Diminished second
Inverse | augmented seventh |
---|---|
Name | |
Other names | — |
Abbreviation | d2[1] |
Size | |
Semitones | 0 |
Interval class | 0 |
Just interval | 128:125[2] |
Cents | |
12-Tone equal temperament | 0 |
Just intonation | 41.1 |
In modern Western tonal music theory, a diminished second is the
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 twelve-tone equal temperament, the diminished second can be viewed as a
In 12-tone
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, 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 semitones |
Equivalent to | Cents | Ratio | |
Pythagorean tuning | A1 |
Opposite of Pythagorean comma | −23.46 | 524288:531441 |
1/12-comma meantone | m2 − A1 | Opposite of schisma | −1.95 | 32768:32805 |
12-tone equal temperament |
m2 − A1 | Unison | 0.00 | 1:1 |
1/6-comma meantone | m2 − A1 | Diaschisma | 19.55 | 2048:2025 |
5-limit tuning |
S3 − S2 | |||
1/4-comma meantone | m2 − A1 | (Lesser) diesis | 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 (A1 = m2 / 2) | 63.16 | :1 |
31-tone equal temperament |
m2 − A1 | Lesser diesis | 38.77 | :1 |
See also
References
- ^ ISBN 978-0-07-294262-0. Specific example of an d2 not given but general example of minor intervals described.
- ISBN 0-8247-4714-3. Minor diesis, diminished second.
- Grove Music Online. Oxford Music Online.
- ^ Benward and Saker (2003), p. 92.