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23edo: Difference between revisions

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==<span style="font-size: 1.4em;">Intervals</span>==
==<span style="font-size: 1.4em;">Intervals</span>==


[[Harmony_of_23edo|[[File:Ciclo_Icositrifonía.png|alt=Ciclo Icositrifonía.png|491x490px|Ciclo Icositrifonía.png]]]]
[[File:Ciclo_Icositrifonía.png|alt=Ciclo Icositrifonía.png|491x490px|link=Harmony_of_23edo]]


23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
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| style="text-align:center;" | D
| style="text-align:center;" | D
| style="text-align:center;" | 1
| style="text-align:center;" | 1
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| style="text-align:center;" | 1
| style="text-align:center;" | 1
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| style="text-align:center;" | Db
| style="text-align:center;" | Db
| style="text-align:center;" | 2b
| style="text-align:center;" | 2b
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| style="text-align:center;" | 2
| style="text-align:center;" | 2
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| style="text-align:center;" | E
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
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| style="text-align:center;" | 4·
| style="text-align:center;" | 4·
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| style="text-align:center;" | Eb
| style="text-align:center;" | Eb
| style="text-align:center;" | 3b
| style="text-align:center;" | 3b
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| style="text-align:center;" | 5
| style="text-align:center;" | 5
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| style="text-align:center;" | Ebb, Fx
| style="text-align:center;" | Ebb, Fx
| style="text-align:center;" | 2#
| style="text-align:center;" | 2#
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| style="text-align:center;" | 6
| style="text-align:center;" | 6
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| style="text-align:center;" | F
| style="text-align:center;" | F
| style="text-align:center;" | 4b
| style="text-align:center;" | 4b
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| style="text-align:center;" | 8
| style="text-align:center;" | 8
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| style="text-align:center;" | G#
| style="text-align:center;" | G#
| style="text-align:center;" | 4
| style="text-align:center;" | 4
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| style="text-align:center;" | 10·
| style="text-align:center;" | 10·
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| style="text-align:center;" | G
| style="text-align:center;" | G
| style="text-align:center;" | 5
| style="text-align:center;" | 5
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| style="text-align:center;" | 11
| style="text-align:center;" | 11
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| style="text-align:center;" | Gb
| style="text-align:center;" | Gb
| style="text-align:center;" | 6b
| style="text-align:center;" | 6b
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| style="text-align:center;" | 12
| style="text-align:center;" | 12
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| style="text-align:center;" | A#
| style="text-align:center;" | A#
| style="text-align:center;" | 5#
| style="text-align:center;" | 5#
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| style="text-align:center;" | 13·
| style="text-align:center;" | 13·
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| style="text-align:center;" | Ab
| style="text-align:center;" | Ab
| style="text-align:center;" | 7b
| style="text-align:center;" | 7b
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| style="text-align:center;" | 15
| style="text-align:center;" | 15
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| style="text-align:center;" | B#
| style="text-align:center;" | B#
| style="text-align:center;" | 6#
| style="text-align:center;" | 6#
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| style="text-align:center;" | 16·
| style="text-align:center;" | 16·
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| style="text-align:center;" | B
| style="text-align:center;" | B
| style="text-align:center;" | 7
| style="text-align:center;" | 7
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| style="text-align:center;" | 17
| style="text-align:center;" | 17
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| style="text-align:center;" | Bb
| style="text-align:center;" | Bb
| style="text-align:center;" | 8b
| style="text-align:center;" | 8b
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| style="text-align:center;" | 18
| style="text-align:center;" | 18
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| style="text-align:center;" | Bbb, Cx
| style="text-align:center;" | Bbb, Cx
| style="text-align:center;" | 7#
| style="text-align:center;" | 7#
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| style="text-align:center;" | 19·
| style="text-align:center;" | 19·
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| style="text-align:center;" | C#
| style="text-align:center;" | C#
| style="text-align:center;" | 8
| style="text-align:center;" | 8
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| style="text-align:center;" | 20
| style="text-align:center;" | 20
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| style="text-align:center;" | C
| style="text-align:center;" | C
| style="text-align:center;" | 9b
| style="text-align:center;" | 9b
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| style="text-align:center;" | 21
| style="text-align:center;" | 21
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| style="text-align:center;" | Cb
| style="text-align:center;" | Cb
| style="text-align:center;" | 8#
| style="text-align:center;" | 8#
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| style="text-align:center;" | 22
| style="text-align:center;" | 22
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| style="text-align:center;" | D#
| style="text-align:center;" | D#
| style="text-align:center;" | 9
| style="text-align:center;" | 9
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| style="text-align:center;" | 23··
| style="text-align:center;" | 23··
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| style="text-align:center;" | D
| style="text-align:center;" | D
| style="text-align:center;" | 1
| style="text-align:center;" | 1
