Re: [tuning-math] Digest Number 1346

i mean Just tones (just intonation). 112 equal temp.hits them all perfectly. the only problem is what to do with such an unwieldy #.

tuning-math@yahoogroups.com wrote:There is 1 message in this issue.

Topics in this digest:

1. Re: Digest Number 1338
From: "Gene Ward Smith"

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Message: 1
Date: Sat, 23 Jul 2005 21:36:13 -0000
From: "Gene Ward Smith"
Subject: Re: Digest Number 1338

--- In tuning-math@yahoogroups.com, elfdream baby
wrote:
> why 112?
> according to my computations, 112 hits all the pure
> tones and is the lowest number to do so. perhaps i was
> off by one.

If you will explain what you count as a pure tone and how close you
need to come to hit one, we can find out. I dount 112 is optimal for
this, though it does make for a nice meantone via 65 steps out of 112.

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Have you tried setting the SCALA notation to e93? That way the 696.429 cents fifth of 112-tET is the generator with the correct notational scheme.

----- Original Message -----
From: elfdream baby
To: tuning-math@yahoogroups.com
Sent: 25 Temmuz 2005 Pazartesi 9:42
Subject: Re: [tuning-math] Digest Number 1346

i mean Just tones (just intonation). 112 equal temp.hits them all perfectly. the only problem is what to do with such an unwieldy #.

--- In tuning-math@yahoogroups.com, elfdream baby <elfdreambaby@y...>
wrote:
> i mean Just tones (just intonation). 112 equal temp.hits them all
> perfectly. the only problem is what to do with such an unwieldy #.
>

With "just intonation" you mean the intervals with low rational
numbers (3/2, 5/4 etc.)? These can never be hit perfectly by any equal
temperament since, in any equal temperament, all intervals (except
one) are irrational.
So what your computations gave you must be some kind of close
approximation. Smaller than 1 cent or something?
--
Hans Straub

Hi there elfdream baby,

Can you show your calculations? Gene and I have been doing these kinds
of calculations for decades and there also have been many papers
published on the topic. No one has found 112-equal to be very good. Of
course, no equal division of the octave will hit any Just ratios
perfectly (other than the octave), because the former consists only of
irrational frequency ratios, while the latter are rational frequency
ratios. Perhaps you meant "almost perfect" and have a very specific
conception of Just Intonation in mind? Please do share it.

Best,
Paul