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| == Gallery of equal divisions == | | == Gallery of equal divisions == |
| ===[[EdVI through edX|…of sixths through tenths]]===
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| * [[EdVI|'''…of sixths (e. g. 5/3 and 11/7)''']]
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| * [[EdVII|'''…of sevenths (e. g. 9/5)''']]
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| * [[EDO|'''...of the Octave/Duple (2/1)''']]
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| * [[EdIX|'''…of ninths (e. g. 9/4)''']]
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| * [[EdX|'''…of tenths (e. g. 7/3)''']]
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| ===[[EdXI and beyond|…of elevenths and beyond]]===
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| * [[EdXI|'''…of elevenths (e. g. 8/3)''']]
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| ** [[EDN|'''...of the Natave (e/1)''']]
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| * [[EdXII|'''…of twelfths (e. g. 3/1)''']]
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| ** [[EDT|'''...of the Tritave/Triple (3/1)''']]
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| *** most famously the [[Bohlen-Pierce|BP]] scale, but lots of others, too
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| * [[EdXIII|'''…of thirteenths (e. g. 10/3)''']]
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| * [[EdXIV|'''…of fourteenths (e. g. 7/2)''']]
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| * [[Ed4|'''...of the Double Octave (4/1)''']]
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| * [[EdXVI|'''…of sixteenths (e. g. 9/2)''']]
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| * [[EdXVII|'''…of seventeenths (e. g. 5/1)''']]
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| ** [[Ed5|'''...of the Just Major 17th (5/1)''']]
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| * [[EdXVIII|'''…of eighteenths (e. g. 11/2)''']]
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| * [[EdXIX|'''…of nineteenths (e. g. 6/1)''']]
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| ** [[Ed6|'''...of the hexatave (6/1)''']]
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| * [[Ed7|'''...of the 7th Natural (7/1)''']]
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| * [[Ed8|'''...of the Triple Octave (8/1)''']]
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| * [[Ed9|'''...of the Double Tritave (9/1)''']]
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| * [[Ed10|'''...of the Just Major 24th (10/1)''']]
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| * [[Ed11|'''...of the 11th Natural (11/1)''']]
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| * [[Ed12|'''...of the Just Perfect 26th (12/1)''']]
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| * [[Ed13|'''...of the 13th Natural (13/1)''']]
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| ===[[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]] |
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| | * [[Ed13/10]] (… of the tridecimal naiadic) |
| | ** 2 – [[Square root of 13 over 10|2ed13/10]] |
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| ===[[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
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| ** 6 - [[6ed4/3|Sextilipyth]] scale
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| ** 9 - [[Noleta]] scale | |
| * '''...of the Septimal Narrow Tritone (7/5)'''
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| ** 4 - [[4ed7/5|Fourth root of 7/5]]
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| ** 11 - [[11ed7/5|Eleventh root of 7/5]]
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| ** 13 - [[13ed7/5|Thirteenth root of 7/5]]
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| * '''...of the Undecimal Semiaugmented Fourth (15/11)'''
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| ** 13 - [[13ed15/11|Thirteenth root of 15/11]]
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| * '''...of the Tridecimal Ultramajor Third (13/10)'''
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| ** 2 - [[Square root of 13 over 10]]
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| ===[[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]]
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| ** 4 - [[4ed5/4|Fourth root of 5/4]]
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| ** 5 - [[5ed5/4|Fifth root of 5/4]]
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| ** 6 - [[6ed5/4|Sixth root of 5/4]]
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| ** 7 - [[7ed5/4|Seventh root of 5/4]]
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| ===[[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]]
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| * '''...of the Pythagorean Whole Tone (9/8)'''
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| ** 9 - [[9ed9/8|Ninth root of 9/8]] | |
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| ===[[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]] |
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| == Equal multiplications == | | == Equal multiplications == |