Trisected
Trisected is the rank-2 temperament tempering out 128/125, 1029/1000, and 1029/1024 in the 7-limit, making it a member of the augmented family, keegic temperaments, and gamelismic clan. Since it tempers out 128/125, the octave is split into 3 ~5/4's, each tuned to 400 ¢ if the octave is pure. Since it tempers out 1029/1024, the perfect fifth is split into three intervals of ~8/7.Since it tempers out 1029/1000, the tritave is split into three intervals of 10/7. This means that every Pythagorean interval is split into three equal parts.
| Trisected |
56/55, 128/125, 1029/1000 (11-limit);
56/55, 91/90, 128/125, 1029/1000 (13-limit)
13-limit 21-odd-limit: 17.5 ¢
13-limit 21-odd-limit: 36 notes
In the 11-limit, the perfect fourth is split into three ~11/10's, thus tempering out 4000/3993. Additionally, the 1/3-octave period represents 14/11, tempering out 56/55 and 176/175. The 13-limit extension equates the ~10/7 with 13/9, tempering out 91/90 and 2197/2187.
For technical data, see Augmented family #Trisected.
Intervals
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Todo: complete section |
Tunings
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Todo: complete section |
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