matju at artengine.ca
Tue Nov 27 17:28:09 CET 2007
On Fri, 23 Nov 2007, Patrice Colet wrote:
> 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
Ok, but this is modulo octaves, so, there's no indication of actual
frequency: 440*2=440 and 440/2=440 in that little world.
And we were not really talking about the traditional music theory vision
of a fundamental. I believe that we were using it to refer to a possibly
hidden gcd (pgcd in French) frequency-wise, a "highest common undertone",
that can be applied to any combination of notes, so that for example, in
ACEG it is à priori worthwhile to consider the highest common undertone of
AC, AE, AG, CE, CG, EG, and then ACE, ACG, AEG, CEG, and then ACEG.
Highest common undertone is quite similar to looking at ratios such as 3/2
for a fifth, 5/4 for a major third, ... except it relativises it with the
actual pitch, because in practice a treble major chord is a lot more
consonant than a bass major chord, for example. (i asked myself the
question: why do bassists so seldom play chords?...)
> FM7 (F A C E G) or G13 (G B D F A C E)...
Those two are only chords containing the original chord. They contain all
of the same relationships, but they also contain additional relationships.
> 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 bars
This is vaguely related to Heisenberg-style uncertainty: you have a
limited number of hints in order to decode a melody, and if there are too
few of them, you can't figure out. But Heisenberg's is only about waves.
Originally it's only about wavicles (wavy particles at atomic level), it's
been generalised to sampling of all waves, and I guess it could be
faithfully generalised to some other transforms than Fourier's, but what
I'm saying here about melodies is ultra-loosely-connected to Heisenberg.
It's actually closer to reading or hearing words in a language and not
knowing which language it is yet: if you read the word «information» it
could be either French or English; if you hear the French word
«information» it could also be Bokmål's «informasjon» and you wouldn't
know unless you can really tell apart Bokmål's accent from all native
French accents just by hearing that word. That said, meaning-wise for that
word, it's pretty much all the same no matter the language. There are
Within one language, there are homophones and homonyms. The homophones
depend on the accent. In my accent and vocabulary, French «bosse», English
«boss» and English «bus» all sound the same, and the latter two can occur
in my French sentences. If I just say one word, the meaning can't be
guessed further than finding a set of several possibilities.
Melodies and scales are a lot more regular than the seemingly random
associations of phonemes with meanings, but still, they have some of the
discrete aspects that are somewhat oblivious to Heisenberg/Fourier. The
only thing that is in common there, is what is called
"under-determination", and also what I'd call "progressive determination":
each note played can tell you a bit more about the scale in use and the
way that the scale is being used and such, or about what could be a change
of scales that has occured but has not been confirmed by the listener's
interpretation yet (happens more in solo single-note than when extra notes
give a much more immediate indication of what's going on).
>> 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
No, we were thinking specifically about close detunings, all those
intervals that are confused with a much simpler interval, and usually,
which *should* be confused. It's the basis of logarithmic temperaments:
2^(7/12) is over 0.1% off from 3/2, and that's one of the best-matching
intervals relative to just temperaments. So, my question is, how do we
deal with that? When is a major third played like 2^(1/3) considered to
be an approximation of 5/4, and when is it considered to be an
approximation of 81/64 or some other?
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| Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada
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