replies to Ray Tomes

[Dave Keenan, TD 186.4]
>
> [Ray Tomes]
>> Of course that means that a minor chord becomes 1/6:1/5:1/4
>> (a sort of inverted major)
>
> Yes. A shame the word "inverted" already has a quite different
> meaning in music. I think I have heard people call it the
> "dual". Note that the minor 7th above is its own dual.

There is a tradition of using the word 'dualism' to describe
this 'inverted major' description of 'minor' in 19th-century
German music theory. It is chiefly associated with the work
of Oettingen and Riemann.

[Ray Tomes]
>
>[me, monz]
>> So, in a musically significant way, the 'common multiple'
>> notation *is* less satisfactory than the 'common divisor'
>> version, Partch's use of it notwithstanding.
>
> Just finished replying to the above and then read this. Are you
> saying the same thing as I am in my second paragraph above?

Yes. Dave Keenan's post appeared before mine and already gave
a better explanation of the same thing I'm saying.

BTW, Dave, thanks for the excellent summary of the complexity
discussion!

[Ray Tomes, TD 187.5]
>
> I saw a home video show recently which consisted of a guy
> playing ...
> [piano] da-da-da-da-dump
> [lid] brrp-brrp brrp-brrp
> [piano] da-da-da-da-dump
> [lid] brrp-brrp brrp-brrp
> where the lid part was sliding the lid closed and then open
> again. It really worked quite well!

John Cage wrote a piece back in 1942 called _The Wonderful Widow
of 18 Springs_. It's scored for soprano singer and piano with
the lid closed.

In other words, the pianist is really a percussionist in this
piece, as his part consists of tapping or pounding various
places on the wood of the piano.

Joseph L. Monzo monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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The current experimental and theoretical understanding of particle masses is
embedded in the conceptual framework of Quantum Field Theory. In this
theory, there is not only an uncertainty relation governing the positions
and momenta of the particles, but also the very number of particles existing
at a given point in time. I have not formally studied QFT, but I know that
some of its predictions, such as the magnetic moment of the electron, are
the most accurate (one part in 10^18) in all of science. You will have to
come to terms with all its successes if you wish to propose a competing view
of the universe. OK, that's enough particle physics for now.

>>One musical point for Ray Tomes: You are incorrect in your assumptions
about
>>composers' intentions and wandering tonics. Many classical pieces have
been
>>analyzed in just intonation and almost invariably they have a net downward
>>drift in JI, sometimes by as much as half an octave.

>I am unsure as to what you are saying here. Are you saying that turning
>a piece into JI commonly (and wrongly) causes this drift in many pieces?

Yes.

>If so, I suggest that this depends very strongly on the algorithm used
>in the process. I dealt with some considerations in this regard a
>couple of weeks ago and it is clear that slightly different algorithms
>can jump to different notes under the same circumstances and introduce
>ratios such as 80/81 etc.

OK, but these jumps are quite foreign to any accepted performance practices,
and many musical situations (such as the chord d-f-g-a-c in C major) could
not be remedied by such jumps anyway -- the 80/81 must vanish.

>>Although a solution involving a constant, upward, compensating drift could
>>certainly help in many situtations, it is difficult to see any grounds on
>>which this could be deemed preferable to the adaptive JI schemes that John
>>A. deLaubenfels (sp?) and I discussed.

>Where is this information?

As I said, look at the tuning archived just before you rejoines, especially
posts entitled "Adaptive JI", and note that I often post from Brett
Barbaro's e-mail account.

>>I think a better description would relate to chaos theory. The opening and
closing of
>>the vocal folds experiences a period-doubling, so the apparent fundamental
and its
>>overtones are still prominent (due to the dynamics and not the filtering)
but the
>>true fundamental is an octave lower. The way the "subharmonic" almost
"jumps" in and
>>out of existence as one varies the mode of singing is a hallmark of a
nonlinear
>>bifurcation. I refer Jim to any of the popular books on chaos theory, such
as Manfred
>>Schroeder's _Fractals, Chaos, and Power Laws_.

>I disagree as it is stated that notes 1/2, 1/3, 1/4, 1/5 the original
>all came in with slight adjustments. That is not chaotic behaviour but
>undertones.

I'm not saying it's chaotic behavior, I'm saying it's the type of behavior
found en route to chaos. What do you mean by "slight adjustements"? And how
do you propose to physically account for the "undertones"? In steady-state
oscillations, resonant cavities can do nothing more than selectively amplify
frequencies already present. The question is how they get there in the first
place.

>I should make a bolder statement in regard to this to Paul. If the
>large playing ground idea is used (which shows what I called C and C-
>etc) then we are in agreement that the piece should end on C and not C--
>or some such if it started on C. This can be achieved by keeping track
>of the CoG (centre of gravity) as we go along and not letting it get too
>far from the starting place. This method will ensure that the "breaks"
>will happen at the most correct places where there is considerable
>ambiguity. Of course this is easier to do well with the whole piece of
>music available than to do in real time where retrospect can play no
>part.

>For example, in the big playing field ...

>D-- A- E- B- F#- C#- G#- D#- A# E# B#
> F- C- G- D- A E B F# C# G# D#
> Ab Eb Bb F C G D A+ E+ B+
> Fb Cb Gb Db Ab+ Eb+ Bb+ F+ C+ G+ D+

>... if we have wandered from D to E to D- and E- we would not want to go
>to D-- but would have a bias built in to pull back to D- instead. Maybe
>even the first time (E to D-) would have pulled back unless the music
>very powerfully made this move. Paul, I'm not sure that we can fully
>resolve this without worked examples.

I would argue that virtually every Western composer since the advent of the
5-limit has been dealing not with the flat playing field you describe above,
but a cylindrical one where the lattice bends back on itself so that
commatic distinctions vanish. Finding the correct place for "breaks" could
certainly be handled as you describe, but would have nothing to do with
anything that went on in the mind of the composer or in the actions of the
finest performers of his/her music. And again, there are cases where by your
reckoning D and D- would have to occur at the same time, in a single
sonority, so even "breaks" would not solve the problem.

Finally, a note on notation. You are using Ben Johnston's notation, where a
perfect fifth above D is not A but A+. This is a very confusing notation and
almost everyone who has tried to use it prefers Daniel Wolf's variant, where
a central Pythagorean row of your playing field would be notated entirely
without +s or -s, and then each row above would gain one more - and each row
below would gain one more +:

D-- A-- E-- B-- F#-- C#-- G#-- D#-- A#-- E#-- B#--
F- C- G- D- A- E- B- F#- C#- G#- D#-
Ab Eb Bb F C G D A E B
Fb+ Cb+ Gb+ Db+ Ab+ Eb+ Bb+ F+ C+ G+ D+

Not only is this simpler and clearer, but it corresponds more closely (at
least for a nice wide stretch of the playing field) to how a 12-tET-trained
performer could play the notes without +s and -s pretty much as usual and
then interpret the + or - as a fixed alteration of pitch. Fokker has
proposed a third alternative, which is that "the commatic stroke is added to
that homonym of a pair, which in the lattice is farther away from the centre
D" (he uses a square lattice). This would also not be a very useful notation
for performers.