21/20
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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]
open this interval in xen-calc
| Interval information |
septimal chromatic semitone,
large septimal chroma
reduced
(Shannon, [math]\sqrt{nd}[/math])
S7 × S8 × S9
[sound info]
English Wikipedia has an article on:
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[1].
See also
- 40/21 – its octave complement
- 10/7 – its fifth complement
- 1ed21/20 - its equal multiplication
- List of superparticular intervals
- Gallery of just intervals
- Septisemi temperaments, where it is tempered out