rh%%SrSSKJr SSKJr SSKJr SSKrSSKJ r J r SSK r SSK r SSK rSSKrSSKJr SSKJr SS KJr SS KJr SS KJr \R,"S 5r"S S\R05r"SS\R05r"SS\R05r"SS\R05r"SS\R05rSrSrSr Sr!Sr"\\\ \!\"/r#Sr$\%"\ RL5S/-r'S4Sjr(Sr)S5S6S jjr*S5S!jr+S"r,S7S#jr-S$r."S%S&5r/"S'S(5r0"S)S*5r1"S+S,5r2"S-S.5r3"S/S0\Rh5r5/r6S1\7S2'\8S3:XaSSKr\Rr"\55 gg)8a A comprehensive, object model of the Xenakis Sieve. :class:`music21.sieve.Sieve` objects can be created from high-level string notations, and used to generate line segments in various representation. Additional functionality is available through associated objects. The :class:`music21.sieve.Sieve` class permits generation segments in four formats. >>> a = sieve.Sieve('3@2|7@1') >>> a.segment() [1, 2, 5, 8, 11, 14, 15, 17, 20, 22, 23, 26, 29, 32, 35, 36, 38, 41, 43, 44, 47, 50, 53, 56, 57, 59, 62, 64, 65, 68, 71, 74, 77, 78, 80, 83, 85, 86, 89, 92, 95, 98, 99] >>> a.segment(segmentFormat='binary') [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1] >>> a.segment(segmentFormat='width') [1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1] >>> len(a.segment(segmentFormat='unit')) 43 A :class:`music21.sieve.CompressionSegment` can be used to derive a Sieve from a ny sequence of integers. >>> a = sieve.CompressionSegment([3, 4, 5, 6, 7, 8, 13, 19]) >>> str(a) '6@1|7@6|8@5|9@4|10@3|11@8' The :class:`music21.sieve.PitchSieve` class provides a quick generation of :class:`music21.pitch.Pitch` lists from Sieves. >>> a = sieve.PitchSieve('13@3|13@6|13@9', 'c1', 'c10', 'f#4') >>> pitches = a() >>> ', '.join([str(p) for p in pitches]) 'F#1, A1, C2, G2, B-2, C#3, G#3, B3, D4, A4, C5, E-5, B-5, C#6, E6, B6, D7, F7, C8, E-8, F#8, C#9, E9, G9' ) annotations) literal_eval)IterableN)gcdlcm)common) environment) exceptions21)interval)pitchsievec\rSrSrSrg) UnitExceptionMN__name__ __module__ __qualname____firstlineno____static_attributes__rG/home/james-whalen/.local/lib/python3.13/site-packages/music21/sieve.pyrrMrrc\rSrSrSrg)ResidualExceptionQrNrrrrrrQrrrc\rSrSrSrg)SieveExceptionUrNrrrrrrUrrrc\rSrSrSrg)CompressionSegmentExceptionYrNrrrrr"r"Yrrr"c\rSrSrSrg)PitchSieveException]rNrrrrr%r%]rrr%{}&|^-@c## 0nSnURUS5nUbX2-nXA;a XC-nXA;aM X1U'OX"-nX!U'X :aUv US-nMF7f)ae Yields the sequence of prime numbers via the Sieve of Eratosthenes. rather than creating a fixed list of a range (z) and crossing out multiples of sequential candidates, this algorithm stores primes under their next possible candidate, thus allowing the generation of primes in sequence without storing a complete range (z). Create a dictionary. Each entry in the dictionary is a key:item pair of (key) the largest multiple of this prime so far found and (item) the prime. The dictionary only has as many entries as found primes. If a candidate is not a key in the dictionary, it is not a multiple of any already-found prime; it is thus a prime. a new entry is added to the dictionary, with the square of the prime as the key. The square of the prime is the next possible multiple to be found. To use this generator, create an instance and then call the .next() method on the instance. >>> a = sieve.eratosthenes() >>> next(a) 2 >>> next(a) 3 We can also specify a starting value for the sequence, skipping over initial primes smaller than this number: >>> a = sieve.eratosthenes(95) >>> next(a) 97 >>> next(a) 101 N)pop)firstCandidateDqpnextMults r eratosthenesr7tsyL A A  EE!TN =uH-#<-hKuHhK" E) s -AAc[U5nUS;agUS-nUS;ag/SQnUS::aX;aggUH nX-S:XdM g US - S pTUS -(dUS -nUS -nUS -(dM[S 5HZn[[R"S US - 5X@5nUS :XaM/[S U5HnXpS - :Xa MI[US U5nM g g) a Returns True if an integer is likely prime or False if it is likely composite using the Rabin Miller primality test. See also here: http://www.4dsolutions.net/ocn/numeracy2.html >>> sieve.rabinMiller(234) False >>> sieve.rabinMiller(5) True >>> sieve.rabinMiller(4) False >>> sieve.rabinMiller(97 * 2) False >>> sieve.rabinMiller(6 ** 4 + 1) # prime True >>> sieve.rabinMiller(123986234193) # divisible by 3, runs fast False )r/T)r0F)r; %)+/5;=CGIOSr#adrr0 