comments sought

http://members.aol.com/chang8828/grouptheory.htm

Oh totally. In modern terms, they just had a way of practically exorcising
Obsessive Compulsive Disorder, Mozart by twiddling out the last power of two
he could, and Beethoven by perpetual change and distraction. This is
something I've only tapped into by being so mentally off balance, I've never
really talked about it, but this is what has me thinking in terms of not
just quantum applications of pitch time and volume, but structure.

I keep going back to Beethoven's first piano sonata, it's almost like a
fractal structure the way things move around and fold into each other.
Almost like origami. I can't ever say exactly what it means to the general
public but I can tell be all the fidget factors he had a solid grip on being
able to balance and calm the mind enraged. Only because if he didn't, in
certain states of mind I wouldn't be able to listen to him. There's a sense
of nested scales in his variations as well. A melody will move up into
arpeggiating a different chord, one note will be a diatonic step away, one
note will be a chromatic step away etc. Well not etc. I don't recall any
specific 17 or 19 implications in altered intervals as they evolved. Other
than the fact that there's an Fb on the first page of the first piano
sonata. I thought that was so cool. Oh actually, no, in his first few
piano sonatas at least, IIRC he works with a span of 19 fifths. Heh.

Mozart, the binary structure didn't surprise me at all. In visualizing the
macro structure of K545 one day, I just sort of said wait is this a joke,
and started making about the equivalent of a Harvard outline chronicling the
piece. Taking things phrase by phrase I managed to knock it down to five
levels, 32 sections. I was pretty sure it trickled down to each individual
note or possibly into the fabric, choice of scale or style or something, but
probably down to the note.

I've felt a sort of inert connection to Beethoven and Mozart as I can relate
to each, the paternal physical abuse and exploitation, respectively. Being
that pressured that young and punished that severely, well, that SPECIFIC
element of abuse has a way of making you a little more OCD than normal.
Musically, your imaginations tend to be structured, to sort of build
yourself a solid structure to escape to. Things become a lot more balanced,
to make up for the chaos directly outside the brain.

Marc

() Any article on Mozart introducing his works by their location
in the movie "Amadeus" is automatically disqualified.

() Mozart's "formula" doesn't look like very much of a formula
at all to me. It looks a loose description -- a lot like the
standard music theory the author (correctly) criticizes at the
beginning of the article. Let's see the "formula" applied from
scratch into something that sounds like Mozart; then we'll talk.

() "practically every musical composition has mathematical
underpinnings" You can use math to describe almost anything.
How deep these descriptions are, how much explanatory power
they have for why we like music, is another thing... "the
chromatic scale is a simple logarithmic equation", for example,
explains nothing.

() "Thus, the beginning of Beethoven's Fifth symphony, when
translated into mathematical language, reads just like the first
chapter of a textbook on group theory, almost sentence for
sentence!" I'll leave this to Gene and those who know group
theory. Doesn't strike me that that much is being said here,
other than a discussion (as opposed to a prediction) of the 5th
symphony using fancy lingo.

() "He wanted to implant the idea of the theme in our brain
before we heard it!" Okay, okay. So what?

() There seems to be a lot of good advice on practicing the piano
on this site, though I'm still working my way through it.

-Carl

> From: Orphon Soul, Inc. <tuning@orphonsoul.com>
> To: Tuning Math <tuning-math@yahoogroups.com>
> Sent: Thursday, February 21, 2002 3:25 PM
> Subject: Re: [tuning-math] comments sought
>
>
> ...
> I keep going back to Beethoven's first piano sonata, it's almost like a
> fractal structure the way things move around and fold into each other.
> Almost like origami.

hmmm... that's really interesting, marc. i can see a lot of
Beethoven's work in that light, now that you mention it.

> I can't ever say exactly what it means to the general
> public but I can tell be all the fidget factors he had a solid grip on
being
> able to balance and calm the mind enraged. Only because if he didn't, in
> certain states of mind I wouldn't be able to listen to him.

that's really interesting.

> There's a sense
> of nested scales in his variations as well. A melody will move up into
> arpeggiating a different chord, one note will be a diatonic step away, one
> note will be a chromatic step away etc. Well not etc. I don't recall any
> specific 17 or 19 implications in altered intervals as they evolved.

hmm ... i don't recall Beethoven using anything that resembles 19,
but i'd say that he certainly implied 17 a l o t in his compositions,
both melodically (the "flat 9th" or "flat 2nd") and harmonically
(frequent "diminished-7th" chords which imply 10:12:14:17).

it's amazing to me how Beethoven could capture in his piano pieces
what i c l e a r l y hear as improvisations. in good performances
of much of his piano music, i can almost see Ludwig himself sitting
at the keyboard making it up on the spot.

