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 19967 days, 6 hours, 35 minutes ago.