Mabilic
Mabilic is a rank-2 regular temperament based around the antidiatonic and armotonic scale structures. 5/2 is split into three generators which are somewhat sharper than a fourth (~520-530 cents), five of which stack (octave-reduced) to make 8/7. Mabilic in its basic form is a 2.5.7 subgroup temperament, because 3 cannot be added without a high complexity or a significant loss of accuracy. Mabilic[7] or [9], Semabila[16], and Trismegistus[25] are reasonable forms.
Extensions of Mabilic include
- Trismegistus (best tuned around 527 cents) which finds 3/2 at 15 generators up, equating it to both three 8/7s (Slendric temperament) and five 5/4s (Magic temperament).
- Mnemonic: tris- is Greek for "thrice"; three 8/7's are equated to 3/2; -megistus refers to the Magic mapping of 2.3.5
- Semabila (best tuned around 530 cents) which finds 4/3 at 10 generators up, equating it to two 8/7s (Semaphore temperament).
- Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.
- In fact, Semabila easily extends to the full 23-limit by finding 16/13 at 12 generators and 16/11 at 8 generators, which is not accurate at all in Trismegistus.
- Semabila also tunes the fifth to 25/17, finding 17 at 7 generators; then 8 generators may be assigned to 23/16. This is possible but less accurate in Trismegistus.
- Mavila (best tuned around 522-528 cents), an exotemperament which sets the generator itself equal to 4/3, and somewhat functions as an opposite to Meantone.
In Meantone, 4 fifths make a 5/4; in Mavila they make a 6/5.
In any tuning, the flat fifth generator may be identified wth 28/19. This produces a 2.5.7.19 temperament with a flat tendency for 19, and justifies the generator as an imperfect fifth of 95/64 created by stacking 5/4 and 19/16.
Intervals
Trismegistus/Mavila:
| Generators | Tuning | Interpretation | |||
|---|---|---|---|---|---|
| 2.5.7.19 | Trismegistus | Mavila | +17.23 interpretation | ||
| 0 | 0 | 1/1 | |||
| 1 | 527 | 19/14 | 4/3 | 23/17, 34/25 | |
| 2 | 1054 | 64/35 | 16/9, 15/8 | ||
| 3 | 381 | 5/4 | 9/7, 24/19 | ||
| 4 | 908 | 32/19 | 5/3 | ||
| 5 | 235 | 8/7 | 10/9 | ||
| 6 | 762 | 25/16 | 32/21 | ||
| 7 | 89 | 21/20 | 15/14 | 17/16 | |
| 8 | 616 | 10/7 | 23/16 | ||
| 9 | 1143 | 40/21 | |||
| 10 | 470 | 21/16 | |||
| 11 | 997 | 34/19 | |||
| 12 | 324 | 6/5 | |||
| 13 | 851 | ||||
| 14 | 178 | 17/15 | |||
| 15 | 705 | 3/2 | |||
Semabila:
| Generators | Tuning | Interpretation (2.3.5.7.19) | Interpretation (2...29) |
|---|---|---|---|
| 0 | 0 | 1/1 | |
| 1 | 530 | 19/14 | 23/17, 34/25, 15/11 |
| 2 | 1060 | 28/15, 64/35 | |
| 3 | 390 | 5/4, 19/15 | 14/11 |
| 4 | 920 | 32/19 | |
| 5 | 250 | 7/6, 8/7 | 15/13 |
| 6 | 780 | 25/16, 19/12 | |
| 7 | 110 | 16/15 | 17/16 |
| 8 | 640 | 10/7 | 23/16, 16/11 |
| 9 | 1170 | ||
| 10 | 500 | 4/3 | |
| 11 | 1030 | 34/19, 29/16, 20/11 | |
| 12 | 360 | 16/13 | |
| 13 | 890 | 5/3 | |
| 14 | 220 | 17/15 | |
| 15 | 750 | 32/21 | 20/13 |
