User:2^67-1/Sandbox

A program to find increasingly better EDns in a given subgroup with a given equave ('increasingly better' is given by decreasing relative error)

import math

def fracmult(a,b):
    g = math.gcd(a[0]*b[0],a[1]*b[1])
    return [a[0]*b[0]//g,a[1]*b[1]//g]

def reciprocal(a):
    return [a[1],a[0]]

def equavereduce(a,b):
    while b[0]*a[1] > a[0]*b[1]:
        b = fracmult(b,reciprocal(a))
    while b[0] < b[1]:
        b = fracmult(b,a)
    return b

def tonalitydiamond(a,b,c):
    return [equavereduce(a,b),equavereduce(a,reciprocal(b)),equavereduce(a,c),equavereduce(a,reciprocal(c)),equavereduce(a,fracmult(b,reciprocal(c))),equavereduce(a,fracmult(c,reciprocal(b)))]

def cents(a):
    return 1200*math.log2(a[0]/a[1])

def centslist(a):
    c = []
    for i in a:
        c.append(cents(i))
    return c

def ednerror(a,e,equave):
    step = cents(equave)/e
    approx = round(a/step,0)*step
    error = math.fabs(a-approx)
    return error

def ednerrorlist(a,e,equave):
    error = []
    for i in a:
        error.append(ednerror(cents(i),e,equave))
    return error

def euc(a):
    total = 0
    for i in a:
        total = total + i**2
    return total**(1/2)

def avg(a):
    total = 0
    for i in a:
        total = total + i
    return total/len(a)
    

best = 10**10

for i in range(1, 100000):
    if avg(ednerrorlist(tonalitydiamond([3,2],[5,2],[7,4]),i,[3,2]))*i < best:
        best = avg(ednerrorlist(tonalitydiamond([3,2],[5,2],[7,4]),i,[3,2]))*i
        print(i)

More programs

import math
def relativeerror(x):
    three = abs(round(x*math.log2(3),0)-x*math.log2(3))
    five = abs(round(x*math.log2(5),0)-x*math.log2(5))
    eleven = abs(round(x*math.log2(11),0)-x*math.log2(11))
    return max(three, five, eleven)

best = 3
for i in range(1,1000000):
    if relativeerror(i) < best:
        print(i)
        best = relativeerror(i)

Output:

1
2
4
7
15
22
87
183
270
494
1171
11105
42348
54624
282560