112/75
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| Ratio | 112/75 |
| Factorization | 24 × 3-1 × 5-2 × 7 |
| Monzo | [4 -1 -2 1⟩ |
| Size in cents | 694.24348¢ |
| Name | marvelous fifth |
| Color name | zgg6, zogugu 6th |
| FJS name | [math]\text{d6}^{7}_{5,5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 13.0362 |
| Weil height (log2 max(n, d)) | 13.6147 |
| Wilson height (sopfr(nd)) | 28 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~3.6276 bits |
[sound info] | |
| open this interval in xen-calc | |
112/75, the marvelous fifth (694.2¢), is 225/224 (7.7¢) below the just fifth 3/2. It often arises in just intonation scales, for instance as the interval from 15/14 to 8/5, or 5/7 to 16/15. Tempering out 225/224 from the scale can be used to make it much less flat, but it is usable as it is, being only half a cent flat from the 19edo fifth of 11\19. Considered as a meantone fifth, it is approximately 5/14-comma meantone.
See also
- File:jid_112_75_pluck_adu_dr220.mp3 – another sound example
- 75/56 - its octave complement
- Gallery of just intervals