Qian's large comma

Interval information

Factorization	2-569 × 3359
Monzo	[-569 359⟩
Size in cents	1.845311¢
Names	Qianlezhi's large comma, 359-comma
FJS name	[math]\displaystyle{ \text{51d}{-35} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	1138
Weil norm (log2 max(n, d))	1138
Wilson norm (sopfr(nd))	2215
Comma size	unnoticeable
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[-569 359⟩, called Qian's large comma, is an unnoticeable 3-limit comma with a size of 1.845 cents. Which 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.

Etymology

The comma is discovered by the ancient Chinese theorist, Qian Lezhi（钱乐之，390—462, pronounces as ch'ien lo-chih）, see Qian's 360 pitches.

In Qian's 360 pitches, this comma can be described as the interval between Huangzhong（黄钟） and Anyun（安运）.

Temperaments

359edo

see

Ratio

1934329451767021421190980423006270754962252499447372679942534652297789463068718331568475476554301659845788554312924531179306109686817232569946089263295619210341718686733067

/1932268761508629172347675945465993672149463664853217499328617625725759571144780212268096883290961288981231808015751088588682539330521493827871454336733540374348490407411712

Old pages

Qianlezhi's large comma[1]

See also

• Unnoticeable comma
• Qian's small comma