r/)absrangepowrandomrandint) nmprimesprimesriyjs r rabinMillerras0 AAF{ AA;F Cx ; 9> q5!q!e a E!ee2Y q!a%(! / 6 q!AEzAq! A  rcUH)n[R"U5(aM [S5e /nUbUR5 USnUSnO9[ [ R "U55nUR5 USnUSn[XES-5H,nX ;aURS5 MURS5 M. U$)a Treat a sequence of integers as defining contiguous binary integers, where provided values are 1's and excluded values are zero. For instance, running [3, 10, 12] through this method gives a 1 for the first entry (signifying 3), 0s for the next six entries (signifying 4-9), a 1 (for 10), a 0 (for 11), and a 1 (for 12). >>> sieve.discreteBinaryPad([3, 10, 12]) [1, 0, 0, 0, 0, 0, 0, 1, 0, 1] >>> sieve.discreteBinaryPad([3, 4, 5]) [1, 1, 1] znon-integer value foundrr0) risNumrsortlistcopydeepcopyrTappend)seriesfixRangexdiscreteminValmaxVal seriesAlts rdiscreteBinaryPadrqs$||A 9: :H !"v./ 12 6A: & ; OOA  OOA  ' Orc|UbUR5 USnUSnO[U5n[U5nX2- n/n[U5S:aaUHYnXb- n[R "U5(a [ U5nUS:waURXt- 5 MHURS5 M[ U$URS5 U$)a  Given a list of numbers, create a proportional spacing across the unit interval. The first entry will always be 0 and the last 1, other entries will be spaced according to their distance between these two units. For instance, for 0, 3, 4 the middle entry will be 0.75 since 3 is 3/4 of the distance between 0 and 4: >>> sieve.unitNormRange([0, 3, 4]) [0.0, 0.75, 1.0] but for [1, 3, 4], it will be 0.666... because 3 is 2/3 of the distance between 1 and 4 >>> sieve.unitNormRange([1, 3, 4]) [0.0, 0.666..., 1.0] rrcr0)reminmaxlenrrdfloatri)rjrkminFoundmaxFoundspanunitvaldifs r unitNormRanger}!s, A;B<v;v;  D D 6{QC.C||C  Cjqy CJ' A K A KrcUS::aS/$US:XaSS/$/nSUS- - n[US- 5HnURX2-5 M URS5 U$)a Given a certain number of parts, return a list unit-interval values between 0 and 1, with as many divisions as parts; 0 and 1 are always inclusive. >>> sieve.unitNormEqual(3) [0.0, 0.5, 1] If parts is 0 or 1, then a single entry of [0] is given: >>> sieve.unitNormEqual(1) [0] r0rr/)rTri)partsrzstepr_s r unitNormEqualrNse zs !1v EAIuqy!A KK !" A rcX:Xa/$X:aUnUnOUnUnSn/nUnX::a!URU5 X- nUS- nX::aM!U(a [U5$U$)aN Given a step size and an a/b min/max range, calculate number of parts to fill step through inclusive a,b, then return a unit interval list of values necessary to cover region. Note that returned values are, by default, normalized within the unit interval. >>> sieve.unitNormStep(0.5, 0, 1) [0.0, 0.5, 1] >>> sieve.unitNormStep(0.5, -1, 1) [0.0, 0.25, 0.5, 0.75, 1] >>> sieve.unitNormStep(0.5, -1, 1, normalized=False) [-1, -0.5, 0.0, 0.5, 1.0] >>> post = sieve.unitNormStep(0.25, 0, 20) >>> len(post) 81 >>> post = sieve.unitNormStep(0.25, 0, 20, normalized=False) >>> len(post) 81 rr0)rir) rab normalizedrnrocountvaluesrls r unitNormSteprhsu4 v u E FA + a    +U## rcvSnUS:XaSnU$X:XaSnU$US:aX -U-nUS:XaU$US-nUS:aMU$)Nrr0'r)c1c2gr{s r _meziriacrsm A Qw  H   H %i6R-Cax HAA %i Hrc4\rSrSrSrSSjrSrS SjrSrg) PrimeSegmenticJ/UlXlX lUR5 g)z A generator of prime number segments, given a start value and desired length of primes. >>> ps = sieve.PrimeSegment(3, 20) >>> ps() [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73] N)segstartlength _fillRange)selfrrs r__init__PrimeSegment.__init__s   rNc/nSnUS-S:XaX:aUS:XaUS-nOUS- nOUn[U5(a#URU5 [U5U:aU$Xs:XaU$Xv:aUS:XaUS-nOUS- nOUS:XaUS-nOUS- nMe)z scan all number in range and return a list of primes provide a max to force stoppage at certain point before the maximum length direction determines which way things go. r/rupr0)rariru)rrrstop directionr _oddBoundaryrXs r_fillRabinMillerPrimeSegment._fillRabinMillers 19>e2D AIAIA1~~ 1 s8v% y $AAAA$AAAA!rcURS:aUR[UR5URSS5nUVs/sHo"*PM nn[ U5UR:a4URSUR[ U5- SS5nX-UlgXlgURURURSS5Ulgs snf)z" fill positive and negative range rdownNr)rrrSrrur)rsegNegrlsegPoss rrPrimeSegment._fillRanges ::>**3tzz?DKKFSF"()&Qb&F)6{T[[(..q$++F 2K9=tE!?!,,TZZdDQDH*s CcURSURS/nUS;a[URU5$US:Xa[URU5$US;a]/n[[ UR5S- 5H4nUR URUS-URU- 5 M6 U$UR$)zn assumes that min and max values are derived from found primes means that primes will always be at boundaries rrcbinbinaryrzwidwidthr0)rrqr}rTruri)r segmentFormatzrr^s r__call__PrimeSegment.