Qian's large comma

Interval information

Factorization	2-569 × 3359
Monzo	[-569 359⟩
Size in cents	1.845311¢
Names	Qian's large comma, 359-comma
FJS name	[math]\text{51d}{-35}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	1138
Weil height (log2 max(n, d))	1138
Wilson height (sopfr(nd))	2215
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.23088 bits
Comma size	unnoticeable
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Qian's large comma, or the 359-comma, is an unnoticeable 3-limit comma with a monzo of [-569 359⟩ and a size of 1.845 cents. It is the amount by which 359 perfect fifths exceed 210 octaves, in other words (3/2)³⁵⁹/2²¹⁰. It is also the amount by which a Mercator's comma exceeds a Qian's small comma.

Temperaments

This comma is tempered out in 359edo and any edo that is divisible by 359 and has its best perfect fifth as the same perfect fifth in 359edo (718edo, 1077edo, 1436edo, etc).

Etymology

According to a 2009 paper by Chen Yingshi, this comma as well as the 306-comma was discovered by the ancient Chinese theorist Qian Lezhi (Simplified Chinese: 钱乐之, 390–462, also romanized as Ch'ien Lo-chih), hence the name. In Qian's 360-tone tuning, this comma can be described as the interval between Huangzhong (黄钟) and Anyun (安运).