Harmonotonic tuning: Difference between revisions
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We can state a few helpful analogies: | We can state a few helpful analogies: | ||
'''(n-) | '''(n-)AQSp : n-EQDp''' | ||
An arithmetic sequence of some kind of quantity Q is analogous to an equal division. Both require an interval '''p''' to be specified. The key difference is that a sequence is potentially open-ended — proceeding forever without repeating (such as the overtone series) — so its parameter '''n''', for the total number of pitches, is optional. | An arithmetic sequence of some kind of quantity Q is analogous to an equal division. Both require an interval '''p''' to be specified. The key difference is that a sequence is potentially open-ended — proceeding forever without repeating (such as the overtone series) — so its parameter '''n''', for the total number of pitches, is optional. | ||
''' | '''OS : AFS :: OD : EFD''' | ||
OS:AFS::OD:EFD | |||
AS:APS::__:EPD | '''AS : APS :: __ : EPD''' | ||
US:ALS::UD:ELD | |||
''' | '''US : ALS :: UD : ELD''' | ||
Each of these rows has the form rational sequence : irrational division :: rational division : irrational division. The first row is for frequency, the second for pitch, and the third for length. | Each of these rows has the form rational sequence : irrational division :: rational division : irrational division. The first row is for frequency, the second for pitch, and the third for length. | ||