__call__s XXa[$((2, ' - -$TXXq1 1 f $ 1- - . .C3txx=1,- DHHQUOdhhqk9;.J88Or)rrr)NrN) rrrrrrrrrrrrrrs #JR$rrc\rSrSrSrSSjrSrSrSrSSjr SS jr S r SS jr SS jr S rSrSrSrSrSrSrSrSrSrg)Residualiz object that represents a modulus and a start point each object stores a range of integers (self._z) from which sections are drawn this range of integers can be changed whenever the section os drawn >>> residual = sieve.Residual(3, 2) NcUc[[S55nX@lXlUS;a [ S5eX0lURS:XaX lOX R-Ul/SQUlSUlg)NrQ)rr0z)negative value must be 0, 1, or a Booleanrintrrzrr) rfrT_z_mr_neg_shift_segmentFormatOptions_segmentFormat)rrYshiftnegrs rrResidual.__init__sg 9U3Z A f #$OP P 77a<K''/DK%B"#rcXlg)z: z is the range of integers to use when generating a list Nrrrs rsetZ Residual.setZ3s rc<[[XS-55Ulg)z^ z is the range of integers to use when generating a list convenience function that fixes max r0NrfrTrrminIntmaxInts r setZRangeResidual.setZRange9 uVaZ01rcUR5R5nXR;a[SU35eXlg)Nzformat not in format options: )striplowerrrrrfmts rsetSegmentFormatResidual.setSegmentFormat@s;iik! ,, ,#&DSE$JK K!rc<Uc URnUc URn/nURS:XaU$XR-UR-nUH(nXUR-:XdMUR U5 M* UR (a3[ R"U5nUHnURU5 M UnOUnUS;a [Xr5$US:Xa [Xr5$US;aUR/[U5S- -nU$US;aU$[US35e)al get a residual subset of this modulus at this n within the integer range provided by z format can be 'int' or 'bin', for integer or binary >>> a = sieve.Residual(3, 2) >>> a.segment(3) [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98] >>> a.segment(3, range(3, 15)) [5, 8, 11, 14] rrrzrr0)rintegerz( not a valid sieve segmentFormat string.) rrrrrirrgrhremoverqr}rur) rrXrrsubsetvaluecompSetrrs rsegmentResidual.segmentHs 9A   //M 77a<M _ 'EDGGO# e$ 99mmA&Gu% CC - -$S, , f $ ( ( . .77)s3x!|,CJ 0 0J#}o5]$^_ _rcUR$)z` period is M; obvious, but nice for completeness >>> a = sieve.Residual(3, 2) >>> a.period() 3 )rrs rperiodResidual.periodws wwrc[R"UR5n[R"UR5n[R"UR5n[ XX0R 5$r)rgrrrrr)rrYrrs rrg Residual.copysI IIdgg  $++&ii "#ww//rc&URXU5$)z calls self.segment(); uses _segmentFormat >>> a = sieve.Residual(3, 2) >>> a() [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98] )rrrXrrs rrResidual.__call__s||A-00rcUS:XaTURS:waURSURS3nOURS3nUR(aSU3nU$URSUR3nUR(aSU3nU$)z7 does not show any logical operator but unary negation classicrz(n+)z(n)r,r-)rrr)rstylerepStrs r representResidual.represents I {{a GG9C }A6 GG9CyyVH  y$++/FyyVH rc"UR5$)ze str representation using M(n + shift) style notation >>> a = sieve.Residual(3, 2) >>> str(a) '3@2' rrs r__str__Residual.__str__s~~rcUcgURUR:Xa5URUR:XaURUR:Xagg)z6 ==, compare residual classes in terms of m and shift rr0rrrrothers r__eq__Residual.__eq__sB = GGuxx KK5<</II+rcjURUR:agURUR:agURUR:XacURUR:agURUR:agURUR:waURS:Xagggg)z allow comparison based on m and shift; if all equal look at neg Still being used internally even though __cmp__ is not used in Python 3 rcr0rNrrs r__cmp__Residual.__cmp__s 77UXX  WWuxx  WW {{U\\)u||+99 *yyA~! !rc0URU5S:Xagg)NrcTFrrs r__lt__Residual.__lt__s << " $rc0URU5S:Xagg)Nr0TFrrs r__gt__Residual.__gt__s << ! #rcUR(aSnOSn[URURXR5$)z( unary neg operators; return neg object rr0)rrrrr)rrs r__neg__Residual.__neg__s0 99CCc77;;rc^UR(dUR(a [S5eURURURURUR5up#[ UR 5[ UR 5-n[U5n[X#SU5$)z &, produces an intersection of two Residual classes returns a new Residual class cannot be done if R under complementation >>> a = sieve.Residual(3, 2) >>> b = sieve.Residual(5, 1) >>> c = a & b >>> str(c) '15@11' z3complemented Residual objects cannot be intersectedr) rr_cmpIntersectionrrsetrrfr)rrrYrXzSetrs r__and__Residual.__and__sw ::#$YZ Z$$TWWehh U\\R477|c%((m+ Ja##rcg)z |, not sure if this can be implemented i.e., a union of two Residual classes can not be expressed as a single Residual, that is intersections can always be reduced, whereas unions cannot be reduced. Nrrs r__or__Residual.