15/14
| Ratio | 15/14 |
| Factorization | 2-1 × 3 × 5 × 7-1 |
| Monzo | [-1 1 1 -1⟩ |
| Size in cents | 119.44281¢ |
| Names | septimal diatonic semitone, septimal major semitone |
| Color name | ry1, ruyo unison |
| FJS name | [math]\text{A1}^{5}_{7}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 7.71425 |
| Weil height (log2 max(n, d)) | 7.81378 |
| Wilson height (sopfr(nd)) | 17 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.26381 bits |
[sound info] | |
| open this interval in xen-calc | |
15/14 is a superparticular ratio with a numerator which is the fifth triangular number. It may be found as the interval between many 7-limit ratios, including:
- 16/15 and 8/7
- 14/13 and 15/13
- 7/6 and 5/4
- 6/5 and 9/7
- 14/11 and 15/11
- 4/3 and 10/7
- 7/5 and 3/2
- 22/15 and 11/7
- 14/9 and 5/3
- 8/5 and 12/7
- 26/15 and 13/7
- 7/4 and 15/8
In combination with 19/17 it forms a good approximation of golden meantone. The untempered combination of five 19/17 and two 15/14 leads to an interval that is sharp to an octave by the mercurial comma: ((19/17)^5 * (15/14)^2 = (2/1) / (mercurial comma))
Terminology
15/14 is traditionally called a diatonic semitone, perhaps for its proximity (and conflation in systems such as septimal meantone) with the classic diatonic semitone 16/15. However, 15/14 is a chromatic semitone in both Helmholtz-Ellis notation and Functional Just System, viewed as the apotome 2187/2048 altered by 5120/5103. Marc Sabat has taken to call it the major chromatic semitone in the same material where 21/20 is also named as the minor diatonic semitone[1].
Approximation
15/14 is very accurately approximated by 10EDO (1\10) and all linus temperaments. The linus comma, 5.6¢, is the amount by which a stack of ten 15/14's falls short of the octave.
References
See also
- 28/15 – its octave complement
- 7/5 – its fifth complement
- List of superparticular intervals
- Gallery of just intervals
- AS15/14 - its ambitonal sequence