15/8: Difference between revisions
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m expanded see also section, added inverse; increased precision to 5 decimal places |
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| Ratio = 15/8 | | Ratio = 15/8 | ||
| Monzo = -3 1 1 | | Monzo = -3 1 1 | ||
| Cents = 1088. | | Cents = 1088.26871 | ||
| Name = major seventh | | Name = major seventh | ||
| Sound = jid_15_8_pluck_adu_dr220.mp3 | | Sound = jid_15_8_pluck_adu_dr220.mp3 | ||
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Since 15 is a perfect fifth above 10 (15/10 = [[3/2]]), [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triads]] can be formed with the 10th harmonic as root and 15th harmonic as perfect fifth. The simplest and most familiar example is the classic minor triad 10:12:15 -- a [[6/5]] with a [[5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 -- a [[13/10]] on bottom and a [[15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit]] inframinor triad 20:23:30. | Since 15 is a perfect fifth above 10 (15/10 = [[3/2]]), [[List_of_root-3rd-P5_triads_in_JI|root-3rd-P5 triads]] can be formed with the 10th harmonic as root and 15th harmonic as perfect fifth. The simplest and most familiar example is the classic minor triad 10:12:15 -- a [[6/5]] with a [[5/4]] stacked on top of it. Another is the Barbados triad, 10:13:15 -- a [[13/10]] on bottom and a [[15/13]] on top. And a particularly uncommon but mentionable example is the [[23-limit]] inframinor triad 20:23:30. | ||
== See also == | |||
* [[16/15]] its [[inverse interval]] | |||
* [[Gallery of just intervals]] | |||
[[Category:5-limit]] | [[Category:5-limit]] | ||
Revision as of 23:07, 26 October 2018
| Interval information |
reduced harmonic
[sound info]
In 5-limit Just Intonation, 15/8 is a major seventh of about 1088.3¢. It is also the 15th overtone (octave-reduced), and appears as a complex consonance in chords such as 8:10:12:15, a just version of a major seventh chord. Since 15 is 3*5, it can be seen as a perfect fifth above a major third or vice versa, and this understanding is compatible with the 1100¢ interval of 12edo.
Since 15 is a perfect fifth above 10 (15/10 = 3/2), root-3rd-P5 triads can be formed with the 10th harmonic as root and 15th harmonic as perfect fifth. The simplest and most familiar example is the classic minor triad 10:12:15 -- a 6/5 with a 5/4 stacked on top of it. Another is the Barbados triad, 10:13:15 -- a 13/10 on bottom and a 15/13 on top. And a particularly uncommon but mentionable example is the 23-limit inframinor triad 20:23:30.