__or__s rc[X5nX-nX%-nSnSn US:waUS:wa X1-nXB-nOX4$US:waX4- U-S:waX4$US:waX4- U-S:XaX4:wa Xg:XaUn UnX4$Xg-U-n [Xg5n X:XC- -U--U -nX4$)z compression by intersection find m,n such that the intersection of two Residuals can be reduced to one Residual. Xenakis p 273. rr0)rr) rm1m2n1n2drrn3m3rs rrResidual._cmpIntersections K W W   7rQwBB6M 61})6M !V"'Q!+"(BB6M1B"!ARW *+r1B6Mr)rrrrrr)rrNrNNreturnrr)rrrr__doc__rrrrrrrgrrrrrrrrrr rrrrrrrsc$* 2"-`^0 1"  6  <$* rrcJ\rSrSrSrS SjrS SjrSrSrSr S r S r S r g) CompressionSegmenti-a Utility to convert from a point sequence to sieve. A z range can be supplied to explicitly provide the complete sieve segment, both positive and negative values. all values in the z range not in the segment are interpreted as negative values. thus, there is an essential dependency on the z range and the realized sieve. No matter the size of the z range, there is a modulus at which one point in the segment can be found. As such, any segment can be reduced to, at a minimum, a residual for each point in the segment, each, for the supplied z, providing a segment with one point. The same segment can then have multiplied logical string representations, depending on the provided z. >>> a = sieve.CompressionSegment([3, 4, 5, 6, 7, 8, 13, 19]) >>> str(a) '6@1|7@6|8@5|9@4|10@3|11@8' >>> b = sieve.CompressionSegment([0, 2, 4, 6, 8]) >>> str(b) '2@0' >>> c = sieve.CompressionSegment([0, 2, 4, 5, 7, 9, 11, 12]) >>> str(c) '5@2|5@4|6@5|7@0' Nc[[R"U55nUR5 /UlUH/nX0R;dMURR U5 M1 [ UR5S::a [S5eURU5 [ UR5Ul UR5 g![a [S5ef=f)Nr0z'segment must have more than one elementz*no Residual classes found for this z range) rfrgrhre_matchrirur"_zUpdater_maxMod_processAssertionError)rsrcrnums rrCompressionSegment.__init__Ks4==%&   C++% ""3' t{{ q -.WX X a477|  \ MMO \-.Z[ [ \s <C C#cUbPURURU5(d [S5eXlURSURSp2gURSURSp2[ [ X#S-55Ulg)Nz-z range must be a superset of desired segmentrrcr0)_subsetrr"rrfrT)rrzMinzMaxs rrCompressionSegment._zUpdatecsz =<< Q//1CEEGTWWR[$QR$5q23DGrcUR$)zW >>> a = sieve.CompressionSegment([3, 4, 5, 6, 7, 8]) >>> b = a() >>> str(b[0]) '1@0' ) _residualsrs rrCompressionSegment.__call__rsrc/n[UR5S:Xa[URS5nU$URHnUR[U55 M SR U5nU$)Nr0rr*)rur*strrijoin)rresStrresObjs rrCompressionSegment.__str__|se t 1 $+,F  // c&k**XXf%F rcRSnUHnXB;dM US-nM U[U5:Xagg)z= True if sub is part of set; assumes no redundancies in each rr0)ru)rsubthisSet commonNumrls rr%CompressionSegment._subsets5 A|%M  C rc SnX@R:af[XASUR5nU"5nURXb5(aXV4$URXc5(aXV4$US-nX@R:aMf[ SUR35e)zG given a point, and SieveSegment, find a modulus and shift that match. r0rza mod was not found less than )rrrr%r)rrXpartwholerYobjrs r_findCompressionSegment._finds ,,1DGG,C%C||C&&xc))xAA,,=dll^LMMrc/Ul[R"UR5nSnU(aUS-nUSnURX1UR5upEUc [ S5eX@R;a<URR U5 UHnXa;dM UR U5 M U(dO U(aMURR5 g)z take a copy of match; move through each value of this list as if it were n; for each n test each modulo (from 1 to len(z) + 1) to find a residual. when found (one will be found), keep it; remove the found segments from the match, and repeat. rr0rNz_find() returned a None object)r*rgrr;r"rirre)rmatchmaxToRunrXr:rrls rrCompressionSegment._processs $++& MHaAzz!DKK8HC{12RSS//)&&s+Az Qh r)rrr*rr) rrrrrrrrrr%r;rrrrrrr-s,:\0 4 N&rrcN\rSrSrSrS)S*SjjrSrSrSrSr S)S jr S r S r S r S rSrSrSrSrSrSrSrSrSrS+SjrSrSrS,SjrSrSrS)SjrSrS)Sjr S r!S!r"S-S.S"jjr#S/S#jr$S0S$jr%S1S2S%jjr&S3S&jr'S'r(S(r)g)4Sieveiz Create a sieve segment from a sieve logical string of any complexity. >>> a = sieve.Sieve('3@11') >>> b = sieve.Sieve('2&4&8|5') >>> c = sieve.Sieve('(5|2)&4&8') NcUc*[U[5(a[[S55nOUc[R "U5(aX lSUlSUlSUl /SQUl SUl 0Ul SUl SUlSUlSUlSUlXlUR$bUR'5 gg) NrQexprrFrrc) isinstancer-rfrTr isListLiker_state_expTyperr_nonCompressible_resLib_resId_expTree _expPeriod_cmpTree _cmpPeriod_usrStr_load)rusrStrrs rrSieve.__init__s 9FC00U3Z A Y6,,V44 /4  #%B" %,.     << # JJL $rc&[R"UR5(a<UR5 UR UR5 UR 5 gUR5 UR 5 UR 5 gr)rrGrQ _resClear_initLoadSegment_initCompression _initParsers rrR Sieve._loadsa   T\\ * * NN   ! !$,, /  ! ! # NN  OO   ! ! #rc"SUl[UR;d<[UR;d([UR;d[ UR;aUR 5 OUR5 SUlSnUR(aSnU$URS:XaSnU$URS:XaSnU$![a SUlNRf=f![a, UR 5 Ns![a SUlNf=ff=f)Ncomplexr0simplerEzno compression possibler intersection) rINEGrMLGROUPRGROUPXOR _cmpSegment IndexErrorrJr TypeError)rmethods rrXSieve._initCompressions" 4== T]]*T]]*$--' *  " .