21/20

Interval information

Ratio	21/20
Factorization	2-2 × 3 × 5-1 × 7
Monzo	[-2 1 -1 1⟩
Size in cents	84.46719¢
Names	septimal minor semitone, septimal chromatic semitone, large septimal chroma
Color name	zg2, zogu 2nd
FJS name	[math]\text{m2}^{7}_{5}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	8.71425
Weil height (log2 max(n, d))	8.78463
Wilson height (sopfr(nd))	19
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.3207 bits
Comma size	medium
S-expressions	S6 × S7, S7 × S8 × S9
[sound info]
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English Wikipedia has an article on:

Septimal chromatic semitone

21/20 is a small semitone of about 85 cents. It may be found in 7-limit just intonation as, for example, the difference between 4/3 and 7/5, 8/7 and 6/5, or 5/3 and 7/4.

Terminology

21/20 is traditionally called a chroma, perhaps for its proximity (and conflation in systems like septimal meantone) with the major chroma 135/128. However, it is a diatonic semitone in both Helmholtz–Ellis notation and Functional Just System, viewed as the Pythagorean minor second 256/243 altered by 5120/5103. Marc Sabat has taken to call it the minor diatonic semitone in the same material where 15/14 is also named as the major chromatic semitone.

See also

• 40/21 – its octave complement
• 10/7 – its fifth complement
• 1ed21/20 – its ambitonal sequence
• List of superparticular intervals
• Gallery of just intervals
• Septisemi temperaments, where it is tempered out