Miscellaneous 16-form scales

Lou Harrison 16-note scale

This 16-note scale byLou Harrison is based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addition to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4).

This may be considered a justly-tuned Armodue scale, though other options are available.

The composer Andrián Pertout used a very similar scale in his composition "Sonus dulcis" (article on archive.org), namely the following (according to Armodue):

Armodue note	Interval	Ratio	Cents
1	unison	1/1	0
1#	major half-tone	16/15	112
2	minor tone	10/9	182
2#	major tone	9/8	204
3	minor third	6/5	316
3#	major third	5/4	386
4	fourth	4/3	498
5	harmonic tritone	45/32	590
5#	cyclic tritone	64/45	610
6	fifth	3/2	702
6#	diminished sixth	8/5	814
7	harmonic sixth	5/3	884
7#	harmonic minor seventh	7/4	969
8	minor seventh	16/9	996
8#	minor seventh	9/5	1018
9	major seventh	15/8	1088

Vector Graphics' just Armodue scale

! untitled scale.scl
! Created using Scale Workshop 3.1.0
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! https://scaleworkshop.plainsound.org/scale/VBpdSlwF9
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Untitled tuning
 16
!
 21/20
 35/32
 8/7
 6/5
 5/4
 64/49
 4/3
 7/5
 3/2
 49/32
 8/5
 5/3
 7/4
 64/35
 40/21
 2/1

A scale which uses many 5- and 7-limit intervals, intended as an alternative scale for Armodue theory that more closely matches 16edo and Armodue's theoretical basis as a 2.5.7 system.