5L 3s: Difference between revisions

Line 506:

=== Tridec (29&37) ===

In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps make a [[4/3]] perfect fourth. [This identification 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.

In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps make a [[4/3]] perfect fourth. [This identification 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 is very close to 29edo's 11\29 (455.17c), 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.

Line 526:

|-

| L (3g - octave)

| 171.43

| 3\21, 171.43

| 165.52

| 4\29, 165.52

| 162.16

| 5\37, 162.16

| 165.65

| 11/10

|-

| s (-5g + 2 octaves)

| 114.29

| 2\21, 114.29

| 124.14

| 3\29, 124.14

| 129.73

| 4\37, 129.73

| 123.91

| 14/13

| 14/13, 15/14

|}

@@ Line 506: / Line 506: @@
 === Tridec (29&37) ===
-In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps make a [[4/3]] perfect fourth. [This identification 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.
+In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps make a [[4/3]] perfect fourth. [This identification 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 is very close to 29edo's 11\29 (455.17c), 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.
@@ Line 526: / Line 526: @@
 |-
 | L (3g - octave)
-| 171.43
+| 3\21, 171.43
-| 165.52
+| 4\29, 165.52
-| 162.16
+| 5\37, 162.16
 | 165.65
 | 11/10
 |-
 | s (-5g + 2 octaves)
-| 114.29
+| 2\21, 114.29
-| 124.14
+| 3\29, 124.14
-| 129.73
+| 4\37, 129.73
 | 123.91
-| 14/13
+| 14/13, 15/14
 |}