Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Digest Number 3488

[monz wrote:]
--- In tuning@yahoogroups.com,
"Gene Ward Smith"
wrote:
>
> --- In tuning@yahoogroups.com,
"monz" 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.
....

My own trifling bit of information to contribute is: in the 1st ed. of New Grove (1980), in the article on horn there is a page reproduced from the last published manual for natural horn, c. 1850, which is a chart showing which notes are stopped/closed, and it gives different fractional amounts of hand-closing for enharmonic notes. I also once saw a late-19th/early-20th c. trombone method with a chart giving different fractional slide positions for enharmonics. This would support Johnny Reinhard. My own take on it is simply that it's proof 12et wasn't widely used or considered as a theoretical basis of music until Schoenberg, contra the 20th c. myth that it dates back to the WTC or whatever, which still pops up from time to time (the myth, not the WTC).

Related to this, I was recently listening to the Bruckner 7th, and there are spots, up to a couple bars at a time or so, where different orchestra sections are notated in different keys, e.g. the brass will be doubling the strings, and the strings are notated in a sharp key and the brass in a flat key. ??

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

🔗monz <monz@tonalsoft.com>

hi Christopher,

--- In tuning@yahoogroups.com,
Christopher John Smith
<christopherjohn_smith@y...>
wrote:
>
>
>
> My own trifling bit of
> information to contribute
> is: in the 1st ed. of
> New Grove (1980), in the
> article on horn there is a
> page reproduced from the
> last published manual for
> natural horn, c. 1850, which
> is a chart showing which
> notes are stopped/closed,
> and it gives different
> fractional amounts of
> hand-closing for enharmonic
> notes.

wow, i would like to get my paws on that manual!

> I also once saw a late-19th/early-20th c. trombone method
> with a chart giving different fractional slide positions
> for enharmonics.

and that one too!

> This would support Johnny Reinhard.

yes, well ... the fact that a recording made in 1923 sounded
to my ears exactly like 55-edo or 1/6-comma meantone, also
goes a long way towards support what Johnny wrote.

> My own take on it is simply that it's proof 12et wasn't
> widely used or considered as a theoretical basis of music
> until Schoenberg, contra the 20th c. myth that it dates back
> to the WTC or whatever, which still pops up from time to
> time (the myth, not the WTC).

the later music of Wagner certainly encouraged composers
to think of the chromatic scale as a 12-tone closed tuning
... whether or not 12-edo is implied i'm not sure.

but certainly, Schoenberg's atonal compositions, and even
moreso, his _Harmonielehre_, got a lot of people thinking
of 12-edo as the "theoretical basis of music" ... and notice
that i prefaced the quote from you with "the" rather than "a",
deliberately. if there's only one thing that Schoenberg
deserves credit for beyond any doubt, it's that.

> Related to this, I was recently listening to the Bruckner 7th,
> and there are spots, up to a couple bars at a time or so,
> where different orchestra sections are notated in different
> keys, e.g. the brass will be doubling the strings, and the
> strings are notated in a sharp key and the brass in a flat key.
> ??

hmm ... as soon as i read that, i thought i recalled seeing
it too ... but i've just thumbed thru the whole score of
Bruckner's 7th, and don't see it. can you cite movement
and measure numbers? ... and in the case of Bruckner, we
probably need to know which version/publisher it is too.

note that, until Tanaka demonstrated passages from Wagner
on his 53-edo "enharmonium" (reed organ) to Bruckner around
1890, Bruckner always taught his students that theoretical
JI commatic differences were irrelevant, because it was
"impossible" to have instruments tuned in JI. he changed
his teaching after Tanaka opened his ears.

for much more on this, see the relevant years in my
long chronology "A Century of New Music in Vienna"

http://tonalsoft.com/monzo/vienna/vienna.htm

-monz

🔗Tom Dent <tdent@auth.gr>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > My own trifling bit of information to contribute
> > is: in the 1st ed. of New Grove (1980), in the
> > article on horn there is a page reproduced from the
> > last published manual for natural horn, c. 1850, which
> > is a chart showing which notes are stopped/closed,
> > and it gives different fractional amounts of
> > hand-closing for enharmonic notes.
>
>
> wow, i would like to get my paws on that manual!
>

I assume just 5ths and 3rds in the harmonic series are OK for
the horn?

> yes, well ... the fact that a recording made in 1923 sounded
> to my ears exactly like 55-edo or 1/6-comma meantone, also
> goes a long way towards support what Johnny wrote.

