Download or view musicalscale.frink in plain text format
// Optimize a musical scale to find the optimal number of notes in an octave.
// Key frequency ratios to evaluate at
// These numbers are the Farey series between 1 and 2, in order of generation.
points= [[3/2, 1],
[4/3, 1/2], [5/3, 1/2],
[5/4, 1/4], [7/5, 1/4], [8/5, 1/4], [7/4, 1/4]] /*
[6/5, 1/8], [9/7, 1/8], [11/8, 1/8], [10/7, 1/8], [11/7, 1/8], [13/8, 1/8], [12/7, 1/8], [9/5, 1/8]] */
bestError = 1000
for root = 2 to million
{
// print["$root\t"]
ratio = 2^(1/root)
sum = 0
for [point, weight] = points
{
// Find optimal number of steps
optSteps = log[point]/log[ratio]
// Error between steps and closest note in this scale
error = abs[(optSteps-round[optSteps])/optSteps]
// We're going to take RMS error
sum = sum + error^2 * weight^2
// println["$point\t$error"]
}
e = sqrt[sum] * root
// print[format[e,1,6]]
// Best so far?
if (e < bestError)
{
// print["\t*"]
println["$root\t$e\t*"]
bestError = e
}
// println[]
}
Download or view musicalscale.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19966 days, 15 hours, 50 minutes ago.