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Dissonant triads in 12TET...is 12TET "half consonance/half dissonance" optimized for composition?

🔗Michael <djtrancendance@...>

1/19/2011 9:59:58 PM

Before I had posted....

So within a 5th interval the following chords from the same root, IMVHO, sound
dissonant in 12TET (9 of them):
C C# D#,
C C# E,
C C# G
C D# E.
C D# F# (diminished...relatively non-clustered)
C E F
C E F#, ("reverse diminished"...not sure of the formal name...relatively
non-clustered)
C F F#
C F# G
....................

Now here are a bunch of ones between the 5th and the octave (9 of them)
C F G#
C F# A (yay, more sour 12TET tritones)
C F# B
C G G#
C G# A
C G# B
C A A# (clusters)
C A B
C A# B
***********************************************

....and now...some with notes both above and below the octave (8 of them)
C C# G#
C C# A
C C# A#
C C# B
C D G#
C D# A
C F# A#
C F# B

That's about 26 "sour" triads total. And if my combinatorics calculations
serve me correctly, gives the root note in a dyad is fixed at C and the other 2
notes at other tones there are nCr = 11 choose 2 = 55 total combinations for
triads starting at C.
Which would make about 47% of the possible triads in 12TET dissonant and 53%
of them consonant...not far at all from a "perfect" 50/50 consonance/dissonance
distribution far as balanced musical options for both consonance and dissonance!
That is...unless you'd argue some of the triads I listed are consonant under
12TET...let me know if you think any of the above triads sound consonant. :-D

My point...is that composition-ally 12TET may well be favored not because it
is "uncannily consonant" (which it certainly is not)...but because it promotes a
fairly even distribution between consonant and dissonant options.

And that, perhaps, we should be on the lookout for microtonal scales and
tunings that feature similar balance far as compositional options for "tension
and resolve"...rather than use an excuse like "people dislike microtonal
scales...because of their unquenchable thirst for 12TET 'hyper-consonance' ".

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