Mabilic
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(Redirected from Trismegistus)
Mabilic is a rank-2 regular temperament based around the antidiatonic scale structure. 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.
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).
- 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 sharp generator may be identified wth 28/19. This produces an accurate 2.5.7.19 temperament, and justifies the generator as an imperfect fifth of 95/64 created by stacking 5/4 and 19/16.
Intervals
| Generators | Tuning (Trismegistus/Mavila) | Tuning (Semabila) | Interpretation (2.5.7) | Interpretation (Trismegistus) | Interpretation (Mavila) | Interpretation (Semabila) |
|---|---|---|---|---|---|---|
| -15 | 495 | 450 | 4/3 | 21/16 | ||
| -14 | 1022 | 980 | ||||
| -13 | 349 | 310 | 6/5 | |||
| -12 | 876 | 840 | 5/3 | |||
| -11 | 203 | 170 | ||||
| -10 | 730 | 700 | 32/21 | 3/2 | ||
| -9 | 57 | 30 | 21/20 | |||
| -8 | 584 | 560 | 7/5 | |||
| -7 | 1111 | 1090 | 40/21 | 28/15 | 15/8 | |
| -6 | 438 | 420 | 32/25 | 21/16 | ||
| -5 | 965 | 950 | 7/4 | 12/7 | ||
| -4 | 292 | 280 | 6/5 | |||
| -3 | 819 | 810 | 8/5 | 14/9 | ||
| -2 | 146 | 140 | 35/32 | 16/15, 9/8 | 15/14 | |
| -1 | 673 | 670 | 3/2 | |||
| 0 | 0 | 0 | 1/1 | |||
| 1 | 527 | 530 | 4/3 | |||
| 2 | 1054 | 1060 | 64/35 | 16/9, 15/8 | 28/15 | |
| 3 | 381 | 390 | 5/4 | 9/7 | ||
| 4 | 908 | 920 | 5/3 | |||
| 5 | 235 | 250 | 8/7 | 7/6 | ||
| 6 | 762 | 780 | 25/16 | 32/21 | ||
| 7 | 89 | 110 | 21/20 | 15/14 | 16/15 | |
| 8 | 616 | 640 | 10/7 | |||
| 9 | 1143 | 1170 | 40/21 | |||
| 10 | 470 | 500 | 21/16 | 4/3 | ||
| 11 | 997 | 1030 | ||||
| 12 | 324 | 360 | 6/5 | |||
| 13 | 851 | 890 | 5/3 | |||
| 14 | 178 | 220 | ||||
| 15 | 705 | 750 | 3/2 | 32/21 |
