5-limit D# and Eb (was: serial bullseye)

Hi Klaus,

> From: klaus schmirler <KSchmir@z.zgs.de>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, January 01, 2002 3:15 PM
> Subject: Re: [tuning] Re: serial bullseye
>
>
>
> monz schrieb:
>
> > I saw that. It was Klaus Schmirler (a microtonal trombonist),
> > discussing a trombone part which had a D# tied to an Eb
> > (which, as Paul pointed out to me, can also be found in Mozart,
> > and certainly in Beethoven).
>
> P.E. accepted that pitches shift in the middle of a note???
> Tell me more.
>
> k

Be careful not to misinterpret that. No, I didn't mean that
Paul accepts pitch-shift in the middle of a note.

What I meant was that I've seen Beethoven scores which have
notated pitches with flats which are then tied to their
enharmonically equivalent sharp, or vice versa, and that Paul
has pointed out to me that Mozart wrote a few things like this
also.

But Paul's point is that Mozart (and Beethoven, and Wagner)
must have had in mind when they wrote these, some form of
temperament in which what he calls a "commatic" unison-vector
disappears, and I agree.

I put "commatic" in quotes because in this 5-limit case the only
comma which might be involved is the Pythagorean comma. Other
unison-vectors which might vanish could be the skhisma, diaschisma,
dieses, or possibly a few others.

Here's a section of the 5-limit rectangular lattice in which I've
notated only the D#'s and Eb's. Observe that notes with the same
notation are a syntonic comma apart. We're already assuming that
*that* vanishes, because the notation of the composers in the
standard late-romantic repertoire never distinguishes it.

4 D# . . . . . . . . . . . . . . . .
3 . . . . D# . . . . . . . . . . . .
2 . . . . . . . . D# . . . . . . . .
1 Eb . . . . . . . . . . . D# . . . .
5^y 0 . . . . Eb . . n^0 . . . . . . . . D#
-1 . . . . . . . . Eb . . . . . . . .
-2 . . . . . . . . . . . . Eb . . . .
-3 . . . . . . . . . . . . . . . . Eb

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
3^x

In this example, we're considering unison-vectors which
connect any of the D#'s with any of the Eb's.

All the D#-Eb pairs on this lattice are:

x,y higher
ratio coordinates ~cents note

skhisma 32805:32768 ( 8, 1) 1.95 D#
Pyth.comma 531441:528244 (12, 0) 23.46 D#
diaschisma 2048:2025 (-4,-2) 19.55 Eb
diesis 128:125 ( 0,-3) 41.06 Eb
648:625 ( 4,-4) 62.57 Eb
6561:6250 ( 8,-5) 84.07 Eb
531441:500000 (12,-6) 105.6 Eb
(16,-7) 127.1 Eb

(Observe that D# is the higher note of the pair for the
skhisma and Pythagorean comma, whereas Eb is for the rest.)

The Beethoven scores in which I've seen these enharmonic ties
are some of his piano sonatas, so there's no question there of
a change in pitch.

Where Paul and I differ is that I *do* accept a pitch-shift in
the middle of a note, particularly in a JI or adaptive-JI context.
But it would be inappropriate in other contexts.

Since Wagner's instrumental medium, like Mahler's, was the orchestra,
intra-note pitch-shift is not entirely out of the question, but I
believe a great deal of analysis would be necessary to determine
where and how much would be appropriate.

-monz

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> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, January 01, 2002 9:37 PM
> Subject: [tuning] 5-limit D# and Eb (was: serial bullseye)
>

>
> Hi Klaus,
>
>
> > From: klaus schmirler <KSchmir@z.zgs.de>
> > To: <tuning@yahoogroups.com>
> > Sent: Tuesday, January 01, 2002 3:15 PM
> > Subject: Re: [tuning] Re: serial bullseye
> >
> >
> >
> > monz schrieb:
> >
> > > I saw that. It was Klaus Schmirler (a microtonal trombonist),
> > > discussing a trombone part which had a D# tied to an Eb
> > > (which, as Paul pointed out to me, can also be found in Mozart,
> > > and certainly in Beethoven).
> >
> > P.E. accepted that pitches shift in the middle of a note???
> Since Wagner's instrumental medium, like Mahler's, was the orchestra,
> intra-note pitch-shift is not entirely out of the question, but I
> believe a great deal of analysis would be necessary to determine
> where and how much would be appropriate.

Well ... of course there's always the idea that a trombone player,
for instance, might have really good ears... :)

-monz

_________________________________________________________
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Get your free @yahoo.com address at http://mail.yahoo.com

> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, January 01, 2002 9:37 PM
> Subject: [tuning] 5-limit D# and Eb (was: serial bullseye)
>
>
> Here's a section of the 5-limit rectangular lattice in which I've
> notated only the D#'s and Eb's.

