I note that the subject of this thread ultimately became:
Developing a notational comma
badness metric.
Things hopped back and forth a bit between this thread and the Magrathean diacritics thread. The final badness metric (that was used indirectly in obtaining the final list of tina commas) was:
From:
viewtopic.php?p=2636#p2636
LPEI_badness = lb(N2D3P9) + (AAS/9.65)^1.7 + 2^(ATE-9.65) + 0.8×AERR
lb() is the base-2 logarithm.
N2D3P9 is as described here:
https://en.xen.wiki/w/N2D3P9
AAS is the absolute value of the apotome slope
= comma_3_exponent - apotome_3_exponent × untempered_comma_cents / untempered_apotome_cents
= comma_3_exponent - 7 × untempered_comma_cents / 113.685c
ATE is the absolute value of the 3-exponent of the comma.
AERR is the absolute value of the error which is the number of inas the comma is away from the nearest whole ina. The ina is the width of the capture zone at the relevant precision level. So AERR always ranges from 0 to 0.5.
"LPEI" stands for "log, power, exponential, identity" which lists the functions applied to the four input values before scaling and adding them.
The LPE notational comma
complexity metric is obtained from the above by omitting the 0.8×AERR term.