> 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.