U 9%e]> @sdZddlmZmZmZmZmZmZddlm Z ddl Z ddl m Z ddl ZddlmZddlmZdd lmZee ed d Ze jed d ZW5QRXeddddddeeeeeefeeeejdddZeddddeee d ejdddZ edddeee deeeefdddZ eddddeeeeejeeeeffdddZ eddddd deeeeejeeeeffdddZ d d!Z!d"d#Z"eddddeeee d ejd$d%d&Z#edddeeee deeeefd$d'd&Z#eddddeeeeeejeeeeffd$d(d&Z#eddddd deeeeeejeeeeffd$d)d&Z#dS)*z#Functions for interval construction) CollectionDictListUnionoverloadIterable)LiteralN)resource_filename) ArrayLike)cache) _FloatLike_cozintervals.msgpackrbF)strict_map_key )level T)bins_per_octavetuningsort)n_binsfmin intervalsrrrreturnc Cst|tr|dkr0d|tjd|td|}q|dkrFt||d}q|dkr`tdg||d }q|d kr|tdd g||d }q|d krtdd d g||d }nt|}t|}t ||}tj dt|| d|}|rt |}||S)aConstruct a set of frequencies from an interval set Parameters ---------- n_bins : int The number of frequencies to generate fmin : float > 0 The minimum frequency intervals : str or array of floats in [1, 2) If `str`, must be one of the following: - `'equal'` - equal temperament - `'pythagorean'` - Pythagorean intervals - `'ji3'` - 3-limit just intonation - `'ji5'` - 5-limit just intonation - `'ji7'` - 7-limit just intonation Otherwise, an array of intervals in the range [1, 2) can be provided. bins_per_octave : int > 0 If `intervals` is a string specification, how many bins to generate per octave. If `intervals` is an array, then this parameter is ignored. tuning : float Deviation from A440 tuning in fractional bins. This is only used when `intervals == 'equal'` sort : bool Sort the intervals in ascending order. Returns ------- frequencies : array of float The frequencies Examples -------- Generate two octaves of Pythagorean intervals starting at 55Hz >>> librosa.interval_frequencies(24, fmin=55, intervals="pythagorean", bins_per_octave=12) array([ 55. , 58.733, 61.875, 66.075, 69.609, 74.334, 78.311, 82.5 , 88.099, 92.812, 99.112, 104.414, 110. , 117.466, 123.75 , 132.149, 139.219, 148.668, 156.621, 165. , 176.199, 185.625, 198.224, 208.828]) Generate two octaves of 5-limit intervals starting at 55Hz >>> librosa.interval_frequencies(24, fmin=55, intervals="ji5", bins_per_octave=12) array([ 55. , 58.667, 61.875, 66. , 68.75 , 73.333, 77.344, 82.5 , 88. , 91.667, 99. , 103.125, 110. , 117.333, 123.75 , 132. , 137.5 , 146.667, 154.687, 165. , 176. , 183.333, 198. , 206.25 ]) Generate three octaves using only three intervals >>> intervals = [1, 4/3, 3/2] >>> librosa.interval_frequencies(9, fmin=55, intervals=intervals) array([ 55. , 73.333, 82.5 , 110. , 146.667, 165. , 220. , 293.333, 330. ]) equalg@rZdtypeZ pythagoreanrrZji3)primesrrZji5Zji7N) isinstancestrnparangefloatpythagorean_intervalsplimit_intervalsarraylenceilmultiplyouterflattenr) rrrrrrratiosZ n_octavesZ all_ratiosr0U/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/librosa/core/intervals.pyinterval_frequenciessDH   r2.rrreturn_factors)rrr4rcCsdSNr0r3r0r0r1r'sr'rcCsdSr5r0r3r0r0r1r'scCsdSr5r0r3r0r0r1r'scst|ttd\}|dk}||d7<|d7<t|rlt|}||}nt|}|rtfdd|DSt d|S)aPythagorean intervals Intervals are constructed by stacking ratios of 3/2 (i.e., just perfect fifths) and folding down to a single octave:: 1, 3/2, 9/8, 27/16, 81/64, ... Note that this differs from 3-limit just intonation intervals in that Pythagorean intervals only use positive powers of 3 (ascending fifths) while 3-limit intervals use both positive and negative powers (descending fifths). Parameters ---------- bins_per_octave : int The number of intervals to generate sort : bool If `True` then intervals are returned in ascending order. If `False`, then intervals are returned in circle-of-fifths order. return_factors : bool If `True` then return a list of dictionaries encoding the prime factorization