12/7: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
less obscure chord example; 4:5:7:9:12 is more often written as 4:5:6:7:9 |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 6: | Line 6: | ||
{{Wikipedia| Septimal major sixth }} | {{Wikipedia| Septimal major sixth }} | ||
In [[7-limit]] [[just intonation]], '''12/7''' is the '''septimal (super)major sixth''' of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as | In [[7-limit]] [[just intonation]], '''12/7''' is the '''septimal (super)major sixth''' of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as [[70:84:105:120|1/(12:10:8:7)]]. It differs from the 5-limit major sixth of [[5/3]] by [[36/35]] – the septimal quartertone – a [[superparticular]] interval of about 48.8¢. It differs from the Pythagorean major sixth of [[27/16]] by [[64/63]] – Archytas' comma – about 27.3¢. And finally, it differs from the harmonic seventh of [[7/4]] by [[49/48]] – the large septimal diesis or slendro diesis – about 35.7¢. 12/7 is the inversion of the septimal subminor third of [[7/6]]. | ||
== Approximation == | |||
{{Interval edo approximation|12/7}} | |||
== See also == | == See also == | ||
Latest revision as of 08:39, 25 December 2025
| Interval information |
septimal major sixth
[sound info]
In 7-limit just intonation, 12/7 is the septimal (super)major sixth of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 1/(12:10:8:7). It differs from the 5-limit major sixth of 5/3 by 36/35 – the septimal quartertone – a superparticular interval of about 48.8¢. It differs from the Pythagorean major sixth of 27/16 by 64/63 – Archytas' comma – about 27.3¢. And finally, it differs from the harmonic seventh of 7/4 by 49/48 – the large septimal diesis or slendro diesis – about 35.7¢. 12/7 is the inversion of the septimal subminor third of 7/6.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 9 | 7\9 | 933.33 | +0.20 | +0.15 |
| 18 | 14\18 | 933.33 | +0.20 | +0.31 |
| 27 | 21\27 | 933.33 | +0.20 | +0.46 |
| 36 | 28\36 | 933.33 | +0.20 | +0.61 |
| 45 | 35\45 | 933.33 | +0.20 | +0.77 |
| 54 | 42\54 | 933.33 | +0.20 | +0.92 |
| 63 | 49\63 | 933.33 | +0.20 | +1.07 |
| 67 | 52\67 | 931.34 | -1.79 | -9.97 |
| 72 | 56\72 | 933.33 | +0.20 | +1.23 |
| 76 | 59\76 | 931.58 | -1.55 | -9.82 |
See also
- 7/6 – its octave complement
- 7/4 – its twelfth complement
- Gallery of just intervals
- File:Ji-12-7-csound-foscil-220hz.mp3 – an alternative sound sample