8/7: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal whole tone, supermajor second, septimal major second, septimal supermajor second | |||
| Name = septimal whole tone, | |||
| Color name = r2, ru 2nd | | Color name = r2, ru 2nd | ||
| Sound = jid_8_7_pluck_adu_dr220.mp3 | | Sound = jid_8_7_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Septimal whole tone}} | {{Wikipedia|Septimal whole tone}} | ||
In [[just intonation]], 8/7 is the ''' | In [[just intonation]], 8/7 is the '''septimal major second''', or '''septimal supermajor second''', of approximately 231.2{{cent}}. Although it falls between the familiar major second and minor third of [[12edo]], most people think of it more like a wide second than a narrow third. It can be found between the 7th and 8th [[harmonic]]s and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3{{cent}}. It is close in size to 5edo's 240{{c}} step. | ||
A stack of three supermajor seconds is close to a perfect fifth ([[3/2]]). The difference is [[1029/1024]] (about 8.4{{c}}), which is tempered out in [[slendric]] systems like [[31edo]]. | |||
== Approximation == | |||
{{Interval edo approximation|8/7}} | |||
== See also == | == See also == | ||
* [[7/4]] – its [[octave complement]] | * [[7/4]] – its [[octave complement]] | ||
| Line 19: | Line 16: | ||
* [[7/6]] – its [[fourth complement]] | * [[7/6]] – its [[fourth complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Supermajor second]] | [[Category:Supermajor second]] | ||
[[Category:Over-7 intervals]] | |||
[[Category:Over-7]] | |||
Latest revision as of 16:02, 11 April 2026
| Interval information |
supermajor second,
septimal major second,
septimal supermajor second
reduced,
reduced subharmonic
[sound info]
In just intonation, 8/7 is the septimal major second, or septimal supermajor second, of approximately 231.2 ¢. Although it falls between the familiar major second and minor third of 12edo, most people think of it more like a wide second than a narrow third. It can be found between the 7th and 8th harmonics and is thus a superparticular ratio. In 7-limit JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh (7/4) and octave. It differs from the Pythagorean major second of 9/8 by 64/63, a microtone of about 27.3 ¢. It is close in size to 5edo's 240 ¢ step.
A stack of three supermajor seconds is close to a perfect fifth (3/2). The difference is 1029/1024 (about 8.4 ¢), which is tempered out in slendric systems like 31edo.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 5 | 1\5 | 240.00 | +8.83 | +3.68 |
| 10 | 2\10 | 240.00 | +8.83 | +7.35 |
| 16 | 3\16 | 225.00 | -6.17 | -8.23 |
| 21 | 4\21 | 228.57 | -2.60 | -4.55 |
| 26 | 5\26 | 230.77 | -0.40 | -0.88 |
| 31 | 6\31 | 232.26 | +1.08 | +2.80 |
| 36 | 7\36 | 233.33 | +2.16 | +6.48 |
| 42 | 8\42 | 228.57 | -2.60 | -9.11 |
| 47 | 9\47 | 229.79 | -1.39 | -5.43 |
| 52 | 10\52 | 230.77 | -0.40 | -1.75 |
| 57 | 11\57 | 231.58 | +0.40 | +1.92 |
| 62 | 12\62 | 232.26 | +1.08 | +5.60 |
| 67 | 13\67 | 232.84 | +1.66 | +9.28 |
| 68 | 13\68 | 229.41 | -1.76 | -9.99 |
| 73 | 14\73 | 230.14 | -1.04 | -6.31 |
| 78 | 15\78 | 230.77 | -0.40 | -2.63 |
See also
- 7/4 – its octave complement
- 21/16 – its fifth complement
- 7/6 – its fourth complement
- Gallery of just intervals