Odd harmonic: Difference between revisions
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An [[odd limit]] is the set of all [[just interval]]s where the largest odd factor in the numerator and denominator both do not exceed a specified bound. For example, the [[5-odd-limit]] consists of all ratios where the only allowable odd factors are 1, 3, and 5; those being [[1/1]], [[6/5]], [[5/4]], [[4/3]], [[3/2]], [[8/5]], [[5/3]], and any whole number of octaves above those intervals. | An [[odd limit]] is the set of all [[just interval]]s where the largest odd factor in the numerator and denominator both do not exceed a specified bound. For example, the [[5-odd-limit]] consists of all ratios where the only allowable odd factors are 1, 3, and 5; those being [[1/1]], [[6/5]], [[5/4]], [[4/3]], [[3/2]], [[8/5]], [[5/3]], and any whole number of octaves above those intervals. | ||
We can also restrict the set of usable intervals to only allow odd harmonics. Such intervals include [[3/1]], [[5/3]], [[9/7]], [[27/25]], etc. Here, using [[3/1]] as the [[interval of equivalence]] (a "tritave") is natural, since the 3rd harmonic is the smallest odd harmonic after the fundamental. [[Edt]]s divide the tritave into a whole number of equal steps, analogous to how [[edo]]s divide the octave. | |||
[[Category:Terms]] | [[Category:Terms]] | ||