%%' (   .F  ]]i 'F ]]h &#F ' *()% *  ..$$&!.,-D). .s<C+CCC D#C55D D D  DcURS5nURS5n[U6nX:Xa X0lX0lgX0l[U6Ulg)zR Lazy period initialization, called only when needed from public period() method. rDcmpN)_resPeriodListrrNrP)rmListExpmListCmplcmExps r _initPeriodSieve._initPeriod;sM&&u-&&u-h  $O$O$O!8nDOrcSUlg)z' Set this Sieve to its expanded state. rDN)rHrs rexpand Sieve.expandKs  rcUb6XR:wa'XlURS5 UR5 UR(agSUlg)z) Set this sieve to its compressed state. Nri)rrVrXrJrHrs rcompressSieve.compressQsA =Q''\G NN5 !  ! ! #  DKrcSURS50nURc-URURS5RUS'U$URUS'U$)z8 Provides a dictionary data representation for exchange logStrrDrr)rrrK _resKeyStrr)rdatas r_getParameterDataSieve._getParameterDataas` dnnU+  77? T__Q%78::DI DI rcXlg)z] Set the z as a list. The z is the range of integers to use when generating a sieve segment. Nrrs rr Sieve.setZps rc<[[XS-55Ulg)zj Set the z as a min and max value. The z is the range of integers to use when generating a sieve segment. r0Nrrs rrSieve.setZRangewrrcUR5R5nXR;a[SU35eXlg)Nzcannot set to format: )rrrrrrs rrSieve.setSegmentFormat~s;iik! 00 0 #9#!?@ @!rcUR5nSR[[US[/5nUSn[ X#5$)z) unary neg operators; return neg object. rErwr)rzr.r_r`rarB)rdataSelfrSrs rr Sieve.__neg__sL))+   X      SMVrc  UR5nUR5nSR[US[[[US[/5n[ US5[ US5-n[ U5n[XF5$)z &, produces an intersection of two >>> a = sieve.Sieve('3@11') >>> b = sieve.Sieve('2&4&8|5') >>> c = sieve.Sieve('(5|2)&4&8') >>> d = a & b >>> str(d) '{2@0&4@0&8@0|5@0}&{3@2}' rErwr)rzr.r`raANDrrfrBrrr dataOtherrSrrs rr Sieve.__and__s))+++-   h     X    8C=!C #$77 JVrc  UR5nUR5nSR[US[[[US[/5n[ US5[ US5-n[ U5n[XF5$)z |, produces a union >>> a = sieve.Sieve('3@11') >>> b = sieve.Sieve('2&4&8|5') >>> d = a | b >>> str(d) '{2@0&4@0&8@0|5@0}|{3@2}' rErwr)rzr.r`raORrrfrBrs rr  Sieve.__or__s))+++-   h     X    8C=!C #$77 JVrc  UR5nUR5nSR[US[[[US[/5n[ US5[ US5-n[ U5n[XF5$)z$ ^, produces exclusive disjunction. rErwr)rzr.r`rarbrrfrBrs r__xor__ Sieve.__xor__s))+++-   h     X    8C=!C #$77 JVrcSn[R"U5(a[U5SSS.$UR5nU(dgUR S5(aUR SS5nUR S5(aUR SS5nUR [ S5nUR [S5nUSS:XaS nUS SR5nOSnU(dg[U5nSn[R"U5(a[U5nSnO7[R"U5(aUSn[U5S :aUS nOSnUUUS .$![[[4a gf=f) a1 process an arg string for proper Residual creation valid syntax for Mod, shift pairs: all valid: MsubN, M@N, M,N, M if M is given alone, shift is assumed to be 0 this method assumes that all brackets have been replaced with parentheses returns a dictionary of args suitable for creating a Residual class r)rYrXrNr3,r-rEr,r0)rYrr)rrdrrfindreplacer`rar NameError SyntaxErrorrerGru)rrSrYrargsrs r_parseResidualSieve._parseResidualsb  <<  V1Q7 7 ;;u  ^^E3/F ;;s  ^^C-F++ !9 CABZ%%'FC  'D <<  D AE   t $ $QA4y1}Q ; 2  s+ EE65E6c[R"U5(a[U5nUS3nURS5S:aUR S[ 5nURS5S:aUR S[ 5nURS5S:aUR S[ 5nURS5S:aUR S[ 5nURS5S:aUR S[ 5nURS 5S:aUR S [5nURS 5S:aUR S [5nURS 5S:aUR S [5nURS 5S:aUR S [5nURS 5S:aUR S [5nUR SS5nU$)a provide synonyms for logical symbols intersection == and, &, * union == or, |, + not == not, - the native format for str representation uses only &, |, - this method converts all other string representations all brackets and braces are replaced with parenthesis parentheses are only used for the internal representation on string representation, braces are restored z@0andr*or+xorr+not[](r rE) rrdrrrrrr_r`ra)rrSs r _parseLogicSieve._parseLogic!s <<  [Fxr]F ;;u  "^^E3/F ;;s q ^^C-F ;;t  !^^D"-F ;;s q ^^C,F ;;u  "^^C,F ;;u  "^^E3/F ;;s q ^^C0F ;;s q ^^C0F ;;s q ^^C0F ;;s q ^^C0FR( rcZ[U5n[U5RSS5nSUS3$)z6 return string necessary to instantiate a set object. rrEzset(r)rfreprr)rvalLists r_setInstantiateStrSieve._setInstantiateStrMs2w-w-''R0gYa  rcSUS3$)Nzr)rresIds rrxSieve._resKeyStrUsE7!}rc"US;a [S5eUS:Xa9/nURH%nX0R;dMURU5 M' U$US:Xa9/nURH%nX0R;dMURU5 M' U$g)z% get residual keys based on library. )rirDzstate must be 'cmp' or 'exp'rirDN)rrKrOrirM)rstatelibKeyskeys r_resKeysSieve._resKeysXs  & !?