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16edo: Difference between revisions

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! [[7mu]]s ([[Wikipedia: hexadecimal |hex]])
! [[7mu]]s ([[Wikipedia: hexadecimal |hex]])
! Approximate <br> Ratios*
! Approximate <br> Ratios*
! colspan="2" | Melodic names, <br> major wider than minor
! index-0 notation
! colspan="2" | Harmonic names, <br> major narrower <br> than minor
! colspan="2" | index-1 notation
! Interval Names <br> Just
! Interval Names <br> Just
! Interval <br> Names <br> Simplified
! Interval Names Simplified
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
Line 95: Line 95:
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:center;" | 1/1
| style="text-align:center;" | 1/1
| style="text-align:center;" | unison
! colspan="2" style="text-align:center;" | unison
| style="text-align:center;" | D
| style="text-align:center;" | D
| style="text-align:center;" | unison
! colspan="2" style="text-align:center;" | Unison
| style="text-align:center;" | D
| style="text-align:center;" | Unison
| style="text-align:center;" | Unison
|-
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
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|96 (60<sub>16</sub>)
|96 (60<sub>16</sub>)
| style="text-align:center;" | 28/27, 27/26
| style="text-align:center;" | 28/27, 27/26
| style="text-align:center;" | aug 0, dim 1st
dim 0, aug 1st
| style="text-align:center;" | aug 1, dim 2nd
| style="text-align:center;" | aug 1, dim 2nd
dim 1, aug 2nd
| style="text-align:center;" | D#, Eb
| style="text-align:center;" | D#, Eb
| style="text-align:center;" | dim 1, aug 2nd
Db, E#
| style="text-align:center;" | Db, E#
| style="text-align:center;" | Minor 2nd
| style="text-align:center;" | Subminor 2nd
Minor 1st
| style="text-align:center;" | Min 2nd
| style="text-align:center;" | Min 2nd
Min 1st
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
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|192 (C0<sub>16</sub>)
|192 (C0<sub>16</sub>)
| style="text-align:center;" | 35/32
| style="text-align:center;" | 35/32
| style="text-align:center;" | minor 1st
major 1st
| style="text-align:center;" | minor 2nd
| style="text-align:center;" | minor 2nd
| style="text-align:center;" | E
major 2nd
| style="text-align:center;" | major 2nd
| style="text-align:center;" | E
| style="text-align:center;" | E
| style="text-align:center;" | Neutral 2nd
| style="text-align:center;" | Neutral 2nd
Neutral 1st
| style="text-align:center;" | Maj 2nd
| style="text-align:center;" | Maj 2nd
Maj 1st
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
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|288 (120<sub>16</sub>)
|288 (120<sub>16</sub>)
| style="text-align:center;" | 8/7
| style="text-align:center;" | 8/7
| style="text-align:center;" | major 1st
minor 1st
| style="text-align:center;" | major 2nd
| style="text-align:center;" | major 2nd
minor 2nd
| style="text-align:center;" | E#
| style="text-align:center;" | E#
| style="text-align:center;" | minor 2nd
Eb
| style="text-align:center;" | Eb
| style="text-align:center;" | Major 2nd,
| style="text-align:center;" | Supermajor 2nd,
 
(Septimal) Whole-Tone
 
Major 1st,


Septimal Whole-Tone
(Septimal) Whole-Tone
| style="text-align:center;" | Perf 2nd
| style="text-align:center;" | Perf 2nd
Perf 1st
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
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|384 (180<sub>16</sub>)
|384 (180<sub>16</sub>)
| style="text-align:center;" | 19/16, 32/27
| style="text-align:center;" | 19/16, 32/27
| style="text-align:center;" | minor 2nd
major 2nd
| style="text-align:center;" | minor 3rd
| style="text-align:center;" | minor 3rd
major 3rd
| style="text-align:center;" | Fb
| style="text-align:center;" | Fb
| style="text-align:center;" | major 3rd
F#
| style="text-align:center;" | F#
| style="text-align:center;" | Minor 3rd
| style="text-align:center;" | Minor 3rd
Major 3rd
| style="text-align:center;" | Min 3rd
| style="text-align:center;" | Min 3rd
Min 2nd
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
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|480 (1E0<sub>16</sub>)
|480 (1E0<sub>16</sub>)
| style="text-align:center;" | 5/4, 16/13, 26/21
| style="text-align:center;" | 5/4, 16/13, 26/21
| style="text-align:center;" | major 2nd
minor 2nd
| style="text-align:center;" | major 3rd
| style="text-align:center;" | major 3rd
| style="text-align:center;" | F
minor 3rd
| style="text-align:center;" | minor 3rd
| style="text-align:center;" | F
| style="text-align:center;" | F
| style="text-align:center;" | Major 3rd
| style="text-align:center;" | Major 3rd
| style="text-align:center;" | Maj 3rd
Minor 3rd
| style="text-align:center;" | Maj 3rd  
Maj 2nd
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
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|576 (240<sub>16</sub>)
|576 (240<sub>16</sub>)
| style="text-align:center;" | 13/10, 35/27
| style="text-align:center;" | 13/10, 35/27
| style="text-align:center;" | aug 3rd
| style="text-align:center;" | aug 2nd, dim 3rd


