53edo: Difference between revisions
+Temperament measures |
Intro, minor cleanup and correction |
||
| Line 4: | Line 4: | ||
| es = | | es = | ||
| ja = | | ja = | ||
}} | }} | ||
The famous ''53 equal division'' divides the octave into 53 equal comma-sized parts of 22.642 cents each. | |||
== Theory == | == Theory == | ||
It is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the [[schisma]], 32805/32768, the [[kleisma]], 15625/15552, the [[amity comma]], 1600000/1594323 and the [[semicomma]], 2109375/2097152. In the 7-limit it tempers out 225/224, [[1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family #Orwell|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 275/273, and gives the optimal patent val for [[Marvel_family #Athene|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo]] and coming before [[59edo]]. | |||
53EDO has also found a certain dissemination as an EDO tuning for [[Arabic,_Turkish,_Persian|Arabic/Turkish/Persian music]]. | 53EDO has also found a certain dissemination as an EDO tuning for [[Arabic,_Turkish,_Persian|Arabic/Turkish/Persian music]]. | ||
| Line 613: | Line 615: | ||
| C upmajor or C up | | C upmajor or C up | ||
|} | |} | ||
For a more complete list, see [[Ups and Downs Notation# | For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]]. | ||
== Relationship to 12-edo == | == Relationship to 12-edo == | ||
| Line 663: | Line 665: | ||
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. | One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds. | ||
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[ | The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224. | ||
=== Selected just intervals by error === | === Selected just intervals by error === | ||
| Line 836: | Line 838: | ||
== Linear temperaments == | == Linear temperaments == | ||
[[List of edo-distinct 53et rank two temperaments]] | * [[List of edo-distinct 53et rank two temperaments]] | ||
== Music == | == Music == | ||