Otonal heptad - Revision history

FloraC: Propose merging

2026-10-11T08:01:35Z

Propose merging

← Older revision		Revision as of 08:01, 11 October 2026
Line 1:		Line 1:
			{{Todo\|inline=1\|merge articles\|comment= [[Otonal heptad]] → [[Harmonics 7–14]] }}

	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.		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.

Sintel: wording

2026-10-11T03:21:39Z

wording

← Older revision		Revision as of 03:21, 11 October 2026
Line 1:		Line 1:
	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 ==		== Intervals ==
Line 61:		Line 61:
	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.		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 ==		== 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		* [[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		* [[11/8]] (551.3 cents) is 48.7 cents flat of the augmented fourth

Sintel at 02:23, 11 October 2026

2026-10-11T02:23:34Z

@@ Line 1: / Line 1: @@
 <pre>
 ! oheptad.scl
@@ Line 14: / Line 89: @@
+!
 </pre>
 [[Category:7-tone scales]]
 [[Category:Just intonation scales]]
 [[Category:Harmonic]]

Sintel: remove the pile of Fokblock

2026-10-11T02:13:11Z

remove the pile of Fokblock

@@ Line 2: / Line 2: @@
 ! oheptad.scl
+!
-Otonal heptad as a 54-wakalix
+Otonal heptad 8:9:10:11:12:13:14:16
+!
@@ Line 13: / Line 13: @@
 /1
+!
 </pre>
 [[Category:7-tone scales]]

Sintel: Sintel moved page Oheptad to Otonal heptad

2026-10-11T02:12:22Z

Sintel moved page Oheptad to Otonal heptad

← Older revision	Revision as of 02:12, 11 October 2026
(No difference)

BudjarnLambeth: Categorised, removed empty lines, added pre tags

2023-05-01T10:11:49Z

Categorised, removed empty lines, added pre tags

Show changes

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>genewardsmith: Imported revision 499334490 - Original comment:

