Diatonic semitone
| Interval information |
diatonic minor second
reduced subharmonic
The 3-limit diatonic semitone, also called the diatonic minor second (m2) and represented by the ratio 256/243, is the smaller of the two seconds (1-step intervals) in the MOS diatonic scale. It is generated by stacking 5 fourths and octave-reducing. In Pythagorean tuning, and thus purely-tuned just intonation, it is approximately 90.2 cents in size, but as an interval in the abstract diatonic scale it may range between 0 and 171 cents, depending on the tuning.
It functions as the small step of the diatonic MOS, and along with the diatonic major second may be used to construct other diatonic intervals. For example, the diatonic minor third is a major second stacked with a minor second. The chromatic semitone is the difference between these two intervals. Note that the chromatic semitone itself is distinct from the diatonic semitone; they are separated by the Pythagorean comma, which separates all enharmonic intervals in Pythagorean tuning, and which, if tempered out, yields 12edo.
As a harmonic interval, the diatonic semitone is usually considered a dissonance, due to its small size and complex ratio.
Scale info
The diatonic scale contains two minor seconds. In the Ionian mode, minor seconds are found on the third and seventh scale degrees; the others have major seconds. The small number of minor seconds compared to major seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are minor.
Just intonation
The diatonic semitone is a product of square superparticulars, denoted S7 * S82. When tempered out, it leads to blackwood temperament, which tunes the 2.3.7 subgroup to 5edo.
