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 to distinct numbers of steps up to [[octave equivalence]]. These are the only perfect ringer scales: | A perfect ringer ''n'' scale is one that by some val can map the first ''n'' odd harmonics to distinct numbers of steps up to [[octave equivalence]]. These are the only perfect ringer scales: | ||
'''Ringer 1:''' 1:2 | '''Ringer 1:''' 1:2 (val: {{val| 1 }}) | ||
'''Ringer 2:''' 2:3:4 | '''Ringer 2:''' 2:3:4 (val: {{val| 2 3 }}) | ||
'''Ringer 3:''' 3:4:5:6 | '''Ringer 3:''' 3:4:5:6 (val: {{val| 3 5 7 }}) | ||
'''Ringer 4:''' 4:5:6:7:8 | '''Ringer 4:''' 4:5:6:7:8 (val: {{val| 4 6 9 11 }}) | ||
'''Ringer 5:''' 5:6:7:8:9:10 | '''Ringer 5:''' 5:6:7:8:9:10 (val: {{val| 5 8 12 14 }}) | ||
'''Ringer 7:''' 7:8:9:10:11:12:13:14 | '''Ringer 7:''' 7:8:9:10:11:12:13:14 (val: {{val| 7 11 16 20 24 26 }}) | ||
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]]. | ||