User:Godtone: Difference between revisions

(9 intermediate revisions by the same user not shown)

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* [[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.

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== My Python 3 code ==

IMPORTANT NOTE: there seems to be ~~a bug~~ for subgroup mappings at the moment, pending investigation, but ideally usage of subgroups should be made far easier too:

IMPORTANT NOTE: there seems to be bugs for subgroup mappings at the moment, pending investigation, but ideally usage of subgroups should be made far easier too:

>>> sg = [2, 3, 7, 11, 13, 17, 19]

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return result

# the length of the mediant path of whichever octave-revoicing gives the interval x the least length

def mediant_complexity(x,revoicing_octs=7):

mincomplexity = 2**30

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print()

return spaces

# there is only finitely many EDOs which provide some simplification of a set of intervals as contrasted to all-distinct

def efficient_edos( n, inconsistencies=0, min_simplifications=1, edos=range(1,1000) ):

if type(n)==int:

n = odd_lim(n)

elif type(n)==list and type(n[0])==int:

n = odd_lim(1,[],n)

results = []

for edo in edos:

v = edo

if type(v)==int:

v = val( lim(max([ prime_idx(len(fact(x))-1) for x in n ])), ed(edo) )

# else v is assumed to be a mapping

m = dict()

for x in n: # collect mappings of intervals

sedo = map_iv(v,x)

if sedo in m:

m[sedo].append(x)

else:

m[sedo] = [x]

if len(inconsistent_ivs_by_val(n,v)) <= inconsistencies:

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>

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=== Installation issues/troubleshooting strategies/recommendations ===

The most potentially difficult part is that depending on what OS you are using, how you have Python installed, what version, etc. there can be complications so that running <code>pip install rtmidi</code> and <code>pip install mido</code> in a terminal does not work, or only appears to work so that there's issues when the code tries to use mido. I list potential issues below, so please read carefully for something applicable to your case if it isn't going smoothly.

'''IMPORTANT: A strange error has been found: Python 3.14 and later versions have removed a functionality used by mido internally, so downgrading to Python 3.12 is required if nothing here works.'''

'''IMPORTANT:''' Before deeming an installation of mido/rtmidi to "not be working", make sure that the issue is not just one of what MIDI ports are being autoselected; see (6.) onwards for details.

@@ 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 466: / Line 466: @@
 == My Python 3 code ==
-IMPORTANT NOTE: there seems to be a bug for subgroup mappings at the moment, pending investigation, but ideally usage of subgroups should be made far easier too:
+IMPORTANT NOTE: there seems to be bugs for subgroup mappings at the moment, pending investigation, but ideally usage of subgroups should be made far easier too:
 <syntaxhighlight lang="python">
 >>> sg = [2, 3, 7, 11, 13, 17, 19]
@@ Line 1,518: / Line 1,518: @@
 	return result
+# the length of the mediant path of whichever octave-revoicing gives the interval x the least length
 def mediant_complexity(x,revoicing_octs=7):
 	mincomplexity = 2**30
@@ Line 1,550: / Line 1,551: @@
 		print()
 	return spaces
+# there is only finitely many EDOs which provide some simplification of a set of intervals as contrasted to all-distinct
+def efficient_edos( n, inconsistencies=0, min_simplifications=1, edos=range(1,1000) ):
+	if type(n)==int:
+		n = odd_lim(n)
+	elif type(n)==list and type(n[0])==int:
+		n = odd_lim(1,[],n)
+	results = []
+	for edo in edos:
+		v = edo
+		if type(v)==int:
+			v = val( lim(max([ prime_idx(len(fact(x))-1) for x in n ])), ed(edo) )
+		# else v is assumed to be a mapping
+		m = dict()
+		for x in n: # collect mappings of intervals
+			sedo = map_iv(v,x)
+			if sedo in m:
+				m[sedo].append(x)
+			else:
+				m[sedo] = [x]
+		if len(inconsistent_ivs_by_val(n,v)) <= inconsistencies:
+			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 1,629: / Line 1,686: @@
 === Installation issues/troubleshooting strategies/recommendations ===
 The most potentially difficult part is that depending on what OS you are using, how you have Python installed, what version, etc. there can be complications so that running <code>pip install rtmidi</code> and <code>pip install mido</code> in a terminal does not work, or only appears to work so that there's issues when the code tries to use mido. I list potential issues below, so please read carefully for something applicable to your case if it isn't going smoothly.
+'''IMPORTANT: A strange error has been found: Python 3.14 and later versions have removed a functionality used by mido internally, so downgrading to Python 3.12 is required if nothing here works.'''
 '''IMPORTANT:''' Before deeming an installation of mido/rtmidi to "not be working", make sure that the issue is not just one of what MIDI ports are being autoselected; see (6.) onwards for details.