Chords of octacot: Difference between revisions

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Below are listed the [[dyadic chord]]s of 11-limit [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.

Octacot has MOS of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-cent equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of ~~88 cents temperament~~. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.

Octacot has MOS of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-[[cent]] equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88cET. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.

= Triads =

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 Below are listed the [[dyadic chord]]s of 11-limit [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.
-Octacot has MOS of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-cent equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.
+Octacot has MOS of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-[[cent]] equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88cET. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.
 = Triads =