User:Eufalesio/Ultimate: Difference between revisions

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The most error you'll get with this system resides in the chain of fifths (~+0.25c), having all other primes accurate to hundreds of a cent. This is in a sense is reminiscent of [[septimal meantone]], which can tune p5 and p7 near-pure by adding error to the fifth chain.

== The special place of 41edo, 94edo and 270edo ==

== The special place of 41edo, 53edo, 94edo and 270edo ==

41edo is the coarsest cassandra edo, with a high ratio of accuracy to simplicity, and being the first ever edo to be distinctly consistent in the 9-odd-limit, making the most out of the next convergent chain of fifths. 94edo is arguably the best cassandra edo, making the most out of the chain of fifths; while more complex it can be extended to the 23-odd-limit; which could be useful to some. Not me.

41edo is the coarsest cassandra edo, with a high ratio of accuracy to simplicity, and being the first ever edo to be distinctly consistent in the 9-odd-limit, making the most out of the next convergent chain of fifths, and supplying

53edo is the second coarsest, being better at some things 41edo is worse, and viceversa. It notably is extremely good in the yatha, with a fairly decent yazatha. It is also one of the best schismic temperaments, with nothing better than it except for 118edo and 171edo. Anything that doesn't use too many 11's and doesn't make much emphasis on 7's, can easily be done with 53edo.

94edo is arguably the best cassandra edo, making the most out of the chain of fifths; while more complex it can be extended to the 23-odd-limit; which could be useful to some. Not me. When the whole 13-limit or 19-limit is desired, better to use 94edo to have everything decently well tuned.

270edo is well known for its unbeatable 13-limit, for which, arguably, no other edo finer or coarser comes even close to its ratio of accuracy to "simplicity". It also technically has some useful interpretations for up to the [[53-limit]] which could be even more useful than that of 311edo, as seen by people like [[Godtone]].

41edo is particularly interesting because joining it with 270edo results in [[newt]], an extremely accurate rank 2 microtemperament of Ultimate that is practically indistinguishable from it. Instead of halving the poma, it halves the fifth, finding the MC "generator" at -41 generators, which firmly places this as a 41edo [[well temperament]].

41edo is particularly interesting because joining it with 270edo results in [[newt]], an extremely accurate rank 2 microtemperament of Ultimate that is practically indistinguishable from it. Instead of halving the poma, it halves the fifth, finding the MC "generator" at -41 generators, which firmly places this (including Ultimate) as a 41edo [[well temperament]].

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 The most error you'll get with this system resides in the chain of fifths (~+0.25c), having all other primes accurate to hundreds of a cent. This is in a sense is reminiscent of [[septimal meantone]], which can tune p5 and p7 near-pure by adding error to the fifth chain.
-== The special place of 41edo, 94edo and 270edo ==
+== The special place of 41edo, 53edo, 94edo and 270edo ==
-edo is the coarsest cassandra edo, with a high ratio of accuracy to simplicity, and being the first ever edo to be distinctly consistent in the 9-odd-limit, making the most out of the next convergent chain of fifths. 94edo is arguably the best cassandra edo, making the most out of the chain of fifths; while more complex it can be extended to the 23-odd-limit; which could be useful to some. Not me.
+edo is the coarsest cassandra edo, with a high ratio of accuracy to simplicity, and being the first ever edo to be distinctly consistent in the 9-odd-limit, making the most out of the next convergent chain of fifths, and supplying
+edo is the second coarsest, being better at some things 41edo is worse, and viceversa. It notably is extremely good in the yatha, with a fairly decent yazatha. It is also one of the best schismic temperaments, with nothing better than it except for 118edo and 171edo. Anything that doesn't use too many 11's and doesn't make much emphasis on 7's, can easily be done with 53edo.
+edo is arguably the best cassandra edo, making the most out of the chain of fifths; while more complex it can be extended to the 23-odd-limit; which could be useful to some. Not me. When the whole 13-limit or 19-limit is desired, better to use 94edo to have everything decently well tuned.
 edo is well known for its unbeatable 13-limit, for which, arguably, no other edo finer or coarser comes even close to its ratio of accuracy to "simplicity". It also technically has some useful interpretations for up to the [[53-limit]] which could be even more useful than that of 311edo, as seen by people like [[Godtone]].
-edo is particularly interesting because joining it with 270edo results in [[newt]], an extremely accurate rank 2 microtemperament of Ultimate that is practically indistinguishable from it. Instead of halving the poma, it halves the fifth, finding the MC "generator" at -41 generators, which firmly places this as a 41edo [[well temperament]].
+edo is particularly interesting because joining it with 270edo results in [[newt]], an extremely accurate rank 2 microtemperament of Ultimate that is practically indistinguishable from it. Instead of halving the poma, it halves the fifth, finding the MC "generator" at -41 generators, which firmly places this (including Ultimate) as a 41edo [[well temperament]].
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