> Other than the fact that there's an Fb on the first page of the first
> piano sonata. I thought that was so cool.

whoa! -- it's getting scary now, you and i have thought so
many similar things. when i first bought an old used copy
of the _32 Sonatas, volume 1_ at Settlement Music School back
in the 1970s, i opened to the first page and that was my exact
response when i saw the Fb: "wow, that's so cool!".

> Oh actually, no, in his first few piano sonatas at least,
> IIRC he [Beethoven] works with a span of 19 fifths. Heh.

it's been a few months now since i worked on it, but i recall
that Mozart used a span of 20 "5ths" in the 1st movement of his
40th Symphony. the Symphony is in G-minor, so G=1/1 gives a
meantone chain from -8 (Cb) to +11 (B#) "5th" generators.

in my MIDI rendition of the beginning of the piece in 55edo
http://www.ixpres.com/interval/monzo/55edo/55edo.htm
i was careful to tune the sharps and flats differently to
reflect Mozart's notation, which had to be done by hand
because none of the programs i know of (Manuel's Scala,
Graham's Midiconv, John deLaubenfels adaptune) can retune
to more than 12 tones per octave.

-monz

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--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

> http://members.aol.com/chang8828/grouptheory.htm

If you take out the drivel pretending to be math, you are left with an analysis of how Mozart and Beethoven use motives to build themes.

In-Reply-To: <003501c1bb52$449655e0$af48620c@dsl.att.net>
monz wrote:

> in my MIDI rendition of the beginning of the piece in 55edo
> http://www.ixpres.com/interval/monzo/55edo/55edo.htm
> i was careful to tune the sharps and flats differently to
> reflect Mozart's notation, which had to be done by hand
> because none of the programs i know of (Manuel's Scala,
> Graham's Midiconv, John deLaubenfels adaptune) can retune
> to more than 12 tones per octave.

What do you mean? Midiconv doesn't have any 12-fetishism! I don't think
Scale does either.

Graham

>What do you mean? Midiconv doesn't have any 12-fetishism!
>I don't think Scala does either.

They don't, but Joe means the MIDI 12-fetishism. If there's
a F# and a Gb in the score, we aren't able to guess which
because they have the same note number in the MIDI-file.
Still doing _all_ notes by hand what Joe does is a waste
of time.

Manuel

> From: <manuel.op.de.coul@eon-benelux.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Friday, February 22, 2002 5:20 AM
> Subject: Re: [tuning-math] Re: comments sought
>
>
> > What do you mean? Midiconv doesn't have any 12-fetishism!
> > I don't think Scala does either.
>
> They don't, but Joe means the MIDI 12-fetishism. If there's
> a F# and a Gb in the score, we aren't able to guess which
> because they have the same note number in the MIDI-file.

thanks for clarifying that, Manuel. yes, the fault is not
with the software designers but with MIDI.

> Still doing _all_ notes by hand what Joe does is a waste
> of time.

that's true, Manuel, and i thank you publicly here for
providing me with the entire Mozart 40th retuned to a
12-tone subset of 55edo by Scala. when i ever find time
to go back to this project, i can continue by starting from
your file and simply changing the pitch-bend on the few
required notes (at least i hope it's a few!).

-monz

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

Another possibility is to see if there are unused note
numbers in the MIDI-file, change the note numbers of the
special notes to those free ones, and retune the whole
file in one go with Scala using a 128-note scale with
the right pitches. Then you don't need to calculate
pitch bends, and you can try different tunings too with
very little effort.

Manuel

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

/tuning-math/message/3366

> http://members.aol.com/chang8828/grouptheory.htm

***Well, this was an interesting read, but I'm dubious at best. In
order to be convinced, I'd like to see more Mozart examples
on "regular staff notation" like a "real" music theory article. It's
quite possible that the examples were selected which just *happened*
to prove the "formula."

I'd need to see vastly more instances of this so-called
Mozart "formula" before I'd believe it really exists and that Mozart
used it to generate his works...

Besides, due to the nature of the way themes are *normally* generated
in "common practice" Western music, with small units of 2, 4,
expanding to 8, 16, etc., almost *all* themes could be expressed by
some kind of common "compound," yes? It's saying more about the
generation of themes in common practice (i.e. dead white male)
Western music than anything else, so it seems.

Regarding the Beethoven, that seems even *more* specious. I don't
know much about "Group Theory" but I can guess that it's expansive
enough that you could included *just about anything* if you angle it
the right way.

This seems like a "spin cycle" worthy of the greatest of washing
machines...

JP