253edo: Difference between revisions

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'''~~253EDO~~''' is the [[EDO|equal division of the octave]] into 253 parts of 4.743083 [[cent]]s each. It's consistent to the 17-limit, approximating the fifth by ~~'''~~148\253~~'''~~ (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[~~Schismatic_family|~~sesquiquartififths]] temperament.

'''253edo''' is the [[EDO|equal division of the octave]] into 253 parts of 4.743083 [[cent]]s each. It is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. It tempers out [[32805/32768]] in the 5-limit; [[2401/2400]] in the 7-limit; [[385/384]], 1375/1372 and [[4000/3993]] in the 11-limit; [[325/324]], [[1575/1573]] and [[2200/2197]] in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[sesquiquartififths]] temperament.

~~<u>'''~~253 ~~tone equal modes:'''</u>~~

253 = 11 × 23, and has subset edos [[11edo]] and [[23edo]].

~~63 32 63 63 32: [[3L_2s~~|~~Pentatonic]]~~

=== Prime harmonics ===

43 43 19 43 43 43 19: [[5L_2s|Pythagorean tuning]]

== Scales ==

* 63 32 63 63 32: [[3L_2s|Pentatonic]]

* 43 43 19 43 43 43 19: [[5L_2s|Pythagorean tuning]]

* 41 41 24 41 41 41 24: [[Meantone|Meantonic tuning]]

* 35 35 35 35 35 35 35 8: [[7L_1s|Porcupine tuning]]

* 33 33 33 11 33 33 33 33 11: [[23edo|"The Hendecapliqued superdiatonic of the Icositriphony"]]

* 31 31 31 18 31 31 31 31 18: [[7L_2s|Superdiatonic tuning]] in the way of Mavila

* 26 26 15 26 26 26 15 26 26 26 15: [[sensi11|Sensi tuning]]

* 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L_3s|Ketradektriatoh tuning]]

~~41 41 24 41 41 41 24: [[Meantone|Meantonic tuning]]~~

~~35 35 35 35 35 35 35 8: [[7L_1s|Porcupine tuning]]~~

~~33 33 33 11 33 33 33 33 11: [[23edo|"The Hendecapliqued superdiatonic of the Icositriphony"]]~~

~~31 31 31 18 31 31 31 31 18: [[7L_2s|Superdiatonic tuning]] in the way of Mavila~~

~~26 26 15 26 26 26 15 26 26 26 15: [[sensi11|Sensi tuning]]~~

~~20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L_3s|Ketradektriatoh tuning]]~~

~~'''PRIME FACTORIZATION:'''~~

~~253 = [[11edo|11]] * [[23edo|23]]~~

[[Category:Equal divisions of the octave]]

[[Category:~~modes]]~~

[[Category:Sesquiquartififths]]

~~[[Category:nano]]~~

~~[[Category:sesquiquartififths]]~~

~~[[Category:superpythagorean~~]]

@@ Line 1: / Line 1: @@
-'''253EDO''' is the [[EDO|equal division of the octave]] into 253 parts of 4.743083 [[cent]]s each. It's consistent to the 17-limit, approximating the fifth by '''148\253''' (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[Schismatic_family|sesquiquartififths]] temperament.
+'''253edo''' is the [[EDO|equal division of the octave]] into 253 parts of 4.743083 [[cent]]s each. It is [[consistent]] to the [[17-odd-limit]], approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. It tempers out [[32805/32768]] in the 5-limit; [[2401/2400]] in the 7-limit; [[385/384]], 1375/1372 and [[4000/3993]] in the 11-limit; [[325/324]], [[1575/1573]] and [[2200/2197]] in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit [[sesquiquartififths]] temperament.
-<u>'''253 tone equal modes:'''</u>
+= 11 × 23, and has subset edos [[11edo]] and [[23edo]].
-32 63 63 32: [[3L_2s|Pentatonic]]
+=== Prime harmonics ===
+{{Harmonics in equal|253}}
-43 19 43 43 43 19: [[5L_2s|Pythagorean tuning]]
+== Scales ==
+* 63 32 63 63 32: [[3L_2s|Pentatonic]]
+* 43 43 19 43 43 43 19: [[5L_2s|Pythagorean tuning]]
+* 41 41 24 41 41 41 24: [[Meantone|Meantonic tuning]]
+* 35 35 35 35 35 35 35 8: [[7L_1s|Porcupine tuning]]
+* 33 33 33 11 33 33 33 33 11: [[23edo|"The Hendecapliqued superdiatonic of the Icositriphony"]]
+* 31 31 31 18 31 31 31 31 18: [[7L_2s|Superdiatonic tuning]] in the way of Mavila
+* 26 26 15 26 26 26 15 26 26 26 15: [[sensi11|Sensi tuning]]
+* 20 20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L_3s|Ketradektriatoh tuning]]
-41 24 41 41 41 24: [[Meantone|Meantonic tuning]]
-35 35 35 35 35 35 8: [[7L_1s|Porcupine tuning]]
-33 33 11 33 33 33 33 11: [[23edo|"The Hendecapliqued superdiatonic of the Icositriphony"]]
-31 31 18 31 31 31 31 18: [[7L_2s|Superdiatonic tuning]] in the way of Mavila
-26 15 26 26 26 15 26 26 26 15: [[sensi11|Sensi tuning]]
-20 20 11 20 20 20 20 11 20 20 20 20 11: [[11L_3s|Ketradektriatoh tuning]]
-'''PRIME FACTORIZATION:'''
-= [[11edo|11]] * [[23edo|23]]
 [[Category:Equal divisions of the octave]]
-[[Category:modes]]
+[[Category:Sesquiquartififths]]
-[[Category:nano]]
-[[Category:sesquiquartififths]]
-[[Category:superpythagorean]]