IFDO: Difference between revisions

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An '''IDO''' ('''inverse-arithmetic division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] according to the inverse-arithmetic mean.

An '''IDO''' ('''inverse-arithmetic frequency division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] according to the inverse-arithmetic mean.

The inverse-arithmetic mean is known in general mathematics as the [[Wikipedia:Harmonic_mean|harmonic mean]], but it would have been confusing to name this tuning a "harmonic division of the octave" because this mathematical sense of harmonic conflicts with the relevant musical sense of harmonic: divisions according to the harmonic mean correspond to ''subharmonic'' sequences, which are the opposite of harmonic sequences. And so "Inverse-arithmetic mean" was coined to avoid this conflict, as well as to point to its relationship with the [[Wikipedia:Arithmetic_mean|arithmetic mean]] (see [[Pythagorean means]]).

Revision as of 02:36, 11 April 2023 view source CompactStar (talk \| contribs) autopatrolled 5,084 edits m CompactStar moved page IDO to IFDO: Name is being changed to this as discussed in talk pages ← Older edit		Revision as of 02:36, 11 April 2023 view source CompactStar (talk \| contribs) autopatrolled 5,084 edits No edit summary Newer edit →
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	An '''IDO''' ('''inverse-arithmetic division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] according to the inverse-arithmetic mean.		An '''IDO''' ('''inverse-arithmetic frequency division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] according to the inverse-arithmetic mean.

	The inverse-arithmetic mean is known in general mathematics as the [[Wikipedia:Harmonic_mean\|harmonic mean]], but it would have been confusing to name this tuning a "harmonic division of the octave" because this mathematical sense of harmonic conflicts with the relevant musical sense of harmonic: divisions according to the harmonic mean correspond to ''subharmonic'' sequences, which are the opposite of harmonic sequences. And so "Inverse-arithmetic mean" was coined to avoid this conflict, as well as to point to its relationship with the [[Wikipedia:Arithmetic_mean\|arithmetic mean]] (see [[Pythagorean means]]).		The inverse-arithmetic mean is known in general mathematics as the [[Wikipedia:Harmonic_mean\|harmonic mean]], but it would have been confusing to name this tuning a "harmonic division of the octave" because this mathematical sense of harmonic conflicts with the relevant musical sense of harmonic: divisions according to the harmonic mean correspond to ''subharmonic'' sequences, which are the opposite of harmonic sequences. And so "Inverse-arithmetic mean" was coined to avoid this conflict, as well as to point to its relationship with the [[Wikipedia:Arithmetic_mean\|arithmetic mean]] (see [[Pythagorean means]]).