5L 4s: Difference between revisions
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Semiquartal tunings can be divided into two major ranges: | Semiquartal tunings can be divided into two major ranges: | ||
# | # "[[hard]]-of-center" semiquartal, generated by semifourths flatter than 3\14 (257.14¢). This implies a diatonic fifth. | ||
#: The generator could be viewed as a 15/13, and the resulting "ultramajor" chords and "inframinor" triads could be viewed as approximating 10:13:15 and 26:30:39. See [[Arto and Tendo Theory]]. | #: The generator could be viewed as a 15/13, and the resulting "ultramajor" chords and "inframinor" triads could be viewed as approximating 10:13:15 and 26:30:39. See [[Arto and Tendo Theory]]. | ||
# | # "[[soft]]-of-center" semiquartal, generated by semifourths sharper than 3\14 (257.14¢). This implies a "[[mavila]]" or superdiatonic fifth. | ||
== Notation == | == Notation == | ||
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== Tuning ranges == | == Tuning ranges == | ||
=== | === Hard-of-basic === | ||
These tunings satisfy the property that 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¢). | |||
The sizes of the generator, large step and small step of 5L 4s are as follows in various semaphore tunings. | The sizes of the generator, large step and small step of 5L 4s are as follows in various semaphore tunings. | ||
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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 can be considered the [[19edo]] (4\19)-to-[[24edo]] (5\24) range, i.e. parahard semiquartal, which also contains [[43edo]] (9\43) and [[62edo]] (13\62). | 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 can be considered the [[19edo]] (4\19)-to-[[24edo]] (5\24) range, i.e. parahard semiquartal, which also contains [[43edo]] (9\43) and [[62edo]] (13\62). | ||
=== | === Soft-of-basic === | ||
These are tunings where two [[semifourth]] generators make a ''superdiatonic'' ([[7L 2s]]) fourth (i.e. 514.29¢ to 533.33¢), 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 this generator. | |||
The sizes of the generator, large step and small step of 5L 4s are as follows in various | The sizes of the generator, large step and small step of 5L 4s are as follows in various soft-of-basic tunings. | ||
{| class="wikitable right-2 right-3 right-4 right-5" | {| class="wikitable right-2 right-3 right-4 right-5" | ||
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