Which recording is that? There are relatively few recordings
from that period where the tuning can be made out with any
certainty.

> > My own take on it is simply that it's proof 12et wasn't
> > widely used or considered as a theoretical basis of music
> > until Schoenberg, contra the 20th c. myth that it dates back
> > to the WTC or whatever, which still pops up from time to
> > time (the myth, not the WTC).
>
> the later music of Wagner certainly encouraged composers
> to think of the chromatic scale as a 12-tone closed tuning
> ... whether or not 12-edo is implied i'm not sure.

Widespread enharmonic modulation (a speciality of Wagner) means
that the key-centres should be placed on a circulating well
temperament, although in tonally stable passages some variation
away from that temperament would be desirable. I wonder what the
first chromatic valve horns (or whatever they had for Tristan)
did for tuning.

> > Related to this, I was recently listening to the Bruckner 7th,
> > and there are spots, up to a couple bars at a time or so,
> > where different orchestra sections are notated in different
> > keys, e.g. the brass will be doubling the strings, and the
> > strings are notated in a sharp key and the brass in a flat key.
> > ??

Most brass are transposing instruments, which muddies the issue
further (particularly when Wagner tubas come into the picture),
but the apparent implication is that such passages are approximated
to 12-ET. When the music is written in remote keys and the composer
works around the 'nasty end' of the cycle of 5ths (for example
between C sharp minor and A flat major), the meantone commas pile
up and become very awkward. The slow movement is in C sharp minor,
which is probably where the enharmonically notated passages occur.

> hmm ... as soon as i read that, i thought i recalled seeing
> it too ... but i've just thumbed thru the whole score of
> Bruckner's 7th, and don't see it.

I suspect his 8th and 9th have more enharmonic equivalences in
them. (You have some theory about Bruckner 9, isn't that so?) Of
course editors have done lots of things to Bruckner over the
years...

> note that, until Tanaka demonstrated passages from Wagner
> on his 53-edo "enharmonium" (reed organ) to Bruckner around
> 1890, Bruckner always taught his students that theoretical
> JI commatic differences were irrelevant, because it was
> "impossible" to have instruments tuned in JI. he changed
> his teaching after Tanaka opened his ears.

Hum, what sort of JI would this be with which one could play
Wagner? (Apart from the Wedding March in Lohengrin.) Adaptive or
not?

Actually, if you are looking for enharmonic clashes, you don't
need to go further than the slow movement of Mozart's String
Quintet in G minor K516, where there is a coincidence of B natural
in the cello and C flat in a violin part (about 2/3 of the way
through the movement) - a very unusual passage for Mozart where he
uses dominant 7ths / minor 9ths with roots separated by successive
minor 3rds.

I would like to know if modern editors have altered the notation
or if Mozart broke his own meantone rules. (Or indeed if the
passage can be played in meantone at all!)

