9802/9801

Interval information

Ratio	9802/9801
Factorization	2 × 3-4 × 11-2 × 132 × 29
Monzo	[1 -4 0 0 -2 2 0 0 0 1⟩
Size in cents	0.1766295¢
Name	kakisma
FJS name	[math]\displaystyle{ \text{d2}^{13,13,29}_{11,11} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	26.5176
Weil norm (log2 max(n, d))	26.5177
Wilson norm (sopfr(nd))	91
Comma size	unnoticeable
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9802/9801, the kakisma, is an unnoticeable 29-limit (specifically 2.3.11.13.29-subgroup) comma measuring about 0.177 ¢. It is the amount by which a stack of two 33/26's fall short of 29/18. Alternatively, it is the amount by which 29/27 exceeds the difference between 13/11 and its fifth complement, 33/26.

Commatic relations

This comma may be found as the difference between the following superparticular ratios:

• 364/363 and 378/377
• 676/675 and 726/725
• 2080/2079 and 2640/2639
• 2784/2783 and 3888/3887
• 4225/4224 and 7425/7424
• 4901/4900 and 9801/9800
• 5083/5082 and 10557/10556
• 5104/5103 and 10648/10647
• 6656/6655 and 20736/20735
• 8281/8280 and 53361/53360
• 8671/8670 and 75141/75140
• 9801/9800 and 96059601/96059600

It factors into the following superparticular ratios:

• 14365/14364 and 30856/30855
• 13311/13310 and 37180/37179
• 12673/12672 and 43264/43263
• 12376/12375 and 47125/47124

Temperaments

Tempering out this comma in the 2.3.11.13.29 subgroup leads to the rank-4 kakic temperament, or in the full 29-limit, the rank-9 kakismic temperament. In either case, it equates 29/27 with the difference between 13/11 and its fifth complement. Any 13-limit temperament can be extended to include prime 29 by tempering out this comma, but as we see above, such an extension works best with accurate 13/11's.

Etymology

This comma's name was casually proposed by Lériendil in 2025 from the Greek root kak- ("bad"), which is the antonym of kal- used to name the kalisma.