Reply to Paul H. Erlich

>>> [Monzo:]
>>> 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
>>>
>>> note a : c : e : g
>>> common subharmonic 10 : 12 : 15 : 18
>>> common harmonic 1/18 : 1/15 : 1/12 : 1/10
>>>
>>> note a : c : e : g
>>> common subharmonic 12 : 14 : 18 : 21
>>> common harmonic 1/21 : 1/18 : 1/14 : 1/12

>> [Mulkers:]
>> I like to add this "diminished" to make it complete:
>> note c : es : ges : a
>> common subharmonic 10 : 12 : 14 : 17
>> common harmonic 1/17 : 1/14 : 1/12 : 1/10

> [Erlich:]
> Note that while Monzo's chords are exact JI chords, Mulkers' diminished
> 7th is only an approximation. A just 10:12:14:17 is not exactly
> 1/17:1/14:1/12:1/10, and vice versa.

[Mulkers:]
I made a mistake. You're right. It's not exact JI.
By the way, the traditional diminished 7th like we know
I think it's an ET4. Am I right?
In fact, I had another chord in mind.
The way I like to notate it, I make less mistakes,
And you can easily see the simplicity of the chord.

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?
I'm looking out for some reply about the
sound appreciation of this kind of chords.

Peter Mulkers