of each interval as `{2: p2, 3: p3}` (meaning `3**p3 * 2**p2`). If `False` (default), return intervals as an array of floating point numbers. Returns ------- intervals : np.ndarray or list of dictionaries The constructed interval set. All intervals are mapped to the range [1, 2). See Also -------- plimit_intervals Examples -------- Generate the first 12 intervals >>> librosa.pythagorean_intervals(bins_per_octave=12) array([1. , 1.067871, 1.125 , 1.201355, 1.265625, 1.351524, 1.423828, 1.5 , 1.601807, 1.6875 , 1.802032, 1.898437]) >>> # Compare to the 12-tone equal temperament intervals: >>> 2**(np.arange(12)/12) array([1. , 1.059463, 1.122462, 1.189207, 1.259921, 1.33484 , 1.414214, 1.498307, 1.587401, 1.681793, 1.781797, 1.887749]) Or the first 7, in circle-of-fifths order >>> librosa.pythagorean_intervals(bins_per_octave=7, sort=False) array([1. , 1.5 , 1.125 , 1.6875 , 1.265625, 1.898437, 1.423828]) Generate the first 7, in circle-of-fifths other and factored form >>> librosa.pythagorean_intervals(bins_per_octave=7, sort=False, return_factors=True) [ {2: 0, 3: 0}, {2: -1, 3: 1}, {2: -3, 3: 2}, {2: -4, 3: 3}, {2: -6, 3: 4}, {2: -7, 3: 5}, {2: -9, 3: 6} ] rrc3s"|]}| |dVqdS))r rNr0).0ipow2Zpow3r0r1 sz(pythagorean_intervals..r ) r$r%modflog2astypeintargsortrangelistpower)rrr4 log_ratios too_smallidxr0r9r1r'sF    cCsrt|}t|}t|d}||}t|d}||}t||t||}t|||d|dS)uCompute the harmonic distance between ratios a and b. Harmonic distance is defined as `log2(a * b) - 2*log2(gcd(a, b))` [#]_. Here we are expressing a and b as prime factorization exponents, and the prime basis are provided in their log2 form. .. [#] Tenney, James. "On ‘Crystal Growth’ in harmonic space (1993–1998)." Contemporary Music Review 27.1 (2008): 47-56. rr )r$r)maximumminimumZarounddot)logsabZa_numZa_denZb_numZb_dengcdr0r0r1__harmonic_distances    rOcCs |t||t|kS)z-Given two tuples of prime powers, break ties.)rJr$abs)rLrMrKr0r0r1_crystal_tie_break!srQ)rrrr4rcCsdSr5r0rrrr4r0r0r1r(&sr(cCsdSr5r0rRr0r0r1r(1scCsdSr5r0rRr0r0r1r(<scCst|}tj|tjd}g}tt|D]>}dgt|}d||<|t|d||<|t|q*|}t } t } tdgt|} | | t| |krtj } d} t |D]\}}d}| D]J}||f| krt |||| ||f<| ||f| ||f<|| ||f7}q|| ks>> librosa.plimit_intervals(primes=[3], bins_per_octave=12) array([1. , 1.05349794, 1.125 , 1.18518519, 1.265625 , 1.33333333, 1.40466392, 1.5 , 1.58024691, 1.6875 , 1.77777778, 1.8984375 ]) >>> # Pythagorean intervals: >>> librosa.pythagorean_intervals(bins_per_octave=12) array([1. , 1.06787109, 1.125 , 1.20135498, 1.265625 , 1.35152435, 1.42382812, 1.5 , 1.60180664, 1.6875 , 1.80203247, 1.8984375 ]) >>> # 12-TET intervals: >>> 2**(np.arange(12)/12) array([1. , 1.05946309, 1.12246205, 1.18920712, 1.25992105, 1.33483985, 1.41421356, 1.49830708, 1.58740105, 1.68179283, 1.78179744, 1.88774863]) Create a 7-bin, 5-limit interval set >>> librosa.plimit_intervals(primes=[3, 5], bins_per_octave=7) array([1. , 1.125 , 1.25 , 1.33333333, 1.5 , 1.66666667, 1.875 ]) The same example, but now in factored form >>> librosa.plimit_intervals(primes=[3, 5], bins_per_octave=7, ... return_factors=True) [ {}, {2: -3, 3: 2}, {2: -2, 5: 1}, {2: 2, 3: -1}, {2: -1, 3: 1}, {3: -1, 5: 1}, {2: -3, 3: 1, 5: 1} ] rrr6rr cSs"i|]\}}|dkr|t|qS)r)r?)r7prCr0r0r1 sz$plimit_intervals..)r$Z atleast_1dr=Zfloat64rAr*appendtuplecopydictrBinf enumeraterOiscloserQpopr)r&r<rJr>r?r@updateziprC)rrrr4rKZseedsr8seedZfrontierZ distancesrrootZscoreZbest_ffpointZHDsZ new_point_Znew_seedZpowsrDr:rErFZfactorsvr0r0r1r(GsrT         )$__doc__typingrrrrrrZtyping_extensionsrmsgpack pkg_resourcesr numpyr$Z numpy.typingr _cacher Z_typingr open__name__Z_fdescloadZ INTERVALSr?r#r&boolZndarrayr2r'rOrQr(r0r0r0r1s      l g