Also in the Requiem there are a lot of enharmonics - now whether
they are Mozart's or Süssmayr's or someone else's I don't know.
Also there is a very odd passage about 2/3 the way through the
first movement of K515 where I suspect Mozart may go 'round the
clock' of the cycle of 5ths, therefore cannot be played in
meantone.

~~~Thomas~~~

🔗Gene Ward Smith <gwsmith@svpal.org>

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

> Actually, if you are looking for enharmonic clashes, you don't
> need to go further than the slow movement of Mozart's String
> Quintet in G minor K516, where there is a coincidence of B natural
> in the cello and C flat in a violin part (about 2/3 of the way
> through the movement) - a very unusual passage for Mozart where he
> uses dominant 7ths / minor 9ths with roots separated by successive
> minor 3rds.
>
> I would like to know if modern editors have altered the notation
> or if Mozart broke his own meantone rules. (Or indeed if the
> passage can be played in meantone at all!)

I imagine a meantone version would require deciding if they all should
be Cb or all B. The roots separated by minor thirds may have a
relationship of an augmented second in there somewhere, making sense
of the whole thing; three minor thirds and an augmented second make up
an octave, but Mozart may have decided not to put any augmented
seconds into the melody line of any one instrument, figuring that the
ensemble would adjust its tuning well enough. I would be surprised if
there was any real difficulty finding a good meantone version for the
passage.

> Also there is a very odd passage about 2/3 the way through the
> first movement of K515 where I suspect Mozart may go 'round the
> clock' of the cycle of 5ths, therefore cannot be played in
> meantone.

Once again, I would be wary of leaping to the conclusion that
something cannot be played in meantone. You need to check and see if
you can actually make a good meantone version. Are you saying it does
something like go around the fifths from C through G# to Eb and then
around to C? It hardly can have done something like go from C through
G# to B#, I presume, but if it did, then it did, and you'd have to
blame it on Mozart.

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > > My own trifling bit of information to contribute
> > > is: in the 1st ed. of New Grove (1980), in the
> > > article on horn there is a page reproduced from the
> > > last published manual for natural horn, c. 1850, which
> > > is a chart showing which notes are stopped/closed,
> > > and it gives different fractional amounts of
> > > hand-closing for enharmonic notes.
> >
> >
> > wow, i would like to get my paws on that manual!
> >
>
> I assume just 5ths and 3rds in the harmonic series are OK for
> the horn?

AFAIK, composers writing for the natural horn expected
the harmonic ratios for 5ths and major-3rds.

> > yes, well ... the fact that a recording made in 1923 sounded
> > to my ears exactly like 55-edo or 1/6-comma meantone, also
> > goes a long way towards support what Johnny wrote.
>
> Which recording is that? There are relatively few recordings
> from that period where the tuning can be made out with any
> certainty.

i don't have any details. i heard it on the radio when i was
about 15 years old, and had my cassette tape recorder running.
so for all of my teenage years, that was the performance
of the Mozart G-minor that i knew. what i do remember the
radio announcer saying, was that it was the first electrical
recording made of a complete symphony.

and i'm not trying to claim that the tuning *could* be
made out with "certainty", whatever that means for
non-electronic music or any music made with instruments
where the pitch can vary as wildly as it can on woodwinds.
but what i do know is exactly what i wrote here before:
when i retuned my MIDI-file into 55-edo, it sounded
*exactly* like what i remember that old recording
sounding like.

> > > My own take on it is simply that it's proof 12et wasn't
> > > widely used or considered as a theoretical basis of music
> > > until Schoenberg, contra the 20th c. myth that it dates back
> > > to the WTC or whatever, which still pops up from time to
> > > time (the myth, not the WTC).
> >
> > the later music of Wagner certainly encouraged composers
> > to think of the chromatic scale as a 12-tone closed tuning
> > ... whether or not 12-edo is implied i'm not sure.
>
> Widespread enharmonic modulation (a speciality of Wagner) means
> that the key-centres should be placed on a circulating well
> temperament,

why do you say that? you seem awfully certain that Wagner
intended well-temperament, and i know of no firm evidence
for that. he may very well have intended 12-edo. in any
case, his harmonic practice definitely put an emphasis
on enharmonic equivalence, which definitely *ain't* meantone
(except for 12-edo, that is).

> > hmm ... as soon as i read that, i thought i recalled seeing
> > it too ... but i've just thumbed thru the whole score of
> > Bruckner's 7th, and don't see it.
>
> I suspect his 8th and 9th have more enharmonic equivalences in
> them. (You have some theory about Bruckner 9, isn't that so?) Of
> course editors have done lots of things to Bruckner over the
> years...

yes, Bruckner has suffered more than just about any other
composer at the hands of his editors, who have felt no
compunction about actually re-composing large sections of
his symphonies.

i don't really have any worked-out theories about Bruckner
... just a hunch, based on the fact that i know his extremely
positive reaction to Tanaka's 53-edo/JI demonstrations.
the harmonies in the slow movement and scherzo of his
9th Symphony are so bizarre in some places, nearly atonal
even, that i wouldn't be surprised if he had 53-edo/JI in
mind for some of those chords. but i don't know if i'll
ever have the time to do a proper analysis, with all the
other things on my plate.

> > note that, until Tanaka demonstrated passages from Wagner
> > on his 53-edo "enharmonium" (reed organ) to Bruckner around
> > 1890, Bruckner always taught his students that theoretical
> > JI commatic differences were irrelevant, because it was
> > "impossible" to have instruments tuned in JI. he changed
> > his teaching after Tanaka opened his ears.
>
> Hum, what sort of JI would this be with which one could play
