o ٷi>@s dZddlmZmZmZmZmZmZddlm Z ddl Z ddl Z ddl mZddlmZddlmZdd lmZed d $Zed Ze jed dZWdn1sUwYWdn1sdwYedddddddededeeeefdededede jfddZedddddeded e d de jfd!d"Z eddd#deded e ddeeeeffd$d"Z edddddeded edee jeeeefffd%d"Z eddddd ddeded edee jeeeefffd&d"Z d'd(Z!d)d*Z"eddddd+ededed e d de jf d,d-Z#eddd#d+ededed e ddeeeeff d.d-Z#eddddd+ededed edee jeeeefff d/d-Z#eddddd dd+ededed edee jeeeefff d0d-Z#dS)1z#Functions for interval construction) CollectionDictListUnionoverloadIterable)LiteralN) ArrayLike)cache) _FloatLike_co)_resource_filez librosa.corezintervals.msgpackrbF)strict_map_key )level T)bins_per_octavetuningsortn_binsfmin intervalsrrrreturnc Cst|trL|dkrd|tjd|td|}n=|dkr#t||d}n2|dkr0tdg||d }n%|d kr>tdd g||d }n|d krKtgd ||d }n t|}t|}t ||}tj dt|| d|}|rut |}||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@rdtype pythagoreanrrji3)primesrrji5ji7)r!r$N) isinstancestrnparangefloatpythagorean_intervalsplimit_intervalsarraylenceilmultiplyouterflattenr) rrrrrrratios n_octaves all_ratiosr7J/home/ubuntu/.local/lib/python3.10/site-packages/librosa/core/intervals.pyinterval_frequenciess: H    r9.rrreturn_factorsr;cCdSNr7r:r7r7r8r,sr,rcCr<r=r7r:r7r7r8r,cCr<r=r7r:r7r7r8r,r>cst|ttd\}|dk}||d7<|d7<t|r6t|}||}nt|}|rHtfdd|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} ] r!rc3s$|] }| |dVqdS))r r!Nr7).0ipow2pow3r7r8 s"z(pythagorean_intervals..r ) r)r*modflog2astypeintargsortrangelistpower)rrr; log_ratios too_smallidxr7rBr8r,s F    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.maximumminimumarounddot)logsaba_numa_denb_numb_dengcdr7r7r8__harmonic_distances   r^cCs |t||t|kS)z-Given two tuples of prime powers, break ties.)rUr)abs)rWrXrVr7r7r8_crystal_tie_break"s r`r"cCr<r=r7r"rrr;r7r7r8r-'r-cCr<r=r7rar7r7r8r-2rbcCr<r=r7rar7r7r8r-=rbcCst|}tj|tjd}g}tt|D]}dgt|}d||<|t|d||<|t|q|}t } t } tdgt|} | | t| |krtj } d} t |D]C\}}d}| D]$}||f| vrt |||| ||f<| ||f| ||f<|| ||f7}qd|| kst|| rt||| |r|} |} q\|| }| ||D]}tt|t|}|| vr||vr||qt| |ksStjt | td}t||\}}|dk}||d7<||d8<|t}|rt|}||}nt|}|r=g}|D](}t }||dkr%|| |d<|ddt|||D||q|Std|S) u Construct p-limit intervals for a given set of prime factors. This function is based on the "harmonic crystal growth" algorithm of [#1]_ [#2]_. .. [#1] Tenney, James. "On ‘Crystal Growth’ in harmonic space (1993–1998)." Contemporary Music Review 27.1 (2008): 47-56. .. [#2] Sabat, Marc, and James Tenney. "Three crystal growth algorithms in 23-limit constrained harmonic space." Contemporary Music Review 27, no. 1 (2008): 57-78. Parameters ---------- primes : array of odd primes Which prime factors are to be used bins_per_octave : int The number of intervals to construct sort : bool If `True` then intervals are returned in ascending order. If `False`, then intervals are returned in crystal growth 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 -------- pythagorean_intervals Examples -------- Compare 3-limit tuning to Pythagorean tuning and 12-TET >>> 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} ] rrr?rr cSs"i|] \}}|dkr|t|qS)r)rI)r@prMr7r7r8 s"z$plimit_intervals..)r) atleast_1drGfloat64rKr/appendtuplecopydictrLinf enumerater^iscloser`popr.r+rFrUrHrIrJupdateziprM)r"rrr;rVseedsrAseedfrontier distancesrrootscorebest_ffpointHDs new_point_new_seedpowsrNrCrOrPfactorsvr7r7r8r-Hsx T            )$__doc__typingrrrrrrtyping_extensionsrmsgpacknumpyr) numpy.typingr _cacher _typingr util.filesr imsgpackopen_fdescload INTERVALSrIr(r+boolndarrayr9r,r^r`r-r7r7r7r8s         l     g