Re: Digest Number 89

[Mulkers, TD 89:]
> 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

Divide the "frequention" you gave by 33
and what do you get? 8:10:12:15, exactly
the chord Erlich was referring to when he
said 15/8 "on top of a major triad".

This is the "standard" 5-limit rationalization
of a "major 7th" chord.

Interestingly, if *all* of its members are measured
from a "common harmonic", the proportions are
exactly the inverse of the "common subharmonic"
proportions:

note c : e : g : b
common subharmonic 8 : 10 : 12 : 15
common harmonic 1/15 : 1/12 : 1/10 : 1/8

Although I've always thought it's a lovely
chord, and I use it a lot, I tend to prefer
its more exotic siblings, like the one I
mentioned in the post you quoted:

c : e : g : bV
12 : 15 : 18 : 22
4 : 5 : 6

(the "V" means roughly a quarter-tone flat, and
the chord is given here in its close position,
not the open one I described)

[Mulkers:]
> 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

Divide the frequencies here by 22, and measured
as an otonal proportion (i.e., from the bottom up),
this chord is 10:12:15:18 - again, the standard
5-limit "minor 7th" chord. And again, the
utonal proportions are the inverse of the otonal:

note a : c : e : g
common subharmonic 10 : 12 : 15 : 18
common harmonics 1/18 : 1/15 : 1/12 : 1/10

And again, this is nice, but try this beautiful
7-limit "minor 7th", which also has this
"inversion similarity" property (I give it
in both your type of measurements and mine):

note a : c : e : g
common subharmonic 1/9 : 1/7 : 1/6
common harmonic 6 : 7 : 9

common subharmonic 1/21 : 1/18 : 1/14 : 1/12
common harmonic 12 : 14 : 18 : 21

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html

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