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Monzo's inversion similarity chords

🔗Peter Mulkers <P.Mulkers@xxx.xxxx>

3/10/1999 11:44:36 AM

Monzo,

Thanks for your reply.
I learned a few new terms more,
and a different kind of notation.

[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

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

[Monzo:]
>The utonal proportions are the inverse of the otonal

I want to ask you something more about these chords.
What's the common sound-appreciation *you* feel?
They feel all extremely static and tensionless to me.
As if they are in perfect balance.
What's the reason for this?
Can this lead us to discover the mystery of tension?
What are your main ideas about tension?

Peter Mulkers (the scale quitter)

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

3/11/1999 3:16:17 PM

>[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

Peter Mulkers wrote,

>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

>[Monzo:]
>>The utonal proportions are the inverse of the otonal

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.