Octave (interval region): Difference between revisions
Tag: Undo |
Tag: Undo |
||
| Line 1: | Line 1: | ||
{{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}} | {{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 octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to 7\7 and [[24edo| | 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. | 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. | ||
| Line 17: | Line 17: | ||
Several notable ones are: | Several notable ones are: | ||
{| class="wikitable" | |||
{| class="wikitable | |- | ||
! Interval | |||
! Size <br>(cents) | |||
! Prime limit | |||
|- | |- | ||
| [[2/1]] | |||
| 1200 | |||
| 2 | |||
|- | |- | ||
| [[1048576/531441]] | | [[1048576/531441]] | ||
| 3 | | 1176.54 | ||
| | | rowspan="2" | 3 | ||
| [[ | |- | ||
| [[531441/262144]] | |||
| 1223.46 | |||
|- | |- | ||
| [[160/81]] | | [[160/81]] | ||
| | | 1178.49 | ||
| | | rowspan="2" | 5 | ||
| | |||
|- | |- | ||
| [[ | | [[81/40]] | ||
| | | 1221.51 | ||
|- | |- | ||
| [[ | | [[35/18]] | ||
| | | 1151.23 | ||
| | | rowspan="10" | 7 | ||
| | |||
|- | |- | ||
| [[ | | [[96/49]] | ||
| | | 1164.30 | ||
|- | |- | ||
| [[ | | [[49/25]] | ||
| | | 1165.02 | ||
|- | |- | ||
| [[63/32]] | | [[63/32]] | ||
| | | 1172.74 | ||
|- | |- | ||
| [[ | | [[125/63]] | ||
| | | 1186.21 | ||
|- | |- | ||
| [[ | | [[252/125]] | ||
| | | 1213.79 | ||
|- | |- | ||
| [[128/ | | [[128/63]] | ||
| | | 1227.26 | ||
|- | |- | ||
| [[ | | [[100/49]] | ||
| | | 1234.98 | ||
|- | |- | ||
| [[ | | [[49/24]] | ||
| | | 1235.70 | ||
|- | |- | ||
| [[ | | [[72/35]] | ||
| | | 1248.77 | ||
|} | |} | ||