Miracle is not especially notable as a 5-limit system, but it seems

to me having triads that beat in sync could be interesting anyway.

Howbeit, here is the lowdown:

Secor polynomial: 5*s^13-5*b*s^7+8*b-12 = 0

Secor for b=0, 5-limit poptimal: 1.06966311063807 or 116.587791307739

cents

From root of 440:

Fifth F = 659.074923710535 Hz

Major third T = 549.229103092098 Hz

Beat of fifth 3*440 - 2*F = 1.85015257893 Hz

Beat of major third 5*440 - 4*T = 3.08358763161 Hz

Beat of minor third 6*T - 5*F = 0 Hz

Fundamental beat = fifth beat / 3 = third beat / 5 = .6167175263 Hz

Secor for b=-1/6, 7-limit poptimal: 1.06965100291870 or

116.568195030691 cents

From root of 440:

Fifth F = 659.030163813727 Hz

Major third T = 549.272622860298 Hz

Beat of fifth 3*440 - 2*F = 1.93967237255 Hz

Beat of major third 5*440 - 4*T = 2.90950855881 Hz

Beat of minor third 6*T - 5*F = .48491809315 Hz

Fundamental beat is minor third beat = .48491809315 Hz

Secor for b=2/3, 11-limit poptimal: 1.06973058849676 or

116.696999787326 cents

From root of 440:

Fifth F = 659.324422707746 Hz

Major third T = 548.986634061637 Hz

Beat of fifth 3*440 - 2*F = 1.35115458451 Hz

Beat of major third 5*440 - 4*F = 4.05346375345 Hz

Beat of minor third 5*F - 6*T = 2.70230916891

Fundamental beat is fifth beat = 1.35115458451 Hz