202edo: Difference between revisions

Line 3:

== Theory ==

202et [[tempering out|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.

202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]] (which explains why 11/9 is inconsistently sharp).

202et [[tempering out|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]], equating a stack of 5 [[33/32]] quarter tones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, wich also tempers out [[540/539]], and the rank-4 rastmic temperament tempering out 243/242.

It extends less well to the [[13-limit]], with harmonic [[13/1|13]] being about halfway between its steps. Nonetheless, the patent val tempers out 351/350, 364/363, 676/675, 729/728, and 2080/2079, supporting [[Breed family#Jovial|jovial]] and [[Breed family#Jovis|jovis]], as well as 13-limit [[harry]].

=== Prime harmonics ===

Line 9:

Line 13:

=== Subsets and supersets ===

Since 202 factors into {{factorization|202}}, 202edo contains [[2edo]] and [[101edo]] as its subsets.

== Regular temperament properties ==

@@ Line 3: / Line 3: @@
 == Theory ==
-et [[tempering out|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.
+edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]] (which explains why 11/9 is inconsistently sharp).
+et [[tempering out|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]], equating a stack of 5 [[33/32]] quarter tones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, wich also tempers out [[540/539]], and the rank-4 rastmic temperament tempering out 243/242.
+It extends less well to the [[13-limit]], with harmonic [[13/1|13]] being about halfway between its steps. Nonetheless, the patent val tempers out 351/350, 364/363, 676/675, 729/728, and 2080/2079, supporting [[Breed family#Jovial|jovial]] and [[Breed family#Jovis|jovis]], as well as 13-limit [[harry]].
 === Prime harmonics ===
@@ Line 9: / Line 13: @@
 === Subsets and supersets ===
 Since 202 factors into {{factorization|202}}, 202edo contains [[2edo]] and [[101edo]] as its subsets.
 == Regular temperament properties ==