I decided to add numbers to each of the notes on my lattice,
so that we can formulate an "algebra of enharmonicity" for
the 5-limit:

4 D#1. . . . . . . . . . . . . . . .
3 . . . . D#2. . . . . . . . . . . .
2 . . . . . . . . D#3. . . . . . . .
1 Eb1 . . . . . . . . . . D#4. . . .
5^y 0 . . . . Eb2. . n^0 . . . . . . . . D#5
-1 . . . . . . . . Eb3. . . . . . . .
-2 . . . . . . . . . . . . Eb4. . . .
-3 . . . . . . . . . . . . . . . . Eb5

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
3^x

All the D#-Eb pairs on this lattice are:
(note the last two columns)

x,y higher lower
ratio coordinates ~cents note subtract note

skhisma 32805:32768 ( 8, 1) 1.95 D#(x+2) - Eb(x)
Pyth.comma 531441:528244 (12, 0) 23.46 D#(x+3) - Eb(x)
diaschisma 2048:2025 (-4,-2) 19.55 Eb(x) - D#(x+1)
diesis 128:125 ( 0,-3) 41.06 Eb(x) - D#(x)
648:625 ( 4,-4) 62.57 Eb(x+1) - D#(x)
6561:6250 ( 8,-5) 84.07 Eb(x+2) - D#(x)
531441:500000 (12,-6) 105.6 Eb(x+3) - D#(x)
(16,-7) 127.1 Eb(x+4) - D#(x)

-monz

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I've played many pieces where I hold a long note and it changes its enharmonic spelling as a bassoonist in orchestras. There is definitely a psychological adjustment. I believe I change the tone on such a shift, rather than change pitch. The changes come from the timbral content moveing to a greater resonance.

BTW, hasn't it been demonstrated that Hayden wanted enharmonic relationships? I believe there was some essay that indicated this.

Johnny Reinhard

--- In tuning@y..., Afmmjr@a... wrote:

> BTW, hasn't it been demonstrated that Hayden wanted enharmonic relationships? I believe there was some essay that indicated this.

It would be interesting to find out more about Haydn's practicces, since he had such complete artistic control of the Esterhazy musical resources.

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

/tuning/topicId_32212.html#32212

>
> 4 D# . . . . . . . . . . . . . . . .
> 3 . . . . D# . . . . . . . . . . . .
> 2 . . . . . . . . D# . . . . . . . .
> 1 Eb . . . . . . . . . . . D# . . . .
> 5^y 0 . . . . Eb . . n^0 . . . . . . . . D#
> -1 . . . . . . . . Eb . . . . . . . .
> -2 . . . . . . . . . . . . Eb . . . .
> -3 . . . . . . . . . . . . . . . . Eb
>
> -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
> 3^x
>
> In this example, we're considering unison-vectors which
> connect any of the D#'s with any of the Eb's.
>
> All the D#-Eb pairs on this lattice are:
>
> x,y higher
> ratio coordinates ~cents note
>
> skhisma 32805:32768 ( 8, 1) 1.95 D#
> Pyth.comma 531441:528244 (12, 0) 23.46 D#
> diaschisma 2048:2025 (-4,-2) 19.55 Eb
> diesis 128:125 ( 0,-3) 41.06 Eb
> 648:625 ( 4,-4) 62.57 Eb
> 6561:6250 ( 8,-5) 84.07 Eb
> 531441:500000 (12,-6) 105.6 Eb
> (16,-7) 127.1 Eb
>
>

Hi Monz...

You might wish to remind the "web viewers" to go "Message
Index" "Expand Messages..."

Otherwise your two charts here come out a mess...

(Glad I tried it the other way... :)

JP

----- Original Message -----
From: jpehrson2 <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, January 02, 2002 8:50 PM
Subject: [tuning] Re: 5-limit D# and Eb (was: serial bullseye)

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_32212.html#32212
>
> ... <diagrams snipped>
>
> Hi Monz...
>
> You might wish to remind the "web viewers" to go "Message
> Index" "Expand Messages..."
>
> Otherwise your two charts here come out a mess...
>
> (Glad I tried it the other way... :)

Hi Joe,

Yes, I've been pretty good about using URLs which point to
the "Expand Messages" versions of the web-based archives.

So why are *you* not doing that?

I'm not even sure if these links work like they should
... I'd appreciate feedback from others.

The message Joe referenced is:
/tuning/topicId_32212.html#32212?expand=1

And the one with the better, updated diagrams is:
/tuning/topicId_32212.html#32219?expand=1

-monz

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Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> I'm not even sure if these links work like they should
> ... I'd appreciate feedback from others.
>
> The message Joe referenced is:
> /tuning/topicId_32212.html#32212?expand=1
>
> And the one with the better, updated diagrams is:
> /tuning/topicId_32212.html#32219?expand=1

> -monz
>
>
Joe,

Your links to this recent stuff seem to work fine.

