Yahoo Tuning Groups Ultimate Backup tuning Re: Mozart tuning

Hey Paul, I'm sending a copy of this to the list.

> > > [Paul]
> > > How about 19? Then the interval matrices will
> > > come out nice.
> >
> > [monz]
> > You say that like it's self-evident. Is it?
> > What connection does 19 have with 55 that will
> > make this happen? I'm intrigued...
>
> [Paul]
> 19 is an MOS of the meantone-fifth generator. Hence
> it will be a CS -- any given specific interval will
> always span the same number of degrees.

Is there info about this somewhere?
Can you point me to it?

I'd like to see the whole list of MOSs of the
meantone-fifth.

As I mention on the webpage
http://www.ixpres.com/interval/monzo/55edo/55edo.htm,
my curiosity is already piqued by the relationship
between 50- and 55-EDO, whereas 53 is a whole
different animal.

So anyway, I guess it would make a lot of
sense to set my 55-EDO subset at 19.
But would I want to use a "standard"
closed conjunct cycle of "5ths"?, say,

Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D#
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

But this doesn't jive with Mozart's tuning either.

Since Chesnut gives the actual Mozart tuning at
20 notes: Ebb, Bbb, Fb, Gb...A#, I think that's
what I should illustrate. Part of my point
in doing this webpage is to recognize the actual
tuning Mozart intended for much of his music.

Now I wonder, why *did* he choose that strange
disjunct tuning, when the nice 19-tone MOS was
readily at hand (almost) within it? Hmmm...

I can't wait to retune his _40th Symphony_ in
20-o-o-55-EDO!! (That's a piece I used many years
ago to make experiments in retuning to JI.)

-monz
http://www.monz.org
All roads lead to n^0

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🔗monz <joemonz@yahoo.com>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> > [Paul]
> > 19 is an MOS of the meantone-fifth generator. Hence
> > it will be a CS -- any given specific interval will
> > always span the same number of degrees.
>
>
> Is there info about this somewhere?
> Can you point me to it?

Dave Keenan has talked extensively about how the continued fraction
expansion of any generator gives you a list of its MOSs.
>
> I'd like to see the whole list of MOSs of the
> meantone-fifth.

It depends _which_ meantone fifth -- for example, the golden fifth
gives you the Fibonacci-like series of MOSs: 5, 7, 12, 19, 31, 50,
81 . . .
>
> So anyway, I guess it would make a lot of
> sense to set my 55-EDO subset at 19.
> But would I want to use a "standard"
> closed conjunct cycle of "5ths"?, say,
>
> Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D#
> -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
>
>
> But this doesn't jive with Mozart's tuning either.

Why not? Just because Mozart left out Cb in his exercises for violin?
>
> Since Chesnut gives the actual Mozart tuning at
> 20 notes: Ebb, Bbb, Fb, Gb...A#,

"The actual Mozart tuning" . . . why don't you read the article?
>
> I can't wait to retune his _40th Symphony_ in
> 20-o-o-55-EDO!! (That's a piece I used many years
> ago to make experiments in retuning to JI.)

20? Why 20? Are you sure there are 20 notated pitches in this piece?
And no Cb? Also, I suggest you read the last two pages of Chesnut's
paper before doing anything along these lines.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_24406.html#24406
>
> > As I mention on the webpage
> > <http://www.ixpres.com/interval/monzo/55edo/55edo.htm>,
>
>
> Drats... I messed up the link in that post. Try this one.
> I've made an extensive update to the page, so that it now
> include's Mozart's actual intended non-keyboard tuning:
> a 20-out-of-55-EDO subset.
>

On this page, you wrote,

>The table and graph below show that 72-EDO, which is gathering
>enthusiasm for adoption as a new tuning standard, provides a pretty
>good approximation to Mozart's tuning.

No, sir. Never. Remember, Monz, when comparing two tuning systems,
one must compare the _intervals_, not the pitches. No subset of 72-
tET will match the intervals of a meantone tuning.

🔗Paul Erlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

----- Original Message -----
From: Paul Erlich <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, June 06, 2001 11:35 AM
Subject: [tuning] Re: Mozart tuning

> > <http://www.ixpres.com/interval/monzo/55edo/55edo.htm>,
>
> On this page, you wrote,
>
> > The table and graph below show that 72-EDO, which is gathering
> > enthusiasm for adoption as a new tuning standard, provides a pretty
> > good approximation to Mozart's tuning.
>
> No, sir. Never. Remember, Monz, when comparing two tuning systems,
> one must compare the _intervals_, not the pitches. No subset of 72-
> tET will match the intervals of a meantone tuning.
>

Right, so the only way I could really give a good comparison
is to compare the interval matrices. Well, I've added a Pythagorean
tuning now too, so there's even *more* work to do... :(

But I did find it fascinating that both 72-EDO and Pythagorean
do provide pretty good approximations of Mozart's 20-o-o-55.