@ @ E>G||--'NN3'$N e^G||--'NN3'$N rc/nURU5H8nURUR5nXB;dM'URU5 M: UR 5 U$)z For all residual classes, get the period, or the value of M, and return these in a list. Remove any redundant values and sort. )rrKrrire)rrmListrr5s rrjSieve._resPeriodListksS =='C S!((*A~ Q(   rc2URSRU55nUc&SRU5nSU3n[SU<S35e[USUSUSUR5nX`R UR U5'UR U5$)zz create a residual object, store in expResidualLib return a string id representation this uses self._z at initialization. rEz cannot parse zbad residual class notation: (rrYrr)rr.rrrrKrx)rrr/resDictjoinedmsgr0s r _resCreateSieve._resCreatexs %%bggfo6 ?WWV_F!&*C #A#!JK K'#,(8!%.$''306 T__U+,u%%rc^X RURU5'URU5$r)rKrx)rrr0s r _resAssignSieve._resAssigns&/5 T__U+,u%%rcUc URn[R"U5(dUb[SU<35eURU"X#5nUR U5$)zu this is where residuals are converted to set evaluating strings z should not be stored; should be a temporary value z"z must be a list of integers, not )rrrGrrKr)rrrXrrs r _resToSetStrSieve._resToSetStrs^ 9A  ##  #EaU!KL L,,u%a+&&w//rc,URS-Ulg)z increment the _resId. r0N)rLrs r_resIdIncrementSieve._resIdIncrementskkAo rc6[[URR555nUH?nUR U5nX0R ;dM%X0R ;dM6[S5e [URR55Ulg)z reset self._resId to the next available number may need to re-label some residual classes if gaps develop ids should be contiguous integer sequence zgap in residual keysN) rTrurKkeysrxrOrMrrL)riValsr^testKeys r _resResetIdSieve._resResetIdsr c$,,++-./Aooa(Gmm+}}0L$%;<< $,,++-. rcUc0UlSUlgUS:Xa8URU5nUHnURU M UR5 gUS:Xa [ S5eg)NrrirDz1Expanded residual classes should never be cleared)rKrLrrr)rrcmpKeysrs rrVSieve._resClearsf =DLDK e^mmE*GLL%     e^ !TU Urcj/Ul[XR5nURcURUlU"5nUHHnURRUR UR U55 UR 5 MJ [RUR5Ulg)z% load from a segments reload _resId. N) rMrrrirrLrrr.)rusrDatasegObjunionr0s rrWSieve._initLoadSegments  #GWW5 77?iiDGF MM f!E F  " . rcP0UlSUl/UlUR[R "UR 55nSnU[U5:XaGOX#nUS:XaSnOX#S- nU[U5S- :XaSnOX#S-nU[;a"URRU5 US-nGOU[:XaUcSn[SUS35eU[:XaUbU[;aSn[SUS35eU[:Xa]UbZU[:XaPUb+U[[[[ 4;aS n[S US35eURRU5 US- nGOU["R$;d U[:Xa/n[R"U5n Sn X)U -[:XaUR[5 U S-n X-[U5:XaO4X)U -n U [;d U [:XaOURU 5 U S-n MFURRUR'URS R)U555 UR+5 X:-nOUS-nGM#UR(d [S 5eS R)UR5Ulg) zF process usrStr string into proper argument dictionaries for Residual rr0Nz(negation cannot be used without operandsz"badly formed logical string (a): (rz,negation cannot be used as a binary operatorz"badly formed logical string (b): (z6negation must be of a group and isolated by delimitersz"badly formed logical string (c): (rEzno residual classes defined)rKrLrMrrgrhrQruBOUNDSrir_rRESIDUALr`rrrbstringdigitsrr.r) rrrwr^char charPreviouscharNextrr/subStartsubLensubChars rrYSieve._initParses    !!$-- "=> CK9DAv# %!e} CK!O#!a%=v~ $$T*E!1@$'I#a%PQQ#+"."h.D$'I#a%PQQ#+*&(!,(b#0FFRC(+McURS)TUU $$T*Q &$#+99Q<V+,3MM#&#aZF )c&k9$%67G&(GsN g.!'! $$T__T[["''&/%RS$$&JEOR|| !>? ? . rc/Ul[R"UR5nUR[5nSnUHnUS:XaM UR[ 5n[ U5S:XaURUSnOP[[ U5S- 5H5nUS:XaURXVnOUnURXVS-nXx-nM7 URRURURU55 UR5 M [RUR5Ulg)z) an unbound sieve, intersection Residual rrEr0N)rOrgrMsplitrrrurKrTrirrLrr.) rrworListr^orGroupandListr^rrs rrSieve._cmpIntersection+s 4==)b! G"}mmC(G7|q #||GAJ7 s7|a/0AAv LL4( WU^4A#$5L1 MM l!K L  ")* . rcp/UlURS5nU(d [S5e[XR5nU"5HHnURR UR URU55 UR5 MJ [RUR5Ulg)z, a bound sieve, uss a newly created segment rDz/empty segment; segment compression not possibleN) rOrrdrrrirrLrrr.)rrrr0s rrcSieve._cmpSegmentKs  ll5!NO O#C1hF MM f!E F  " . rc Uc URnUc URnUc URnUS:Xa![R"UR5nO)US:Xa![R"UR 5nOSnUR U5n[SSSU5nURU"55nURSUS-5nUH$n URXRXU55nM& UR[S5nUR[S 5n[US S [0005n [#U 5n U R%5 US ;a ['X5$US:Xa [)X5$US;a=/n [+[-U 5S- 5Hn U R/XS-X- 5 M U $U $![an [!S US 35U eSn A ff=f)aR Return a sieve segment in various formats. >>> a = sieve.Sieve('3@11') >>> a.segment('exp') [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98] >>> c = sieve.Sieve('(5|2)&4&8') >>> c.segment('cmp', segmentFormat='wid') [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8] NrDrirEr0rr,rr __builtins__rzbadly formed logical string (rrzr)rHrrrgrMrOrrrrrr`raevalrrrrfrerqr}rTruri)rrrXrrevalStrrr0setStrrrserr^s rr Sieve.segment^s& =KKE 9A   //M E>ii .G e^ii .GG}}U#!Q1%((2//#v|4Cooc+<+CC3i  - -$S, , f $ ( ( . .C3s8a<( CAJ/1)JJ#  /y:  sF66 GGGcURnURS:XaUR5 US:Xa UR$US:Xa UR$[ S5e)z Return the period of the sieve. >>> a = sieve.Sieve('3@11') >>> a.period() 3 >>> b = sieve.Sieve('2&4&8|5') >>> b.period() 40 >>> c = sieve.Sieve('(5|2)&4&8') >>> c.period() 40 * Changed in v9: state is taken from the object. rcrDrizState must be exp or cmp)rHrNrnrP ValueError)rrs rr Sieve.periodsS(  ??b     E>?? " e^?? "78 8rc<URURXU5$r)rrHrs rrSieve.