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| == Examples == | | == Examples == |
| === Tridec === | | === Tridec === |
| In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps to a [[4/3]] perfect fourth. [This identification may come in handy since many altered oneirotonic modes have three consecutive large steps.] Based on the JI interpretations of the [[29edo]] and [[37edo]] tunings, 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 455.2178¢, which is very close to 29edo's 11\29 (455.17¢), but we could accept any generator between 17\45 (453.33¢) and 8\21 (457.14¢), if we stipulate that the 3/2 has to be between [[7edo]]'s fifth and [[5edo]]'s fifth.
| | Tridec is a temperament generated by a generator near 455.2178¢ (for example, [[29edo|11\29]] or [[37edo|14\37]]) and has an 8-note MOS. If you restrict to the 8-note MOS, Tridec is an 2.7/5.11/5.13/5 temperament that tempers the chord 5:7:11:13; one generator represents a 13/10, three generators represent a 11/10, -4 generators represent a 7/5. |
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| Tridec essentially contains all the notes of 2.3.5 [[porcupine]] temperament and satisfies all its relations; hence it is essentially the same as 13-limit [[Ammonite]]; however, provided you restrict yourself to the 8-note MOS, you're using it as a non-over-2 temperament. | | Tridec essentially contains all the notes of 2.3.5 [[porcupine]] temperament and satisfies all its relations; hence it is essentially the same as 13-limit [[Ammonite]]; however, provided you restrict yourself to the 8-note MOS, you're using it as a non-over-2 temperament. |
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| The sizes of the generator, large step and small step of oneirotonic are as follows in various tridec tunings.
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| {| class="wikitable right-2 right-3 right-4 right-5"
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| |-
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| !
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| ! [[21edo]]
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| ! [[29edo]]
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| ! [[37edo]]
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| ! Optimal ([[POTE]]) tuning
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| ! JI intervals represented (2.3.7/5.11/5.13/5 subgroup)
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| |-
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| | generator (g)
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| | 8\21, 457.14
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| | 11\29, 455.17
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| | 14\37, 454.05
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| | 455.22
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| | 13/10
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| |-
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| | L (3g - octave)
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| | 3\21, 171.43
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| | 4\29, 165.52
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| | 5\37, 162.16
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| | 165.65
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| | 11/10
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| |-
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| | s (-5g + 2 octaves)
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| | 2\21, 114.29
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| | 3\29, 124.14
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| | 4\37, 129.73
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| | 123.91
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| | 14/13, 15/14
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| |}
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| === Sensi === | | === Sensi === |