> Wagner? (Apart from the Wedding March in Lohengrin.) Adaptive or
> not?

not adaptive-JI ... i just responded to you yesterday
pointing out that 53-edo does not do adaptive-JI.

however, 53-edo *is* a remarkably good approximation
of a large section of the 5-limit JI lattice, and it
is an outstanding approximation of pythagorean tuning.
you can see this here:

http://tonalsoft.com/enc/bingo.htm#53

compare the lily-white 53-edo lattice with the fancy
colors or shades of grey (indicating amount of error)
all over the lattices for the other EDOs.

indeed, the very G-minor Symphony that started this discussion
is filled with some very unusual tonal moves -- Schoenberg
cites one brief passage from the 1st movement in _Harmonielehre_,
where there are simultaneously both upper and lower
neighboring-tones which resolve onto minor triads ... but
those combined neighboring-tones make some very strange
6-note chords.

and then there's the famous passage from the last movement
of the same symphony, where the whole orchestra, in unison,
plays a series consisting of all 12 notes of the chromatic
scale. if Mozart really intended to have the piece tuned
in a subset of 55-edo, then the very fact that he made
sure to use 12 notes here might be an indication that he
was thinking in 12-edo for this one spot.

> I would like to know if modern editors have altered the notation
> or if Mozart broke his own meantone rules. (Or indeed if the
> passage can be played in meantone at all!)

i don't know about Mozart ... in fact usually in Mozart
scores i see both notes of an enharmonic pair during the
course of the piece.

but i *do* know, because i've studied his manuscripts,
that Mahler's editors have changed the notation of some
notes in his scores -- and i wish they hadn't. i am quite
firmly convinced that Mahler intended 31-edo for his
symphonies at least some of the time, if not all. and
almost all of his double-sharps have been converted to
the enharmonically equivalent naturals in the Critical
Edition.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
>
> > http://tonalsoft.com/enc/bingo.htm#53
> >
> > compare the lily-white 53-edo lattice with the fancy
> > colors or shades of grey (indicating amount of error)
> > all over the lattices for the other EDOs.
>
> We don't have colored bingo cards for 34, 46 or 53.
> How far would we need to go to start seeing colors for
> 53?

i already explained that the colorless bingo-card lattice
for 53-edo is colorless *because* the error for that part
of the 5-limit lattice is so small.

for 53-edo, the whole Euler-genus from 3^(-12...+12)*5^(-7...+7)
is colorless, which means that the bingo-card lattice for 53
for that Euler-genus gives the same degrees of 53 as the best
approximation to JI ... which, in essence, means that there's
no discernable error for that part of the lattice. the error
starts to appear at around 5^-8 and 5^8 for these exponents
of 3 -- specifically, you'd see some blue on the 5^8 row for
postive exponents of 3, and some orange for the 5^-8 for
negative exponents of 3. my cutoff points along the 5-axis
for the lattices on the webpage happens to be just under the
appearance of error in 53-edo.

but 53-edo's approximation to pythagorean is much better still,
so you don't begin to see any error along the 3-axis until
you get all the way to 3^+/-166.

> Bingo cards for 34 and 46 should be possible.

done, on a slightly bigger lattice than for the other EDOs.

http://tonalsoft.com/enc/bingo.htm

> > but i *do* know, because i've studied his manuscripts,
> > that Mahler's editors have changed the notation of some
> > notes in his scores -- and i wish they hadn't. i am quite
> > firmly convinced that Mahler intended 31-edo for his
> > symphonies at least some of the time, if not all. and
> > almost all of his double-sharps have been converted to
> > the enharmonically equivalent naturals in the Critical
> > Edition.
>
> A critical edition should not do this without citing what
> Mahler actually had in score. Shoddy scholarship!

of course you know i agree 100% with that opinion!
i'm a member of the International Gustav Mahler Society
(you would never have guessed, right?), and they are
right now in the process of coming out with 2nd editions
of the Critical Edition, with much revision going on.
i'll write to them and put in my vote for citing Mahler's
original notations ... i think i did already, but don't
remember.

-monz

🔗Tom Dent <tdent@auth.gr>

Thanks for your careful reply... see below.

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

> (...) for all of my teenage years, that was the performance
> of the Mozart G-minor that i knew. what i do remember the
> radio announcer saying, was that it was the first electrical
> recording made of a complete symphony.

Too bad, I have Googled for it with no success. If only there was
a list of all historic recordings of Symphony no.40...

> when i retuned my MIDI-file into 55-edo, it sounded
> *exactly* like what i remember that old recording
> sounding like.

> > Widespread enharmonic modulation (a speciality of Wagner) means
> > that the key-centres should be placed on a circulating well
> > temperament,
>
> why do you say that? you seem awfully certain that Wagner
> intended well-temperament, and i know of no firm evidence
> for that. he may very well have intended 12-edo.

Ah, I meant 'anything that approximates to 12-ET'. Which includes 12-
ET itself. Sorry for any terminological confusion.

> (...) famous passage from the last movement
> of the same symphony, where the whole orchestra, in unison,
> plays a series consisting of all 12 notes of the chromatic
> scale. if Mozart really intended to have the piece tuned
> in a subset of 55-edo, then the very fact that he made
> sure to use 12 notes here might be an indication that he
> was thinking in 12-edo for this one spot.

Those 12 notes do fit nicely into a mean-tone framework modulating
through a few closely related keys... the radical nature of the
passage is due to the lack of harmony and cadences, so the
listener has to deduce what the (very rapid) modulations are.

(...)
> i am quite
> firmly convinced that Mahler intended 31-edo for his
> symphonies at least some of the time, if not all.

Did you give a reason somewhere why it would be 31 and not 43 or
55?

Best,
~~~T~~~

