5L 3s: Difference between revisions
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=== Tridec (29&37) === | |||
In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates the large step to a "porcupine generator" of 160c to 171c, i.e. nine 13/10 generators make a [[4/3]] perfect fourth. [Some altered oneirotonic modes have three large steps.] Based on the tuning's [[29edo]] and [[37edo]] interpretations, it can in fact be viewed as a 2.3.7/5.11/5.13/5 temperament, i.e. a [[Non-over-2 temperament|non-over-2 temperament]] that approximates the chord 5:7:11:13:15. The optimal generator is 455.2178c, which 29edo's 11\29 (455.17c) is very close to, but we could accept any generator between 17\45 (453.33c) and 8\21 (457.14c), if we stipulate that the 3/2 has to be between [[7edo]]'s fifth and [[5edo]]'s fifth. | |||
The sizes of the generator, large step and small step of oneirotonic are as follows in various tridec tunings. | |||
{| class="wikitable right-2 right-3 right-4 right-5" | |||
|- | |||
! | |||
! [[21edo]] | |||
! [[29edo]] | |||
! [[37edo]] | |||
! Optimal ([[POTE]]) tuning | |||
! JI intervals represented (2.3.7/5.11/5.13/5 subgroup) | |||
|- | |||
| generator (g) | |||
| 8\21, 457.14 | |||
| 11\29, 455.17 | |||
| 14\37, 454.05 | |||
| 455.22 | |||
| 13/10 | |||
|- | |||
| L (3g - octave) | |||
| 171.43 | |||
| 165.52 | |||
| 162.16 | |||
| 165.65 | |||
| 11/10 | |||
|- | |||
| s (-5g + 2 octaves) | |||
| 114.29 | |||
| 124.14 | |||
| 129.73 | |||
| 123.91 | |||
| 14/13 | |||
|} | |} | ||