Equal-step tuning: Difference between revisions

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== Gallery of equal divisions ==
== Gallery of equal divisions ==
===[[EdVI through edX|…of sixths through tenths]]===
* [[EdVI|'''…of sixths (e. g. 5/3 and 11/7)''']]
* [[EdVII|'''…of sevenths (e. g. 9/5)''']]
* [[EDO|'''...of the Octave/Duple (2/1)''']]
* [[EdIX|'''…of ninths (e. g. 9/4)''']]
* [[EdX|'''…of tenths (e. g. 7/3)''']]
===[[EdXI and beyond|…of elevenths and beyond]]===
* [[EdXI|'''…of elevenths (e. g. 8/3)''']]
** [[EDN|'''...of the Natave (e/1)''']]
* [[EdXII|'''…of twelfths (e. g. 3/1)''']]
** [[EDT|'''...of the Tritave/Triple (3/1)''']]
*** most famously the [[Bohlen-Pierce|BP]] scale, but lots of others, too
* [[EdXIII|'''…of thirteenths (e. g. 10/3)''']]
* [[EdXIV|'''…of fourteenths (e. g. 7/2)''']]
* [[Ed4|'''...of the Double Octave (4/1)''']]
* [[EdXVI|'''…of sixteenths (e. g. 9/2)''']]
* [[EdXVII|'''…of seventeenths (e. g. 5/1)''']]
** [[Ed5|'''...of the Just Major 17th (5/1)''']]
* [[EdXVIII|'''…of eighteenths (e. g. 11/2)''']]
* [[EdXIX|'''…of nineteenths (e. g. 6/1)''']]
** [[Ed6|'''...of the hexatave (6/1)''']]
* [[Ed7|'''...of the 7th Natural (7/1)''']]
* [[Ed8|'''...of the Triple Octave (8/1)''']]
* [[Ed9|'''...of the Double Tritave (9/1)''']]
* [[Ed10|'''...of the Just Major 24th (10/1)''']]
* [[Ed11|'''...of the 11th Natural (11/1)''']]
* [[Ed12|'''...of the Just Perfect 26th (12/1)''']]
* [[Ed13|'''...of the 13th Natural (13/1)''']]


===[[EdV|...of fifths (e. g. 3/2 and 13/9)]]===
* [[Ed16/15]] (… of the classic diatonic semitone)
* [[EDF|'''...of the Perfect Fifth (3/2)''']]
** 8 – [[Delta scale]] (8ed16/15)
** most famously Carlos Alpha, Beta and Gamma, but lots of others, too
 
* '''...of the Tridecimal High Tritone (13/9)'''
* [[Ed9/8]] (… of the whole tone)
** 11 - [[11ed13/9|Eleventh root of 13 over 9]]
** 9 – [[9ed9/8]]
* '''...of the Septimal High Tritone (10/7)'''
 
** 8 - [[8ed10/7|Eighth root of 10 over 7]]
* [[Ed5/4]] (… of the classic major third)
** 2 – [[2ed5/4]]
** 3 – [[3ed5/4]]
** 4 – [[4ed5/4]]
** 5 – [[5ed5/4]]
** 6 – [[6ed5/4]]
** 7 – [[7ed5/4]]
 
* [[Ed13/10]] (… of the tridecimal naiadic)
** 2 – [[Square root of 13 over 10|2ed13/10]]


===[[EdIV|...of fourths (e. g. 4/3 and 15/11)]]===
* [[Ed4/3]] (… of the perfect fourth)
* '''...of the Perfect Fourth (4/3)'''
** 3 [[Cube Root of P4|3ed4/3]]
** 3 - [[Cube_Root_of_P4|Cube root of 4/3]]
** 9 [[Noleta]] (9ed4/3)
** 5 - [[5ed4/3|Quintilipyth]] scale
** 6 - [[6ed4/3|Sextilipyth]] scale
** 9 - [[Noleta]] scale
* '''...of the Septimal Narrow Tritone (7/5)'''
** 4 - [[4ed7/5|Fourth root of 7/5]]
** 11 - [[11ed7/5|Eleventh root of 7/5]]
** 13 - [[13ed7/5|Thirteenth root of 7/5]]
* '''...of the Undecimal Semiaugmented Fourth (15/11)'''
** 13 - [[13ed15/11|Thirteenth root of 15/11]]
* '''...of the Tridecimal Ultramajor Third (13/10)'''
** 2 - [[Square root of 13 over 10]]


===[[EdIII|...of thirds (e. g. 9/7, 5/4, 11/9, and 6/5)]]===
* [[Ed13/9]] (… of the tridecimal high tritone)
* [[Ed5/4|'''...of the Just Major Third (5/4)''']]
** 11 – [[11ed13/9]]
** 2 - [[2ed5/4|Square root of 5/4]]
** 3 - [[3ed5/4|Cube root of 5/4]]
** 4 - [[4ed5/4|Fourth root of 5/4]]
** 5 - [[5ed5/4|Fifth root of 5/4]]
** 6 - [[6ed5/4|Sixth root of 5/4]]
** 7 - [[7ed5/4|Seventh root of 5/4]]


===[[Equal divisions of the whole tone|...of whole tones (e. g. 8/7, 9/8, and 10/9)]]===
* [[EDF]] (… of the perfect fifth, [[3/2]])
* '''...of the Septimal Whole Tone (8/7)'''
** most famously Carlos Alpha, Beta and Gamma, but lots of others, too
** 5 - [[5ed8/7|Fifth root of 8/7]]
* '''...of the Pythagorean Whole Tone (9/8)'''
** 9 - [[9ed9/8|Ninth root of 9/8]]


===[[Equal divisions of the semitone|...of semitones (e. g. 15/14, 16/15, and 25/24)]]===
* [[Ed5/3]] (… of [[5/3]])
* '''...of the Classic Diatonic Semitone (16/15)'''
* [[Ed9/5]] (… of [[9/5]])
** 8 - [[Delta scale]]
* [[Edo]] (… of the [[octave]], 2/1)
* [[Ed9/4]] (… of [[9/4]])
* [[Ed7/3]] (… of [[7/3]])
* [[Ed8/3]] (… of [[8/3]])
* [[EDN]] (… of the [[natave]], e/1)
* [[EDT]] (… of the [[tritave]]/twelfth, 3/1)
** most famously the [[Bohlen-Pierce|BP]] scale, but lots of others, too
* [[Ed10/3]]
* [[Ed7/2]]
* [[Ed4]]
* [[Ed5]]
* [[Ed6]]
* [[Ed7]]
* [[Ed8]]
* [[Ed9]]
* [[Ed10]]
* [[Ed11]]
* [[Ed12]]
* [[Ed13]]


== Equal multiplications ==
== Equal multiplications ==