Re: [tuning-math] Digest Number 1348

hi guys,
how did i come up with 112 ?
I did not start with ratios.
i used the decimal values of the pure tones.
i then took note of the various distances between them
and then filled in notes at appropriate spots till all
the distances were equal. when this was achieved, the
count was 112.
am i clear in my explanation?
edb.
--- tuning-math@yahoogroups.com wrote:

> There are 3 messages in this issue.
>
> Topics in this digest:
>
> 1. Re: Digest Number 1346
> From: "Ozan Yarman"
> <ozanyarman@superonline.com>
> 2. Re: Digest Number 1346
> From: "hstraub64"
> <hstraub64@telesonique.net>
> 3. Re: Digest Number 1346
> From: "Paul Erlich"
> <perlich@aya.yale.edu>
>
>
>
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>
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>
> Message: 1
> Date: Mon, 25 Jul 2005 14:42:41 +0300
> From: "Ozan Yarman" <ozanyarman@superonline.com>
> Subject: Re: Digest Number 1346
>
> 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 #.
>
> [This message contained attachments]
>
>
>
>
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>
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>
> Message: 2
> Date: Mon, 25 Jul 2005 15:18:15 -0000
> From: "hstraub64" <hstraub64@telesonique.net>
> Subject: Re: Digest Number 1346
>
> --- 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
>
>
>
>
>
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>
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>
> Message: 3
> Date: Mon, 25 Jul 2005 20:39:27 -0000
> From: "Paul Erlich" <perlich@aya.yale.edu>
> Subject: Re: Digest Number 1346
>
> 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
>
>
>
>
>
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>
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--- In tuning-math@yahoogroups.com, elfdream baby <elfdreambaby@y...>
wrote:
> hi guys,
> how did i come up with 112 ?
> I did not start with ratios.
> i used the decimal values of the pure tones.
> i then took note of the various distances between them
> and then filled in notes at appropriate spots till all
> the distances were equal. when this was achieved, the
> count was 112.
> am i clear in my explanation?

Not really, as it is impossible to fill in the pure tones so that all
the distances are equal. You can do it in such a way that the
approximate distances are equal, by adjusting the pure tones a little,
but that hardly forces you to do it by dividing the octave in 112
equal parts.

> elfdream baby <elfdreambaby@y...> wrote:
>> hi guys,
>> how did i come up with 112 ?
>> I did not start with ratios.
>> i used the decimal values of the pure tones.
>> i then took note of the various distances between them
>> and then filled in notes at appropriate spots till all
>> the distances were equal. when this was achieved, the
>> count was 112.
>> am i clear in my explanation?
>
>Not really, as it is impossible to fill in the pure tones so that all
>the distances are equal. You can do it in such a way that the
>approximate distances are equal, by adjusting the pure tones a little,
>but that hardly forces you to do it by dividing the octave in 112
>equal parts.

More importantly, you forgot to tell us which "pure tones" you
used.

-Carl