15/14
| Interval information |
septimal major semitone
reduced
[sound info]
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
- 7/6 and 5/4
- 6/5 and 9/7
- 4/3 and 10/7
- 7/5 and 3/2
- 14/9 and 5/3
- 8/5 and 12/7
- 7/4 and 15/8
It also arises in higher limits as:
Terminology
15/14 is traditionally called a diatonic semitone, perhaps for its proximity (and conflation in systems such as septimal meantone and marvel) with the classic diatonic semitone 16/15. However, 15/14 is a chromatic semitone in both Helmholtz–Ellis notation and the 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.
In combination with 19/17 it forms a good approximation of golden meantone. The untempered combination of five 19/17's and two 15/14's leads to an interval that is sharp to an octave by the mercurial comma: (19/17)5 × (15/14)2 = 2 / (mercurial comma).
Temperaments
The following linear temperaments are generated by a ~15/14:
In addition, several 10th-octave temperaments treat ~15/14 as the period, including decoid and linus.
See also
References
- ↑ Marc Sabat. Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space. Plainsound Music Edition, 2008.