18/17

Interval information

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{nd}[/math])	~4.29182 bits
Comma size	medium
[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 17/16.

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