However, I've noted problems trying to resolve
a number of older posts, where the only technique
which will properly display the "spaces" (hence, all
the painstaking ASCII lattice works), is to select
"reply" or "forward". Then I am only able to *VIEW*
(and cannot print-out) the message. When I email
such to myself (as has been proposed on this list
as a solution), it's garbage (or close enough).

I fear that this points to some significant differences
between the archived *pre-yahoo debacle* and the archived
*post-yahoo debacle* stuff (as you have been recently
posting).

Check it out for yourself (I wish you/all better luck!)...

/tuning/topicId_16878.html#26302?expand=1

J Gill

Alas, emailed it to myself using Yahoo "forward".
All that work to have it apparantly non-printable!
See this message link, as well:

/tuning/topicId_16723.html#16723?expand=1

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > I'm not even sure if these links work like they should
> > ... I'd appreciate feedback from others.
> >
> > The message Joe referenced is:
> > /tuning/topicId_32212.html#32212?expand=1
> >
> > And the one with the better, updated diagrams is:
> > /tuning/topicId_32212.html#32219?expand=1
>
> > -monz
> >
> >
> Joe,
>
> Your links to this recent stuff seem to work fine.
>
> However, I've noted problems trying to resolve
> a number of older posts, where the only technique
> which will properly display the "spaces" (hence, all
> the painstaking ASCII lattice works), is to select
> "reply" or "forward". Then I am only able to *VIEW*
> (and cannot print-out) the message. When I email
> such to myself (as has been proposed on this list
> as a solution), it's garbage (or close enough).
>
> I fear that this points to some significant differences
> between the archived *pre-yahoo debacle* and the archived
> *post-yahoo debacle* stuff (as you have been recently
> posting).
>
> Check it out for yourself (I wish you/all better luck!)...
>
> /tuning/topicId_16878.html#26302?expand=1
>
>
> J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

> Alas, emailed it to myself using Yahoo "forward".
> All that work to have it apparantly non-printable!
> See this message link, as well:
>
> /tuning/topicId_16723.html#16723?expand=1
>
> J Gill
>
>
J Gill: To clarify what it is that I find -

IF you use a link such as that above (where
the symbols '?expand=1' are appended to the
messages original identifier, THEN it is FUBARed.

IF you navigate directly to the message , then
select the "Expand Messages" selection, the
message *WILL* display correctly (but one is
not able access the "Forward" or "Reply" functions
in order to email to oneself.

But, at least it is plain-text, so copy/paste
techniques into Notepad, Wordpad, and Word
*do* work ...

J Gill

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

/tuning/topicId_32212.html#32255

>
> ----- Original Message -----
> From: jpehrson2 <jpehrson@r...>
> To: <tuning@y...>
> Sent: Wednesday, January 02, 2002 8:50 PM
> Subject: [tuning] Re: 5-limit D# and Eb (was: serial bullseye)
>
>
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > /tuning/topicId_32212.html#32212
> >
> > ... <diagrams snipped>
> >
> > Hi Monz...
> >
> > You might wish to remind the "web viewers" to go "Message
> > Index" "Expand Messages..."
> >
> > Otherwise your two charts here come out a mess...
> >
> > (Glad I tried it the other way... :)
>
>
> Hi Joe,
>
>
> Yes, I've been pretty good about using URLs which point to
> the "Expand Messages" versions of the web-based archives.
>
> So why are *you* not doing that?
>

Hi Monz...

Well, I *will* in the future, if that works. *However* I was just
refering to your *original* post, which looked like a jumble without
the "Expand Messages" notice.

I think a simple line like: "To view correctly, please use "Message
Index-Expand Messages" is all that is needed..."

Unless you feel that everybody knows that... but it's easy to
forget...

??

JP

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

/tuning/topicId_32212.html#32257

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> >
> > I'm not even sure if these links work like they should
> > ... I'd appreciate feedback from others.
> >
> > >
> Check it out for yourself (I wish you/all better luck!)...
>
> /tuning/topicId_16878.html#26302?expand=1
>
>
> J Gill

Hello J. Gill!

This printed fine for me. The problem was, it was not "fully
expanded" for some reason, and I had to select that option again.

However, after doing that, it printed fine in its "true" lattice
form...

I also tried other earlier posts that printed out fine...

best,

Joe

monz schrieb:
> Be careful not to misinterpret that. No, I didn't mean that
> Paul accepts pitch-shift in the middle of a note.
>
> What I meant was that I've seen Beethoven scores which have
> notated pitches with flats which are then tied to their
> enharmonically equivalent sharp, or vice versa, and that Paul
> has pointed out to me that Mozart wrote a few things like this
> also.
>
> But Paul's point is that Mozart (and Beethoven, and Wagner)
> must have had in mind when they wrote these, some form of
> temperament in which what he calls a "commatic" unison-vector
> disappears, and I agree.

