Odd harmonic: Difference between revisions
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An '''odd harmonic''' is a [[harmonic]] where the [[frequency ratio]] is an odd number. Odd harmonics are significant in that they create distinct [[pitch class]]es, since any even harmonic is a whole number of [[2/1|octave]]s above an odd harmonic. | An '''odd harmonic''' is a [[harmonic]] where the [[frequency ratio]] is an odd number. The first few odd harmonics are [[1/1]], [[3/1]], [[5/1]], [[7/1]], [[9/1]], [[11/1]], etc. Odd harmonics are significant in that they create distinct [[pitch class]]es, since any even harmonic is a whole number of [[2/1|octave]]s above an odd harmonic. | ||
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. | ||
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[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Odd limit]] | [[Category:Odd limit]] | ||
Latest revision as of 18:50, 17 March 2026
An odd harmonic is a harmonic where the frequency ratio is an odd number. The first few odd harmonics are 1/1, 3/1, 5/1, 7/1, 9/1, 11/1, etc. Odd harmonics are significant in that they create distinct pitch classes, since any even harmonic is a whole number of octaves above an odd harmonic.
An odd limit is the set of all just intervals 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. Edts divide the tritave into a whole number of equal steps, analogous to how edos divide the octave.