Daquin CD

I am not holding a classical harpsichord CD in just intonation
in my hands every day, so here's the title. Highly recommended.

Louis-Claude Daquin: Premier Livre de Pie`ces de Clavecin,
Suites 1-4. Anne Robert, historical harpsichord Hemsch (1751).
BNL Productions, 1991, BNL 112809. Auvidis distribution. DDD 78'20"
Intonation pure.
Exactly which tuning is not specified. Anne Robert has also recorded
works of Balbastre (on CCS-ADDA) and Froberger (on BNL).

Manuel Op de Coul coul@ezh.nl

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On Mon, 23 Jun 1997, Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) wrote:

>The fact that octaves are often not equal to 2, but slightly more than 2,
>has nothing to do with harmonic series or inharmonic partials. The
>effect is most pronounced when sine waves are used; I believe a large
>experiment found that the average subject deemed two sine waves
>equivalent when they differed by 1209 cents. The typical 2nd harmonic of
>a piano string is more like 1203 cents.

I don't know about the structure of the ear, but that is an interesting
idea. However I do believe that in nature there are definite
frequencies at ratios near to but not exactly equal to 2.

One particularly interesting example is found in the periods of
revolution of 3 of the 4 Galilean satellites of Jupiter. They are all
being repelled by the action of tidal forces, with the strongest action
on the innermost. However as they get near to exact 1:2 ratios it sets
up a strong resonance which forces the next outer one away from an exact
1:2 resonance. The result is as follows:

Jupiter Satellite I II III

Period (days) 1.76913780 3.55118108 7.15455312
Frequency (nHz) 6542.21173 3259.21822 1617.72145

I - 2xII II - 2xIII
Beat frequency (nHz) 23.77530 23.77531

Ratio II/beat 137.0842 137.0841

The interesting thing is that not only are the beats between each
adjacent pair of satellites the same, but the ratio of these to the
middle satellite period of 137.0841 is very similar to a number found in
atomic physics called the fine structure constant which is 1/137.0360.

The two ratios II/I and III/II are 1206.3 and 1212.7 cents respectively.
It rather seems that nature likes to operate at a little distance from
exact resonance.

-- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory --
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm

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I have great difficulty with statements about a supposed preference for
stretched octaves. Once you get out of the ''piano zones'', the evidence
starts to collapse. My recent posting on Javanese gamelan was one examplethat showed a statistically equal preference for larger, just or smaller
octaves, and my experiences with other musics are similar - when the tuner
wants the octave to beat, it doesn't matter if it is because the octaves
are smaller or larger than a 2:1.

I asked the maker of my gamelan what he thought about the ''pleng'' tuning
for the octaves I had chosen. His reply was that, in effect, I had made aconsumer choice against a particular shimmering quality caused by beatingand that singers and rebab players would have to be more careful in the
upper register because of the unisons, but that the tuning was not an
unacceptable one. He added that the tuning was more restfull, more
''Javanese'' than ''Balinese''. So, the rationale he gave for the non-just
octaves was related to timbre and difficulty in performance due to a lackof fuzziness around the pitches, to some cultural referents, and not at all
to a intervallic preference for stretching. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
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