Diminished second
Inverse  augmented seventh 

Name  
Other names   
Abbreviation  d2^{[1]} 
Size  
Semitones  0 
Interval class  0 
Just interval  128:125^{[2]} 
Cents  
Equal temperament  0 
24 equal temperament  50 
Just intonation  41.1 
In modern Western tonal music theory, a diminished second is the interval produced by narrowing a minor second by one chromatic semitone.^{[1]} It is enharmonically equivalent to a perfect unison.^{[3]} Thus, 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 twelvetone 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.
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]}
Size in different tuning systems
In tuning systems other than twelvetone equal temperament, the diminished second 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).

In 12tone equal temperament, the diminished second is identical to the unison ( play ), because both semitones have the same size. In 19tone equal temperament, on the other hand, it is identical to the chromatic semitone and is a respectable 63.16 cents wide. It shows a similar size in thirdcomma meantone, where it coincides with the greater diesis (62.57 cents). The most commonly used meantone temperaments fall between these extremes, giving it an intermediate size.
In Pythagorean tuning, however, the interval actually shows a descending direction, i.e. a ratio below unison, and thus a negative size (−23.46 cents), equal to the opposite of a Pythagorean comma. Such is also the case in twelfthcomma meantone, although that diminished second is only a twelfth of the Pythagorean one (−1.95 cents, the opposite of a schisma).
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 S_{1}, S_{2}, S_{3}, S_{4} are semitones as defined in fivelimit tuning#Size of intervals. Notice that for 5limit tuning, 1/6, 1/4, and 1/3comma meantone, the diminished second coincides with the corresponding commas.
Tuning system  Definition of diminished second  Size  

Difference between semitones 
Equivalent to  Cents  Ratio  
Pythagorean tuning  m2 − A1  Opposite of Pythagorean comma  −23.46  524288:531441 
1/12comma meantone  m2 − A1  Opposite of schisma  −1.95  32768:32805 
12tone equal temperament  m2 − A1  Unison  0.00  1:1 
1/6comma meantone  m2 − A1  Diaschisma  19.55  2048:2025 
5limit tuning  S_{3} − S_{2}  
1/4comma meantone  m2 − A1  (Lesser) diesis  41.06  128:125 
5limit tuning  S_{3} − S_{1}  
1/3comma meantone  m2 − A1  Greater diesis  62.57  648:625 
5limit tuning  S_{4} − S_{1}  
19tone equal temperament  m2 − A1  Chromatic semitone (A1 = m2 / 2)  63.16  2^{1/19}:1 
See also
Sources
 1 2 Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.54. ISBN 9780072942620. Specific example of an d2 not given but general example of minor intervals described.
 ↑ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 0824747143. Minor diesis, diminished second.
 ↑ Rushton, Julian. "Unison (prime)]". Grove Music Online. Oxford Music Online. Retrieved August 2011. Check date values in:
accessdate=
(help) (subscription needed)  ↑ Benward & Saker (2003), p.92.