__call__s||DKK}==rc /nUnSnUS:aUn Xu-n US;a1URURU[[X55U5n O0URURU[[X55S5n XkSS-nXu-nUS-n[ U5U:aOUS:aMUSUn [ U 5U:wa [ S5eUS:Xa[ U [U SU S S-55$US ;a[U [U SU S S-55$U $) z Collect sieve segment points for the provided length and format. >>> a = sieve.Sieve('3@11') >>> a.collect(10, 100, 10, 'int') [102, 105, 108, 111, 114, 117, 120, 123, 126, 129] rrrrNr0z/desired length of sieve segment cannot be foundrzrcr)rrHrfrTrurr}rq) rrXzMinimumrrzStepfoundr5 zExtendCountr&r'segmentPartialrs rcollect Sieve.collects6*  U"D9D 00!%dkk1.253D.E}"V"&dkk1.253D.Eu"N1--E A'!+L5zV##U"(GVn s8v  !RS S F " eCFCGaK&@A A / /$S%AB! *DE EJrcRUc URnUS:Xa![R"UR5nO)US:Xa![R"UR5nOSnUR U5nUH0nUR XPR URU55nM2 U$)zz style of None is use for users; adds | to single residuals style abs (absolute) does not add | tos single residual class rDrirE)rHrgrMrOrrrKr)rrrrrrs rrSieve.represents =KKE E>))DMM*C e^))DMM*CC}}U#C++c<<#4#>#>u#EFC rc"UR5$rrrs rr Sieve.__str__s~~r) rPrOrNrMrIrJrLrKrrrHrQrr)rSzstr | list[str]rzlist[int] | None)r list[int])rN)NrNN)rz*t.Literal['cmp'] | t.Literal['exp'] | Nonerrrr)rQ) rXrrrrrrr-rrrr)NN)*rrrrrrrRrXrnrqrtrzrrrrrr rrrrrxrrjrrrrrrVrWrYrrcrrrrrrrrrrrBrBs%8 $> -   2"   6 6 .;z)X!& &"& 0& / V /$V/v/@/*9=  K5K  KZ9>> 9 99 9  9  9 9v* rrBcL\rSrSrSrSS SjjrSrS SjrSrg) PitchSievei$aP Quick utility generator of :class:`music21.pitch.Pitch` lists from :class:`music21.sieve.Sieve` objects. >>> ps = sieve.PitchSieve('6@0', 'c4', 'c8') >>> [str(p) for p in ps()] ['C4', 'F#4', 'C5', 'F#5', 'C6', 'F#6', 'C7', 'F#7', 'C8'] >>> a = sieve.PitchSieve('4@7') >>> [str(p) for p in a()] ['E-3', 'G3', 'B3', 'E-4', 'G4', 'B4'] NcXl[UR5UlUb[R"U5UlO[R"S5UlUb[R"U5UlO[R"S5UlUb[R"U5UlO%[R"UR 5UlUb[U5Ul gXPl g)Nc3c5) sieveStringrB sieveObjectr Pitch pitchLower pitchUpper pitchOriginrgrhrveld)rrr r r r s rrPitchSieve.__init__2s '#((8(8"9  !#kk*5DO#kk$/DO  !#kk*5DO#kk$/DO  "${{;7D #}}T__=D  ?SzDHHrc URRnURRn[[ [ U5[ US-555nUR RnURS:XaJURXC5n/nUH/n[R"5nXxlURU5 M1 U$[URXSS9n [[ [U 555nURXCS5n /n[ [U 55H<n XS:XdM [R"5nXUlURU5 M> U$)a Return a sieve segment as a list of :class:`music21.pitch.Pitch` objects, mapped to the range between pitchLower and pitchUpper. >>> a = sieve.PitchSieve('4@7&5@4') >>> a() [] >>> a = sieve.PitchSieve('13@3|13@6|13@9', 'c1', 'c10') >>> ', '.join([str(p) for p in a()]) 'E-1, F#1, A1, E2, G2, B-2, F3, G#3, B3, F#4, A4, C5, G5, B-5, C#6, G#6, B6, D7, A7, C8, E-8, B-8, C#9, E9, B9' >>> a = sieve.PitchSieve('3@0', 'c4', 'c5', 'c4', 0.5) >>> a.eld 0.5 The following is a microtonal pitch sieve; presently these are not displayed; true values are [0, 1.5, 3.0, 4.5, 6.0, 7.5, 9.0, 10.5, 12.0] >>> pitches = a() >>> ', '.join([str(p) for p in pitches]) 'C4, C#~4, E-4, E~4, F#4, G~4, A4, B`4, C5' True values: [0.5, 2.0, 3.5, 5.0, 6.5, 8.0, 9.5, 11.0] >>> a = sieve.PitchSieve('3@0', 'c4', 'c5', 'c#4', 0.5) >>> pitches = a() >>> ', '.join([str(p) for p in pitches]) 'C~4, D4, E`4, F4, F#~4, G#4, A~4, B4' r0F)rr)r psr rfrTrr r rr r rirru) rminPSmaxPSrrXsieveSegIntegerssieveSegpsNumr5rbinSegr^s rrPitchSieve.