Mathematics of MOS: Difference between revisions

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== Classification of MOS scales ==

Since MOS scales always consist of some number of large steps and some number of small steps, they can be classified simply by the number of large steps and the number of small steps, in the form #L #s—e.g., the diatonic scale can be described as 5L 2s (5 large steps and 2 small steps) or simply [5, 2]. It is typical to ignore the period when specifying MOS scales and instead use the number of large and small steps that make up the interval of equivalence (typically assumed to be the octave—a frequency ratio of 2/1—unless otherwise specified). For instance, the diminished scale in 12-TET is typically classified as ~~4L4s~~ rather than ~~1L1s~~, since there are 4 large and 4 small steps that make up an octave.

Since MOS scales always consist of some number of large steps and some number of small steps, they can be classified simply by the number of large steps and the number of small steps, in the form #L #s—e.g., the diatonic scale can be described as 5L 2s (5 large steps and 2 small steps) or simply [5, 2]. It is typical to ignore the period when specifying MOS scales and instead use the number of large and small steps that make up the interval of equivalence (typically assumed to be the octave—a frequency ratio of 2/1—unless otherwise specified). For instance, the diminished scale in 12-TET is typically classified as 4L 4s rather than 1L 1s, since there are 4 large and 4 small steps that make up an octave.

Alternatively, we could give a mediant for a Farey pair associated to the MOS, where this mediant is less than any generator for the MOS. In other words, we use the right hand part of the Farey pair interval, which means we must replace ''g'' with {{nowrap|1 − ''g''}} and use the complementary pair if ''g'' is in the left hand side. This method is rarely used in discussions, however.

@@ Line 63: / Line 63: @@
 == Classification of MOS scales ==
-Since MOS scales always consist of some number of large steps and some number of small steps, they can be classified simply by the number of large steps and the number of small steps, in the form #L&nbsp;#s—e.g., the diatonic scale can be described as 5L&nbsp;2s (5 large steps and 2 small steps) or simply [5,&nbsp;2]. It is typical to ignore the period when specifying MOS scales and instead use the number of large and small steps that make up the interval of equivalence (typically assumed to be the octave—a frequency ratio of 2/1—unless otherwise specified). For instance, the diminished scale in 12-TET is typically classified as 4L4s rather than 1L1s, since there are 4 large and 4 small steps that make up an octave.
+Since MOS scales always consist of some number of large steps and some number of small steps, they can be classified simply by the number of large steps and the number of small steps, in the form #L&nbsp;#s—e.g., the diatonic scale can be described as 5L&nbsp;2s (5 large steps and 2 small steps) or simply [5,&nbsp;2]. It is typical to ignore the period when specifying MOS scales and instead use the number of large and small steps that make up the interval of equivalence (typically assumed to be the octave—a frequency ratio of 2/1—unless otherwise specified). For instance, the diminished scale in 12-TET is typically classified as 4L&nbsp;4s rather than 1L&nbsp;1s, since there are 4 large and 4 small steps that make up an octave.
 Alternatively, we could give a mediant for a Farey pair associated to the MOS, where this mediant is less than any generator for the MOS. In other words, we use the right hand part of the Farey pair interval, which means we must replace ''g'' with {{nowrap|1 − ''g''}} and use the complementary pair if ''g'' is in the left hand side. This method is rarely used in discussions, however.