-monz
http://www.monz.org
"All roads lead to n^0"

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🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> I'd like to see the whole list of MOSs of the
> meantone-fifth.

Monz, you should download Dave Keenan's MOS-finding spreadsheet:

http://www.uq.net.au/~zzdkeena/Music/MyhillCalculator.xls

Just put in the size of the generator next to "Generator" and it does
the rest. Normally you'll keep "Intvl of equiv" at 1200.

For example, if I type in the 1/6-syntonic-comma meantone generator,
698.3706, I see that the MOSs are 1, 2, 3, 5, 7, 12, 19, 31, 43, 55,
67, and 122. The proper MOSs are in the leftmost yellow column are
are 1, 2, 5, 7, 12, 55, 67, and 122. If I type in the Woolhouse
optimal meantone generator, 696.1648, I see that the MOSs are 1, 2,
3, 5, 7, 12, 19, 31, and 50. Of these, only 3 is improper.

For my decatonic scale, I'll type in my optimal generator of
708.8143, and change "Intvl of equiv" to 600. The resulting proper
MOSs are 1, 5, 6, 11, 193 . . . indicating 2, 10, 12, 22, and 386
tones per octave, respectively. So my use of 10, 12, and 22-tone-per-
octave proper MOS scales with this generator pretty much exhausts
the "interesting" possibilities within the limits of human endeavor
(no 386-tET guitars coming anytime soon!)

If I try the RMS-optimal 9-limit MIRACLE generator, 116.7297 cents,
and of course an interval of equivalence of 1200 cents, I see MOSs at
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 21, 31, 41, 72, 113 . . . you see
blackjack, canasta, etc. are of course all in there. Question for
Dave Keenan: what happened to 9? That should be the next improper MOS
after 8 . . . why is it missing? Is this a bug?

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Question for Dave Keenan: what happened to 9? That should be the
> next improper MOS after 8 . . . why is it missing? Is this a bug?

Yes. It's a bug. I fixed it a while ago but failed to upload the fix.
Sorry. It's there now.

I also changed the term "interval of equivalence" to "period", which
is short for "interval of periodicity", the term Clampitt uses. It's a
better term because it doesn't imply any psychoacoustic equivalence
for the interval at which the scale repeats.

http://www.uq.net.au/~zzdkeena/Music/MyhillCalculator.xls

Regards,
-- Dave Keenan

🔗D.Stearns <STEARNS@CAPECOD.NET>

Dave Keenan wrote,

<<I also changed the term "interval of equivalence" to "period", which
is short for "interval of periodicity", the term Clampitt uses. It's a
better term because it doesn't imply any psychoacoustic equivalence
for the interval at which the scale repeats.>>

This is also the term I've always used for exactly this same thing on
this list, and for the same "doesn't imply any psychoacoustic
equivalence" type of generalized reasons. Though I never have read
Clampitt, I did adopt his term "trivalence" from his posting here, and
suggested bivalence in place of Myhill's property for the same type of
generalized reasons.

--Dan Stearns

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, June 06, 2001 12:23 PM
> Subject: [tuning] Re: Mozart tuning
>
>
> I wrote,
> >
> > Remember, Monz, when comparing two tuning systems,
> > one must compare the _intervals_, not the pitches. No subset of 72-
> > tET will match the intervals of a meantone tuning.
>
> For example, your 72-tET version of this tuning has a fifth from E to
> B that is 19 cents flat. BLECCHHH! (Sorry if that was too
> intellectual for you.)

and

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 07, 2001 12:29 PM
>Subject: [tuning] Re: Mozart tuning
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > But I did find it fascinating that both 72-EDO and Pythagorean
> > do provide pretty good approximations of Mozart's 20-o-o-55.
>
> I disagree. When the E-B fifth is 19 cents flat, I wouldn't call that
> a "pretty good" anything in regard to Mozart.

OK, I've added interval matrices for both the 20-tone subset
of 55-EDO which Mozart used in teaching composition to Thomas
Atwood, and for the 20-tone subset of 72-EDO which I chose
to approximate Mozart's tuning.

http://www.ixpres.com/interval/monzo/55edo/55edo.htm

No more opinions from me... just the facts.

-monz
http://www.monz.org
"All roads lead to n^0"

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🔗Afmmjr@aol.com

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> and for the 20-tone subset of 72-EDO which I chose
> to approximate Mozart's tuning.
>
> http://www.ixpres.com/interval/monzo/55edo/55edo.htm
>
> No more opinions from me... just the facts.

