Qian's small comma

Interval information

Factorization	2485 × 3-306
Monzo	[485 -306⟩
Size in cents	1.769735¢
Names	Qian's small comma, sasktel comma, 306-comma
Color name	s44w30, lequadsawa 30th
FJS name	[math]\text{43d30}[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	969.999
Weil height (log2 max(n, d))	970
Wilson height (sopfr(nd))	1888
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.22745 bits
Comma size	unnoticeable
open this interval in xen-calc

Qian's small comma, also known as the sasktel comma or 306-comma, is an unnoticeable 3-limit comma with a monzo of [485 -306⟩, and a size of 1.7697 cents. It is the difference between 306 just perfect fifths and 179 octaves, in other words 2¹⁷⁹/(3/2)³⁰⁶. It is also the amount by which a Pythagorean comma exceeds a stack of six Mercator's commas, or the amount by which a 41-comma exceeds a stack of five Mercator's commas.

Temperaments

This comma is tempered out in 306edo and any edo that is divisible by 306 and has its best perfect fifth as the same perfect fifth in 306edo (612edo, 918edo, 1224edo, etc).

Etymology

According to a 2009 paper by Chen Yingshi, this comma as well as the 359-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 Yizhao (亿兆) and Qinghuangzhong (清黄钟), or between Kezhong (克终) and Zhishi (执始), etc.

Sasktel comma was first attested on this wiki in 2011. It is unclear how this name was coined.