Re: Harmonic reduction

[Lukas-Fabian Moser]

Hi Urs,

> The use case is the following: The example I attached shows a few ways
> to visualize the harmonic structure of (dodecaphonic) polyphonic music.
> But I would like to have this as a kind of live preview when working
> out counterpoints (with students). Therefore I don't need an analysis
> toolkit like Humdrum. Although: There actually might be tools to
> analyze the resulting MIDI files from a LilyPond compilation, and it
> would be possible to write a script that takes the Humdrum output to
> generate some LilyPond code that is then compiled. Hm, while writing
> the previous sentence this looks like an intriguing idea, but it's way
> too short for being able to use that on Wednesday :-(

But I think it would be desirable to avoid using MIDI as an intermediate 
step at all costs: For, as far as I know, MIDI only knows "chromatic" 
pitches and has no way of distinguishing enharmonic equivalents.

This might be sort-of acceptable for dodecaphonic music (I tend to 
disagree: Dodecaphonic music has always been written by composers with a 
strong background in classical diatonic theory, and it should not be 
taken for granted that they just tossed a coin when deciding on the 
enharmonic spelling of a given pitch), but it's obviously a no-go for 
pieces governed by classical tonality.


Moreover, your initial example manifestly exhibits what is known as the 
"segmentation problem" in many flavours of musical analysis: Which notes 
are to be grouped together in ordner to obtain a meaningful analysis of 
harmony/voice leading/etc.?

For instance, it's quite hard to (algorithmically) decide which notes in 
the attached Chopin are to be considered when analysing "the harmonic 
progression" of the piece - except of course if you claim (erroneously, 
I think) that "harmony" only lives in the lower staff here.

As another example, there's the famous bar in the first prelude of the 
Well-Tempered Clavier (see attachmend) where, for the first (and 
basically only) time in the piece, squashing all the pitches in a given 
bar together does not yield a meaningful chord. (And in fact, there is 
some debate on which pitch should be considered as part of the 
underlying chord here: Many people say b, but there a strong reasons to 
instead consider the c as a chord tone instead, hence regarding the 
harmony as a 43 instead of a 642.)

Also, Schönberg gave (in his Harmonielehre) funny examples of 
"impossible" sonorities taken from Bach's Motetten by just stopping the 
music at the right (or wrong?) time, together with equally funny jibes 
against the "aestheticians", or from Mozart's symphonies (also attached).


Maybe all I'm saying here is that any such automated tool for "musical 
analysis" would have to be highly configurable.

Lukas

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