Rodan comma

Interval information

Ratio	131072000/129140163
Factorization	220 × 3-17 × 53
Monzo	[20 -17 3⟩
Size in cents	25.70613¢
Names	rodan comma, roda
Color name	sasa-triyo 2nd, ssy32
FJS name	[math]\text{m2}^{5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	53.9101
Weil height (log2 max(n, d))	53.9316
Wilson height (sopfr(nd))	106
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.28325 bits
Comma size	small
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The rodan comma (monzo: [20 -17 3⟩, ratio: 131072000/129140163), otherwise known as the roda, is a small 5-limit comma of about 25.7 cents. As part of the syntonic–diatonic equivalence continuum, it is the difference between the Pythagorean diatonic semitone (256/243) and a stack of three syntonic commas. It is also the amount by which a stack of three acute whole tones (729/640) falls short of the perfect fifth.

Temperaments

Tempering out this comma leads to the 5-limit version of rodan.