Slendric
Slendric, a member of the gamelismic clan, has 8/7 as a generator, and three of them make a 3/2. Thus the gamelisma, 1029/1024, is tempered out. Since 1029/1024 is a relatively small comma (8.4 cents), and the error is distributed over several intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents).
The disadvantage, if you want to think of it that way, is that approximations to the 5th harmonic do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large complexity. Possible extensions of slendric to the full 7 limit include mothra, rodan, and guiron. Mothra tempers out 81/80; rodan and guiron are more complex.
This article concerns the basic 2.3.7 subgroup temperament, slendric itself.
Slendric was originally named "wonder" by Margo Schulter.[1]
Interval chains
| 296.81 | 530.50 | 764.19 | 997.88 | 31.56 | 265.25 | 498.94 | 732.63 | 966.31 | 0. | 233.69 | 467.37 | 701.06 | 934.75 | 1168.44 | 202.12 | 435.81 | 669.50 | 903.19 |
| 32/27 | 49/36 | 14/9 | 16/9 | 49/48 | 7/6 | 4/3 | 32/21 | 7/4 | 1/1 | 8/7 | 21/16 | 3/2 | 12/7 | 96/49 | 9/8 | 9/7 | 72/49 | 27/16 |
Chords
Scales
5-note and 6-note (both proper)
There is a 5-note MOS, Lssss, in which L is 7/6 and s is 8/7; and a 6-note MOS, LLLLLs, in which L is 8/7 and s is the characteristic small interval of slendric representing both 64/63 and 49/48.
Both of these scales are somewhat lacking in harmonic resources relative to similar-sized scales of other temperaments. Even within the 2.3.7 subgroup, archy and semaphore have pentatonic scales with more consonant intervals and chords; or if more accuracy is desired a 2.3.7 JI scale could be used.
Slendric really shines when used with larger scales than these. The 5-note MOS, however, has a special role in organizing the intervals of slendric because it is so close to 5edo (see below).
11-note (LsLsLsLsLss, improper)
The 11-note MOS has 9/8 "whole tones" in alternation with ~32 cent "sixth tones", with the exception of one pair of adjacent "sixth tones".
| Small ("minor") interval | 31.56 | 63.13 | 265.25 | 296.81 | 498.94 | 530.50 | 732.63 | 764.19 | 966.31 | 997.88 |
| JI intervals represented | 7/6 | 32/27 | 4/3 | 49/36 | 32/21 | 14/9 | 7/4 | 16/9 | ||
| Large ("major") interval | 202.12 | 233.69 | 435.81 | 467.37 | 669.50 | 701.06 | 903.19 | 934.75 | 1136.87 | 1168.44 |
| JI intervals represented | 9/8 | 8/7 | 9/7 | 21/16 | 72/49 | 3/2 | 27/16 | 12/7 |
Alternate way of organizing intervals
Instead of organizing the intervals according to larger and larger MOSes (none of which are proper until at least 26 notes), the intervals of slendric can be organized according to how many steps of 5edo, or equivalently the 5-note MOS, they correspond to. The "major" interval of a class is the one that's just larger than the corresponding 5edo interval, and the "minor" interval is just smaller.
| Steps of 5edo | 1 | 2 | 3 | 4 |
| "Augmented" interval | 296.81 | 530.50 | 764.19 | 997.88 |
| JI intervals represented | 32/27 | 49/36 | 14/9 | 16/9 |
| "Major" interval | 265.25 | 498.94 | 732.63 | 966.31 |
| JI intervals represented | 7/6 | 4/3 | 32/21 | 7/4 |
| "Minor" interval | 233.69 | 467.37 | 701.06 | 934.75 |
| JI intervals represented | 8/7 | 21/16 | 3/2 | 12/7 |
| "Diminished" interval | 202.12 | 435.81 | 669.50 | 903.19 |
| JI intervals represented | 9/8 | 9/7 | 72/49 | 27/16 |
Relationship with EDOs
Notable EDOs that support slendric include 31, 36, 41, and 77. CTE slendric is extremely well-approximated by 2160edo.
Scala files
Music and listening examples
- Slendric[11] wailing on SoundCloud