Septimal chromatic semitone

In music, a septimal chromatic semitone or minor semitone^[1] is the interval 21:20 (Play^ⓘ). It is about 84.47 cents. The septimal chromatic semitone may be derived from the harmonic series as the interval between the twentieth and twenty-first harmonics.

The septimal chromatic semitone equals a just chromatic semitone (25:24) plus a septimal semicomma (126:125).

When added to the 15:14 semitone, the 21:20 semitone and 28:27 semitone produce the 9:8 tone (major tone) and 10:9 tone (minor tone), respectively.

References

^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. ISBN 0-8247-4714-3.

Intervals

Twelve-
semitone
(post-Bach
Western)

(Numbers in brackets
are the number of
semitones in the
interval.)

Perfect	unison (0) fourth (5) fifth (7) octave (12)
Major	second (2) third (4) sixth (9) seventh (11)
Minor	second (1) third (3) sixth (8) seventh (10)
Augmented	unison (1) second (3) third (5) fourth (6) fifth (8) sixth (10) seventh (12)
Diminished	second (0) third (2) fourth (4) fifth (6) sixth (7) seventh (9) octave (11)
Compound	ninth (13 or 14) tenth (15 or 16) eleventh (17 or 18) twelfth (18 or 19) thirteenth (20 or 21) fourteenth (22 or 23) fifteenth (24)

Other
tuning
systems

24-tone equal temperament
(Numbers in brackets refer
to fractional semitones.)

Neutral	quarter tone (1⁄2) second (1+1⁄2) third (3+1⁄2) major fourth (5+1⁄2) minor fifth (6+1⁄2) sixth (8+1⁄2) seventh (10+1⁄2)

Just intonations
(Numbers in brackets
refer to pitch ratios.)

7-limit	septimal quarter tone (36:35) septimal third tone (28:27) septimal chromatic semitone (21:20) septimal diatonic semitone (15:14) supermajor second (8:7) subminor third (7:6) supermajor third (9:7) subminor fifth (7:5) supermajor fourth (10:7) subminor seventh (7:4)
Higher-limit	minor diatonic semitone (17-limit)

Other
intervals

Groups	Microtone 5-limit Comma Pseudo-octave Pythagorean interval Subminor and supermajor
Semitones	Pythagorean limma Pythagorean apotome Major limma
Quarter tones	Quarter tone Septimal quarter tone Undecimal quarter tone
Commas	Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma (27.3 cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma (13.8 cents) Kleisma (8.1 cents) Septimal kleisma (7.7 cents) Schisma (1.95 cents) Breedsma (0.72 cents) Ragisma (0.4 cents)
Measurement	Cent Centitone Millioctave Savart
Others	Wolf Ditone Semiditone Secor Incomposite interval

List of pitch intervals

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