Re: [tuning] bridges to 19/16

> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, August 09, 2001 10:34 AM
> Subject: [tuning] bridges to 19/16 (was: Higher primes, not Greek)
>
>
> And centuries or possibly millennia before Eratosthenes,
> a music-theorist analyzing 19-limit ratios would have found
> that 19/16 is very nearly the same as the common Pythagorean
> "minor 3rd" with the ratio 32/27. This is another 3==19 bridge
> which is a little over twice the size of Eratosthenes's
> (or about 3&1/3 cents).
>
>
> ratio ~cents delta cents
> of 19/16 from this
>
> 2^(3/12) 1.189207115 300 -2.486983868
> 19/16 1.1875 297.5130161
> 32/27 1.185185185 294.1349974 3.378018728

I had intended to include the ratio of the (32/27)==(19/16) bridge:
it's 513/512, calculated in fraction and prime-factor forms as follows:

2 3 19

19/16 |-4 0 1|
/ 32/27 - | 5 -3 0|
------- ------------
513/512 |-9 3 1|

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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Hi, Joe! I knew I could depend on an incredibly erudite response from
you (chuckle)! Very much appreciated, too. Clearly out of my element
on much of the history regarding these tuning issues. In response to
your feedback, I probably should temper (ha-ha!) my phraseology,
namely "virtually universal acceptance" (of 12t-ET).

I simply refer to the 19th-century period in which some of the major
romantics like Schubert and Brahms frequently used enharmonic
modulations that don't really work in justly tuned harmonies. I
assumed that 12 EDO was behind that, and this is when the minor mode
began to be used with greater frequency (which seems subjectively
true to me just from musical exposure to the period, but don't ask me
to document that, since I'm explicitly quoting here from the
assessments of my acquaintance precisely to elicit this kind of
feedback, Joe).

Also I wasn't trying to establish that this period represented the
first instances of such intervals. Only pointing to the alleged
synchronicity among various phenomena such as increased use of 12 EDO
tuning, a sudden surge in using the minor mode, and frequent use of
enharmonic modulations, especially those based on the ambiguity of
diminished 7ths in 12t-ET, thereby clearly implicating it.

A correction to an earlier statement of mine in this thread:
"This 16:20:24 triad is not as stable to my ear as the ET virtually
perfect 16:19:24 triad for this very reason, I would conjecture."

The 16:20:24 ratios constitute a MAJOR triad and not the 6:5 minor
3rd of the just minor triad. I should have said 10:12:15 instead of
16:20:24 so the corrected statement reads:

This 10:12:15 triad is not as stable to my ear as the ET virtually
perfect 16:19:24 triad for this very reason, I would conjecture.

--- In tuning@y..., BobWendell@t... wrote:
>
> I simply refer to the 19th-century period in which some of the
major
> romantics like Schubert and Brahms frequently used enharmonic
> modulations that don't really work in justly tuned harmonies. I
> assumed that 12 EDO was behind that,

I don't think your assumption can be very far off here. Like you, I
also don't see what Monz was "disagreeing" with -- it seems he was
talking about a different issue entirely.