Groven and 171-tone equal temperament?

I remember, years ago, reading the New Grove entry on microtonality, to find
one composer listed as using 171-tone equal temperament. My best
recollection was that is was Groven, but after years of hearing Groven
referred to as a 36-tone JI composer, I tried to flush that from my memory.
So now it turns out that Groven used 1/8-schisma temperament. Well, a
1/8-schisma tempered fifth is 701.711 cents, while 100/171 octave is 701.754
cents. Close enough, but the questions remain: Did New Grove actually say
that? If so, did they get it from something Groven actually said or wrote,
or did someone else note this approximation? 118-tone equal temperament
comes closer, with a fifth of 701.695 cents, so where did 171-tET come from
(if not my own confusion)?

To tuning listers: this is of interest partially to fill out Joe Monzo's ET
table, and partially because 171 (along with 22) just came up as the most
common periodicity block size using Fokker's unison vectors of 225:224 or
smaller. Also, 171-tET has a maximum error of 0.40 cents in the 9-limit,
making it the lowest ET to improve on 99-tET's figure of 2.15 cents. In fact
171 is best for its size for the 7-limit and even the 5-limit (just barely
beating 118), but not the 3-limit, where 53 is better. Wildly speculating
(given his interest in the seljefl�yte): maybe Groven chose 171 over 118
because 171 is consistent through the 13-limit while 118 is consistent only
though the 11-limit?

> [Paul Erlich, TD 309.10]
>
> Wildly speculating (given his interest in the seljefl�yte):
> maybe Groven chose 171 over 118 because 171 is consistent
> through the 13-limit while 118 is consistent only though
> the 11-limit?

Bravo, Paul! I think you may be on to something here.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
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| - Erv Wilson |
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I wrote,

>> Wildly speculating (given his interest in the seljefl�yte):
>> maybe Groven chose 171 over 118 because 171 is consistent
>> through the 13-limit while 118 is consistent only though
>> the 11-limit?

Joe Monzo wrote,

>Bravo, Paul! I think you may be on to something here.

Apparently not. David Code, who maintains the Groven site, says Groven never
mentioned 171-tET and Code couldn't even find 171-tET mentioned in the New
Grove. I'm sure I saw it in the New Grove once -- must have been a different
edition.

I don't have a copy of Grove's Dictionary of Music and Musicians in any edition among the books in my music library, as best as I can recall. It is over a thousand dollars new, as I recall from receiving ads to buy it. I wouldn't be inclined to trust it for accuracy in such heavy math in any case, but might refer to a regional library's copy if I needed to, which I have done in the past, to resolve the difference between Guiseppe and Umberto Giordano, for instance. I don't recall anyone else referring to a scale, theoretical or otherwise, with that many tones per octave.

>>> "Paul H. Erlich" <PErlich@Acadian-Asset.com> 09/13 4:27 PM >>>
From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

I wrote,

>> Wildly speculating (given his interest in the seljefl�yte):
>> maybe Groven chose 171 over 118 because 171 is consistent
>> through the 13-limit while 118 is consistent only though
>> the 11-limit?

Joe Monzo wrote,

>Bravo, Paul! I think you may be on to something here.

Apparently not. David Code, who maintains the Groven site, says Groven never
mentioned 171-tET and Code couldn't even find 171-tET mentioned in the New
Grove. I'm sure I saw it in the New Grove once -- must have been a different
edition.

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On Mon, 13 Sep 1999, John F. Sprague wrote:
> I don't have a copy of Grove's Dictionary of Music and Musicians in
> any edition among the books in my music library, as best as I can
> recall.

I have it here at work, but I have to get going. I'll look tomorrow--
but I'll tell you now that I've read just about all the entries I can
find in Grove about any tuning or temperament related subjects, and I
don't remember any mention of any ETs as high as 171.

--pH <manynote@library.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Do you like to gamble, Eddie?
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