__call__Rs$D"""" s5z3uqy>2 3      88q=#//5 H)KKM"*&#488UeLGU3w<()A%%aE2FH3v;'9> A":ADOOA& ( rcRURR5nUS:a[[US-55nOSnURSUSS9n/n[ U5H8upV[ R "X`R-5nURU5 M: U(d [S5eU$)a Return a list of Interval objects that defines the complete structure of this :class:`music21.sieve.Sieve`. >>> a = sieve.PitchSieve('3@0') >>> a.getIntervalSequence() [] >>> a = sieve.PitchSieve('3@0|7@0') >>> a.sieveObject.segment() [0, 3, 6, 7, 9, 12, 14, 15, 18, 21, 24, 27, 28, 30, 33, 35, 36, 39, 42, 45, 48, 49, 51, 54, 56, 57, 60, 63, 66, 69, 70, 72, 75, 77, 78, 81, 84, 87, 90, 91, 93, 96, 98, 99] >>> a.sieveObject.period() 21 >>> a.getIntervalSequence() [, , , , , , , , ] This is the PitchSieve for a major scale: >>> b = sieve.PitchSieve('(-3@2 & 4) | (-3@1 & 4@1) | (3@2 & 4@2) | (-3 & 4@3)') >>> b.getIntervalSequence() [, , , , , , ] iɚ;r0Nrr)rzinterval segment has no values) rrrfrT enumerater Intervalr rir%)rr5r widthSegmentspostr^r intervalObjs rgetIntervalSequencePitchSieve.getIntervalSequencesP    # # % y=U1q5\"AA((AU(C (*!-0HA"++EHH,<=K KK $1 %&FG G r)r r r r rr)NNNr0)r  str | Noner r r r r z int | float)rzlist[interval.Interval]) rrrrrrrrrrrrrr$sL )-(,)-"# %&'   @>@=rrcJ\rSrSrSrSrSrSrSrSr Sr S r S r S r g ) Testic(URSS5 g)NT) assertEqualrs r testDummyTest.testDummys t$rcjSnUHnU[U5S-- nM US[U5S- nUS- nU$)Nrz, rr/r)r-ru)rlistInoutr5s rpitchOut Test.pitchOutsEA 3q6D= C!CHqL! s  rcn[S5n/SQnUH up4pV[X55n[XF5nX-nM" g)Nr9))r9r:r/r;)rr:r0r9)r;rr9r/)r) rrtestArgsr rrrrr^s rtestIntersectionTest.testIntersections9 QK?&NBB A AA'rc j/SQnUH)n[U5nU"S[[S555nM+ g)N)z-5 | 4 & 4sub3 & 6 | 4 & 4z2 or 4 and 4 & 6 or 4 & 4r9)r/rr:)r0r:r=r?r)rBrfrT)rr-argtestObjdummys rtestSieveParseTest.testSieveParses2CCjGAtE"I/Ercr[SSS5n[S5nURUR4nU"5ng)Nz-5 | 4 & 4sub3 & 6b3zf#4)rr r )runused_testObjr5r6s rtestSievePitchTest.testSievePitchs9#$8$F12""G$6$66 rcj/SQnUH)n[U5n[[U55nU"5nM+ g)N))r9r: ) rr:r?r3$*)rr:r>)r/r9rr;r1 rRr=r?r@rArBrBrC)rr/rr;r<rEr=r?rFr2r?r@rArB) r0r/r9rr;r:r<r1rErR)iirr/r0)rrBr-)rrr!r:sObjr6s r testTimePointTest.testTimePoint s3C$S)CS?DFErc[[S55nSn[X!5nUR[ U5S5 Sn[X!5nUR[ U5S5 Sn[X!5nUR[ U5S5 Sn[X!5nUR[ U5S 5 S n[X!5nUR[ U5S 5 g) NrQz"3@2 & 4@1 | 2@0 & 3@1 | 3@3 | -4@2z3@2&4@1|2@0&3@1|3@0|-4@2z5-(3@2 & -4@1 & -(12@3 | 12@8) | (-2@0 & 3@1 | (3@3)))z)-{3@2&-4@1&-{12@3|12@8}|{-2@0&3@1|{3@0}}}z[(8@0 | 8@1 | 8@7) & (5@1 | 5@3)] | [(8@0 | 8@1 | 8@2) & 5@0] | [8@3 & (5@0 | 5@1 | 5@2 | 5@3 | 5@4)] | [8@4 & (5@0 | 5@1 | 5@2 | 5@3 | 5@4)] | [(8@5 | 8@6) & (5@2 | 5@3 | 5@4)] | (8@1 & 5@2) | (8@6 & 5@1)z{{8@0|8@1|8@7}&{5@1|5@3}}|{{8@0|8@1|8@2}&5@0}|{8@3&{5@0|5@1|5@2|5@3|5@4}}|{8@4&{5@0|5@1|5@2|5@3|5@4}}|{{8@5|8@6}&{5@2|5@3|5@4}}|{8@1&5@2}|{8@6&5@1}z4(-3@2 & 4) | (-3@1 & 4@1) | (3@2 & 4@2) | (-3 & 4@3)z*{-3@2&4@0}|{-3@1&4@1}|{3@2&4@2}|{-3@0&4@3}zV(-(13@3 | 13@5 | 13@7 | 13@9) & 11@2) | (-(11@4 | 11@8) & 13@9) | (13@0 | 13@1 | 13@6)zB{-{13@3|13@5|13@7|13@9}&11@2}|{-{11@4|11@8}&13@9}|{13@0|13@1|13@6})rfrTrBr$r-)rrrSrs r testSieveTest.testSieves s 5 &  Q!;<H &  Q!LMR &  QI J H &  Q!MN) &  Q] _rcSSKJn URSSS5nURUR U"55S5 URSSSSS9nURUR U"55S 5 g) Nrr z3@0|7@0rc6z\[C2, E-2, F#2, G2, A2, C3, D3, E-3, F#3, A3, C4, E-4, E4, F#4, A4, B4, C5, E-5, F#5, A5, C6]r/r z5[C2, D2, F#2, C3, E3, F#3, C4, F#4, C5, F#5, G#5, C6]music21r rr$r*rr s1s rtestPitchSieveATest.testPitchSieveA=su!   it 4 rt,B C  it  ; rt,P RrcSSKJn URSSSSS9nURUR U"55S5 URS SSSS9nURUR U"55S 5 g) NrrSz1@0rrTg?rUa[C2, C~2, C#2, C#~2, D2, D~2, E-2, E`2, E2, E~2, F2, F~2, F#2, F#~2, G2, G~2, G#2, G#~2, A2, A~2, B-2, B`2, B2, B~2, C3, C~3, C#3, C#~3, D3, D~3, E-3, E`3, E3, E~3, F3, F~3, F#3, F#~3, G3, G~3, G#3, G#~3, A3, A~3, B-3, B`3, B3, B~3, C4, C~4, C#4, C#~4, D4, D~4, E-4, E`4, E4, E~4, F4, F~4, F#4, F#~4, G4, G~4, G#4, G#~4, A4, A~4, B-4, B`4, B4, B~4, C5, C~5, C#5, C#~5, D5, D~5, E-5, E`5, E5, E~5, F5, F~5, F#5, F#~5, G5, G~5, G#5, G#~5, A5, A~5, B-5, B`5, B5, B~5, C6]z3@0z[C2, C#~2, E-2, E~2, F#2, G~2, A2, B`2, C3, C#~3, E-3, E~3, F#3, G~3, A3, B`3, C4, C#~4, E-4, E~4, F#4, G~4, A4, B`4, C5, C#~5, E-5, E~5, F#5, G~5, A5, B`5, C6]rVrXs rtestPitchSieveBTest.testPitchSieveBIs}!  eT4S  9 rt,Z [  eT4S  9 rt,- .rrN)rrrrr%r*r.r7r<rMrPrZr]rrrrr"r"s2% 0 _B R.rr"z list[type] _DOC_ORDER__main__)r/r)rjz Iterable[int]rr)rr0T):r __future__rastrcollections.abcrrgmathrrrVrtypingtunittestrWrr r r r Environment environLocalMusic21Exceptionrrrr"r%r`rarrrbrr_rfrrr7rarqr}rrrrrrrBrTestCaser"r___annotations__rmainTestrrrrns+X#$   &&w/  L11  55  \22  ,"?"?  ,77      &#r3 '   # &=@?L$N*Z4/n 4XXxTTpSS~r  r  pkkBv.8  v.| J z Tr