17/16: Difference between revisions
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17/16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], the small septendecimal semitone, which measures about 99¢. The difference between them is [[289/288]], about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out. | 17/16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], the small septendecimal semitone, which measures about 99¢. The difference between them is [[289/288]], about 6¢. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out. | ||
17/16 is almost exactly 1/3 of the [[6/5]] minor third. The difference between 6/5 and three 17/16 semitones is [[24576/24565]], an interval of approximately 0.8¢. | 17/16 is almost exactly 1/3 of the [[6/5]] minor third. The difference between 6/5 and three 17/16 semitones is [[24576/24565]], an interval of approximately 0.8¢. It is almost exactly 1/8 of [[13/8]], with the difference between 13/8 and (17/16)^8 being approximately 0.9¢. The difference between ten 17/16s and 11/6 is approximately 0.2¢, while the difference between 13 17/16s and 11/5 is approximately 0.6¢. | ||
== Terminology and notation == | == Terminology and notation == | ||