Hi Monz, please try not to get upset at me . . .

If you chose a subset of 72-tET to approximate Mozart's tuning, then you're implying that a
subset of 72-tET _can_ approximate Mozart's tuning in a musically useful way. In my opinion,
the only subset of 72-tET that is even barely appropriate for Mozart is 12-tET . . . the thirds are
not great, but at least you don't get any 19-cent-flat fifths between E and B or any other 'perfect
fifths'. But clearly the 12-tET solution is uninteresting from a microtonality perspective. So I think
that presenting a 72-tET approximation to Mozart's tuning on your webpage, even without
opinions, can be misleading. OK, no further comments from me on this subject. I should just
make my own webpages. If anyone knows how to get lots of web space free or very cheap,
e-mail me.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., Afmmjr@a... wrote:
> Are you guys saying (Paul and Monz) that Leopold Mozart suggested his readers
> read Werckmeister in a list of 3 names associated with temperament,

No. (what are you referring to?)

> but
> Wolfgang jumped ship to meantone?

No.

> Wouldn't such a switch (since Wolfgang was
> Leopold's most important teacher) be recorded in history some way?

History records that the Mozarts used well-temperaments, not meantone, on their keyboards.
History also records that the Mozarts taught string intonation in a mild meantone, in accord with
Tosi, Quantz, and what was simply considered "correct intonation" (the word _temperament_
was not used for meantone in those days) in their time. However, the teaching of string
intonation in meantone creates some practical problems in a few enharmonic modulations to be
found in Mozart's scores.

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, June 09, 2001 10:56 AM
> Subject: [tuning] Re: Mozart tuning
>

> > http://www.ixpres.com/interval/monzo/55edo/55edo.htm
>
> Hi Monz, please try not to get upset at me . . .
>

Hi Paul. I wasn't getting upset... just tired of adding
to that webpage! But I'm glad that your criticism inspired
me to do more work on it.

> If you chose a subset of 72-tET to approximate Mozart's
> tuning, then you're implying that a subset of 72-tET
> _can_ approximate Mozart's tuning in a musically useful
> way. In my opinion, the only subset of 72-tET that is
> even barely appropriate for Mozart is 12-tET . . . the
> thirds are not great, but at least you don't get any
> 19-cent-flat fifths between E and B or any other 'perfect
> fifths'. But clearly the 12-tET solution is uninteresting
> from a microtonality perspective. So I think that presenting
> a 72-tET approximation to Mozart's tuning on your webpage,
> even without opinions, can be misleading.

OK, hopefully *this* is my last comment about it ...for now. ;-)

I think I've stated quite plainly on my webpages your opinion
of this, but this explanation does flesh it out a bit more.
Perhaps I'll add it in, or perhaps I'll just finally scrap
the idea of the 72-EDO approximation to Mozart tuning.

What about the bit comparing Mozart's 20-o-o-55 to Pythagorean?
Any comments on that? It looks to me to have roughly the
same margins of error as 72-EDO. And of course, this comparison
goes quite a way toward another comparison I hinted at on
the page: that between 55-EDO and 53-EDO. (Paul knows but
some others may not: 53-EDO is audibly identical to a
53-tone Pythagorean cycle.)

-monz
http://www.monz.org
"All roads lead to n^0"

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🔗Paul Erlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

Wow... hard for me to believe that this was already a week ago.

Anyway,

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, June 06, 2001 11:31 AM
> Subject: [tuning] Re: Mozart tuning
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > I can't wait to retune his _40th Symphony_ in
> > 20-o-o-55-EDO!! (That's a piece I used many years
> > ago to make experiments in retuning to JI.)
>
> 20? Why 20? Are you sure there are 20 notated pitches in this piece?
> And no Cb? Also, I suggest you read the last two pages of Chesnut's
> paper before doing anything along these lines.

Yup, thanks. I've read Chesnut's paper again, and am midway thru
a second reading (well, *this* time's second reading... I read
it years ago.)

In between writing postings to various tuning lists, I've been
hard at work retuning my MIDI-file of Mozart's famous _40th Symphony_
into a subset of 55-EDO.

I've only analyzed the pitch-naming in the 1st and 3rd movements
so far, and I've found some very interesting things. Mozart uses
a 19-tone cycle from Gb to B# in the 1st movement, and a 13-tone
cycle from Ab to G# in the 3rd (Minuet).

The pitch-naming in the Minuet is fairly straightforward, with
only one significant formal curiosity. But the 1st movement has
*layers* of significant shifts in pitch-naming that help to
articulate formal divisions, which I will elaborate later when
I've gotten more work done.

And I suspect that the 4th movement will prove to be even richer
in material like this, as it is by far the most chromatic movement
in the piece (and one of the most chromatic in all of Mozart's output).

Anyway, this mp3 is only the very very beginning (the first 27 seconds),
but it's so beautiful that I simply had to share it:
</tuning/files/monz/55k550bg.mp3>.

(Sorry about the cryptic filename... my ancient version of
Cakewalk is strictly 8+3. And mp3 quality is deliberately not
very great, to keep file size down. Hmmm... when I download it
my media player "doesn't recognize it"... weird. Hope the rest
of you can hear it.)

As always, I introduced very significant _rubato_ into the tempo,
and as usual with me, the overall pace is quite a bit slower than
what most of you are familiar with. In fact, I'm still not at all
happy with my tempi here, but have at least taken a stab at what
I'd like them to be... much more polishing still required.

What's really interesting is that it's *too* slow for me. And I
know exactly why this happened. When I began working on the
_rubato_, some of the vertical sonorities just sounded so cool
that I slowed down those beats to bring them out more. In the
process, I distorted a lot of the smooth flow that I had already
achieved.

Oh well.... enjoy it anyway...
it's darn good if I say so myself. ;-)

To my ears, this tuning has brought out a vieled, misty
quality in this piece that I've heard good live performers get
sometimes, but never dreamed of achieving in a MIDI-file!
Certainly 12-EDO never did it. The violins almost sound
as if they have mutes on. Listen especially to the
expressiveness in the inner voices.

Sheesh... this really sheds a whole new light on Mozart's genius!!

-monz
http://www.monz.org
"All roads lead to n^0"

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🔗Paul Erlich <paul@stretch-music.com>

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 14, 2001 1:12 PM
> Subject: [tuning] Re: Mozart tuning
>

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > Yup, thanks. I've read Chesnut's paper again, and am midway thru
> > a second reading (well, *this* time's second reading... I read
> > it years ago.)
>
> OK -- don't miss those last two pages, though.

I suppose you're referring to Chesnut's admonitions regarding
enharmonicity in some of Mozart's pieces. I'm sure I'll encounter
some of that in the 40th Symphony, especially in the last movement,
but I decided to just jump in and start swimming. I'll deal with
that stuff when I'm up against it... so far, no problems.

Did you listen to my short opening excerpt, Paul?
/tuning/files/monz/55k550bg.mp3

What do you think?

(BTW, I mentioned that my Windows Media Player had trouble playing
this when I clicked the download link to open it. When I chose
"save" as my download option instead, it worked OK.)

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> Did you listen to my short opening excerpt, Paul?

Yes, I did.

> What do you think?

The tuning sounds right, as there are clearly no enharmonic problems
so far . . . I'll refrain from comment about the phrasing, since I'm
so used to 20th century recordings of the piece, and not an expert on
period performance . . . As for the timbres, I was a lot happier with
how my soundcard sounded on Herman's Pachelbel MIDI files than with
what I'm hearing here . . . what did you use as your sound generation
device for this .mp3? (You can reply on metatuning)

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 14, 2001 2:06 PM
> Subject: [tuning] Re: Mozart tuning
>

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > Did you listen to my short opening excerpt, Paul?
>
> Yes, I did.
>
> > What do you think?
>
> The tuning sounds right, as there are clearly no enharmonic problems
> so far . . . I'll refrain from comment about the phrasing, since I'm
> so used to 20th century recordings of the piece, and not an expert on
> period performance . . . As for the timbres, I was a lot happier with
> how my soundcard sounded on Herman's Pachelbel MIDI files than with
> what I'm hearing here . . . what did you use as your sound generation
> device for this .mp3? (You can reply on metatuning)

I'm using Yamaha's XG100 SoftSynth. I'm not really crazy about
the sounds, either, but my soundcard on my new PC really sucks,
so softsynth is my only option right now.

Re: the phrasing: This is still a quickie... haven't done the
polishing-up on phrasing, dynamics, etc.

-monz
http://www.monz.org
"All roads lead to n^0"

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🔗John A. deLaubenfels <jdl@adaptune.com>

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: John A. deLaubenfels <jdl@adaptune.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 14, 2001 2:41 PM
> Subject: [tuning] Re: Mozart tuning
>
>
> Monz, any chance you could post a GM version of what you've got so far?
> I've got serious bandwidth problems. Thanks!

/tuning/files/monz/55K550BG.MID

If anyone out there wants to make a better mp3 than the one
I've done, be my guest. Please save it in the same place
as the one I've uploaded.

-monz
http://www.monz.org
"All roads lead to n^0"

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