User:Eufalesio/Ultimate: Difference between revisions

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is 41&53&217, otherwise known by in the wiki as ''[[cassaschismic]]'' (technical info inside), but since this is my page I will simply call it '''~~ultimate~~'''. My reasoning of this will become clear. Or at least, I expect you to understand why it's clear in my mind.

is 41&53&217, otherwise known by in the wiki as ''[[cassaschismic]]'' (technical info inside), but since this is my page I will simply call it '''Ultimate'''. My reasoning of this will become clear. Or at least, I expect you to understand why it's clear in my mind.

== Quick definition ==

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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.

'''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.

'''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.

270edo and 311edo inherit a chain of fifths that is consistent with cassandra, which itself is an extension of the circle of fifths. The only adition is a single edostep, and respectively, the entire 13-limit is tuned to unfathomable precision, and the 41-limit is fully accessible and very well tuned. However, I prefer sticking to the 13-limit, so 270edo is an optimal equal tuning.

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217edo could ''in theory'' be used with binary valve or key systems in woodwinds, granted they have the intonation precision to reliably hit pitches within a maximum error of 2.7649 cents. Which I know won't happen. Best course would be to tune the instrument to 31edo plus a slide to nudge everything into the right place, but that's not ultimate. That's [[birds]].

=== 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 ==

Of all the equal tunings supported by Ultimate, the best ones are 94edo and 270edo. They have the key property of being even, and thus also tempers out the [[kalisma]], allowing the poma to be split in halves. Using them this way is reminiscent of [[Gariwizmic]], a very similar temperament to Ultimate, but with the minicomma found deep in the generator chain, not independent. This is useful for easier navigation within a DAW.

It's possible to use Gariwizmic wholesale, but I wouldn't recommend it. For that, Ultimate is a much better choice overall. Gariwizmic would only provide the structure, not the tuning.

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-is 41&53&217, otherwise known by in the wiki as ''[[cassaschismic]]'' (technical info inside), but since this is my page I will simply call it '''ultimate'''. My reasoning of this will become clear. Or at least, I expect you to understand why it's clear in my mind.
+is 41&53&217, otherwise known by in the wiki as ''[[cassaschismic]]'' (technical info inside), but since this is my page I will simply call it '''Ultimate'''. My reasoning of this will become clear. Or at least, I expect you to understand why it's clear in my mind.
 == Quick definition ==
@@ Line 138: / Line 138: @@
 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.
-'''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.
+'''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.
 edo and 311edo inherit a chain of fifths that is consistent with cassandra, which itself is an extension of the circle of fifths. The only adition is a single edostep, and respectively, the entire 13-limit is tuned to unfathomable precision, and the 41-limit is fully accessible and very well tuned. However, I prefer sticking to the 13-limit, so 270edo is an optimal equal tuning.
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 edo could ''in theory'' be used with binary valve or key systems in woodwinds, granted they have the intonation precision to reliably hit pitches within a maximum error of 2.7649 cents. Which I know won't happen. Best course would be to tune the instrument to 31edo plus a slide to nudge everything into the right place, but that's not ultimate. That's [[birds]].
+=== 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 ==
+Of all the equal tunings supported by Ultimate, the best ones are 94edo and 270edo. They have the key property of being even, and thus also tempers out the [[kalisma]], allowing the poma to be split in halves. Using them this way is reminiscent of [[Gariwizmic]], a very similar temperament to Ultimate, but with the minicomma found deep in the generator chain, not independent. This is useful for easier navigation within a DAW.
+It's possible to use Gariwizmic wholesale, but I wouldn't recommend it. For that, Ultimate is a much better choice overall. Gariwizmic would only provide the structure, not the tuning.