Octave (interval region): Difference between revisions
where the heck else does octave less diesis go, these articles are meant to cover the entire range of intervals |
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{{About|the interval region|the octave as a just ratio|2/1}} | {{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 1140 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]]. 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 1140 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]]. 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]]. | ||
Revision as of 04:51, 27 February 2025
- This page is about the interval region. For the octave as a just ratio, see 2/1.
A perfect octave (P8) or octave (8ve) is an interval that is approximately 1200 cents in size. While a rough tuning range for octaves is sharper than 1140 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. Other intervals are also classified as perfect octaves, sometimes called wolf octaves or imperfect octaves, if they are reasonably mapped to 7\7 and 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- 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 region of attraction of low harmonic entropy, 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.
Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to commas and dieses.
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Todo: review
Mention concordance before harmonic entropy, since harmonic entropy is a single model of concordance |
In just intonation
The only "perfect" octave is the interval 2/1, which can be stacked to produce all other 2-limit intervals. It is 1200 cents in size, by definition. However, various "out-of-tune" octaves exist, usually flat or sharp of an octave by a small interval such as a comma.
Several notable ones are:
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Todo: complete list |
In tempered scales
As the just octave of 2/1 is the interval being equally divided in EDOs, it is represented perfectly in all of them. The following table lists other octave-sized intervals (> 1140 cents) that exist in various significant EDOs.
| EDO | Suboctaves |
|---|---|
| 22 | TBD |
| 24 | |
| 25 | |
| 26 | |
| 27 | |
| 29 | |
| 31 | |
| 34 | |
| 41 | |
| 53 |
2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).
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Todo: complete table |
| View • Talk • EditInterval classification | |
|---|---|
| Interval regions | |
| Unison and octave | Unison • Comma and diesis • Octave |
| Seconds | Minor second • Neutral second • Major second |
| Thirds | Minor third • Neutral third • Major third |
| Fourths and fifths | Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth |
| Sixths | Minor sixth • Neutral sixth • Major sixth |
| Sevenths | Minor seventh • Neutral seventh • Major seventh |
| Interseptimal intervals | Interseptimal 2nd-3rd • Interseptimal 3rd-4th • Interseptimal 5th-6th • Interseptimal 6th-7th |
| Interval qualities | |
| Diatonic qualities | Diminished • Minor • Perfect • Major • Augmented |
| Tuning ranges | Neutral (interval quality) • Submajor and supraminor • Pental major and minor • Novamajor and novaminor • Neogothic major and minor • Supermajor and subminor • Ultramajor and inframinor |