Diminished second

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Diminished second

In modern Western tonal music theory, a diminished second is the interval produced by narrowing a minor second by one chromatic semitone.[1] In twelve-tone equal temperament, it is enharmonically equivalent to a perfect unison;[3] therefore, it is the interval between notes on two adjacent staff positions, or having adjacent note letters, altered in such a way that they have no pitch difference in twelve-tone equal temperament. An example is the interval from a B to the C immediately above; another is the interval from a B to the C immediately above.

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In particular, it may be regarded as the "difference" between a diatonic and chromatic semitone. 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.

Being diminished, it is considered a dissonant interval.[4]

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Diminished second Play

Size in different tuning systems

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Perspective

In tuning systems other than 12-tone equal temperament and its multiples, the diminished second is a distinct interval. It can be 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. Hence for example C is narrower (or sometimes wider) than D by a diminished second interval, however large or small that may happen to be (see image below).[citation needed]

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Diminished second in quarter-comma meantone (also known as lesser diesis), coinciding with the interval from C to D, defined as the difference between m2 and A1 (117.1 76.0 = 41.1 cents). Play

In 12-tone equal temperament, the diminished second is identical to the unison (play), because the chromatic and diatonic semitones have the same size. In 19-tone equal temperament, which extends 13-comma meantone, it is identical to the chromatic semitone and is a respectable 63.16 cents wide. The most commonly used meantone temperaments fall between these extremes, giving it an intermediate size.

However, in 53-tone equal temperament, which extends Pythagorean tuning, the interval actually shows a descending direction, i.e. a ratio below unison, and thus a negative size, going one step down. In general, this applies for all tunings with fifths wider than 700 cents.

The table below summarizes the definitions of the diminished second in the main tuning systems. In the column labeled "Difference between semitones", m2 is the minor second (diatonic semitone), A1 is the augmented unison (chromatic semitone), and S1, S2, S3, S4 are semitones as defined in five-limit tuning#Size of intervals. Notice that for 5-limit tuning, 16-, 15-, 14-, and 13-comma meantone, the diminished second coincides with the corresponding commas.

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Tuning systemDefinition of diminished secondSize
Difference between
semitones
Equivalent toCentsRatio
Pythagorean tuningm2 A1Opposite of Pythagorean comma23.46524288:531441
1/12-comma meantonem2 A1Opposite of schisma1.9532768:32805
12-tone equal temperamentm2 A1Unison0.001:1
1/6-comma meantonem2 A1Diaschisma19.552048:2025
5-limit tuningS3 S2
1/5-comma meantonem2 A128.16
1/4-comma meantonem2 A1(Lesser) diesis41.06128:125
5-limit tuningS3 S1
1/3-comma meantonem2 A1Greater diesis62.57648:625
5-limit tuningS4 S1
19-tone equal temperamentm2 A1Chromatic semitone (A1 = m2 / 2)63.16:1
31-tone equal temperamentm2 A1Lesser diesis38.77:1
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