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 ! ! https://scaleworkshop.plainsound.org/scale/VBpdSlwF9 ! 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.