniel,

A first translation would likely lead to a second; no translations leads to
hearsay.

Maybe it is a surprise to you, Daniel, but I read German and French. Do you
read Latin enough to read Salinas? (I don't.) It seems arrogant to leave
the readers of different languages to hearsay. A translation can bring a
reader of a second language much closer to the true intentions of the author.

Additionally, there is jargon to be deciphered, the regular occurrence of
language dialects, and political/cultural contexts to consider. I believe
those who read original languages really have some obligation to translate
critical texts hundreds of years old, if they indeed consider themselves educators.

Johnny

p.s. I note your bias towards CDs that are the result of studio recordings
versus live recordings of performances. Since I strongly disagree with you on
this, I would like separate egress to live recorded music, much as I do
through the AFMM and its label PITCH.

_________________________

With all due respect, Johnny , there are a number of us around here
who are able to read these in the original languages. Why should a
translation --adding yet another level of distance from the original
text -- be any more trustworthy?

djw

************************************** See what's new at http://www.aol.com

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

> p.s. I note your bias towards CDs that are the result of studio
recordings
> versus live recordings of performances. Since I strongly disagree
with you on
> this, I would like separate egress to live recorded music, much as
I do
> through the AFMM and its label PITCH.
>

No, my personal bias is towards the use of recordings only for music
not expressly intended for recorded media. As a test, I spent the
year of 2006 trying not to intentionally listening to any recordings
unless the work was composed for and existed only in a recorded
format (e.g. classical tape music). I discovered that, as a result,
I ended up listening to much more live music, played more music
myself, and did a lot more sight-reading than had been my habit. It
was an invaluable experience as a musician, and since then I now find
that I listen only seldom to recordings -- I don't even have a cd
player in my studio any more, and am firmly back into a live music
habit. More importantly, I think, I have recovered some sense of the
difference in presence between a music played in a wonderful room
with musicians scattered throughout the space and music that comes
out of loudspeakers; it's not a distinction between bad and good, but
a recovery of the distinct qualities of each experience. I happen to
like real players in real rooms, and I prefer my own music to be made
that way; other musicians have other preferences which I respect, but
I'd hope that they respect mine as well.

This doesn't mean that I don't value recordings as documents -- I
need my fix of Carlos Kleiber's Seventh with some regularity, and
with the recent passing of Pak Cokro, turning to his recordings was a
real source of solace -- but rather that those documents are taken in
some perspective. I don't particularly buy the arguments about
recordings making music more accessible to the world at large; I have
had more than a small taste -- through a lot of ghosted film scoring
over the years -- of what "access" actually means and what
commodification can do to an art work, and I'd like to spare my own
music all of that. Moreover, my own music has never been made in a
spirit in which such access has much meaning. If I write incidental
music for a stage play, that's how it should be heard; or if I write
for an extraordinary musician friend, like Hildegard Kleeb, than it's
supposed to be heard live and played by her. The world is full of
generic products, _Gebrauchsmusik_, playable anywhere anytime by
anyone, and given that, I can only recognize a need to recover some
specificity, some texture, a local and personal taste.

djw

Thank you, Daniel, for expressing your views. They are completely
understandable. Clearly, I misunderstood your very particular sense of listening to
recordings. Congratulations on accomplishing your listening tasks.

Since CDs are soon to be relegated to history as a technology, we are truly
in a brave new land. My hope is that live music has a renaissance.

Johnny

************************************** See what's new at http://www.aol.com

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Daniel Wolf <djwolf@> wrote:
> >
> > I agree with Carl's characterization, and will add two comments,
> > the first is that, given the ubiquity of meantone, "key
> > characters" in the meantone era, within the typical major
> > tonality (key) range (Bb-D, plus either Eb or A) were probably
> > due to a complex of reasons and associations (tessitura, in
> > general; keys favored by particular instruments due either to
> > technique or tradition), of which the specific intonation of a
> > key was probably least important, with one exception.
>
> Thank you, Daniel. I tried to argue this here about key
> characters of the well temperament era, and had a hard time
> convincing anyone. I can't remember if I remembered to argue
> that they predate well temperament.

The Lindley review has a number of quotations from the 17th century,
mainly France, which make it fairly clear that the use of 'wrong'
enharmonic pitches, due to the limited tonal range of the keyboard,
was one clear difference (possibly among many) in the embryonic
concept of key character. I think Hugyens had some remark about E
minor's character differing from D minor on account of the high D#. (F
minor is at the other end of the spectrum...) The corollary is that C
major and D major are practically *not* different in character.

The more pitches you have per octave - 14 was fairly common in German-
and and Italian-speaking areas, 19 also cropping up - the less
unorthodox your intonation will be, and the less cause you have to
consider keyboard-based key character.

The first list of key characters coming from Charpentier around 1700
might be seen as including some such keyboard-based features, but
otherwise reads as rather haphazard or arbitrary. At that date we also
have the complication of 'temperament ordinaire' which, if one
consults the sources,

http://harpsichords.pbwiki.com/Temperament_Ordinaire

was, at that epoch, probably a mixture of meantone with three or four
notes interpolated between the ends of the chain of regular fifths, in
effect spreading the 'wolf' fifth around so as to eliminate it. This
also spreads the meantone key characters (understood as resulting from
a range Eb-G#) around so that, conceivably, E major might have had a
milder version of the overbright quality of B major, and C minor some
degree of the funereality of F minor.

> > the tonal plan of a work like Messiah
> > seems to me to be closely connected to the limits on minor
> > tonalities

Is there a 'work like Messiah' apart from Messiah itself? But I think
I see what you might mean. The remark is rather cryptic though. Can
you be more specific? Check the recitatives and 'He was despised'
before making any broad statement about tonal plans.

Handel's keyboard suites certainly didn't respect any such limits...

~~~T~~~