15/8: Difference between revisions

Line 4:

| Monzo = -3 1 1

| Cents = 1088.26871

| Name = classic major seventh

| Name = classic/just major seventh

| Color name = y7, yo 7th

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

| Sound = jid_15_8_pluck_adu_dr220.mp3

}}

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 ==

@@ Line 4: / Line 4: @@
 | Monzo = -3 1 1
 | Cents = 1088.26871
-| Name = classic major seventh
+| Name = classic/just major seventh
 | Color name = y7, yo 7th
 | FJS name = M7<sup>5</sup>
 | Sound = jid_15_8_pluck_adu_dr220.mp3
 }}
-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 ==