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
>
>
> Thanks for your careful reply... see below.
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > (...) for all of my teenage years, that was the performance
> > of the Mozart G-minor that i knew. what i do remember the
> > radio announcer saying, was that it was the first electrical
> > recording made of a complete symphony.
>
> Too bad, I have Googled for it with no success. If only there was
> a list of all historic recordings of Symphony no.40...

i was searching Google about it yesterday too, and couldn't
find anything at all.

> (...)
> > i am quite
> > firmly convinced that Mahler intended 31-edo for his
> > symphonies at least some of the time, if not all.
>
> Did you give a reason somewhere why it would be 31 and
> not 43 or 55?

http://tonalsoft.com/monzo/vienna/vienna.htm

right near the beginning, i list my original speculations,
and the very first one is:

>> * The likelihood that Mahler intended meantone tuning
>> to be used for his symphonies, at least partly, based
>> on the possibility of his familiarity with the teachings
>> of Josef Petzval on 31edo during Mahler's stay at the
>> University of Vienna, and on his later remarks to
>> Schoenberg lamenting that "European music, in giving
>> up Meantone tuning, had suffered a great loss".

and under "1877", the details:

>> During Mahler's attendance at the University of Vienna,
>> Josef Petzval is teaching his students about 31edo and
>> meantone, and demonstrating instruments he has had
>> constructed in those tunings. Decades later, Mahler's
>> remarks to Schoenberg indicate that he was familiar
>> enough with meantone to complain about its replacement
>> with 12edo.

i just posted the whole quote from Mahler to Schoenberg,
in another message to this list.

Mahler mentioned that would could not imagine the effect
of the unequal intervals unless one had heard them, so
it's obvious that he had ... and i simply put 2 and 2
together and reason that since Petzval was at the U. of
Vienna demonstrating 31-edo at exactly the time Mahler
attended, then he must have heard 31-edo then.

the big question is: exactly where and when was 55-edo
still being used as the tuning paradigm for orchestral
playing? was Mahler familiar with it at all?

Mahler had befriended Schoenberg in 1904, and had many
arguments with him over theoretical matters, but
supported Schoenberg's work in composition right up
to the end of his life. we all know Schoenberg's ideas
about 12-edo, and how it was supposed to be a tempering
of 11-limit JI ... presumably Mahler picked up some of
this from Schoenberg, and thus, his comments on what
European music had lost as a result of meantone's
replacement by 12-edo.

we microtonalists also know that 12-edo is essentially
the same as 1/11-comma meantone ... Mahler specifically
meant a meantone which had two different sized semitones,
which would be all other meantones except 12-edo.

since the emphasis of Mahler's comment was on the
different key colorations produced by the unequal
intervals, he was presumably talking about a type of
meantone where the difference between the two sizes
of semitones was fairly large ... this would indicate
something closer to the 19-edo/31-edo end of the meantone
spectrum. in meantones like 43-edo and 55-edo, the
sizes of the semitones are closer, and thus the
different keys would not sound as different.

also, it must be pointed out that this key-coloration
does not occur if one extends the meantone chain out
far enough to get rid of all the wolves. the chain
has to be stopped at a fairly low cardinality in
order to produce the wolves which produce the different
key colors.

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

Re: [tuning] Digest Number 3488

🔗Christopher John Smith <christopherjohn_smith@yahoo.com>

🔗monz <monz@tonalsoft.com>

🔗Tom Dent <tdent@auth.gr>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

🔗Tom Dent <tdent@auth.gr>

🔗monz <monz@tonalsoft.com>

🔗monz <monz@tonalsoft.com>