2014-03-30T11:00:28Z

**Imported revision 499334490 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference: 
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-03-30 11:00:28 UTC</tt>. 
: The original revision id was <tt>499334490</tt>. 
: The revision comment was: <tt></tt> 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. 
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">! oheptad.scl
!
Otonal heptad as a 54-wakalix
7
!
9/8
5/4
11/8
3/2
13/8
7/4
2/1
!
! Fokblock([33/32, 22/21, 55/52, 15/14, 99/91], [6, 2, 3, 4, 2])
! = Fokblock([33/32, 27/26, 22/21, 55/52, 15/14], [6, 2, 1, 3, 4])
! = Fokblock([33/32, 27/26, 55/52, 15/14, 99/91], [6, 4, 3, 4, 1])
! = Fokblock([36/35, 22/21, 96/91, 15/14, 99/91], [3, 2, 0, 4, 5])
! = Fokblock([40/39, 22/21, 55/52, 15/14, 99/91], [0, 2, 6, 4, 2])
! = Fokblock([40/39, 22/21, 96/91, 15/14, 99/91], [3, 2, 0, 4, 5])
! = Fokblock([40/39, 27/26, 22/21, 55/52, 15/14], [0, 2, 1, 6, 4])
! = Fokblock([40/39, 27/26, 55/52, 15/14, 99/91], [0, 4, 6, 4, 1])
! = Fokblock([40/39, 33/32, 22/21, 15/14, 99/91], [3, 6, 2, 4, 2])
! = Fokblock([40/39, 33/32, 22/21, 96/91, 15/14], [3, 5, 2, 2, 4])
! = Fokblock([40/39, 33/32, 27/26, 15/14, 99/91], [3, 6, 4, 4, 1])
! = Fokblock([40/39, 33/32, 27/26, 22/21, 15/14], [3, 6, 2, 1, 4])
! = Fokblock([40/39, 33/32, 80/77, 22/21, 96/91], [3, 6, 4, 2, 2])
! = Fokblock([40/39, 36/35, 22/21, 15/14, 99/91], [0, 0, 2, 4, 5])
! = Fokblock([40/39, 36/35, 22/21, 55/52, 15/14], [0, 2, 2, 5, 4])
! = Fokblock([40/39, 65/63, 80/77, 22/21, 15/14], [3, 4, 0, 1, 6])
! = Fokblock([40/39, 80/77, 22/21, 96/91, 15/14], [3, 1, 2, 2, 6])
! = Fokblock([55/54, 40/39, 22/21, 55/52, 15/14], [4, 0, 1, 5, 4])
! = Fokblock([55/54, 40/39, 27/26, 22/21, 15/14], [6, 0, 5, 1, 4])
! = Fokblock([55/54, 40/39, 36/35, 55/52, 15/14], [2, 0, 1, 5, 4])
! = Fokblock([55/54, 40/39, 65/63, 22/21, 15/14], [6, 0, 1, 1, 6])
! = Fokblock([55/54, 40/39, 65/63, 27/26, 22/21], [6, 0, 4, 6, 1])
! = Fokblock([66/65, 36/35, 22/21, 96/91, 15/14], [5, 3, 2, 0, 6])
! = Fokblock([66/65, 36/35, 22/21, 96/91, 99/91], [2, 3, 2, 0, 6])
! = Fokblock([66/65, 40/39, 22/21, 96/91, 15/14], [5, 3, 2, 0, 6])
! = Fokblock([66/65, 40/39, 22/21, 96/91, 99/91], [2, 3, 2, 0, 6])
! = Fokblock([66/65, 40/39, 36/35, 22/21, 15/14], [5, 0, 0, 2, 6])
! = Fokblock([66/65, 40/39, 36/35, 22/21, 99/91], [2, 0, 0, 2, 6])
! = Fokblock([66/65, 40/39, 65/63, 80/77, 15/14], [1, 3, 2, 0, 6])
! = Fokblock([66/65, 40/39, 80/77, 22/21, 15/14], [2, 3, 0, 2, 6])
! = Fokblock([78/77, 40/39, 36/35, 22/21, 15/14], [1, 0, 2, 2, 6])
! = Fokblock([78/77, 40/39, 36/35, 22/21, 55/52], [4, 0, 2, 2, 6])
! = Fokblock([78/77, 40/39, 65/63, 22/21, 15/14], [0, 0, 4, 1, 6])
