205edo: Difference between revisions

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== Theory ==

205edo can serve as a tuning for various temperaments, such as [[~~Ragismic microtemperaments #Amity|~~amity]] or [[~~Hemifamity family #Laka|~~laka]], and supplies the [[optimal patent val]] for [[~~Hemifamity temperaments #Quanic|~~quanic]] in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, [[640/637]], the rank ~~five~~ temperament for which it also supplies the optimal patent val.

205edo can serve as a tuning for various temperaments, such as [[amity]] or [[laka]], and supplies the [[optimal patent val]] for [[quanic]] in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, [[640/637]], the rank-5 temperament for which it also supplies the optimal patent val.

In the 5-limit it tempers out 1600000/1594323, the [[amity comma]], and {{monzo| 38 -2 -15 }}, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out [[4375/4374]], [[5120/5103]], [[6144/6125]] ~~and~~ [[540/539]]. Using its alternative mapping {{val| 205 325 476 575 }} (205d) it can also be used for [[~~Gamelismic clan #Hemithirds|~~hemithirds ~~temperament~~]]~~; the~~ 13-limit version of this, {{val| 205 325 476 575 709 759 }} (205d), is especially noteworthy~~. It factors into primes as 5 × 41~~, ~~a fact some advocates of the division make use of;~~ it ~~is also 2460~~/~~12, so that a single step is precisely 12~~ [[~~mina~~]]s.

In the 5-limit it tempers out 1600000/1594323, the [[amity comma]], and {{monzo| 38 -2 -15 }}, the [[hemithirds comma]], and is an excellent tuning for 5-limit amity. The [[patent val]] {{val| 205 325 476 576 }} tempers out [[4375/4374]], [[5120/5103]], [[6144/6125]] in the 7-limit; [[540/539]], 1331/1323, and 2420/2401 in the 11-limit. Using its alternative mapping {{val| 205 325 476 '''575''' }} (205d) it can also be used for [[hemithirds]] temperament, where it tempers out 385/384 and 441/440. The 13-limit version of this, {{val| 205 325 476 575 709 759 }} (205d), is especially noteworthy, where it tempers out [[196/195]] and [[1001/1000]].

205et tempers out 540/539, so that it allows [[swetismic chords]]; 640/637, so that it allows [[huntmic chords]]; 352/351, so that it allows [[minthmic chords]]; 1188/1183 and 540/539, so that it allows [[kestrel chords]]; and 847/845, so that it allows the [[cuthbert triad]]. This makes it a tuning of exceptional fludity for its degree of accuracy.

205et tempers out [[540/539]], so that it allows [[swetismic chords]]; [[640/637]], so that it allows [[huntmic chords]]; [[352/351]], so that it allows [[minthmic chords]]; [[1188/1183]] and 540/539, so that it allows [[kestrel chords]]; and [[847/845]], so that it allows the [[cuthbert triad]]. This makes it a tuning of exceptional fludity for its degree of accuracy.

=== Prime ~~intervals~~ ===

205 factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina]]s.

=== Prime harmonics ===

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 == Theory ==
-edo can serve as a tuning for various temperaments, such as [[Ragismic microtemperaments #Amity|amity]] or [[Hemifamity family #Laka|laka]], and supplies the [[optimal patent val]] for [[Hemifamity temperaments #Quanic|quanic]] in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, [[640/637]], the rank five temperament for which it also supplies the optimal patent val.
+edo can serve as a tuning for various temperaments, such as [[amity]] or [[laka]], and supplies the [[optimal patent val]] for [[quanic]] in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, [[640/637]], the rank-5 temperament for which it also supplies the optimal patent val.
-In the 5-limit it tempers out 1600000/1594323, the [[amity comma]], and {{monzo| 38 -2 -15 }}, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[540/539]]. Using its alternative mapping {{val| 205 325 476 575 }} (205d) it can also be used for [[Gamelismic clan #Hemithirds|hemithirds temperament]]; the 13-limit version of this, {{val| 205 325 476 575 709 759 }} (205d), is especially noteworthy. It factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina]]s.
+In the 5-limit it tempers out 1600000/1594323, the [[amity comma]], and {{monzo| 38 -2 -15 }}, the [[hemithirds comma]], and is an excellent tuning for 5-limit amity. The [[patent val]] {{val| 205 325 476 576 }} tempers out [[4375/4374]], [[5120/5103]], [[6144/6125]] in the 7-limit; [[540/539]], 1331/1323, and 2420/2401 in the 11-limit. Using its alternative mapping {{val| 205 325 476 '''575''' }} (205d) it can also be used for [[hemithirds]] temperament, where it tempers out 385/384 and 441/440. The 13-limit version of this, {{val| 205 325 476 575 709 759 }} (205d), is especially noteworthy, where it tempers out [[196/195]] and [[1001/1000]].
-et tempers out 540/539, so that it allows [[swetismic chords]]; 640/637, so that it allows [[huntmic chords]]; 352/351, so that it allows [[minthmic chords]]; 1188/1183 and 540/539, so that it allows [[kestrel chords]]; and 847/845, so that it allows the [[cuthbert triad]]. This makes it a tuning of exceptional fludity for its degree of accuracy.
+et tempers out [[540/539]], so that it allows [[swetismic chords]]; [[640/637]], so that it allows [[huntmic chords]]; [[352/351]], so that it allows [[minthmic chords]]; [[1188/1183]] and 540/539, so that it allows [[kestrel chords]]; and [[847/845]], so that it allows the [[cuthbert triad]]. This makes it a tuning of exceptional fludity for its degree of accuracy.
-=== Prime intervals ===
+factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 [[mina]]s.
+=== Prime harmonics ===
 {{Primes in edo|205}}