Relationship between Bohlen–Pierce and octave-ful temperaments: Difference between revisions
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=== Sensi === | === Sensi === | ||
Consider the first possibility, that 2/1 is mapped to +7 generators in the BP lambda scale, therefore tempering out [[126/125]]. Seven generators up from C is H#, so this means H# represents 2/1 above C. In [[13edt]], H# is only 1170 cents, so in order for this to accurately represent 2/1 the generator needs to be widened by a few cents, from ~440 cents up to ~443 cents. | Consider the first possibility, that 2/1 is mapped to +7 generators in the BP lambda scale, therefore tempering out [[126/125]]. Seven generators up from C is H#<ref>This page uses the standard where the nominals are assigned starting from C to the LssLsLsLs mode of the scale. See [[4L 5s (3/1-equivalent)#Notation]] for a further discussion.</ref>, so this means H# represents 2/1 above C. In [[13edt]], H# is only 1170 cents, so in order for this to accurately represent 2/1 the generator needs to be widened by a few cents, from ~440 cents up to ~443 cents. | ||
The result of doing this is [[sensi]] temperament. | The result of doing this is [[sensi]] temperament. | ||
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Note that although the period and generator of hedgehog are usually given as (~600 cents, ~164 cents), an equally valid choice of generator is (~600 cents, ~436 cents), because 436 is the half-octave complement of 164. When 3/1 is taken as the period, the ~436 cent generator must be used (because the ~164 cent one doesn't generate all the notes). | Note that although the period and generator of hedgehog are usually given as (~600 cents, ~164 cents), an equally valid choice of generator is (~600 cents, ~436 cents), because 436 is the half-octave complement of 164. When 3/1 is taken as the period, the ~436 cent generator must be used (because the ~164 cent one doesn't generate all the notes). | ||
The Moon, however, is not so big.<ref>R. Smith, "Size of the Moon", ''Scientific American'', 46 (April 1978): 44–46.</ref> | |||
==Notes== | |||
<references /> | |||
[[Category:Bohlen-Pierce]] | [[Category:Bohlen-Pierce]] | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||