7/6: Difference between revisions
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{{Wikipedia|Septimal minor third}} | {{Wikipedia|Septimal minor third}} | ||
In [[7-limit]] [[just intonation]], '''7/6''' is the '''subminor third''' <ref>[[Hermann von Helmholtz|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal minor third'''. At about 267 cents, it is smaller than both the [[5-limit]] minor third ([[6/5]], ~316 cents) and the familiar [[12edo]] minor third (300 cents). In contrast to [[5/4]] and [[6/5]], 7/6 is noticeably more consonant than it's counterpart [[9/7]], and a [[6:7:9]] subminor triad can sound very stable compared to a [[14:18:21]] supermajor triad. It can also be used with [[8/7]] in a [[6:7:8]] triad dividing [[4/3]] rather than [[3/2]], though this chord is better voiced as 4: | In [[7-limit]] [[just intonation]], '''7/6''' is the '''subminor third''' <ref>[[Hermann von Helmholtz|Hermann L. F. von Helmholtz]] (1875). ''On the sensations of tone as a physiological basis for the theory of music'', p. 284.</ref> or '''septimal minor third'''. At about 267 cents, it is smaller than both the [[5-limit]] minor third ([[6/5]], ~316 cents) and the familiar [[12edo]] minor third (300 cents). In contrast to [[5/4]] and [[6/5]], 7/6 is noticeably more consonant than it's counterpart [[9/7]], and a [[6:7:9]] subminor triad can sound very stable compared to a [[14:18:21]] supermajor triad. It can also be used with [[8/7]] in a [[6:7:8]] triad dividing [[4/3]] rather than [[3/2]], though this chord is better voiced as 4:6:7. | ||
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Revision as of 08:55, 17 December 2025
| Interval information |
septimal minor third
reduced
[sound info]
In 7-limit just intonation, 7/6 is the subminor third [1] or septimal minor third. At about 267 cents, it is smaller than both the 5-limit minor third (6/5, ~316 cents) and the familiar 12edo minor third (300 cents). In contrast to 5/4 and 6/5, 7/6 is noticeably more consonant than it's counterpart 9/7, and a 6:7:9 subminor triad can sound very stable compared to a 14:18:21 supermajor triad. It can also be used with 8/7 in a 6:7:8 triad dividing 4/3 rather than 3/2, though this chord is better voiced as 4:6:7.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 9 | 2\9 | 266.67 | -0.20 | -0.15 |
| 18 | 4\18 | 266.67 | -0.20 | -0.31 |
| 27 | 6\27 | 266.67 | -0.20 | -0.46 |
| 36 | 8\36 | 266.67 | -0.20 | -0.61 |
| 45 | 10\45 | 266.67 | -0.20 | -0.77 |
| 54 | 12\54 | 266.67 | -0.20 | -0.92 |
| 63 | 14\63 | 266.67 | -0.20 | -1.07 |
| 67 | 15\67 | 268.66 | +1.79 | +9.97 |
| 72 | 16\72 | 266.67 | -0.20 | -1.23 |
| 76 | 17\76 | 268.42 | +1.55 | +9.82 |
Temperaments
7/6 can be used as a generator for several temperaments, most notably orwell, where two subminor thirds reach 11/8, three reach 8/5, and seven reach 3/2. It also generates septimin.
It is almost perfectly approximated by 2\9, and is represented as such in the septiennealimmal clan, including ennealimmal.
See also
- 12/7 – its octave complement
- 9/7 – its fifth complement
- 8/7 – its fourth complement
- 7/3 – the interval plus one octave may sound even more consonant
- Gallery of just intervals
References
- ↑ Hermann L. F. von Helmholtz (1875). On the sensations of tone as a physiological basis for the theory of music, p. 284.