15/8: Difference between revisions
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| Monzo = -3 1 1 | | Monzo = -3 1 1 | ||
| Cents = 1088.26871 | | Cents = 1088.26871 | ||
| Name = classic major seventh | | Name = classic/just major seventh | ||
| Color name = y7, yo 7th | | Color name = y7, yo 7th | ||
| FJS name = M7<sup>5</sup> | | FJS name = M7<sup>5</sup> | ||
| Sound = jid_15_8_pluck_adu_dr220.mp3 | | Sound = jid_15_8_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[5-limit]] [[ | 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]]), [[ | 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 == | == See also == | ||
Revision as of 13:51, 9 September 2021
| 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.