Mabilic and trismegistus: Difference between revisions

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{{Infobox regtemp|Optimization method=POTE|Generator tuning=527.236|Mapping=1; -3 5|Subgroups=2.5.7; 2.3.5.7|Title=Mabilic; trismegistus|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)|Generator=175/128|Edo join 1=16|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 cents. Mabilic, as a result, tempers out the '''mabilisma''' 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[Mavila family#Armodue|armodue]] temperament. As such, mabilic can be associated with MOS scales like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not 3/2, [[2L 5s#Notation|melodic]] chain-of-fifths notation makes some amount of sense to use here.

Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.

Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Similarly, since 8/7 is at 5 steps, trismegistus is a slendric temperament.Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.

There is an alternative extension, '''semabila''' ([[Mabila family#Semabila]]), which is a semaphore temperament (hence its name) and thus finds 4/3 at 10 generators.

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 {{Infobox regtemp|Optimization method=POTE|Generator tuning=527.236|Mapping=1; -3 5|Subgroups=2.5.7; 2.3.5.7|Title=Mabilic; trismegistus|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072  (2.3.5.7)|Generator=175/128|Edo join 1=16|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 cents. Mabilic, as a result, tempers out the '''mabilisma''' 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[Mavila family#Armodue|armodue]] temperament. As such, mabilic can be associated with MOS scales like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not 3/2, [[2L 5s#Notation|melodic]] chain-of-fifths notation makes some amount of sense to use here.
-Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.
+Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Similarly, since 8/7 is at 5 steps, trismegistus is a slendric temperament.Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.
 There is an alternative extension, '''semabila''' ([[Mabila family#Semabila]]), which is a semaphore temperament (hence its name) and thus finds 4/3 at 10 generators.