Subminor and supermajor
In
| diminished | subminor | minor | neutral | major | supermajor | augmented | |
|---|---|---|---|---|---|---|---|
| seconds | D
|
≊ D
|
D♭ | D
|
D | ≊ D
|
D♯ |
| thirds | E
|
≊ E
|
E♭ | E
|
E | ≊ E
|
E♯ |
| sixths | A
|
≊ A
|
A♭ | A
|
A | ≊ A
|
A♯ |
| sevenths | B
|
≊ B
|
B♭ | B
|
B | ≊ B
|
B♯ |
Traditionally, "supermajor and superminor, [are] the names given to certain thirds [9:7 and 17:14] found in the justly intoned scale with a natural or subminor seventh."[2]
Subminor second and supermajor seventh
Thus, a subminor second is intermediate between a
- ⓘ). Another example is the ratio 28:27, or 62.96 cents (C
♯- ⓘA supermajor seventh is an interval intermediate between a
♯); the ratio 27:14, or 1137.04 cents (B
ⓘ); and 35:18, or 1151.23 cents (C ⓘSubminor third and supermajor sixth
A subminor third is in between a minor third and a diminished third. An example of such an interval is the ratio 7:6 (E♭), or 266.87 cents,[3][4] the septimal minor third, the inverse of the supermajor sixth. Another example is the ratio 13:11, or 289.21 cents (E↓♭).
A supermajor sixth is noticeably wider than a major sixth but noticeably narrower than an augmented sixth, and may be a just interval of 12:7 (A).[5][6][7] In 24 equal temperament A = B. The septimal major sixth is an interval of 12:7 ratio (A ⓘ),[8][9] or about 933 cents.[10] It is the inversion of the 7:6 subminor third.
Subminor sixth and supermajor third
A subminor sixth or septimal sixth is noticeably narrower than a minor sixth but noticeably wider than a
A supermajor third is in between a major third and an augmented third, enharmonically equivalent to the minor fourth. An example of such an interval is the ratio 9:7, or 435.08 cents, the septimal major third (E). Another example is the ratio 50:39, or 430.14 cents (E♯).
Subminor seventh and supermajor second
A subminor seventh is an interval between a minor seventh and a diminished seventh. An example of such an interval is the 7:4 ratio, the harmonic seventh (B♭).
A supermajor second (or supersecond
Use
Composer
19 equal temperament has several intervals which are simultaneously subminor, supermajor, augmented, and diminished, due to tempering and enharmonic equivalence (both of which work differently in 19-ET than standard tuning). For example, four steps of 19-ET (an interval of roughly 253 cents) is all of the following: subminor third, supermajor second, augmented second, and diminished third.
See also
References
- ^ ISBN 978-0-89579-414-7..
- ^ a b Brabner, John H. F. (1884). The National Encyclopaedia, vol. 13, p. 182. London. [ISBN unspecified]
- ISBN 978-1-60206-639-7.
- ^ Miller 1988, p. XLII.
- ^ ISBN 0-89579-507-8.
- ^ Proceedings of the Royal Society of London, vol. 30, p. 531. Harvard University.
- ^ Journal of the Society of Arts, vol. 25, p. 670.
- ISBN 0-306-80106-X.
- ISBN 0-8247-4714-3.
- ^ Helmholtz 2007, p. 456.
- ^ John Fonville. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p. 122, Perspectives of New Music, vol. 29, no. 2 (Summer 1991), pp. 106–137.
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