Septimal whole tone: Difference between revisions
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In music, the '''septimal whole tone''' or '''supermajor second''' {{Audio|Septimal major second on C.mid|play}} is the [[musical interval]] exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 [[cent (music)|cents]] wide in [[just intonation]]<ref name="M&L">Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. ISBN 0252031202.</ref> and 250 cents in the [[quarter tone scale]]. The term ''septimal'' refers to the fact that it utilizes the seventh harmonic of the [[harmonic series (music)|harmonic series]], which is combined with the eighth.<ref name="M&L"/> |
In music, the '''septimal whole tone''' or '''supermajor second''' {{Audio|Septimal major second on C.mid|play}} is the [[musical interval]] exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 [[cent (music)|cents]] wide in [[just intonation]]<ref name="M&L">Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. ISBN 0252031202.</ref> and 250 cents in the [[quarter tone scale]]. The term ''septimal'' refers to the fact that it utilizes the [[Harmonic seventh|seventh harmonic]] of the [[harmonic series (music)|harmonic series]], which is combined with the eighth.<ref name="M&L"/> |
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This interval does not fit easily into equally-tempered tuning systems. The standard [[12 equal temperament]] used in most western music does not come close to this interval. The [[19 equal temperament]] offers a closer, but still poor match for this interval, but it does not distinguish between this interval and the [[septimal minor third]], which it has a better fit for. The [[22 equal temperament]] distinguishes between these two intervals, but it still matches the septimal whole tone poorly. The [[31 equal temperament]] is the smallest widely used equal temperament that matches this interval closely; 26 equal temperament provides an even closer match to the septimal whole tone (and its inversion, the [[harmonic seventh]]), but due to the significant flatness of its major thirds and fifths, this tuning is little used. |
This interval does not fit easily into equally-tempered tuning systems. The standard [[12 equal temperament]] used in most western music does not come close to this interval. The [[19 equal temperament]] offers a closer, but still poor match for this interval, but it does not distinguish between this interval and the [[septimal minor third]], which it has a better fit for. The [[22 equal temperament]] distinguishes between these two intervals, but it still matches the septimal whole tone poorly. The [[31 equal temperament]] is the smallest widely used equal temperament that matches this interval closely; 26 equal temperament provides an even closer match to the septimal whole tone (and its inversion, the [[harmonic seventh]]), but due to the significant flatness of its major thirds and fifths, this tuning is little used. |
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Revision as of 22:26, 19 July 2009
| Inverse | harmonic seventh |
|---|---|
| Name | |
| Other names | Septimal whole tone, Supermajor second |
| Abbreviation | M2 |
| Size | |
| Semitones | ~2.5 |
| Interval class | ~2.5 |
| Just interval | 8:7 |
| Cents | |
| 12-Tone equal temperament | 200 |
| 24-Tone equal temperament | 250 |
| Just intonation | 231 |
In music, the septimal whole tone or supermajor second is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 cents wide in just intonation[1] and 250 cents in the quarter tone scale. The term septimal refers to the fact that it utilizes the seventh harmonic of the harmonic series, which is combined with the eighth.[1]
This interval does not fit easily into equally-tempered tuning systems. The standard 12 equal temperament used in most western music does not come close to this interval. The 19 equal temperament offers a closer, but still poor match for this interval, but it does not distinguish between this interval and the septimal minor third, which it has a better fit for. The 22 equal temperament distinguishes between these two intervals, but it still matches the septimal whole tone poorly. The 31 equal temperament is the smallest widely used equal temperament that matches this interval closely; 26 equal temperament provides an even closer match to the septimal whole tone (and its inversion, the harmonic seventh), but due to the significant flatness of its major thirds and fifths, this tuning is little used.
Sources
 | This music theory article is a stub. You can help Wikipedia by expanding it. |
| Twelve- semitone (post-Bach Western) |
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| Other tuning systems |
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| Other intervals |
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