TUNING digest 926

Op de Coul:

>Well, like Huygens was also involved with clocks, Harrison was also
>involved with tuning. His temperament has a fifth of 695.493 cents,
>almost 3/10-comma meantone. As such it offers a compromise between
>good minor thirds and good major thirds with the minor thirds about
>twice as good. The fifths are rather rough.

This is none other than the tuning that Charles Lucy has attached his name
to and has been trying to sell as a musical panacea for the past several years.
David B. Doty jinetwk@dnai.com
Just Intonation Network http://www.dnai.com/~jinetwk
Phone:(415) 824-5325 535 Stevenson Street
FAX: (415) 864-8726 San Francisco, CA 94103


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Daniel wrote:

> From what I have read, Lucy's own descriptions of ''his scale'' are
> deficient in many points, both mathematical and musical. His insistance
> that his scale has something to do with _pi_ is almost as perplexing as his
> failure to recognize that it has a lot to do with _phi_, ....

No it has. Harrison's major third is equal to 2^(1/pi) or 381.9719 cents.
The whole discussion started on 29-OCT-1994.

> Erv Wilson has pointed out that the reason tunings like these (Harrison,
> Lucy) are so pleasant despite the poor fifths is that the triads produce
> first order difference tones that are scale members.

The difference tones in Harrison's scale are not exactly on the mark.
A-C: 1.6030037 Hertz, 96.1802225 beats/min.
C-E: 3.2766052 Hertz, 196.5963142 beats/min.
ratio: 2.044041
I haven't read the article but I can get the reference if anyone wants it.
There is also something in Barbour's "Tuning and Temperament".

Manuel Op de Coul coul@ezh.nl

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Well, I think Dan's point is that Harrison's and Lucy's pi-based
definition has nebulous value to many microtonalists, except as a close
approximation to Erv Wilson's meta-meantone tuning. It's easy to imagine -
perhaps completely falsely - Harrison or Lucy thinking, "1/3 octave is just
too sharp for a major third. Hey I know, I'll use 1/pi instead! Pi's a
magic number!"

I personally am prone to go one step further: to attribute only limited
significance to Erv's meta-meantone definition as well, because,
1. Only occasionally do major triads get voiced as 4:5:6 approximations
with
no octave displacements or doubling,
2. At least in the definition alone, doesn't address how the harmonics of
those tones beat against each other, and
3. In most musical contexts, objective tones pretty much drown out
difference
tones anyway. I certainly do acknowledge a handful of important
exceptions, like solo duets on high-pitched instruments, but those are,
in
the big musical picture, exceptions.
Perhaps I'd change that opinion after working out the math of how
beat-frequencies are affected by harmonics, octave displacement, and
doubling.

But as I've said before, I certainly don't want my comments here to
discourage anybody from experimenting with LucyTuning. In my limited
experimentation with it, it struck me as perfectly reasonable and usable
tuning.

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