18/17
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| Ratio | 18/17 |
| Subgroup monzo | 2.3.17 [1 2 -1⟩ |
| Size in cents | 98.954592¢ |
| Name | small septendecimal semitone |
| Color name | 17u1, su unison |
| FJS name | [math]\text{A1}_{17}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 8.25739 |
| Weil height (log2 max(n, d)) | 8.33985 |
| Wilson height (sopfr (nd)) | 25 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.64663 bits |
[sound info] | |
| open this interval in xen-calc | |
In 17-limit just intonation, 18/17 is the small septendecimal semitone of about 99¢. It is very close to 12edo's "half step" of 100¢, and fairly close to the "large septendecimal semitone" of 17/16 (~105¢).
Terminology and notation
Conceptualization systems disagree on whether 17/16 should be a diatonic semitone or a chromatic semitone, and as a result the disagreement propagates to all intervals of HC17. See 17-limit for a detailed discussion.
For 18/17 specifically:
- In the Functional Just System, it is a chromatic semitone, separated by 4131/4096 from the Pythagorean augmented unison (2187/2048).
- In Helmholtz-Ellis notation, it is a diatonic semitone, separated by 2187/2176 from the Pythagorean minor second (256/243).
The term small septendecimal semitone omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the large septendecimal semitone of 18/17.
See also
- 17/9 – its octave complement
- 17/12 – its fifth complement
- Gallery of just intervals
- List of superparticular intervals
- 1ed18/17 – equal multiplication of this interval