Reply to Peter Mulkers

>> [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

That's the 8:10:12:15 (let's remove factors of two and call it 1:3:5:15)
chord that Joe Monzo and I were originally discussing in this thread.

>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

That's my favorite too, and it can be called 10:12:15:18 if you're used
to working with the harmonic series. My second-favorite minor 7th chord
is 12:14:18:21. Each of these minor seventh chords has all six intervals
within the 9-limit, and yet neither one is a subset of a 9-limit
otonality or utonality. I discoved this last year, and Graham Breed
added an 11-limit example, 18:22:27:33, which is not a subset of an
11-limit otonality or utonality. In a sense, these are the chords Partch
forgot (see Graham's page http://www.cix.co.uk/~gbreed/ass.htm).

>note e : g : bes : des
>common subharmonic 5 : 6 : 7
>common harmonic : 1/7 : 1/6 : 1/5
>otonal 25 : 30 : 35 : 42
>utonal 1/42 : 1/35 : 1/30 : 1/25

>Is this exact JI?

Yes, this is an exact, mirror-symmetrical JI chord. The outer interval,
42:25, can be turned into a consonant 5:3 without affecting the other
intervals much by putting the chord in meantone tuning (where it would
be spelled e g a# c#).