Sparkisma: Difference between revisions
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The '''sparkisma''', with a ratio of '''14400/14399''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] that separates the lynchisma ([[120/119]]) and the biyatisma ([[121/120]]), as well as the amount by which a stack consisting of [[7/4]], [[121/64]] and [[17/16]] falls short of [[225/128]], the Neapolitan augmented sixth, upon [[octave reduction]]. Tempering this out in the full 17-limit results in the '''sparkismic temperament''', or in the 2.3.5.7.11.17 subgroup, the '''spark temperament'''. | The '''sparkisma''', with a ratio of '''14400/14399''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] that separates the lynchisma ([[120/119]]) and the biyatisma ([[121/120]]), as well as the amount by which a stack consisting of [[7/4]], [[121/64]] and [[17/16]] falls short of [[225/128]], the Neapolitan augmented sixth, upon [[octave reduction]]. It is also equal to the difference between ([[99/70]])/([[11/10]])<sup>3</sup> = 900/847 and [[17/16]], so because of the relation to stacking 11/10's and to the half-octave interval 99/70 one may want to temper [[9801/9800]] too (and possibly also [[4000/3993|S10/S11]] if you want to equate (11/10)<sup>3</sup> with 4/3). Tempering this out in the full 17-limit results in the '''sparkismic temperament''', or in the 2.3.5.7.11.17 subgroup, the '''spark temperament'''. | ||
== See also == | == See also == | ||
Revision as of 19:36, 2 August 2024
| Interval information |
reduced
The sparkisma, with a ratio of 14400/14399, is an unnoticeable 17-limit superparticular comma that separates the lynchisma (120/119) and the biyatisma (121/120), as well as the amount by which a stack consisting of 7/4, 121/64 and 17/16 falls short of 225/128, the Neapolitan augmented sixth, upon octave reduction. It is also equal to the difference between (99/70)/(11/10)3 = 900/847 and 17/16, so because of the relation to stacking 11/10's and to the half-octave interval 99/70 one may want to temper 9801/9800 too (and possibly also S10/S11 if you want to equate (11/10)3 with 4/3). Tempering this out in the full 17-limit results in the sparkismic temperament, or in the 2.3.5.7.11.17 subgroup, the spark temperament.