User:Akselai/Programs - Revision history

Akselai: Created page with "A list of programs that implement technical xenharmonic concepts. A good algorithm is worth a thousand tables. == Delta-rational chords ==
2024-02-14T20:20:53Z

Created page with "A list of programs that implement technical xenharmonic concepts. A good algorithm is worth a thousand tables. == Delta-rational chords == <syntaxhighlight lang="python..."

New page
A list of programs that implement technical xenharmonic concepts.

A good algorithm is worth a thousand tables.

== [[Delta-rational chord]]s ==
<syntaxhighlight lang="python">
def argmin(list1):
return list1.index(min(list1))

def closest_denom(x, n):
return round(n/x)

def chord_differential(chord, ji, eps):
ji = [x + eps for x in ji]
ji_diff = [abs(ji[i]/ji[0] - chord[i]) for i in range(len(ji))]
df = max(ji_diff)
return df

def find_minimum(f, min, max):
return find_minimum_a(f, min, max, 40)

def find_minimum_a(f, min, max, partitions):
if max - min < 0.00001:
return [(min + max) / 2, f((min + max) / 2)]
values = [float(f(min + (max-min) / partitions * i)) for i in range(0, partitions+1)]
m = argmin(values)
return find_minimum_a(f, min + (max-min) / partitions * (m-1), min + (max-min) / partitions * (m+1), 5)

def delta_rational(chord, limit, offset):
chord = [1] + chord
smallest = 10
result = []
for l in range(1, limit+1):
ji = [closest_denom(chord[-1]/x, l) for x in chord]
df = chord_differential(chord, ji, offset)
if df <= smallest:
result = [ji, df]
smallest = df
return result

def as_plus_notation(chord):
return ' '.join(['+' + str(chord[i+1] - chord[i]) for i in range(len(chord) - 1)])

# PARAMETERS HERE
edo = 10
limit = 19

def f_t(i, j, t):
return delta_rational([2^(i/edo), 2^(j/edo)], limit, t)[1]

for i in range(1, edo):
for j in range(i+1, edo):
minim = find_minimum(lambda t: f_t(i, j, t), -0.5, 0.5)
if minim[1] <= 0.01:
res = delta_rational([2^(i/edo), 2^(j/edo)], limit, minim[0])
print("chord: 0-" + str(i) + "-" + str(j))
print(res[0])
print(as_plus_notation(res[0]), 'offset:', float('%.5g' % minim[0]))
print('score: %s' % float('%.3g' % res[1]))
print('-' * 16)
</syntaxhighlight>