! = Fokblock([78/77, 55/54, 40/39, 22/21, 15/14], [1, 4, 0, 1, 6])
! = Fokblock([78/77, 55/54, 40/39, 22/21, 55/52], [4, 4, 0, 1, 6])
! = Fokblock([78/77, 55/54, 40/39, 36/35, 15/14], [1, 2, 0, 1, 6])
! = Fokblock([78/77, 55/54, 40/39, 36/35, 55/52], [4, 2, 0, 1, 6])
! = Fokblock([78/77, 65/63, 80/77, 22/21, 15/14], [3, 4, 0, 1, 6])
! = Fokblock([78/77, 66/65, 40/39, 22/21, 15/14], [0, 2, 0, 2, 6])
! = Fokblock([78/77, 66/65, 40/39, 65/63, 15/14], [0, 1, 0, 2, 6])
! = Fokblock([78/77, 66/65, 65/63, 80/77, 15/14], [3, 1, 2, 0, 6])
! = Fokblock([78/77, 66/65, 80/77, 22/21, 15/14], [3, 2, 0, 2, 6])
! = Fokblock([144/143, 40/39, 27/26, 22/21, 15/14], [0, 3, 5, 1, 4])
! = Fokblock([144/143, 40/39, 33/32, 22/21, 15/14], [2, 3, 5, 1, 4])
! = Fokblock([144/143, 40/39, 33/32, 80/77, 22/21], [2, 3, 6, 4, 1])
! = Fokblock([144/143, 40/39, 33/32, 80/77, 96/91], [4, 3, 6, 4, 1])
! = Fokblock([144/143, 40/39, 33/32, 96/91, 15/14], [4, 3, 5, 1, 4])
! = Fokblock([144/143, 40/39, 65/63, 22/21, 15/14], [0, 3, 1, 1, 6])
! = Fokblock([144/143, 40/39, 65/63, 27/26, 22/21], [0, 3, 4, 6, 1])
! = Fokblock([144/143, 40/39, 80/77, 22/21, 15/14], [2, 3, 1, 1, 6])
! = Fokblock([144/143, 40/39, 80/77, 96/91, 15/14], [4, 3, 1, 1, 6])
! = Fokblock([144/143, 55/54, 27/26, 22/21, 15/14], [0, 3, 5, 1, 4])
! = Fokblock([144/143, 55/54, 65/63, 22/21, 15/14], [0, 3, 1, 1, 6])
! = Fokblock([144/143, 55/54, 65/63, 27/26, 22/21], [0, 3, 4, 6, 1])
</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>oheptad</title></head><body>! oheptad.scl 
! 
Otonal heptad as a 54-wakalix 
7 
! 
9/8 
5/4 
11/8 
3/2 
13/8 
7/4 
2/1 
! 
! Fokblock([33/32, 22/21, 55/52, 15/14, 99/91], [6, 2, 3, 4, 2]) 
! = Fokblock([33/32, 27/26, 22/21, 55/52, 15/14], [6, 2, 1, 3, 4]) 
! = Fokblock([33/32, 27/26, 55/52, 15/14, 99/91], [6, 4, 3, 4, 1]) 
! = Fokblock([36/35, 22/21, 96/91, 15/14, 99/91], [3, 2, 0, 4, 5]) 
! = Fokblock([40/39, 22/21, 55/52, 15/14, 99/91], [0, 2, 6, 4, 2]) 
! = Fokblock([40/39, 22/21, 96/91, 15/14, 99/91], [3, 2, 0, 4, 5]) 
! = Fokblock([40/39, 27/26, 22/21, 55/52, 15/14], [0, 2, 1, 6, 4]) 
! = Fokblock([40/39, 27/26, 55/52, 15/14, 99/91], [0, 4, 6, 4, 1]) 
! = Fokblock([40/39, 33/32, 22/21, 15/14, 99/91], [3, 6, 2, 4, 2]) 
! = Fokblock([40/39, 33/32, 22/21, 96/91, 15/14], [3, 5, 2, 2, 4]) 
! = Fokblock([40/39, 33/32, 27/26, 15/14, 99/91], [3, 6, 4, 4, 1]) 
! = Fokblock([40/39, 33/32, 27/26, 22/21, 15/14], [3, 6, 2, 1, 4]) 
! = Fokblock([40/39, 33/32, 80/77, 22/21, 96/91], [3, 6, 4, 2, 2]) 
! = Fokblock([40/39, 36/35, 22/21, 15/14, 99/91], [0, 0, 2, 4, 5]) 
! = Fokblock([40/39, 36/35, 22/21, 55/52, 15/14], [0, 2, 2, 5, 4]) 
