User:Godtone: Difference between revisions

(4 intermediate revisions by the same user not shown)

Line 9:

* [[User:Godtone/zeta]]

Whose significance is backed up by the more psychoacoustically-informed tuning metrics I've designed (<code>optimal_edo_sequence</code>s from [[#My Python 3 code]]):

* [[User:Godtone/optimal edo sequences]]

* [[User:Godtone/optimal edo sequences]] (and [[User:Godtone/strict_optimal_edo_sequences]])

...as well as by my own knowledge of tuning theory.

Line 1,574:

if len(n) - len([ sedo for sedo in m ]) >= min_simplifications:

results.append(edo)

return results

# the following definitions are equivalent in the set of commas considered 7-limit dieses:

# dieses(4,odd_lim(9),odd_lim(9)) == dieses(4,odd_lim(9),odd_lim(7)) == dieses(5,odd_lim(9),odd_lim(7))

def dieses( max_n=4, gs=odd_lim(9), targets=None, show=False, minerr=steps(20000/19683,1)/4 ):

if not targets:

targets = gs

dieses_found = dict()

for g in gs:

for target in targets+[(2,1)]:

for n in range(2,max_n+1):

candidate = reduce(div_iv( target, mul_iv(*[g]*n) ))

if steps(candidate,1)>1/2:

candidate = div_iv((2,1),(candidate))

if steps(candidate,1)/n >= steps(20000/19683,1)/4 and steps(250/243,1) >= steps(candidate,1):

if candidate not in dieses_found:

dieses_found[candidate] = []

dieses_found[candidate].append(( n, g, target, steps(candidate,ed(1200))/n ))

if show:

for diesis in dieses_found:

mindamage = min([ dieses_found[diesis][k][3] for k in range(len( dieses_found[diesis] )) ])

if mindamage >= minerr:

def equiv(d):

return ', '.join([ '('+striv(eq[1])+')^'+str(eq[0])+' ~ '+striv(eq[2])+' (~'+

str( int(eq[3]*100+.5)/100 )[:5]+'c)' for eq in dieses_found[d] ])

print(

pad( striv(diesis), 12 ),

pad( str( int(mindamage*100+.5)/100 )[:6]+'c', 7, '.' ),

equiv(diesis)

)

results = [diesis for diesis in dieses_found]

results.sort(key=lambda x: as_float(x))

return results

</syntaxhighlight>

@@ Line 9: / Line 9: @@
 * [[User:Godtone/zeta]]
 Whose significance is backed up by the more psychoacoustically-informed tuning metrics I've designed (<code>optimal_edo_sequence</code>s from [[#My Python 3 code]]):
-* [[User:Godtone/optimal edo sequences]]
+* [[User:Godtone/optimal edo sequences]] (and [[User:Godtone/strict_optimal_edo_sequences]])
 ...as well as by my own knowledge of tuning theory.
@@ Line 1,574: / Line 1,574: @@
 			if len(n) - len([ sedo for sedo in m ]) >= min_simplifications:
 				results.append(edo)
+	return results
+# the following definitions are equivalent in the set of commas considered 7-limit dieses:
+# dieses(4,odd_lim(9),odd_lim(9)) == dieses(4,odd_lim(9),odd_lim(7)) == dieses(5,odd_lim(9),odd_lim(7))
+def dieses( max_n=4, gs=odd_lim(9), targets=None, show=False, minerr=steps(20000/19683,1)/4 ):
+	if not targets:
+		targets = gs
+	dieses_found = dict()
+	for g in gs:
+		for target in targets+[(2,1)]:
+			for n in range(2,max_n+1):
+				candidate = reduce(div_iv( target, mul_iv(*[g]*n) ))
+				if steps(candidate,1)>1/2:
+					candidate = div_iv((2,1),(candidate))
+				if steps(candidate,1)/n >= steps(20000/19683,1)/4 and steps(250/243,1) >= steps(candidate,1):
+					if candidate not in dieses_found:
+						dieses_found[candidate] = []
+					dieses_found[candidate].append(( n, g, target, steps(candidate,ed(1200))/n ))
+	if show:
+		for diesis in dieses_found:
+			mindamage = min([ dieses_found[diesis][k][3] for k in range(len( dieses_found[diesis] )) ])
+			if mindamage >= minerr:
+				def equiv(d):
+					return ', '.join([ '('+striv(eq[1])+')^'+str(eq[0])+' ~ '+striv(eq[2])+' (~'+
+						str( int(eq[3]*100+.5)/100 )[:5]+'c)' for eq in dieses_found[d] ])
+				print(
+					pad( striv(diesis), 12 ),
+					pad( str( int(mindamage*100+.5)/100 )[:6]+'c', 7, '.' ),
+					equiv(diesis)
+				)
+	results = [diesis for diesis in dieses_found]
+	results.sort(key=lambda x: as_float(x))
 	return results
 </syntaxhighlight>