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7-limit comma name proposal

πŸ”—Gene Ward Smith <gwsmith@svpal.org>

10/3/2003 12:48:16 PM

Here are some proposed 7-limit interval names, where ennealimma has
been used as an organizing principle. The number at the top of the
comma classes is the number of 612-et steps. Any comments?

"super" = 2401/2400, "sub" = 2400/2401, "hyper" = 4375/4374, "hypo" =
4374/4375

61
15/14 oversemitone

57
16/15 semitone

43
21/20 undersemitone

36
25/24 chroma

25
1029/1000 superquartone
250/243 hyperquartone
36/35 quartone

18
49/48 major semichroma
50/49 minor semichroma

15
3125/3072 overseptimum

14
686/675 superseptimum
64/63 septimum

11
875/864 hyperdidymus
81/80 didymus

10
2048/2025 diaschisma

7
245/243 hypersemiseptimum
126/125 semiseptimum
4000/3969 hyposemisemptmum
1728/1715 subsemisemptimum

4
1029/1024 superkleis
15625/15552 kleisma (hyperkleis)
225/224 kleis
19683/19600 hypokleis
16875/16807 subkleis

3
3136/3125 superbeta
5120/5103 hyperbeta
6144/6125 beta

1
65625/65536 hyperschisma
32805/32768 schisma

πŸ”—Andreas Sparschuh <a_sparschuh@...>

3/4/2009 12:52:53 PM

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@...> wrote:
>
> Here are some proposed 7-limit interval names,
... Any comments?
>
> "super" = 2401/2400, "sub" = 2400/2401,
or
http://hexadecimal.florencetime.net/from_Nippur_cubit_to_Viennese_ell.htm

Three 7-smooth kommata of Ratios in 7-smooth factors
Value

(commun) komma = 2400/2401 = (2^5 ÃΒ— 3^1 ÃΒ— 5^1) : (7^4) = 1.000 416

poppy(-seed komma) = 4375 / 4374 = (5^4 ÃΒ— 7^1):(2^1 ÃΒ— 3^7) = 1.000 229 -

metric (komma) = 250 047 / 250 000 = (3^6 ÃΒ— 7^3):(2^4 ÃΒ— 5^6)=1.000 188

http://en.wikipedia.org/wiki/Ragisma
>"hyper" = 4375/4374, "hypo" = 4374/4375

also found in the German defintion of length etalons
http://de.wikipedia.org/wiki/Vormetrische_L%C3%A4ngenma%C3%9Fe
as
"
* 2401:2400 = 2^0 ÃΒ— 3^0 ÃΒ— 5^0 ÃΒ— 7^4:2^5 ÃΒ— 3^1 ÃΒ— 5^2 ÃΒ— 7^0=1,000 416. Es handelt sich hierbei um das so genannte (common) comma,
also das (gemeine) Komma.
* 4375:4374 = 2^0 ÃΒ— 3^0 ÃΒ— 5^4 ÃΒ— 7^1:2^1 ÃΒ— 3^7 ÃΒ— 5^0 ÃΒ— 7^0 âΒ‰¤ 1,000 229. Es handelt sich hierbei um das so genannte "poppy-seed-comma",
also das Mohnkorn-Komma.

or also used in Carolingian coinmaking
http://de.wikipedia.org/wiki/Karlspfund
"So gelten bei den Längenmaßen z.B. 1/2400 oder 1/4374, also die 7-glatten Ratios 2401 : 2400 und 4375 : 4374, sowie ihre Reziprokwerte nicht als eigentliche Ratios, sondern nur als Kommata. "
tr:
'The gained precision of accuracy 1/2400 or 1/4373 depends
on the the 7-smooth ratios 2401:2400 and 4375:4374,
and theirs reciprocal values, not considered as actual ratios,
but only as commata.'

> 64/63 septimum
http://en.wikipedia.org/wiki/Septimal_comma

bye
A.S.