Diminished second
Encyclopedia
In modern Western tonal music theory a diminished second is the interval between notes on two adjacent staff positions, or having adjacent note letters, whose alterations cause them, in ordinary equal temperament, to have no pitch difference, such as B and C or B and C. The two notes may more often be described as Enharmonic equivalents.
More specifically, in other tunings and repertoires from Western culture
, a diminished second is the minute (smaller than a semitone) pitch interval
produced by narrowing
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. Being diminished, it is considered a dissonant
interval.
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. 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).
, the diminished second is identical to the unison
, 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
s wide. It shows a similar size in third-comma meantone
, where it coincides with the greater diesis
(62.57 cents). The most commonly used meantone temperament
s 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 twelfth-comma meantone, although that diminished second is only about 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 semitone
s, m2 is the minor second (diatonic semitone), A1 is the augmented unison (chromatic semitone), and S1, S2, S3, S4 are semitones as defined in 5-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.
More specifically, in other tunings and repertoires from Western culture
Western culture
Western culture, sometimes equated with Western civilization or European civilization, refers to cultures of European origin and is used very broadly to refer to a heritage of social norms, ethical values, traditional customs, religious beliefs, political systems, and specific artifacts and...
, a diminished second is the minute (smaller than a semitone) pitch interval
Pitch interval
In musical set theory, a pitch interval is the number of semitones that separates one pitch from another, upward or downward.They are notated as follows:For example C4 to D4 is 3 semitones:While C4 to D5 is 15 semitones:...
produced by narrowing
Diminution
In Western music and music theory, diminution has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of shorter, usually melodic, values...
a minor second
Minor second
In modern Western tonal music theory a minor second is the interval between two notes on adjacent staff positions, or having adjacent note letters, whose alterations cause them to be one semitone or half-step apart, such as B and C or C and D....
, 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. Being diminished, it is considered a dissonant
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
interval.
The diminished second can be also viewed as a comma
Comma (music)
In music theory, a comma is a minute interval, the difference resulting from tuning one note two different ways. The word "comma" used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F tuned using the D-based Pythagorean tuning...
, the minute interval between two enharmonically equivalent
Enharmonic
In modern musical notation and tuning, an enharmonic equivalent is a note , interval , or key signature which is equivalent to some other note, interval, or key signature, but "spelled", or named, differently...
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).
Size in different tuning systems
In 12-tone equal temperamentEqual temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
, the diminished second is identical to the unison
Unison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
, 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 (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
s wide. It shows a similar size in third-comma meantone
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
, where it coincides with the greater diesis
Diesis
In classical music from Western culture, a diesis is either an accidental , or a comma type of musical interval, usually defined as the difference between an octave and three justly tuned major thirds , equal to 128:125 or about 41.06 cents...
(62.57 cents). The most commonly used meantone temperament
Meantone temperament
Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of...
s fall between these extremes, giving it an intermediate size.
In Pythagorean tuning
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
, however, the interval actually shows a descending direction, i.e. a ratio below unison
Unison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
, and thus a negative size (−23.46 cents), equal to the opposite of a Pythagorean comma
Pythagorean comma
In musical tuning, the Pythagorean comma , named after the ancient mathematician and philosopher Pythagoras, is the small interval existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B , or D and C...
. Such is also the case in twelfth-comma meantone, although that diminished second is only about a twelfth of the Pythagorean one (−1.95 cents, the opposite of a schisma
Schisma
In music, the schisma is the ratio between a Pythagorean comma and a syntonic comma and equals 32805:32768, which is 1.9537 cents...
).
The table below summarizes the definitions of the diminished second in the main tuning systems. In the column labeled "Difference between semitone
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....
s, m2 is the minor second (diatonic semitone), A1 is the augmented unison (chromatic semitone), and S1, S2, S3, S4 are semitones as defined in 5-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.
| Tuning system | Definition of diminished second | Size | ||
|---|---|---|---|---|
| Difference between semitone 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.... s |
Equivalent to | Cents Cent (music) The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each... |
Ratio Interval ratio In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3:2 , 1.5, and may be approximated by an equal tempered perfect fifth which is 27/12, 1.498... |
|
| Pythagorean tuning Pythagorean tuning Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant... |
m2 − A1 | Opposite of Pythagorean comma Pythagorean comma In musical tuning, the Pythagorean comma , named after the ancient mathematician and philosopher Pythagoras, is the small interval existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B , or D and C... |
−23.46 | 524288:531441 |
| 1/12-comma meantone Meantone temperament Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal temperament, the opposite of... |
m2 − A1 | Opposite of schisma Schisma In music, the schisma is the ratio between a Pythagorean comma and a syntonic comma and equals 32805:32768, which is 1.9537 cents... |
−1.95 | 32768:32805 |
| 12-tone equal temperament | m2 − A1 | Unison Unison In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance... |
0.00 | 1:1 |
| 1/6-comma meantone | m2 − A1 | Diaschisma Diaschisma The diaschisma is a small musical interval defined as the difference between three octaves and four perfect fifths plus two major thirds . It can be represented by the ratio 2048:2025 and is about 19.5 cents... |
19.55 | 2048:2025 |
| 5-limit tuning | S3 − S2 | |||
| 1/4-comma meantone Quarter-comma meantone Quarter-comma meantone, or 1/4-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. This method is a variant of Pythagorean tuning... |
m2 − A1 | (Lesser) diesis Diesis In classical music from Western culture, a diesis is either an accidental , or a comma type of musical interval, usually defined as the difference between an octave and three justly tuned major thirds , equal to 128:125 or about 41.06 cents... |
41.06 | 128:125 |
| 5-limit tuning | S3 − S1 | |||
| 1/3-comma meantone | m2 − A1 | Greater diesis | 62.57 | 648:625 |
| 5-limit tuning | S4 − S1 | |||
| 19-tone equal temperament | m2 − A1 | Chromatic semitone 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.... (A1 = m2 / 2) |
63.16 | 21/19:1 |