152-EDO as adaptive-JI (was: IM conversation with Monz)

> From: monz <joemonz@yahoo.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Thursday, January 31, 2002 1:33 AM
> Subject: Re: [tuning-math] IM conversation with Monz
>
>
> That's cool! So in other words, a 38-tone subset of 152-EDO would
> give you a nice adaptive-JI based on 1/3-comma meantone?

Oops ... I should have been more specific. I meant a 38-tone
subset of 152-EDO which is two 19-EDOs, ~1/3-comma apart.

And 2^(1/152) is ~1/3-comma.

So it's two 19-EDOs which are one 152-EDO degree apart.

Got it. AWESOME! Now *THIS* looks like a tuning I'd like
to explore more!!

-monz

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> From: monz <joemonz@yahoo.com>
> To: <tuning-math@yahoogroups.com>
> Sent: Thursday, January 31, 2002 2:02 AM
> Subject: [tuning-math] 152-EDO as adaptive-JI (was: IM conversation with
Monz)
>
>
> > [me, monz]
> > That's cool! So in other words, a 38-tone subset of 152-EDO would
> > give you a nice adaptive-JI based on 1/3-comma meantone?
>
>
> Oops ... I should have been more specific. I meant a 38-tone
> subset of 152-EDO which is two 19-EDOs, ~1/3-comma apart.
>
> And 2^(1/152) is ~1/3-comma.
>
> So it's two 19-EDOs which are one 152-EDO degree apart.
>
> Got it. AWESOME! Now *THIS* looks like a tuning I'd like
> to explore more!!

Ah ... 152-EDO gets more and more interesting the more I look
at it!

So, since 19-EDO is a meantone, the lattice wraps into a cylinder.

And since 1 step of 152-EDO is ~1/3-comma, you only need *3*
chains of 19-EDO each separated by 1 step of 152-EDO, in order
to represent the entire infinite JI lattice! And you don't
get comma problems! *WAY* cool !!!!!!

So the 57-tone subset of 152-EDO which is three 19-EDOs starting
on the 1st, 2nd, and 3rd 152-EDO degrees is really some sort of
magical tuning for us adaptive-JI fans!

It looks like this might be the tuning I've been looking for
for my Mahler retunings. Thanks BIGTIME, Paul!

-monz

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--- In tuning-math@y..., "monz" <joemonz@y...> wrote:

> Ah ... 152-EDO gets more and more interesting the more I look
> at it!
>
> So, since 19-EDO is a meantone, the lattice wraps into a cylinder.
>
> And since 1 step of 152-EDO is ~1/3-comma, you only need *3*
> chains of 19-EDO each separated by 1 step of 152-EDO, in order
> to represent the entire infinite JI lattice! And you don't
> get comma problems! *WAY* cool !!!!!!

Umm, something slipped up somewhere. Each 19-tET chain itself
represents the entire JI lattice already. But if you want larger and
larger chords in JI, you need more and more of the 19-tET chains.
Nothing special happens when you have 3 chains.

> So the 57-tone subset of 152-EDO which is three 19-EDOs starting
> on the 1st, 2nd, and 3rd 152-EDO degrees is really some sort of
> magical tuning for us adaptive-JI fans!

Nope. You need as many 19-tET chains as the piece dictates.