53edo: Difference between revisions
Get back prime table and +link to wikipedia |
|||
| Line 13: | Line 13: | ||
| Augmented 1sn = 5\53 ≈ 113¢ | | Augmented 1sn = 5\53 ≈ 113¢ | ||
}} | }} | ||
{{Wikipedia| 53 equal temperament }} | |||
The famous '''53 equal divisions of the octave''' ('''53edo'''), or '''53(-tone) equal temperament''' ('''53tet''', '''53et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 53 [[equal]] comma-sized parts of around 22.6 [[cent]]s each. | The famous '''53 equal divisions of the octave''' ('''53edo'''), or '''53(-tone) equal temperament''' ('''53tet''', '''53et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 53 [[equal]] comma-sized parts of around 22.6 [[cent]]s each. | ||
== Theory == | == Theory == | ||
53edo 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), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] (10485760000/10460353203). 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 [[Big Brother]] temperament, which tempers out both, as well as [[Semicomma family #Orwell|11-limit orwell temperament]], which also tempers out the 11-limit comma [[176/175]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[540/539]], [[625/624]], [[676/675]], and [[2080/2079]], and gives the optimal patent val for [[Marvel family #Athene|athene temperament]]. It is the seventh [[The Riemann Zeta Function and Tuning#Zeta EDO lists|strict zeta edo]] and the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]]. | 53edo 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), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] (10485760000/10460353203). 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 [[Big Brother]] temperament, which tempers out both, as well as [[Semicomma family #Orwell|11-limit orwell temperament]], which also tempers out the 11-limit comma [[176/175]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[540/539]], [[625/624]], [[676/675]], and [[2080/2079]], and gives the optimal patent val for [[Marvel family #Athene|athene temperament]]. It is the seventh [[The Riemann Zeta Function and Tuning#Zeta EDO lists|strict zeta edo]] and the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]]. | ||
| Line 24: | Line 23: | ||
It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit. | It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit. | ||
=== Prime harmonics === | |||
{{Primes in edo|53}} | |||
== Intervals == | == Intervals == | ||
| Line 874: | Line 876: | ||
| [[Untriton]] / [[aufo]] | | [[Untriton]] / [[aufo]] | ||
|} | |} | ||
== Music == | == Music == | ||
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3 Bach WTC1 Prelude 1 in 53] by Bach and [[Mykhaylo Khramov]] | * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3 Bach WTC1 Prelude 1 in 53] by Bach and [[Mykhaylo Khramov]] | ||
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3 Bach WTC1 Fugue 1 in 53] by Bach and Mykhaylo Khramov | * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3 Bach WTC1 Fugue 1 in 53] by Bach and Mykhaylo Khramov | ||