Octave (interval region): Difference between revisions

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A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as ~~perfect~~ octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to 7\7 and [[24edo|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].

A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to 7\7 and [[24edo|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].

The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave.

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 {{About|the interval region|the octave as a just ratio|2/1}}
 {{Wikipedia}}
-A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as perfect octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to 7\7 and [[24edo|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].
+A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to 7\7 and [[24edo|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].
 The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments.  As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave.