15/8: Difference between revisions

Line 4:

| Monzo = -3 1 1

| Cents = 1088.26871

| Name = major seventh

| Name = classic major seventh

| Color name = y7, yo 7th

| FJS name = M7<sup>5</sup>

| Sound = jid_15_8_pluck_adu_dr220.mp3

~~| Color name = y7, yo 7th~~

}}

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]].

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]]), [[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~~]]

* [[16/15]] – its [[octave complement]]

* [[Gallery of just intervals]]

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[[Category:Seventh]]

[[Category:Major seventh]]

[[Category:~~Sound example~~]]

[[Category:Listen]]

[[Category:Overtone]]

@@ Line 4: / Line 4: @@
 | Monzo = -3 1 1
 | Cents = 1088.26871
-| Name = major seventh
+| Name = classic major seventh
+| Color name = y7, yo 7th
+| FJS name = M7<sup>5</sup>
 | Sound = jid_15_8_pluck_adu_dr220.mp3
-| Color name = y7, yo 7th
 }}
-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]].
+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]]), [[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]]
+* [[16/15]] – its [[octave complement]]
 * [[Gallery of just intervals]]
@@ Line 22: / Line 23: @@
 [[Category:Seventh]]
 [[Category:Major seventh]]
-[[Category:Sound example]]
+[[Category:Listen]]
 [[Category:Overtone]]