Chromatic semitone: Difference between revisions
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{{Infobox interval|2187/2048|names=Chromatic semitone, augmented unison|name=Chromatic semitone, augmented unison|Name=Chromatic semitone, augmented unison, apotome}} | {{Infobox interval|2187/2048|names=Chromatic semitone, augmented unison|name=Chromatic semitone, augmented unison|Name=Chromatic semitone, augmented unison, apotome}} | ||
The 3-limit '''chromatic semitone''', also called the '''augmented unison''' ('''A1''') or the '''apotome''' (ə-POT-ə-mee) and represented by the ratio '''2187/2048,''' is the difference between the large and small steps of the MOS [[diatonic]] scale. It is generated by stacking 7 [[Perfect fifth|fifths]] and octave-reducing. In [[Pythagorean tuning|Pythagorean]] tuning (and thus purely-tuned [[just intonation]]), it is approximately {{Cents from ratio|2187/2048|ratio=2187/2048}} cents in size, but as an interval involved in the structure of the abstract diatonic scale it ranges from 0 to 240 cents depending on the tuning. | The 3-limit '''chromatic semitone''', also called the '''augmented unison''' ('''A1''') or the '''apotome''' (''ə-POT-ə-mee'') and represented by the ratio '''2187/2048,''' is the difference between the large and small steps of the MOS [[diatonic]] scale, therefore being a type of [[Interval arithmetic|unison]] (in terms of interval arithmetic, at least) and a type of [[semitone]]. It is generated by stacking 7 [[Perfect fifth|fifths]] and octave-reducing. In [[Pythagorean tuning|Pythagorean]] tuning (and thus purely-tuned [[just intonation]]), it is approximately {{Cents from ratio|2187/2048|ratio=2187/2048}} cents in size, but as an interval involved in the structure of the abstract diatonic scale it ranges from 0 to 240 cents depending on the tuning. In 12edo, it is tuned to 100 cents (the same as the [[diatonic semitone]]); flatter tunings narrow it (leading to a "mellower" diatonic scale), and sharper tunings widen it. | ||
The chromatic semitone is significant in music notation. As it is the difference between, for example, the [[diatonic major third]] and [[diatonic minor third]], it is the interval represented by the # and b accidentals used in standard music notation. The chromatic semitone is distinct from the [[diatonic semitone]], which is the diatonic minor second and differs from the [[diatonic major second]] by a chromatic semitone. | The chromatic semitone is significant in music notation. As it is the difference between, for example, the [[diatonic major third]] and [[diatonic minor third]], it is the interval represented by the # and b accidentals used in standard music notation. The chromatic semitone is distinct from the [[diatonic semitone]], which is the diatonic minor second and differs from the [[diatonic major second]] by a chromatic semitone. | ||
Latest revision as of 03:15, 16 October 2026
| Interval information |
augmented unison,
apotome
reduced harmonic
The 3-limit chromatic semitone, also called the augmented unison (A1) or the apotome (ə-POT-ə-mee) and represented by the ratio 2187/2048, is the difference between the large and small steps of the MOS diatonic scale, therefore being a type of unison (in terms of interval arithmetic, at least) and a type of semitone. It is generated by stacking 7 fifths and octave-reducing. In Pythagorean tuning (and thus purely-tuned just intonation), it is approximately 113.7 cents in size, but as an interval involved in the structure of the abstract diatonic scale it ranges from 0 to 240 cents depending on the tuning. In 12edo, it is tuned to 100 cents (the same as the diatonic semitone); flatter tunings narrow it (leading to a "mellower" diatonic scale), and sharper tunings widen it.
The chromatic semitone is significant in music notation. As it is the difference between, for example, the diatonic major third and diatonic minor third, it is the interval represented by the # and b accidentals used in standard music notation. The chromatic semitone is distinct from the diatonic semitone, which is the diatonic minor second and differs from the diatonic major second by a chromatic semitone.
As a harmonic interval, the chromatic semitone is a harsh dissonance due to its size, though tuning the diatonic interval qualities further apart (such as in arto and tendo theory) can alleviate that somewhat. In 5edo, it is a consonant 8/7 interval much like the diatonic major second.
Scale info
The chromatic semitone, being an interval with a fifthspan of more than 6, does not appear in the diatonic scale itself, but it is often an important interval to account for when discussing the tuning of diatonic.
Just intonation
In just intonation, the chromatic semitone is a 3-limit interval. When tempered out, it leads to the whitewood temperament, where the MOS diatonic scale collapses to 7edo.
