User:BudjarnLambeth/The intervals I see as important: Difference between revisions
Created page with "The following are all the 16-integer-limit consonant intervals available in an octave, simplified to their simplest form (by taking them to a higher octave to simplify the fraction), then sorted with most consonant (ie mathematically simplest) first. (^in a higher octave) HYPERCONSONANCES 2/1 (octave) 3/1 (perf 5th^) CONSONANCES 5/1 (maj 3rd^) 4/3 (perf 4th) 5/3 (maj 6th) 7/1 (submin 7th^) 9/1 (large maj 2nd^) 7/3 (submin 3rd^) AMBISONANCES 6/5 (min 3rd) 11/..." |
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The following are all the 16-integer-limit consonant intervals available in an octave, simplified to their simplest form (by taking them to a higher octave to simplify the fraction), then sorted with most consonant (ie mathematically simplest) first. | The following are all the 16-integer-limit consonant intervals available in an octave, simplified to their simplest form (by taking them to a higher octave to simplify the fraction), then sorted with most consonant (ie mathematically simplest) first. | ||
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(^in a higher octave) | (^in a higher octave) | ||
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16/13 (tridec neu 3rd) | 16/13 (tridec neu 3rd) | ||
16/15 (small neu 2nd) | 16/15 (small neu 2nd) | ||
</pre> | |||
Any ''general-purpose'' tuning system should approximate all hyperconsonances within 10 cents or less, all consonances within 20 cents, and all ambisonances within 30 cents. It should also try to have as few notes as possible that do not approximate any of those three categories of interval, because every note that isn't approximating one of them is a wolf interval that adds a 'bitter' taste to the tuning, and a tuning cannot survive very much bitterness. | Any ''general-purpose'' tuning system should approximate all hyperconsonances within 10 cents or less, all consonances within 20 cents, and all ambisonances within 30 cents. It should also try to have as few notes as possible that do not approximate any of those three categories of interval, because every note that isn't approximating one of them is a wolf interval that adds a 'bitter' taste to the tuning, and a tuning cannot survive very much bitterness. | ||