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<ul><li>the dots indicate which frets on a 23-edo guitar would have dots.<ul><li>based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</li></ul></li></ul>
<ul><li>the dots indicate which frets on a 23-edo guitar would have dots.<ul><li>based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</li></ul></li></ul>
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| style="text-align:center;" | Kleisma
| style="text-align:center;" | Kleisma
| style="text-align:center;" | Semicomma Majeur
| style="text-align:center;" | Semicomma Majeur
| style="text-align:center;" |  
| style="text-align:center;" |
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| style="text-align:center;" | 36/35
| style="text-align:center;" | 36/35
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| style="text-align:right;" | 48.77
| style="text-align:right;" | 48.77
| style="text-align:center;" | Septimal Quarter Tone
| style="text-align:center;" | Septimal Quarter Tone
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" |
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| style="text-align:center;" | 525/512
| style="text-align:center;" | 525/512
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| style="text-align:center;" | Avicennma
| style="text-align:center;" | Avicennma
| style="text-align:center;" | Avicenna's Enharmonic Diesis
| style="text-align:center;" | Avicenna's Enharmonic Diesis
| style="text-align:center;" |  
| style="text-align:center;" |
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| style="text-align:center;" | 4000/3969
| style="text-align:center;" | 4000/3969
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| style="text-align:right;" | 13.47
| style="text-align:right;" | 13.47
| style="text-align:center;" | Octagar
| style="text-align:center;" | Octagar
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" |
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| style="text-align:center;" | 6144/6125
| style="text-align:center;" | 6144/6125
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| style="text-align:right;" | 5.36
| style="text-align:right;" | 5.36
| style="text-align:center;" | Porwell
| style="text-align:center;" | Porwell
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" |
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| style="text-align:center;" | 100/99
| style="text-align:center;" | 100/99
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| style="text-align:right;" | 17.40
| style="text-align:right;" | 17.40
| style="text-align:center;" | Ptolemisma
| style="text-align:center;" | Ptolemisma
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" |
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| style="text-align:center;" | 441/440
| style="text-align:center;" | 441/440
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| style="text-align:right;" | 3.93
| style="text-align:right;" | 3.93
| style="text-align:center;" | Werckisma
| style="text-align:center;" | Werckisma
| style="text-align:center;" |  
| style="text-align:center;" |
| style="text-align:center;" |  
| style="text-align:center;" |
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| | 10 10 3
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| | 9 9 5
| | 9 9 5
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| | 8 8 7
| | 8 8 7
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| | 7 7 7 2
| | 7 7 7 2
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| | 7 2 7 7
| | 7 2 7 7
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| | 6 6 6 5
| | 6 6 6 5
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| | 6 5 6 6
| | 6 5 6 6
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| | 5 4 5 5 4
| | 5 4 5 5 4
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| | 5 4 5 4 5
| | 5 4 5 4 5
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| | 7 1 7 7 1
| | 7 1 7 7 1
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| | 7 1 7 1 7
| | 7 1 7 1 7
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| | 5 5 5 5 3
| | 5 5 5 5 3
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| | 5 3 5 5 5
| | 5 3 5 5 5
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| | 4 4 4 4 4 3
| | 4 4 4 4 4 3
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|-
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| | 4 3 4 4 4 4
| | 4 3 4 4 4 4
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| | 5 1 5 1 5 1 5
| | 5 1 5 1 5 1 5
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|-
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| | 3 4 3 3 4 3 3
| | 3 4 3 3 4 3 3
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| | 3 3 4 3 3 3 4
| | 3 3 4 3 3 3 4
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| | 3 3 3 4 3 3 4
| | 3 3 3 4 3 3 4
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| | 3 3 3 4 3 4 3
| | 3 3 3 4 3 4 3
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| | 2 5 2 5 2 5 2
| | 2 5 2 5 2 5 2
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| | 3 2 3 3 3 3 3 3
| | 3 2 3 3 3 3 3 3
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| | '''3 3 3 1 3 3 3 3 1'''
| | '''3 3 3 1 3 3 3 3 1'''
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|-
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| | 3 3 1 3 3 3 1 3 3
| | 3 3 1 3 3 3 1 3 3
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| | 3 2 3 2 3 2 3 2 3
| | 3 2 3 2 3 2 3 2 3
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|-
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| | 2 2 1 2 2 1 2 2 1 2 2 1 2 1
| | 2 2 1 2 2 1 2 2 1 2 2 1 2 1
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| | '''2 1 2 2 1 2 2 1 2 2 1 2 2 1'''
| | '''2 1 2 2 1 2 2 1 2 2 1 2 2 1'''
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| | 1 1 1 4 1 1 1 1 4 1 1 1 1 4
| | 1 1 1 4 1 1 1 1 4 1 1 1 1 4
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| | 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
| | 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
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| | '''2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1'''
| | '''2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1'''
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| | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
| | 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
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[[Category:todo:unify_precision]]
[[Category:todo:unify_precision]]
[[Category:twentuning]]
[[Category:twentuning]]
[[Category:IMPORTDEBUG - Image in Link]]
Retrieved from "https://en.xen.wiki/w/23edo"