dim 4th
dim 2nd, aug 3rd
| style="text-align:center;" | dim 3rd, aug 4th
dim 3rd, aug 4th
| style="text-align:center;" | F#, Gb
| style="text-align:center;" | F#, Gb
| style="text-align:center;" | dim 3rd,
Fb, G#
| style="text-align:center;" | Sub-4th, Supermajor 3rd


aug 4th
Sub-3rd,
| style="text-align:center;" | Fb, G#
| style="text-align:center;" | Sub-4th,


Supermajor 3rd
Supermajor 2nd
| style="text-align:center;" | Min 4th
| style="text-align:center;" | Min 4th  
Min 3rd
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
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|672 (2A0<sub>16</sub>)
|672 (2A0<sub>16</sub>)
| style="text-align:center;" | 19/14, 27/20, 52/35, 256/189
| style="text-align:center;" | 19/14, 27/20, 52/35, 256/189
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | perfect 3rd
| style="text-align:center;" | G
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | G
| style="text-align:center;" | G
| style="text-align:center;" | Wide 4th
| style="text-align:center;" | Wide 4th
| style="text-align:center;" | Maj 4th
Wide 3rd
| style="text-align:center;" | Maj 4th  
Maj 3rd
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
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|768 (300<sub>16</sub>)
|768 (300<sub>16</sub>)
| style="text-align:center;" | 7/5, 10/7
| style="text-align:center;" | 7/5, 10/7
| style="text-align:center;" | aug 4th
| style="text-align:center;" | aug 3rd, dim 4th
dim 3rd, aug 4th
| style="text-align:center;" | aug 4th,


dim 5th
dim 5th
| style="text-align:center;" | G#, Ab
 
| style="text-align:center;" | dim 4th,
dim 4th,


aug 5th
aug 5th
| style="text-align:center;" | Gb, A#
| style="text-align:center;" | G#, Ab
Gb, A#
| style="text-align:center;" | Tritone
| style="text-align:center;" | Tritone
| style="text-align:center;" | Aug 4th,
| style="text-align:center;" | Aug 4th, Dim 5th


Dim 5th
Aug 3rd, Dim 4th
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
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|864 (360<sub>16</sub>)
|864 (360<sub>16</sub>)
| style="text-align:center;" | 28/19, 40/27, 35/26, 189/128
| style="text-align:center;" | 28/19, 40/27, 35/26, 189/128
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | A
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | A
| style="text-align:center;" | A
| style="text-align:center;" | Narrow 5th
| style="text-align:center;" | Narrow 5th
Narrow 4th
| style="text-align:center;" | Min 5th
| style="text-align:center;" | Min 5th
Min 4th
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
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|960 (3C0<sub>16</sub>)
|960 (3C0<sub>16</sub>)
| style="text-align:center;" | 20/13, 54/35
| style="text-align:center;" | 20/13, 54/35
| style="text-align:center;" | aug 5th
| style="text-align:center;" | aug 4th, dim 5th
 
dim 4th, aug 5th
dim 6th
| style="text-align:center;" | aug 5th, dim 6th
dim 5th, aug 6th
| style="text-align:center;" | A#, Bb
| style="text-align:center;" | A#, Bb
| style="text-align:center;" | dim 5th, aug 6th
Ab, B#
| style="text-align:center;" | Ab, B#
| style="text-align:center;" | Super-5th, Subminor 6th
| style="text-align:center;" | Super-5th,
Super-4th, Subminor 5th
 
