Diminished second

diminished second
Inverse	augmented seventh
Name
Other names	-
Abbreviation	dim.2
Size
Semitones	0
Interval class	0
Just interval	128:125
Cents
12-Tone equal temperament	0
24-Tone equal temperament	50
Just intonation	41.1

In classical music from Western culture, a diminished second is the minute (smaller than a semitone) musical interval produced by diminishing a minor second, or diatonic semitone, by a chromatic semitone. It is therefore the difference between the diatonic and chromatic semitones. For instance, the interval from B to C is a diatonic semitone, the interval from B to B♯ is a chromatic semitone, and their difference, the interval from B♯ to C is a diminished second.

The diminished second can be also viewed as a comma, the minute interval between two enharmonically equivalent notes tuned in a slightly different way. This makes it a highly variable quantity between tuning systems. In standard equal temperament, in fact, it is identical to the unison (play^ⓘ), because both semitones have the same size. In 19 equal temperament, on the other hand, it is identical to the chromatic semitone and is a respectable 63.2 cents wide. It is similar in third-comma meantone, where the interval is 62.6 cents. The most commonly used meantone temperaments (such as quarter-comma meantone) fall between these extremes, giving it an intermediate size. In Pythagorean tuning, however, the interval actually appears below unison in the Pythagorean interval table. Such is also the case in twelfth-comma meantone, although that diminished second is only a twelfth of the distance below unison.

Three major thirds in succession plus a diminished second make up an octave, and therefore the diminished second is sometimes considered to be a diesis, which in just intonation and in quarter-comma meantone is a ratio of 128/125, or about 41 cents (play^ⓘ). In other tuning systems, the diminished second has a different size, and typically is assigned a different name (e.g. greater diesis, schisma, diaschisma, Pythagorean comma).

The diminished second is significant in relation to musical notation, since enharmonic pairs of intervals, in the sense of intervals identical in equal temperament differ by a diminished second. Hence for example G♯ is less than A♭ by a diminished second interval, however large or small that may happen to be.

See also