The hendrix chord, a 7#9no5 chord, has several possible JI interpretations.
| Harmonics
|
4:8:10:14:16:19
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| Intervals from root
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1/2 – 1/1 – 5/4 – 7/4 – 2/1 – 19/8
|
| Cents from root
|
-1200¢ 0¢ 386¢ 969¢ 1200¢ 1498¢
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| Step intervals
|
2/1, 5/4, 7/5, 8/7, 19/16
|
| Step cents
|
1200¢, 386¢, 583¢, 231¢, 298¢
|
| Prime limit
|
19
|
| Genus
|
5 ⋅ 7 ⋅ 19 (665)
|
| Intervallic odd limit
|
19
|
| Otonal odd limit
|
19
|
| Utonal odd limit
|
665
|
| Consistent edos (d ≥ 1.5)
|
4edo, 12edo, 16edo*, 25edo*, …
|
|
|
In the 19-limit it may be tuned as 4:8:10:14:16:19, an extended harmonic seventh chord.
| Harmonics
|
6:12:15:21:24:28
|
| Intervals from root
|
1/2 – 1/1 – 5/4 – 7/4 – 2/1 – 7/3
|
| Cents from root
|
-1200¢ 0¢ 386¢ 969¢ 1200¢ 1467¢
|
| Step intervals
|
2/1, 5/4, 7/5, 8/7, 7/6
|
| Step cents
|
1200¢, 386¢, 583¢, 231¢, 267¢
|
| Prime limit
|
7
|
| Genus
|
3 ⋅ 5 ⋅ 7 (105)
|
| Intervallic odd limit
|
15
|
| Otonal odd limit
|
21
|
| Utonal odd limit
|
35
|
| Consistent edos (d ≥ 1.5)
|
10edo*, 12edo, 21edo, 22edo, …
|
|
|
In the 7-limit it may be tuned as 6:12:15:21:24:28, also an extended harmonic seventh chord.
| Harmonics
|
10:20:25:36:40:48
|
| Intervals from root
|
1/2 – 1/1 – 5/4 – 9/5 – 2/1 – 12/5
|
| Cents from root
|
-1200¢ 0¢ 386¢ 1018¢ 1200¢ 1516¢
|
| Step intervals
|
2/1, 5/4, 36/25, 10/9, 6/5
|
| Step cents
|
1200¢, 386¢, 631¢, 182¢, 316¢
|
| Prime limit
|
5
|
| Genus
|
32 ⋅ 52 (225)
|
| Intervallic odd limit
|
25
|
| Otonal odd limit
|
25
|
| Utonal odd limit
|
75
|
| Consistent edos (d ≥ 1.5)
|
12edo, 15edo, 19edo**, 31edo, …
|
|
|
In the 5-limit it may be tuned as 10:20:25:36:40:48, an extended major-minor seventh chord.
It can also be tuned as an essentially tempered chord that splits the difference between the 19/8 10th and the 7/3 10th. This chord tempers out the hendrix comma of 57/56. It is notable for existing in 12-EDO; other equal divisions with hendrix chords include the 9, 10, 14, 16, 17, 21, 22, 26, and 31 equal divisions.
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Todo: review
The paragraph about tempering 57/56 needs more explanation, and may be incorrect.
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