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'''Mabilic''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] scale structure. [[5/4|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''' is a rank-2 [[regular temperament]] based around the [[antidiatonic]] scale structure. [[5/4|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 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.
{{Cat|Temperaments}}


Extensions of Mabilic include  
Extensions of Mabilic include  
Line 14: Line 16:
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
!Generators
!Tuning (Trismegistus/Mavila)
!Tuning (Semabila)
!Interpretation (2.5.7)
!Interpretation (Trismegistus)
!Interpretation (Mavila)
!Interpretation (Semabila)
|-
|-
! Generators !! Tuning (Trismegistus/Mavila) !! Tuning (Semabila) !! Interpretation (2.5.7) !! Interpretation (Trismegistus) !! Interpretation (Mavila) !! Interpretation (Semabila)
| -15
|495
|450
|
|4/3
|
|21/16
|-
|-
| -15|| 495|| 450|| || 4/3|| || 21/16
| -14
|1022
|980
|
|
|
|
|-
|-
| -14|| 1022|| 980|| || || ||  
| -13
|349
|310
|
|
|
|6/5
|-
|-
| -13|| 349|| 310|| || || || 6/5
| -12
|876
|840
|
|5/3
|
|
|-
|-
| -12|| 876|| 840|| || 5/3|| ||  
| -11
|203
|170
|
|
|
|
|-
|-
| -11|| 203|| 170|| || || ||  
| -10
|730
|700
|
|32/21
|
|3/2
|-
|-
| -10|| 730|| 700|| || 32/21|| || 3/2
| -9
|57
|30
|
|
|21/20
|
|-
|-
| -9|| 57|| 30|| || || 21/20||  
| -8
|584
|560
|7/5
|
|
|
|-
|-
| -8|| 584|| 560|| 7/5|| || ||
| -7
|1111
|1090
|
|40/21
|28/15
|15/8
|-
|-
| -7|| 1111|| 1090|| || 40/21|| 28/15|| 15/8
| -6
|438
|420
|32/25
|
|21/16
|
|-
|-
| -6|| 438|| 420|| 32/25|| || 21/16||
| -5
|965
|950
|7/4
|
|
|12/7
|-
|-
| -5|| 965|| 950|| 7/4|| || || 12/7
| -4
|292
|280
|
|
|6/5
|
|-
|-
| -4|| 292|| 280|| || || 6/5||  
| -3
|819
|810
|8/5
|
|14/9
|
|-
|-
| -3|| 819|| 810|| 8/5|| || 14/9||
| -2
|146
|140
|35/32
|
|16/15, 9/8
|15/14
|-
|-
| -2|| 146|| 140|| 35/32|| || 16/15, 9/8|| 15/14
| -1
|673
|670
|
|
|3/2
|
|-
|-
| -1|| 673|| 670|| || || 3/2||  
|0
|0
|0
|1/1
|
|
|
|-
|-
| 0|| 0|| 0|| 1/1|| || ||  
|1
|527
|530
|
|
|4/3
|
|-
|-
| 1|| 527|| 530|| || || 4/3||
|2
|1054
|1060
|64/35
|
|16/9, 15/8
|28/15
|-
|-
| 2|| 1054|| 1060|| 64/35|| || 16/9, 15/8|| 28/15
|3
|381
|390
|5/4
|
|9/7
|
|-
|-
| 3|| 381|| 390|| 5/4|| || 9/7||  
|4
|908
|920
|
|
|5/3
|
|-
|-
| 4|| 908|| 920|| || || 5/3||
|5
|235
|250
|8/7
|
|
|7/6
|-
|-
| 5|| 235|| 250|| 8/7|| || || 7/6
|6
|762
|780
|25/16
|
|32/21
|
|-
|-
| 6|| 762|| 780|| 25/16|| || 32/21||
|7
|89
|110
|
|21/20
|15/14
|16/15
|-
|-
| 7|| 89|| 110|| || 21/20|| 15/14|| 16/15
|8
|616
|640
|10/7
|
|
|
|-
|-
| 8|| 616|| 640|| 10/7|| || ||  
|9
|1143
|1170
|
|
|40/21
|
|-
|-
| 9|| 1143|| 1170|| || || 40/21||
|10
|470
|500
|
|21/16
|
|4/3
|-
|-
| 10|| 470|| 500|| || 21/16|| || 4/3
|11
|997
|1030
|
|
|
|
|-
|-
| 11|| 997|| 1030|| || || ||  
|12
|324
|360
|
|6/5
|
|
|-
|-
| 12|| 324|| 360|| || 6/5|| ||
|13
|851
|890
|
|
|
|5/3
|-
|-
| 13|| 851|| 890|| || || || 5/3
|14
|-
|178
| 14|| 178|| 220|| || || ||  
|220
|-
|
| 15|| 705|| 750|| || 3/2|| || 32/21
|
|
|
|-
|-
|15
|705
|750
|
|3/2
|
|32/21
|}


{{Cat|Temperaments}}
{{Navbox regtemp}}
{{Navbox regtemp}}

Revision as of 11:36, 22 February 2026

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



View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Gentle-fifth temperaments • Archy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperament Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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