In music, a **subminor interval** is an interval that is noticeably wider than a diminished interval but noticeably narrower than a minor interval. It is found in between a minor and diminished interval, thus making it below, or subminor to, the minor interval. A **supermajor interval** is a musical interval that is noticeably wider than a major interval but noticeably narrower than an augmented interval. It is found in between a major and augmented interval, thus making it above, or supermajor to, the major interval. The inversion of a supermajor interval is a subminor interval, and there are four major and four minor intervals, allowing for eight supermajor and subminor intervals, each with variants.

diminished | subminor | minor | neutral | major | supermajor | augmented | |
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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]}

Thus, a subminor second is intermediate between a minor second and a diminished second (enharmonic to unison). An example of such an interval is the ratio 26:25, or 67.90 cents (D- ). Another example is the ratio 28:27, or 62.96 cents (C♯- ).

A supermajor seventh is an interval intermediate between a major seventh and an augmented seventh. It is the inverse of a subminor second. Examples of such an interval is the ratio 25:13, or 1132.10 cents (B♯); the ratio 27:14, or 1137.04 cents (B ); and 35:18, or 1151.23 cents (C ).

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.

A subminor sixth or septimal sixth is noticeably narrower than a minor sixth but noticeably wider than a diminished sixth, enharmonically equivalent to the major fifth. The sub-minor sixth is an interval of a 14:9 ratio^{[6]}^{[7]} (A♭) or alternately 11:7.^{[5]} (G↑- ) The 21st subharmonic (see subharmonic) is 729.22 cents.

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♯).

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^{[2]}) is intermediate to a major second and an augmented second. An example of such an interval is the ratio 8:7, or 231.17 cents,^{[1]} also known as the septimal whole tone (D- ) and the inverse of the subminor seventh. Another example is the ratio 15:13, or 247.74 cents (D♯).

Composer Lou Harrison was fascinated with the 7:6 subminor third and 8:7 supermajor second, using them in pieces such as *Concerto for Piano with Javanese Gamelan*, *Cinna* for tack-piano, and *Strict Songs* (for voices and orchestra).^{[12]} Together the two produce the 4:3 just perfect fourth.^{[13]}

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.

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^{a}^{b}Miller, Leta E., ed. (1988).*Lou Harrison: Selected keyboard and chamber music, 1937-1994*. p. XLIII. ISBN 978-0-89579-414-7.. - ^
^{a}^{b}Brabner, John H. F. (1884).*The National Encyclopaedia*, vol. 13, p. 182. London. [ISBN unspecified] **^**Helmholtz, Hermann L. F. von (2007).*On the Sensations of Tone*. pp. 195, 212. ISBN 978-1-60206-639-7.**^**Miller 1988, p. XLII.- ^
^{a}^{b}Andrew Horner, Lydia Ayres (2002).*Cooking with Csound: Woodwind and Brass Recipes*, p. 131. ISBN 0-89579-507-8. - ^
^{a}^{b}Royal Society (Great Britain) (1880, digitized February 26, 2008).*Proceedings of the Royal Society of London*, vol. 30, p. 531. Harvard University. - ^
^{a}^{b}Society of Arts (Great Britain) (1877, digitized November 19, 2009).*Journal of the Society of Arts*, vol. 25, p. 670. **^**Partch, Harry (1979).*Genesis of a Music*, p. 68. ISBN 0-306-80106-X.**^**Haluska, Jan (2003).*The Mathematical Theory of Tone Systems*, p. xxiii. 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.**^**Miller and Lieberman (2006), p. 72.^{[incomplete short citation]}**^**Miller & Lieberman (2006), p. 74. "The subminor third and supermajor second combine to create a pure fourth (8⁄7 x 7⁄6 = 4⁄3)."^{[incomplete short citation]}

Twelve- semitone (post-Bach Western) |
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Other tuning systems |
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Other intervals |
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