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In modern Western tonal music theory, a diminished second is the interval produced by narrowing a 
minor second
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent no ...
by one chromatic semitone
In modern Western tonal music theory an augmented unison or augmented prime is the interval between two notes on the same staff position, or denoted by the same note letter, whose alterations cause them, in ordinary equal temperament, to be one ...
.Bruce Benward and Marilyn Saker (2003). ''Music: In Theory and Practice, Vol. I'', p. 54. . Specific example of an d2 not given but general example of minor intervals described. It is enharmonic
In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written n ...
ally equivalent to a perfect unison
In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm.
Definition
Unison or per ...
. 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 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.
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
In music, consonance and dissonance are categorizations of simultaneous or successive Sound, sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness ...
interval.Benward and Saker (2003), p. 92.
Size in different tuning systems
In tuning systems other than twelve-tone equal temperament, the diminished second can be viewed as acomma
The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...
, the minute interval between two enharmonically equivalent
In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written no ...
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 12-tone equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
, the diminished second is identical to the unison
In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm.
Definition
Unison or per ...
(), because both semitones have the same size. In 19-tone equal temperament, on the other hand, it is identical to the chromatic semitone and is a respectable 63.16 cent
Cent may refer to:
Currency
* Cent (currency), a one-hundredth subdivision of several units of currency
* Penny (Canadian coin), a Canadian coin removed from circulation in 2013
* 1 cent (Dutch coin), a Dutch coin minted between 1941 and 1944
* ...
s wide. It shows a similar size in third-comma meantone
Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. Mea ...
, where it coincides with the greater diesis
In classical music from Western culture, a diesis ( , plural dieses ( , "difference"; Greek: δίεσις "leak" or "escape"Benson, Dave (2006). ''Music: A Mathematical Offering'', p.171. . Based on the technique of playing the aulos, where p ...
(62.57 cents). The most commonly used meantone temperament
Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. Me ...
s fall between these extremes, giving it an intermediate size.
In Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: Mc ...
, however, the interval actually shows a descending direction, i.e. a ratio below unison
In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm.
Definition
Unison or per ...
, and thus a negative size (−23.46 cents), equal to the opposite of a Pythagorean comma
In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C ...
. Such is also the case in twelfth-comma meantone, although that diminished second is only a twelfth of the Pythagorean one (−1.95 cents, the opposite of a schisma
In music, the schisma (also spelled ''skhisma'') is the interval between a Pythagorean comma (531441:524288) and a syntonic comma (81:80) and equals or 32805:32768 = 1.00113, which is 1.9537 cents (). It may also be defined as:
* the differe ...
).
The table below summarizes the definitions of the diminished second in the main tuning systems. In the column labeled "Difference between semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent no ...
s", m2 is the minor second (diatonic semitone), A1 is the augmented unison (chromatic semitone), and S, S, S, S are semitones as defined in five-limit tuning#Size of intervals. Notice that for 5-limit tuning, 1/6-, 1/4-, and 1/3-comma meantone, the diminished second coincides with the corresponding commas.
See also
* List of musical intervals *List of pitch intervals
Below is a list of intervals expressible in terms of a prime limit (see Terminology), completed by a choice of intervals in various equal subdivisions of the octave or of other intervals.
For commonly encountered harmonic or melodic intervals ...
*List of meantone intervals
The following is a list of intervals of extended meantone temperament. These intervals constitute the standard vocabulary of intervals for the Western common practice era. Here 12-EDO refers to the size of the interval in 12 equal divisions of th ...
*Comma (music)
In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Strictly speaking, there are only two kinds of comma, the syntonic comma, "the difference between a just major 3rd and four jus ...
References