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 perfect mosfourth 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.

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 perfect mosfourth generators make a [[4/3]] perfect fourth. [This identification for the fifth may come in handy since 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.

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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 perfect mosfourth 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.
+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 perfect mosfourth generators make a [[4/3]] perfect fourth. [This identification for the fifth may come in handy since 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.