Sinarabian comma

Interval information

Ratio	85293/85184
Factorization	2-6 × 38 × 11-3 × 13
Monzo	[-6 8 0 0 -3 1⟩
Size in cents	2.213842¢
Name	Sinarabian comma
Color name	lathotrilu unison
FJS name	[math]\displaystyle{ \text{A1}^{13}_{11,11,11} }[/math]
Special properties	reduced
Tenney height (log2 nd)	32.7584
Weil height (log2 max(n, d))	32.7603
Wilson height (sopfr(nd))	82
Comma size	unnoticeable
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The Sinarabian comma is an 13-limit (also 2.3.11.13 subgroup) unnoticeable comma with a ratio of 85293/85184 and a value of approximately 2 cents.

This comma is identifiable as the amount by which a stack of two 88/81 artoneutral seconds falls short of a 13/11 Neo-Gothic minor third, and also the amount by which a stack of three 11/9 artoneutral thirds fall short of 117/64, and even the comma that separates 1053/1024 and 1331/1296.

In terms of comma relations, it separates 243/242 from 352/351, separates 144/143 from a stack of two instances of 243/242, and, is the sum of the frameshift comma and the tridecapyth comma.

Etymology and Implications

The name of this comma comes from a portmanteau of "Ibn Sina" and "Alpharabian", and was given by Aura on the basis of a series of connections between intervals that he found and shared with Margo Schulter, who took note of the following implications, here paraphrased in part by Aura.

One of the major commatic relations is between the rastma (243/242) on one hand, which occurs in the tuning of the mode of Zalzal by al-Farabi (c. 870-950) as the distinction between his steps of 12/11 (150.637c) and the smaller 88/81 (143.498c), and, on the other hand, the major minthma (352/351, 4.925c) described by Ibn Sina (c.980-1037) in noting the "resemblance" between certain complex superpartient ratios and nearby simpler superparticular ratios, e.g. 128/117 (155.562c) and the simpler 12/11, or 88/81 and the simpler 13/12 (138.573c). These comparisons relate to the adjacent intervals included in the tetrachords al-Farabi and Ibn Sina favor to realize the 'oudist Mansur Zalzal's tuning favoring a middle third:

Al-Farabi:

             0.0c---203.910c--354.547c----498.045c
             1/1--------9/8-------27/22-------4/3
             9:8--------12:11--------88:81
             203.910c-----150.637c---143.498

Ibn Sina:

             0.0c------203.910c.   342.483c 498.045c
             1/1----------9/8-------39/32------4/3
             9:8---------13:12------128:117
             203.910c--138.573c---155.562c

In effect, the Sinarabian comma serves as a kind of bridge between these two tetrachords and tunings, hence its name. More details to come.