5L 4s: Difference between revisions
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=== Semaphore === | === Semaphore === | ||
We can view [[semaphore]] as any 5L 4s tuning where two [[semifourth]] generators make a ''diatonic'' ([[5L 2s]]) fourth, i.e. any tuning where the semifourth is between 1\5 (240¢) or 3\14 (257.14¢). One important sub-range of semaphore is given by stipulating that two semifourth generators must make a ''meantone'' fourth; i.e. that four fifths should approximate a [[5/4]] major third. This results in [[godzilla]] temperament, which is supported by [[19edo]] and [[24edo]]. | We can view [[semaphore]] as any 5L 4s tuning where two [[semifourth]] generators make a ''diatonic'' ([[5L 2s]]) fourth, i.e. any tuning where the semifourth is between 1\5 (240¢) or 3\14 (257.14¢). One important sub-range of semaphore is given by stipulating that two semifourth generators must make a ''meantone'' fourth; i.e. that four fifths should approximate a [[5/4]] major third. This results in [[godzilla]] temperament, which is supported by [[19edo]] and [[24edo]]. | ||
The sizes of the generator, large step and small step of oneirotonic are as follows in various petrtri tunings. | |||
{| class="wikitable right-2 right-3 right-4 right-5" | |||
|- | |||
! | |||
! [[14edo]] | |||
! [[19edo]] | |||
! [[24edo]] | |||
| [[29edo]] | |||
|- | |||
| generator (g) | |||
| 3\14, 257.14 | |||
| 4\19, 252.63 | |||
| 5\24, 250. | |||
| 6\29, 248.28 | |||
|- | |||
| L (octave - 4g) | |||
| 171.43 | |||
| 189.47 | |||
| 200.00 | |||
| 206.90 | |||
|- | |||
| s (5g - octave) | |||
| 85.71 | |||
| 63.16 | |||
| 50.00 | |||
| 41.38 | |||
|} | |||
=== Superpelog === | === Superpelog === | ||
For convenience' sake, we can view [[superpelog]] as any 5L 4s tuning where two [[semifourth]] generators make a ''superdiatonic'' ([[7L 2s]]) fourth, i.e. any tuning where the semifourth is between 3\14 (257.14¢) and 2\9 (266.67¢). [[23edo]]'s 5\23 (260.87¢) is an example of a superpelog generator. | For convenience' sake, we can view [[superpelog]] as any 5L 4s tuning where two [[semifourth]] generators make a ''superdiatonic'' ([[7L 2s]]) fourth, i.e. any tuning where the semifourth is between 3\14 (257.14¢) and 2\9 (266.67¢). [[23edo]]'s 5\23 (260.87¢) is an example of a superpelog generator. | ||
{| class="wikitable right-2 right-3 right-4 right-5" | |||
|- | |||
! | |||
! [[23edo]] | |||
! [[32edo]] | |||
! [[37edo]] | |||
|- | |||
| generator (g) | |||
| 5\23, 252.63 | |||
| 7\32, 262.50 | |||
| 8\37, 259.46 | |||
|- | |||
| L (octave - 4g) | |||
| 156.52 | |||
| 150.00 | |||
| 162.16 | |||
|- | |||
| s (5g - octave) | |||
| 104.35 | |||
| 112.50 | |||
| 97.30 | |||
|} | |||
== Notation == | == Notation == | ||