Syntonic–kleismic equivalence continuum

The syntonic-enneadecal equivalence continuum is a continuum of 5-limit temperaments which equate a number of syntonic commas (81/80) with the enneadeca ([-14 -19 19⟩).

All temperaments in the continuum satisfy (81/80)ⁿ ~ [-14 -19 19⟩. Varying n results in different temperaments listed in the table below. It converges to meantone as n approaches infinity. If we allow non-integer and infinite n, the continuum describes the set of all 5-limit temperaments supported by 19edo (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of n is approximately 0.1309..., and temperaments having n near this value tend to be the most accurate ones.

Temperaments in the continuum

n	Temperament	Comma
		Ratio	Monzo
0	Enneadecal		[-14 -19 19⟩
1	Countermeantone		[-10 -23 20⟩
2	Sensi	78732/78125	[2 9 -7⟩
3	19 & 169c		[2 31 -22⟩
4	19 & 162c		[-2 35 -23⟩
5	Unicorn	1594323/1562500	[-2 13 -8⟩
…	…	…	…
∞	Meantone	81/80	[-4 4 -1⟩