Talk:Keemic temperaments: Difference between revisions

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== 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.

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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))

: I chose to keep quindecal but the 13-limit extension is now rectified. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:04, 7 July 2026 (UTC)

@@ 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.
@@ 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.
-—[[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))
+: I chose to keep quindecal but the 13-limit extension is now rectified. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:04, 7 July 2026 (UTC)