User talk:Godtone: Difference between revisions

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: --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 13:20, 7 May 2026 (UTC)

:: I generally did not find missing information, problem is that I found too much of it, specially in 53edo.

:: The key points I believe you'd agree on:

::* Garibaldi is a natural extension of schismic.

::* 10/9 - 9/8 - 8/7 are made equidistant, and the distance is a 81/80 ~ 64/63 ~ pythcomma. 5120/5103 is tempered out.

::* 41edo and 53edo are the coarsest tunings to support it. Its choice depends on whether to optimize for prime 11 or prime 13.

::* 41edo has a hemififth 11/9~27/22, good 11-limit, bad 15/13, 13/10.

::* 53edo has a hemifourth ~15/13, great 2.3.5.13, bad 14/11; 11/9 and 27/22 are made too far apart.

::* Both support cassandra, which extends garibaldi equating 39/32~11/9, and (10/9)^2 = ~16/13. 352/351 and 325/324 are tempered out.

::* 94edo, their sum, is close to optimal for cassandra.

::* 135edo and 147edo also support cassandra but with more inconsistencies.

:: How can we express them with max concision? On the topic of S-expression, I can't agree that S-expressions are easier to remember than ratios... I don't chunk them, I have to parse them. 5120/5103, 225/224, 32805/32768, 531441/524288, all are to me as a single thing, alongside many other commas whose ratios, monzos, names I've memorized. I find ratios, monzos or names much easier to memorize (within reason), and I alternate between the three. --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 16:29, 7 May 2026 (UTC)

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 : --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 13:20, 7 May 2026 (UTC)
+:: I generally did not find missing information, problem is that I found too much of it, specially in 53edo.
+:: The key points I believe you'd agree on:
+::* Garibaldi is a natural extension of schismic.
+::* 10/9 - 9/8 - 8/7 are made equidistant, and the distance is a 81/80 ~ 64/63 ~ pythcomma. 5120/5103 is tempered out.
+::* 41edo and 53edo are the coarsest tunings to support it. Its choice depends on whether to optimize for prime 11 or prime 13.
+::* 41edo has a hemififth 11/9~27/22, good 11-limit, bad 15/13, 13/10.
+::* 53edo has a hemifourth ~15/13, great 2.3.5.13, bad 14/11; 11/9 and 27/22 are made too far apart.
+::* Both support cassandra, which extends garibaldi equating 39/32~11/9, and (10/9)^2 = ~16/13. 352/351 and 325/324 are tempered out.
+::* 94edo, their sum, is close to optimal for cassandra.
+::* 135edo and 147edo also support cassandra but with more inconsistencies.
+:: How can we express them with max concision? On the topic of S-expression, I can't agree that S-expressions are easier to remember than ratios... I don't chunk them, I have to parse them. 5120/5103, 225/224, 32805/32768, 531441/524288, all are to me as a single thing, alongside many other commas whose ratios, monzos, names I've memorized. I find ratios, monzos or names much easier to memorize (within reason), and I alternate between the three. --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 16:29, 7 May 2026 (UTC)