21/20
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Ratio | 21/20 |
Factorization | 2^{-2} × 3 × 5^{-1} × 7 |
Monzo | [-2 1 -1 1⟩ |
Size in cents | 84.467193¢ |
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 (log_{2} nd) | 8.71425 |
Weil height (log_{2} 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 |
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
- List of superparticular intervals
- Gallery of just intervals
- Septisemi temperaments, where it is tempered out