4000/3993: Difference between revisions
| Line 16: | Line 16: | ||
Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. | Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. | ||
Tempering it out with S9/S10 = [[8019/8000]] (so that three [[10/9]]'s are also an [[11/8]]) allows us to also temper the semiparticular [[243/242]] = ([[3/2|12/8]])/([[11/9]])<sup>2</sup> = S9/S11 leading to [[Gravity_family#Larry|Larry]] in the [[Gravity family]]. | Tempering it out with the trimitone comma S9/S10 = [[8019/8000]] (so that three [[10/9]]'s are also an [[11/8]]) allows us to also temper the semiparticular [[243/242]] = ([[3/2|12/8]])/([[11/9]])<sup>2</sup> = S9/S11 leading to [[Gravity_family#Larry|Larry]] in the [[Gravity family]]. | ||
Tempering it out with both the [[schisma]] and [[trimitone comma]] gives a description of [[65edo]] in the no-7's [[11-limit]], making it an excellent way to extend schismic to include prime 11. | |||
These are just a few examples, but there is a massive wealth of possible high-accuracy temperaments that temper out this comma. | These are just a few examples, but there is a massive wealth of possible high-accuracy temperaments that temper out this comma. | ||
[[Category:Wizardharry]] | [[Category:Wizardharry]] | ||
Revision as of 20:08, 7 April 2023
| Interval information |
pine comma
Triluyo comma
4000/3993, the wizardharry comma (from wizard and harry (named after Harry Partch)) or pine comma (for its relevance and importance to 7L 1s) is an unnoticeable 11-limit comma with a size of roughly 3.03 cents. It is the amount by which a stack of three 11/10 submajor seconds falls short of the 4/3 perfect fourth, therefore it is equal to (12/9)/(11/10)3 = S10/S11.
In terms of commas, it is trivially the difference between S10 = 100/99 and S11 = 121/120 or less trivially between S12/S14 = 540/539 and S99 = 9801/9800. It factors into 13-limit commas as (1575/1573)(2080/2079) or (625/624)(6656/6655).
Temperaments
Tempering it out means the fourth is divided into an equal stepped tetrachord, the step of which is a "trienfourth" (from "1/3 of a fourth") or "submajor second" and because it is an ultraparticular it makes 12/11 and 10/9 equidistant from 11/10.
On the low-accuracy end, this may be reminiscent of how the porcupine comma splits 4/3 into three 10/9's instead and it is for these reasons that 2.3.5.11 porkypine equates 11/10 with the superparticulars adjacent to it of 12/11 and 10/9, tempering S10 and S11 as the porcupine comma is 250/243 = S102 * S11 so through porkypine we make porcupine as efficient and elegant as it can reasonably be.
Tempering it out along with the schisma results in the rank-2 tertiaschis temperament.
Tempering it out with the trimitone comma S9/S10 = 8019/8000 (so that three 10/9's are also an 11/8) allows us to also temper the semiparticular 243/242 = (12/8)/(11/9)2 = S9/S11 leading to Larry in the Gravity family.
Tempering it out with both the schisma and trimitone comma gives a description of 65edo in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.
These are just a few examples, but there is a massive wealth of possible high-accuracy temperaments that temper out this comma.