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Another major sixth is the 12:7 septimal major sixth or supermajor sixth, the inversion of the septimal minor third, of approximately 933 cents. [4] The septimal major sixth (12/7) is approximated in 53-tone equal temperament by an interval of 41 steps, giving an actual frequency ratio of the (41/53) root of 2 over 1, approximately 928 cents.
The size of an interval between two notes may be measured by the ratio of their frequencies.When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (), 2:1 (), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third).
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 Play ⓘ), [8] [9] or about 933 cents. [10] It is the inversion of the 7:6 subminor third.
Comparison between tunings: Pythagorean, equal-tempered, quarter-comma meantone, and others.For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to ...
Augmented sixth Play ⓘ.. In music, an augmented sixth (Play ⓘ) is an interval produced by widening a major sixth by a chromatic semitone. [1] [4] For instance, the interval from C to A is a major sixth, nine semitones wide, and both the intervals from C ♭ to A, and from C to A ♯ are augmented sixths, spanning ten semitones.
Other variants of augmented sixth chords can be found in the repertoire, and are sometimes given whimsical geographical names. For example: 4– ♭ 6–7– ♯ 2; (F–A ♭ –B–D ♯) is called by one source an Australian sixth, and 1- 2 - ♯ 4 - ♯ 6 (C - D - F ♯ - A ♯) sometimes called the Japanese sixth, Blackadder, or Ikisugi chord.
A major interval is one semitone larger than a minor interval. The words perfect, diminished, and augmented are also used to describe the quality of an interval.Only the intervals of a second, third, sixth, and seventh (and the compound intervals based on them) may be major or minor (or, rarely, diminished or augmented).
However, this does not mean that these notes must be played within an octave of the root, nor the extended notes in seventh chords should be played outside of the octave, although it is commonly the case. 6 is particularly common in a minor sixth chord (also known as minor/major sixth chord, as the 6 refers to a major sixth interval).