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Definition | == Definition == | ||
Bathomotonic is the approach to generating scales or intervals based on step sizes. "Bathomos" is the ancient Greek for degree or step (of a process) and "tonic" means "of or relating to tones." | Bathomotonic is the approach to generating scales or intervals based on step sizes. "Bathomos" is the ancient Greek for degree or step (of a process) and "tonic" means "of or relating to tones." | ||
A Bathomotonic approach to generating a scale first defines step sizes or elemental interval sizes, then exploits those steps or elemental intervals to build larger component intervals out of them until a final interval is reached (usually the octave, but, generally, this could be any interval). | A Bathomotonic approach to generating a scale first defines step sizes or elemental interval sizes, then exploits those steps or elemental intervals to build larger component intervals out of them until a final interval is reached (usually the octave, but, generally, this could be any interval). | ||
Examples | == Examples == | ||
For example, in [[12edo]], the most basic elemental step size is 100 cents. The chromatic scale is built out of only that step. If one considers 100 cents as a semitone step and 200 cents as a whole tone step, though, it is possible to use the same approach with two step sizes to create the chromatic scale, the whole tone scale, the major scale, the natural minor scale, all of the classical modes, and several other scales, simply by combining steps of 100 cents and 200 cents in different combinations, with the only other constraint being that the scale contains a final interval of 1200 cents. | |||
For example, in 12edo, the most basic elemental step size is 100 cents. The chromatic scale is built out of only that step. If one considers 100 cents as a semitone step and 200 cents as a whole tone step, though, it is possible to use the same approach with two step sizes to create the chromatic scale, the whole tone scale, the major scale, the natural minor scale, all of the classical modes, and several other scales, simply by combining steps of 100 cents and 200 cents in different combinations, with the only other constraint being that the scale contains a final interval of 1200 cents. | |||
In general, any number of equal divisions of any interval can be given the same treatment to generate scales based on whichever base interval is used. | In general, any number of equal divisions of any interval can be given the same treatment to generate scales based on whichever base interval is used. | ||
Another classic example is Ptolemy's intense diatonic scale, which can be constructed through this approach with the following elementary intervals: | Another classic example is [[wikipedia:Ptolemy's_intense_diatonic_scale|Ptolemy's intense diatonic scale]], which can be constructed through this approach with the following elementary intervals: | ||
h (the half step) 16:15 (111.73 cents) | h (the half step) 16:15 (111.73 cents) | ||
w (the lesser whole step) 10:9 ( 182.40 cents) | |||
w (the lesser whole step) 10:9 (182.40 cents) | |||
W (the greater whole step) 9:8 (203.91 cents) | W (the greater whole step) 9:8 (203.91 cents) | ||
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W w h W w W h | W w h W w W h | ||
The generalization of this treatment of JI intervals proposed by Ptolemy and by Gioseffo Zarlino was exploited to generate Bozuji tuning. | The generalization of this treatment of [[Just intonation|JI]] intervals proposed by [[wikipedia:Ptolemy|Ptolemy]] and by [[wikipedia:Gioseffo_Zarlino|Gioseffo Zarlino]] was exploited to generate [[Bozuji tuning]]. | ||
== See also == | |||
[[DKW theory]] | |||
[[Category:Method]] | |||
[[Category:Bathomotonic]] | |||
Latest revision as of 01:41, 13 November 2025
Definition
Bathomotonic is the approach to generating scales or intervals based on step sizes. "Bathomos" is the ancient Greek for degree or step (of a process) and "tonic" means "of or relating to tones."
A Bathomotonic approach to generating a scale first defines step sizes or elemental interval sizes, then exploits those steps or elemental intervals to build larger component intervals out of them until a final interval is reached (usually the octave, but, generally, this could be any interval).
Examples
For example, in 12edo, the most basic elemental step size is 100 cents. The chromatic scale is built out of only that step. If one considers 100 cents as a semitone step and 200 cents as a whole tone step, though, it is possible to use the same approach with two step sizes to create the chromatic scale, the whole tone scale, the major scale, the natural minor scale, all of the classical modes, and several other scales, simply by combining steps of 100 cents and 200 cents in different combinations, with the only other constraint being that the scale contains a final interval of 1200 cents.
In general, any number of equal divisions of any interval can be given the same treatment to generate scales based on whichever base interval is used.
Another classic example is Ptolemy's intense diatonic scale, which can be constructed through this approach with the following elementary intervals:
h (the half step) 16:15 (111.73 cents)
w (the lesser whole step) 10:9 (182.40 cents)
W (the greater whole step) 9:8 (203.91 cents)
and then combining the steps in the order:
W w h W w W h
The generalization of this treatment of JI intervals proposed by Ptolemy and by Gioseffo Zarlino was exploited to generate Bozuji tuning.