Dave Keenan's musical complexity

[Monzo:]
> I've always thought that 15/8
> is a pretty consonance in a chord -
> is it more, or less, consonant
> than 7/4?

[Hahn:]
> A 15/8 alone vs. a 7/4 alone?
> You better believe the 7/4 is more
> consonant!

I agree with that - I specifically said
"in a chord" because we were talking
about the possible influence of a
"numerary nexus" or common multiple
of a triad or higher-ad on the way
we perceive the consonance of the
chord as a whole and the individual
intervals within the chord:

[Wolf:]
>(5) Euler's _gradus suavatis_ function:
> [...]
> (c) for ratios:
> convert a ratio to a segment of the
> harmonic series, then compute the
> least common multiple of the terms.

I didn't *necessarily* mean "on top
of a major triad" - I like the
8:12:15:20 voicing even better myself.

(It's outside this particular question, but
another "major 7th" chord I like more and more,
with this same voicing, is 6:9:11:15, with
the 11/6 "neutral 7th".)

(Hey, you non-theory types: how's that for
adding a practical bit at the end of a
technical post?)

-monz

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hello Monzo

> [Monzo:]
>
> (It's outside this particular question, but
> another "major 7th" chord I like more and more,
> with this same voicing, is 6:9:11:15, with
> the 11/6 "neutral 7th".)

My favorite "major 7th" chord goes like this:

note c : e : g : b
common subharmonic ratio 4 : 5 : 6
common harmonics ratio 1/6 : 1/5 : 1/4
frequention (Hz) 264 : 330 : 396 : 495

My favorite "minor 7th" chord goes like this:

note a : c : e : g
common subharmonic ratio 4 : 5 : 6
common harmonics ratio 1/6 : 1/5 : 1/4
frequention (Hz) 220 : 264 : 330 : 396

Peter Mulkers (the scale-quitter)