Otonal heptad: Difference between revisions

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The '''otonal heptad''' is the seven-note [[just intonation]] scale 8:9:10:11:12:13:14:16: the harmonics 8 through 14 ~~and~~ the octave. It is a common diatonic~~-like~~ scale, and also sometimes called "the overtone scale" (see [[overtone scale]]). It is a rotation of [[Harmonics 7–14|harmonics 7–14]]: starting that scale on its second degree, the 8th harmonic. It is also [[Harmonics 8–16|harmonics 8–16]] without the 15th harmonic. As a [[13-limit]] scale built from consecutive harmonics, all of its notes share the same fundamental.

The '''otonal heptad''' is the seven-note [[just intonation]] scale 8:9:10:11:12:13:14:16: the harmonics 8 through 14, plus the octave. It is a common diatonic scale, and also sometimes called "the overtone scale" (see [[overtone scale]]). It is a rotation of [[Harmonics 7–14|harmonics 7–14]]: starting that scale on its second degree, the 8th harmonic. It is also [[Harmonics 8–16|harmonics 8–16]] without the 15th harmonic. As a [[13-limit]] scale built from consecutive harmonics, all of its notes share the same fundamental.

== Intervals ==

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The steps of the scale are [[9/8]], [[10/9]], [[11/10]], [[12/11]], [[13/12]], [[14/13]] and [[8/7]]. All but the last are [[superparticular]] steps between consecutive harmonics, and the last is the 14:16 step that closes the octave.

Above the root, the scale contains the [[4:5:6~~:7|~~harmonic seventh chord]] (~~1/1,~~ 5~~/4, 3/2,~~ 7/4), as well as 4:5:6 ~~(the major triad) and 4:5~~:7:9:11:13 (an extended harmonic 13th chord). It has no perfect fourth and no major seventh.

Above the root, the scale contains the [[just major triad]] (4:5:6), the [[harmonic seventh chord]] (4:5:6:7), as well as 4:5:6:7:9:11:13 (an extended harmonic 13th chord). It has no perfect fourth and no major seventh.

== Relation to the acoustic scale ==

The scale approximates the '''acoustic scale''' (also called the ''overtone scale'' or ''lydian dominant'' scale in jazz): a diatonic scale with a raised fourth and a lowered seventh, the fourth mode of the ascending melodic minor scale. The name is commonly said to come from the scale's resemblance to this segment of the harmonic series. In terms of the diatonic degrees, the ~~otonal heptad~~ is 1, 2, 3, {{sharp}}4, 5, 6, {{flat}}7~~, with some deviations from~~ [[12edo]]:

The scale approximates the '''acoustic scale''' (also called the ''overtone scale'' or ''lydian dominant'' scale in jazz): a diatonic scale with a raised fourth and a lowered seventh, the fourth mode of the ascending melodic minor scale. The name is commonly said to come from the scale's resemblance to this segment of the harmonic series. In terms of the diatonic degrees, the acoustic scale is 1, 2, 3, {{sharp}}4, 5, 6, {{flat}}7. The common [[12edo]] version deviates significantly from the just intervals:

* [[5/4]] (386.3 cents) is 13.7 cents flat of the 12edo major third

* [[11/8]] (551.3 cents) is 48.7 cents flat of the augmented fourth

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-The '''otonal heptad''' is the seven-note [[just intonation]] scale 8:9:10:11:12:13:14:16: the harmonics 8 through 14 and the octave. It is a common diatonic-like scale, and also sometimes called "the overtone scale" (see [[overtone scale]]). It is a rotation of [[Harmonics 7–14|harmonics 7–14]]: starting that scale on its second degree, the 8th harmonic. It is also [[Harmonics 8–16|harmonics 8–16]] without the 15th harmonic. As a [[13-limit]] scale built from consecutive harmonics, all of its notes share the same fundamental.
+The '''otonal heptad''' is the seven-note [[just intonation]] scale 8:9:10:11:12:13:14:16: the harmonics 8 through 14, plus the octave. It is a common diatonic scale, and also sometimes called "the overtone scale" (see [[overtone scale]]). It is a rotation of [[Harmonics 7–14|harmonics 7–14]]: starting that scale on its second degree, the 8th harmonic. It is also [[Harmonics 8–16|harmonics 8–16]] without the 15th harmonic. As a [[13-limit]] scale built from consecutive harmonics, all of its notes share the same fundamental.
 == Intervals ==
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 The steps of the scale are [[9/8]], [[10/9]], [[11/10]], [[12/11]], [[13/12]], [[14/13]] and [[8/7]]. All but the last are [[superparticular]] steps between consecutive harmonics, and the last is the 14:16 step that closes the octave.
-Above the root, the scale contains the [[4:5:6:7|harmonic seventh chord]] (1/1, 5/4, 3/2, 7/4), as well as 4:5:6 (the major triad) and 4:5:7:9:11:13 (an extended harmonic 13th chord). It has no perfect fourth and no major seventh.
+Above the root, the scale contains the [[just major triad]] (4:5:6), the [[harmonic seventh chord]] (4:5:6:7), as well as 4:5:6:7:9:11:13 (an extended harmonic 13th chord). It has no perfect fourth and no major seventh.
 == Relation to the acoustic scale ==
-The scale approximates the '''acoustic scale''' (also called the ''overtone scale'' or ''lydian dominant'' scale in jazz): a diatonic scale with a raised fourth and a lowered seventh, the fourth mode of the ascending melodic minor scale. The name is commonly said to come from the scale's resemblance to this segment of the harmonic series. In terms of the diatonic degrees, the otonal heptad is 1, 2, 3, {{sharp}}4, 5, 6, {{flat}}7, with some deviations from [[12edo]]:
+The scale approximates the '''acoustic scale''' (also called the ''overtone scale'' or ''lydian dominant'' scale in jazz): a diatonic scale with a raised fourth and a lowered seventh, the fourth mode of the ascending melodic minor scale. The name is commonly said to come from the scale's resemblance to this segment of the harmonic series. In terms of the diatonic degrees, the acoustic scale is 1, 2, 3, {{sharp}}4, 5, 6, {{flat}}7. The common [[12edo]] version deviates significantly from the just intervals:
 * [[5/4]] (386.3 cents) is 13.7 cents flat of the 12edo major third
 * [[11/8]] (551.3 cents) is 48.7 cents flat of the augmented fourth