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
--- 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 × 3^1 × 5^1) : (7^4) = 1.000 416
poppy(-seed komma) = 4375 / 4374 = (5^4 × 7^1):(2^1 × 3^7) = 1.000 229 -
metric (komma) = 250 047 / 250 000 = (3^6 × 7^3):(2^4 × 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 × 3^0 × 5^0 × 7^4:2^5 × 3^1 × 5^2 × 7^0=1,000 416. Es handelt sich hierbei um das so genannte (common) comma,
also das (gemeine) Komma.
* 4375:4374 = 2^0 × 3^0 × 5^4 × 7^1:2^1 × 3^7 × 5^0 × 7^0 ≤ 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.