Subminor 6th
| style="text-align:center;" | Maj 5th
| style="text-align:center;" | Maj 5th
Maj 4th
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
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|1056 (420<sub>16</sub>)
|1056 (420<sub>16</sub>)
| style="text-align:center;" | 8/5, 13/8, 21/13
| style="text-align:center;" | 8/5, 13/8, 21/13
| style="text-align:center;" | minor 5th
major 5th
| style="text-align:center;" | minor 6th
| style="text-align:center;" | minor 6th
| style="text-align:center;" | B
major 6th
| style="text-align:center;" | major 6th
| style="text-align:center;" | B
| style="text-align:center;" | B
| style="text-align:center;" | Minor 6th
| style="text-align:center;" | Minor 6th
Minor 5th
| style="text-align:center;" | Min 6th
| style="text-align:center;" | Min 6th
Min 5th
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
Line 245: Line 273:
|1152 (480<sub>16</sub>)
|1152 (480<sub>16</sub>)
| style="text-align:center;" | 27/16, 32/19
| style="text-align:center;" | 27/16, 32/19
| style="text-align:center;" | major 6th
| style="text-align:center;" | major 5th
minor 5th
| style="text-align:center;" | minor 6th
major 6th
| style="text-align:center;" | B#
| style="text-align:center;" | B#
| style="text-align:center;" | minor 6th
Bb
| style="text-align:center;" | Bb
| style="text-align:center;" | Major 6th
| style="text-align:center;" | Major 6th
Major 5th
| style="text-align:center;" | Maj 6th
| style="text-align:center;" | Maj 6th
Maj 5th
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
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|1248 (4E0<sub>16</sub>)
|1248 (4E0<sub>16</sub>)
| style="text-align:center;" | 7/4
| style="text-align:center;" | 7/4
| style="text-align:center;" | minor 6th
major 6th
| style="text-align:center;" | minor 7th
| style="text-align:center;" | minor 7th
major 7th
| style="text-align:center;" | Cb
| style="text-align:center;" | Cb
| style="text-align:center;" | major 7th
C#
| style="text-align:center;" | C#
| style="text-align:center;" | (Septimal) Minor 7th
| style="text-align:center;" | Subminor 7th,
(Septimal) Minor 6th
 
Septimal Minor 7th
| style="text-align:center;" | Perf 7th
| style="text-align:center;" | Perf 7th
Perf 6th
|-
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 14
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|1344 (540<sub>16</sub>)
|1344 (540<sub>16</sub>)
| style="text-align:center;" | 64/35
| style="text-align:center;" | 64/35
| style="text-align:center;" | major 6th
minor 6th
| style="text-align:center;" | major 7th
| style="text-align:center;" | major 7th
| style="text-align:center;" | C
minor 7th
| style="text-align:center;" | minor 7th
| style="text-align:center;" | C
| style="text-align:center;" | C
| style="text-align:center;" | Neutral 7th
| style="text-align:center;" | Neutral 7th
Neutral 6th
| style="text-align:center;" | Min 7th
| style="text-align:center;" | Min 7th
Min 6th
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
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|1440 (5A0<sub>16</sub>)
|1440 (5A0<sub>16</sub>)
| style="text-align:center;" | 27/14, 52/27
| style="text-align:center;" | 27/14, 52/27
| style="text-align:center;" | aug 7th
| style="text-align:center;" | aug 6th
 
dim 7th
 
dim 6th,
 
aug 7th
| style="text-align:center;" | aug 7th,


dim 8ve
dim 8ve
| style="text-align:center;" | C#, Db
 
| style="text-align:center;" | dim 7th,
dim 7th,


aug 8ve
aug 8ve
| style="text-align:center;" | Cb, D#
| style="text-align:center;" | C#, Db
| style="text-align:center;" | Supermajor 7th
Cb, D#
| style="text-align:center;" | Major 7th
Major 6th
| style="text-align:center;" | Maj 7th
| style="text-align:center;" | Maj 7th
Maj 6th
|-
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 16
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|1536 (600<sub>16</sub>)
|1536 (600<sub>16</sub>)
| style="text-align:center;" | 2/1
| style="text-align:center;" | 2/1
| style="text-align:center;" | 8ve
! colspan="2" style="text-align:center;" | 8ve
| style="text-align:center;" | D
7th
| style="text-align:center;" | 8ve
| style="text-align:center;" | D
| style="text-align:center;" | D
| style="text-align:center;" | Octave
! colspan="2" style="text-align:center;" | Octave
| style="text-align:center;" | Octave
Seventh
|}
|}
*based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.
*based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.
Retrieved from "https://en.xen.wiki/w/16edo"