Ringer scale: Difference between revisions
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A perfect Ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics (up to [[octave equivalence]]) to distinct numbers of steps. It is likely that only a small finite number of perfect Ringer scales exist. Here are the known ones so far (to be expanded as/if more are found): | A perfect Ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics (up to [[octave equivalence]]) to distinct numbers of steps. It is likely that only a small finite number of perfect Ringer scales exist. Here are the known ones so far (to be expanded as/if more are found): | ||
Ringer | ('''Ringer 1:''' 1:2) | ||
Ringer | '''Ringer 2:''' 2:3:4 | ||
Ringer | '''Ringer 3:''' 3:4:5:6 | ||
Ringer | '''Ringer 4:''' 4:5:6:7:8 | ||
Ringer 7: 7:8:9:10:11:12:13:14 | '''Ringer 5:''' 5:6:7:8:9:10 | ||
'''Ringer 7:''' 7:8:9:10:11:12:13:14 | |||
Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]]. | Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]]. | ||