User:Eufalesio/Ultimate: Difference between revisions

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However, if you forego p5 and p13 for the chain of fifths, you end up with [[gary]]. Gary is a serendipitious temperament, the same as cassandra but optimized for the [[zala]]. 135edo is an essentially perfect tuning, reaching sub-cent levels of error in the subgroup, with a poma of 26.<u>6</u> c.

Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent generator for p5 and p13, which acts as 385/384~352/351~5120/~~51023~~... etc, being around 4.4c; so I call it the "minicomma". It doesn't begin to make sense up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.

Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent generator for p5 and p13, which acts as 385/384~352/351~5120/5103... etc, being around 4.4c; so I call it the "minicomma". It doesn't begin to make sense up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.

'''The key reasons''' on why Ultimate is ultimate, is ultimately due to the fact that 270edo and 311edo are inside the supported equal tunings, because going any further would make the edosteps not discernible, and because no other edo in their vicinity is as good as them. Beyond that, I see no reason to use edos.

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=== Ultimate ''sensu stricto'' ===

It is possible to forego edos altogether and use Ultimate as is, providing the absolute best tuning possible. However, it's a rank-3 system. It has no extra unisons unlike the equal tunings. This is reserved for when 270edo is not just enough, and beating is something to avoid as much as possible.

== The special place of 94edo and 270edo ==

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 However, if you forego p5 and p13 for the chain of fifths, you end up with [[gary]]. Gary is a serendipitious temperament, the same as cassandra but optimized for the [[zala]]. 135edo is an essentially perfect tuning,  reaching sub-cent levels of error in the subgroup, with a poma of 26.<u>6</u> c.
-Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent generator for p5 and p13, which acts as 385/384~352/351~5120/51023... etc, being around 4.4c; so I call it the "minicomma". It doesn't begin to make sense up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.
+Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent generator for p5 and p13, which acts as 385/384~352/351~5120/5103... etc, being around 4.4c; so I call it the "minicomma". It doesn't begin to make sense up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.
 '''The key reasons''' on why Ultimate is ultimate, is ultimately due to the fact that 270edo and 311edo are inside the supported equal tunings, because going any further would make the edosteps not discernible, and because no other edo in their vicinity is as good as them. Beyond that, I see no reason to use edos.
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 === Ultimate ''sensu stricto'' ===
 It is possible to forego edos altogether and use Ultimate as is, providing the absolute best tuning possible. However, it's a rank-3 system. It has no extra unisons unlike the equal tunings. This is reserved for when 270edo is not just enough, and beating is something to avoid as much as possible.
 == The special place of 94edo and 270edo ==