pat at mamalala.org
Fri Nov 23 21:09:49 CET 2007
Hello, I'd like to add some 0.5 cents experiment...
Mathieu Bouchard a écrit :
> On Tue, 20 Nov 2007, Charles Henry wrote:
>> Yes, but there is evidence for the fundamental bass that occurs
>> between pairs of notes, with a strength dependent on those ratios.
>> Complex harmonies could have multiple fundamentals. It's a mystery to
>> me how harmony/rhythm work at a fundamental level.
> Well, so far, most of the time you see "fundamental", there's only one
> at a time, for each block of music you want to figure out the
> fundamental of.
Symmetric chords has as much tones as it has notes, diminished chords,
has four fundamentals, also a minor seven chord might be relative with
three major scales, and we have the choice between different chords with
the same bunch of notes.
eg: A C E G is both Am7, and C6 (C E G A), or FM7 (F A C E G) or G13 (G
B D F A C E)... This is what you are explaining later:
> But different fundamentals can be extracted for any
> given interval, and those intervals can be a window sliding through
> time, looking at any "dinote" (pair of notes), and there can be multiple
> windows of different sizes that account for different levels of human
> memory and of musical understanding... (?) I think that we could analyse
> music using whole networks of fundamentals...
Hardness of understanding increases when window size diminishes, like
a blues we could play with only one scale with a little understanding,
or all scales with applying knowledge of harmony all along the twelve
> and also, a theory of musical understanding should be resistant to
> "detuning", because many forms of detuning are used in music and yet
> humans can automatically figure out what the fundamental is _intended_
> to be (rather than what it is physically).
Dominant chords can contain all the notes that aren't into the
fundamental chord, so we know by experience that the moment after this
dissonant ambiance, the next sound will be different but nearly the one
we've heard before,.
From fundamental the dominant chord contains the nearest intervals,
the fifth and the fourth are mathematicaly the simpliest non-integer
intervals, the seventh is the preceding frequency of the fundamental in
tempered major scale (when 9b is used it goes more complicated...).
>> The topology bullshit was plainly bullshit. But I was trying to
>> stretch what I know, and try to see a way for song-structure and
>> rhythm to take on more than one dimension.
The fundamental appear in harmony once we know an amount of
informations determinded by edges expressed with rythm.
Following the dominant ==> fundamental motion explained just before,
odd beats would contain fundamentals and even beats would contain dominants.
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