4000/3993: Difference between revisions
| Line 10: | Line 10: | ||
== Temperaments == | == 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. | 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 [[250/243|porcupine comma]] splits 4/3 into three [[10/9]]'s instead and it is for these reasons that 2.3.5.11 [[Porcupine_family#2.3.5.11_subgroup_.28porkypine.29|porkypine]] equates 11/10 with the [[superparticular]]s adjacent to it of 12/11 and 10/9, tempering S10 and S11 as the porcupine comma is [[250/243]] = S10<sup>2</sup> * S11 so through porkypine we make [[porcupine]] as efficient and elegant as it can reasonably be. | On the low-accuracy end, this may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 into three [[10/9]]'s instead and it is for these reasons that 2.3.5.11 [[Porcupine_family#2.3.5.11_subgroup_.28porkypine.29|porkypine]] equates 11/10 with the [[superparticular]]s adjacent to it of 12/11 and 10/9, tempering S10 and S11 as the porcupine comma is [[250/243]] = S10<sup>2</sup> * S11 so through porkypine we make [[porcupine]] as efficient and elegant as it can reasonably be. | ||