5L 4s: Difference between revisions
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There are not really good temperament interpretations for 5L 4s scales except for semaphore or godzilla (and even [[semaphore]] is debatable as a temperament because it is so inaccurate), but 5L 4s tunings can be divided into two major ranges: | There are not really good temperament interpretations for 5L 4s scales except for semaphore or godzilla (and even [[semaphore]] is debatable as a temperament because it is so inaccurate), but 5L 4s tunings can be divided into two major ranges: | ||
# [[Semaphore]] generated by semifourths flatter than 3\14 (257.14¢). This implies a diatonic fifth. | # [[Semaphore]] generated by semifourths flatter than 3\14 (257.14¢). This implies a diatonic fifth. | ||
# [[ | # [[Superpelog]], or [[bug]], generated by semifourths sharper than 3\14 (257.14¢). This implies a "[[mavila]]" or superdiatonic fifth. | ||
== Scale tree == | == Scale tree == | ||
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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]]. | ||
=== | === Superpelog === | ||
For convenience' sake, we can view [[ | 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 bug generator. | ||
== Notation == | == Notation == | ||