Octave (interval region): Difference between revisions
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{{About|the interval region|the octave as a just ratio|2/1}} | |||
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, the term ''octave'' tends to imply a function within music that only works with intervals that are exactly (or almost exactly) 1200 cents, corresponding to a [[just]] [[ratio]] of [[2/1]]. | |||
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]]. | |||
{{todo|inline=1|review|comment=Mention concordance before harmonic entropy, since harmonic entropy is a single model of concordance}} | |||
== In just intonation == | == In just intonation == | ||
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Several notable ones are: | Several notable ones are: | ||
{{todo|inline=1|complete list}} | |||
== In tempered scales == | == In tempered scales == | ||
As the just octave of 2/1 is the interval being equally divided in [[EDO | As the just octave of 2/1 is the interval being equally divided in [[EDO]]s, it is represented perfectly in all of them. The following table lists other octave-sized intervals (> 1140 cents) that exist in various significant EDOs. | ||
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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). | 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). | ||
{{todo|inline=1|complete table}} | |||
{{Navbox intervals}} | {{Navbox intervals}} | ||
Revision as of 05:52, 26 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, the term octave tends to imply a function within music that only works with intervals that are exactly (or almost exactly) 1200 cents, corresponding to a just ratio of 2/1.
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.
|
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 | |
|---|---|
| Seconds and thirds | Unison • Comma and diesis • Semitone • Neutral second • Major second • (Interseptimal second-third) • Minor third • Neutral third • Major third |
| Fourths and fifths | (Interseptimal third-fourth) • Perfect fourth • Superfourth • Tritone • Subfifth • Perfect fifth • (Interseptimal fifth-sixth) |
| Sixths and sevenths | Minor sixth • Neutral sixth • Major sixth • (Interseptimal sixth-seventh) • Minor seventh • Neutral seventh • Major seventh • Octave |
| 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 |