! = Fokblock([40/39, 65/63, 80/77, 22/21, 15/14], [3, 4, 0, 1, 6]) 
! = Fokblock([40/39, 80/77, 22/21, 96/91, 15/14], [3, 1, 2, 2, 6]) 
! = Fokblock([55/54, 40/39, 22/21, 55/52, 15/14], [4, 0, 1, 5, 4]) 
! = Fokblock([55/54, 40/39, 27/26, 22/21, 15/14], [6, 0, 5, 1, 4]) 
! = Fokblock([55/54, 40/39, 36/35, 55/52, 15/14], [2, 0, 1, 5, 4]) 
! = Fokblock([55/54, 40/39, 65/63, 22/21, 15/14], [6, 0, 1, 1, 6]) 
! = Fokblock([55/54, 40/39, 65/63, 27/26, 22/21], [6, 0, 4, 6, 1]) 
! = Fokblock([66/65, 36/35, 22/21, 96/91, 15/14], [5, 3, 2, 0, 6]) 
! = Fokblock([66/65, 36/35, 22/21, 96/91, 99/91], [2, 3, 2, 0, 6]) 
! = Fokblock([66/65, 40/39, 22/21, 96/91, 15/14], [5, 3, 2, 0, 6]) 
! = Fokblock([66/65, 40/39, 22/21, 96/91, 99/91], [2, 3, 2, 0, 6]) 
! = Fokblock([66/65, 40/39, 36/35, 22/21, 15/14], [5, 0, 0, 2, 6]) 
! = Fokblock([66/65, 40/39, 36/35, 22/21, 99/91], [2, 0, 0, 2, 6]) 
! = Fokblock([66/65, 40/39, 65/63, 80/77, 15/14], [1, 3, 2, 0, 6]) 
! = Fokblock([66/65, 40/39, 80/77, 22/21, 15/14], [2, 3, 0, 2, 6]) 
! = Fokblock([78/77, 40/39, 36/35, 22/21, 15/14], [1, 0, 2, 2, 6]) 
! = Fokblock([78/77, 40/39, 36/35, 22/21, 55/52], [4, 0, 2, 2, 6]) 
! = Fokblock([78/77, 40/39, 65/63, 22/21, 15/14], [0, 0, 4, 1, 6]) 
! = Fokblock([78/77, 55/54, 40/39, 22/21, 15/14], [1, 4, 0, 1, 6]) 
! = Fokblock([78/77, 55/54, 40/39, 22/21, 55/52], [4, 4, 0, 1, 6]) 
! = Fokblock([78/77, 55/54, 40/39, 36/35, 15/14], [1, 2, 0, 1, 6]) 
! = Fokblock([78/77, 55/54, 40/39, 36/35, 55/52], [4, 2, 0, 1, 6]) 
! = Fokblock([78/77, 65/63, 80/77, 22/21, 15/14], [3, 4, 0, 1, 6]) 
! = Fokblock([78/77, 66/65, 40/39, 22/21, 15/14], [0, 2, 0, 2, 6]) 
! = Fokblock([78/77, 66/65, 40/39, 65/63, 15/14], [0, 1, 0, 2, 6]) 
! = Fokblock([78/77, 66/65, 65/63, 80/77, 15/14], [3, 1, 2, 0, 6]) 
! = Fokblock([78/77, 66/65, 80/77, 22/21, 15/14], [3, 2, 0, 2, 6]) 
! = Fokblock([144/143, 40/39, 27/26, 22/21, 15/14], [0, 3, 5, 1, 4]) 
! = Fokblock([144/143, 40/39, 33/32, 22/21, 15/14], [2, 3, 5, 1, 4]) 
! = Fokblock([144/143, 40/39, 33/32, 80/77, 22/21], [2, 3, 6, 4, 1]) 
! = Fokblock([144/143, 40/39, 33/32, 80/77, 96/91], [4, 3, 6, 4, 1]) 
! = Fokblock([144/143, 40/39, 33/32, 96/91, 15/14], [4, 3, 5, 1, 4]) 
! = Fokblock([144/143, 40/39, 65/63, 22/21, 15/14], [0, 3, 1, 1, 6]) 
! = Fokblock([144/143, 40/39, 65/63, 27/26, 22/21], [0, 3, 4, 6, 1]) 
! = Fokblock([144/143, 40/39, 80/77, 22/21, 15/14], [2, 3, 1, 1, 6]) 
! = Fokblock([144/143, 40/39, 80/77, 96/91, 15/14], [4, 3, 1, 1, 6]) 
! = Fokblock([144/143, 55/54, 27/26, 22/21, 15/14], [0, 3, 5, 1, 4]) 
! = Fokblock([144/143, 55/54, 65/63, 22/21, 15/14], [0, 3, 1, 1, 6]) 
! = Fokblock([144/143, 55/54, 65/63, 27/26, 22/21], [0, 3, 4, 6, 1])</body></html></pre></div>