11-tet harmonies

Paul wrote:

>At the end of "Turquoise Dabo Girl", you have what sounds sort of
>like a 4:6:7:9 chord. Now 4:7:9 is actually very accurate in 11-tET,
>but of course the "6" isn't represented at all. Did you map this down
>to 654 cents, or up to 763 cents? I'm guessing the former, but
>actually I'm not quite sure. I have a very good ear, but evidently
>when you screw with the timbres, you're removing its usual points of
>reference!

Well, I never worked out any "music theory" for 11-tet, but
I just looked back at the midi file of the dabo girl,
and the last measure contains the following midi note numbers:

43 45 54 56 63 67 74 78

Since this is mapped to 11-tet, there are 11 midi numbers in an octave,
thus 45-56-67-78 are all octaves, and 43-54, 67-78, and 63-74
are octaves... however, theyre not all sounded at once - the last two
chords are:

43-54-63-67-74-78 which "resolves" to
45-56-63-67-74-78 half way through the measure.

Removing octave redundancies this is

54-63-67 resolving to
56-63

So the final resolution is to a dyad, not a triad.
Now its time for me to scratch my head... what are these chords?
What are the roots? What kind of harmony is this?

--- In MakeMicroMusic@y..., sethares@e... wrote:

> 54-63-67 resolving to
> 56-63
>
> So the final resolution is to a dyad, not a triad.

Well, I heard a tetrad . . . aren't there other notes sustaining from
earlier soundings?

> Now its time for me to scratch my head... what are these chords?
> What are the roots? What kind of harmony is this?

56-63 would be, I presume, 7 steps of 11-tET . . . or 14 steps of 22-
tET . . . which is about 1 cent off a just 14:9. I said I heard a 7:9
on top, but of course one of your voices may easily have had an
octave transposition built into it or something . . .