Talk:Keemic temperaments: Difference between revisions
Created page with "== Pentadecal == The 11-limit extension is problematic and as we can see the other extension has much lower badness. This is becuz pentadecal tempers out 64827/64000 and suggests using the identity 64827/64000 = (121/120)⋅(441/440)<sup>2</sup>, which competes with the keemic path of extension using the identity 875/864 = (100/99)⋅(385/384), and is evidenced by the fact that both 45 and 60 are kinda dual-11 systems. Another problem is the extension of the other 11-l..." |
No edit summary |
||
| Line 1: | Line 1: | ||
== Pentadecal == | == Pentadecal and undeka == | ||
The 11-limit extension is problematic and as we can see the other extension has much lower badness. This is becuz pentadecal tempers out 64827/64000 and suggests using the identity 64827/64000 = (121/120)⋅(441/440)<sup>2</sup>, which competes with the keemic path of extension using the identity 875/864 = (100/99)⋅(385/384), and is evidenced by the fact that both 45 and 60 are kinda dual-11 systems. | The 11-limit extension of pentadecal is problematic and as we can see the other extension has much lower badness. This is becuz pentadecal tempers out 64827/64000 and suggests using the identity 64827/64000 = (121/120)⋅(441/440)<sup>2</sup>, which competes with the keemic path of extension using the identity 875/864 = (100/99)⋅(385/384), and is evidenced by the fact that both 45 and 60 are kinda dual-11 systems. | ||
Another problem is the extension of the other 11-limit extension to the 13-limit. It should be 15 & 45f. The 45f val should be used as it's significantly better, and of course 15 is better than 15f. This is the same mapping of 13 as the above 11-limit extension. Therefore only these two mappings are worth documenting: 15 & 45f and 15 & 45ef. | Another problem is the extension of the other 11-limit extension to the 13-limit. It should be 15 & 45f. The 45f val should be used as it's significantly better, and of course 15 is better than 15f. This is the same mapping of 13 as the above 11-limit extension. Therefore only these two mappings are worth documenting: 15 & 45f and 15 & 45ef. | ||
| Line 6: | Line 6: | ||
If we can't come up with appropriate names for them right now, I think both 11-limit extensions should be deleted and it should be presented as 2.3.5.7.13. | If we can't come up with appropriate names for them right now, I think both 11-limit extensions should be deleted and it should be presented as 2.3.5.7.13. | ||
—[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:19, 25 June 2026 (UTC) | Undeka is more naturally a no-13 17-limit temperament, so we should catalog it as such. | ||
—[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:19, 25 June 2026 (UTC) (last updated [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:40, 5 July 2026 (UTC)) | |||
Revision as of 10:40, 5 July 2026
Pentadecal and undeka
The 11-limit extension of pentadecal is problematic and as we can see the other extension has much lower badness. This is becuz pentadecal tempers out 64827/64000 and suggests using the identity 64827/64000 = (121/120)⋅(441/440)2, which competes with the keemic path of extension using the identity 875/864 = (100/99)⋅(385/384), and is evidenced by the fact that both 45 and 60 are kinda dual-11 systems.
Another problem is the extension of the other 11-limit extension to the 13-limit. It should be 15 & 45f. The 45f val should be used as it's significantly better, and of course 15 is better than 15f. This is the same mapping of 13 as the above 11-limit extension. Therefore only these two mappings are worth documenting: 15 & 45f and 15 & 45ef.
If we can't come up with appropriate names for them right now, I think both 11-limit extensions should be deleted and it should be presented as 2.3.5.7.13.
Undeka is more naturally a no-13 17-limit temperament, so we should catalog it as such.
—FloraC (talk) 11:19, 25 June 2026 (UTC) (last updated FloraC (talk) 10:40, 5 July 2026 (UTC))