But my point was that in actual practice, possibly going
back to the times of Wagner, it stayed there, being played
as a shift in intonation as the spelling changes, on the
beat. (Every time this has been pointed out to me, the tenor
was like, this guy Wagner certainly knew his craft. There
was no mention of commas, let alone unison vectors, nor
would i have understood it at that time.)

klaus

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "unidala" <JGill99@i...> wrote:
>
> /tuning/topicId_32212.html#32257
>
> > --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > >
> > > I'm not even sure if these links work like they should
> > > ... I'd appreciate feedback from others.
> > >
> > > >
> > Check it out for yourself (I wish you/all better luck!)...
> >
> > /tuning/topicId_16878.html#26302?expand=1
> >
> >
> > J Gill
>
> Hello J. Gill!
>
> This printed fine for me. The problem was, it was not "fully
> expanded" for some reason, and I had to select that option again.
>
> However, after doing that, it printed fine in its "true" lattice
> form...
>
> I also tried other earlier posts that printed out fine...
>
> best,
>
> Joe

J Gill: So you are saying that if you just *press the same
button twice*, that it is a different result (which works)???

Will try it, but that sure sounds weird ...

J Gill

--- In tuning@y..., "unidala" <JGill99@i...> wrote:

/tuning/topicId_32212.html#32272

> J Gill: So you are saying that if you just *press the same
> button twice*, that it is a different result (which works)???
>
> Will try it, but that sure sounds weird ...
>
>
> J Gill

This is what happened to me... I don't know why it didn't work the
first time, but I pressed it again and got the print out... Maybe
the *link* doesn't always "activate" it properly, and you have to do
it manually sometimes.... Just a thought.

best,

Joe

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

> But Paul's point is that Mozart (and Beethoven, and Wagner)
> must have had in mind when they wrote these, some form of
> temperament in which what he calls a "commatic" unison-vector
> disappears, and I agree.

Because of the vertical diminished sixth, correct?
>
> I put "commatic" in quotes because in this 5-limit case the only
> comma which might be involved

*NOT* the only comma which might be involved?

> is the Pythagorean comma. Other
> unison-vectors which might vanish could be the skhisma, diaschisma,
> dieses, or possibly a few others.

Right, these too.

>
> Here's a section of the 5-limit rectangular lattice in which I've
> notated only the D#'s and Eb's. Observe that notes with the same
> notation are a syntonic comma apart. We're already assuming that
> *that* vanishes, because the notation of the composers in the
> standard late-romantic repertoire never distinguishes it.
>
>
> 4 D# . . . . . . . . . . . . . . . .
> 3 . . . . D# . . . . . . . . . . . .
> 2 . . . . . . . . D# . . . . . . . .
> 1 Eb . . . . . . . . . . . D# . . . .
> 5^y 0 . . . . Eb . . n^0 . . . . . . . . D#
> -1 . . . . . . . . Eb . . . . . . . .
> -2 . . . . . . . . . . . . Eb . . . .
> -3 . . . . . . . . . . . . . . . . Eb
>
> -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
> 3^x
>
> In this example, we're considering unison-vectors which
> connect any of the D#'s with any of the Eb's.
>
> All the D#-Eb pairs on this lattice are:
>
> x,y higher
> ratio coordinates ~cents note
>
> skhisma 32805:32768 ( 8, 1) 1.95 D#
> Pyth.comma 531441:528244 (12, 0) 23.46 D#
> diaschisma 2048:2025 (-4,-2) 19.55 Eb
> diesis 128:125 ( 0,-3) 41.06 Eb
> 648:625 ( 4,-4) 62.57 Eb

That's the "other" diesis, four minor thirds, its name depends on
whom you ask.
>
> Where Paul and I differ is that I *do* accept a pitch-shift in
> the middle of a note, particularly in a JI or adaptive-JI context.

And you differ from me there how? I *also* accept those -- big time!
Hello? :)

> But it would be inappropriate in other contexts.
>
> Since Wagner's instrumental medium, like Mahler's, was the
orchestra,
> intra-note pitch-shift is not entirely out of the question, but I
> believe a great deal of analysis would be necessary to determine
> where and how much would be appropriate.

The Mozart case which spawned this had a vertical diminished sixth
and not a fifth if the notation is taken as an open meantone system.
Mozart is in the process of modulating between the extreme flat keys
and the extreme sharp keys, and doesn't bother to make all the
enhamonic changes simultaneous. So to me, the enharmonicity of the
notation is clear.