AFDO: Difference between revisions

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An '''AFDO''' ('''arithmetic frequency division of the octave''') or '''ODO''' ('''otonal division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] according to an [[Wikipedia: Arithmetic progression|arithmetic progression]] of frequency.

For example, in [[12afdo]] the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an AFDO system, the ''difference'' between interval ratios is equal (they form an arithmetic progression), rather than their ''ratios'' between interval ratios being equal as in EDO systems (a geometric progression). All AFDOs are subsets of [[just intonation]]. ~~AFDOs with more divisors such as [[Highly composite equal division|highly composite]] AFDOs generally have more useful just intervals~~.

For example, in [[12afdo]] the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an AFDO system, the ''difference'' between interval ratios is equal (they form an arithmetic progression), rather than their ''ratios'' between interval ratios being equal as in [[EDO]] systems (a geometric progression). All integer AFDOs are subsets of [[just intonation]], and up to transposition, any integer AFDO is a superset of a smaller integer AFDO and a subset of a larger integer AFDO (i.e. ''n''-afdo is a superset of (''n'' - 1)-afdo and a subset of (''n'' + 1)-afdo for any integer ''n'' > 1).

When treated as a scale, the AFDO is equivalent to the [[overtone scale]]. An AFDO is equivalent to an ODO ([[otonal division]] of the octave). It may also be called an EFDO ([[equal frequency division]] of the octave), however, this more general acronym is typically reserved for divisions of irrational intervals, unlike the octave.

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 An '''AFDO''' ('''arithmetic frequency division of the octave''') or '''ODO''' ('''otonal division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] according to an [[Wikipedia: Arithmetic progression|arithmetic progression]] of frequency.
-For example, in [[12afdo]] the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an AFDO system, the ''difference'' between interval ratios is equal (they form an arithmetic progression), rather than their ''ratios'' between interval ratios being equal as in EDO systems (a geometric progression). All AFDOs are subsets of [[just intonation]]. AFDOs with more divisors such as [[Highly composite equal division|highly composite]] AFDOs generally have more useful just intervals.
+For example, in [[12afdo]] the first degree is [[13/12]], the second is 14/12 ([[7/6]]), and so on. For an AFDO system, the ''difference'' between interval ratios is equal (they form an arithmetic progression), rather than their ''ratios'' between interval ratios being equal as in [[EDO]] systems (a geometric progression). All integer AFDOs are subsets of [[just intonation]], and up to transposition, any integer AFDO is a superset of a smaller integer AFDO and a subset of a larger integer AFDO (i.e. ''n''-afdo is a superset of (''n'' - 1)-afdo and a subset of (''n'' + 1)-afdo for any integer ''n'' > 1).
 When treated as a scale, the AFDO is equivalent to the [[overtone scale]]. An AFDO is equivalent to an ODO ([[otonal division]] of the octave). It may also be called an EFDO ([[equal frequency division]] of the octave), however, this more general acronym is typically reserved for divisions of irrational intervals, unlike the octave.