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.
• 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.
  • Mavila and trismegistus can be considered co-structural temperaments.

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