rhCn SrSSKJr SSKrSSKrSSKJr SSKJr SSKJ r SSKJ r \ R"S5r "S S \R5rS rSS jrSS jrSSjrSrSSjrSrSSjrSSjrSrS SjrS!SjrSrSr"SS\R:5r\\\\\\\\\\\\\/ r\ S:XaSSKr\RB"\5 gg)"z This module defines the L, P, and R objects and their related transformations as called on a :class:`~music21.chord.Chord`, according to Neo-Riemannian theory. ) annotationsN) exceptions21)chord) enharmonics) environmentzanalysis.neoRiemannianc\rSrSrSrg) LRPException!N)__name__ __module__ __qualname____firstlineno____static_attributes__r X/home/james-whalen/.local/lib/python3.13/site-packages/music21/analysis/neoRiemannian.pyr r !srr cURVs/sHoRPM nn[R"U5nUR 5n[ R "U5nXElU$s snf)au Returns a copy of chord `c` with pitches simplified. Uses `:meth:music21.analysis.enharmonics.EnharmonicSimplifier.bestPitches` >>> c = chord.Chord('B# F- G') >>> c2 = analysis.neoRiemannian._simplerEnharmonics(c) >>> c2 >>> c3 = analysis.neoRiemannian._simplerEnharmonics(c2) Returns a copy even if nothing has changed. >>> c2 is c3 False )pitchesnameWithOctaverEnharmonicSimplifier bestPitchescopydeepcopy)cp pitchListes newPitchesnewChords r_simplerEnharmonicsr $sZ$,-9959a!!9I5  ) )) 4B!J}}QH! O 6sA*cUR5(aSnUR5nO6UR5(aSnURnOUSLa [ S5eU$[ XU5nUR UlU$)a L transforms a major or minor triad through the 'Leading-Tone exchange'. A C major chord, under L, will return an E minor chord, by transforming the root to its leading tone, B. >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = analysis.neoRiemannian.L(c1) >>> c2.pitches (, , ) Chords must be major or minor triads: >>> c3 = chord.Chord('C4 D4 E4') >>> analysis.neoRiemannian.L(c3) Traceback (most recent call last): music21.analysis.neoRiemannian.LRPException: Cannot perform L on this chord: not a major or minor triad If `raiseException` is `False` then the original chord is returned. >>> c4 = analysis.neoRiemannian.L(c3, raiseException=False) >>> c4 is c3 True Accepts any music21 chord, with or without octave specified: >>> noOctaveChord = chord.Chord([0, 3, 7]) >>> chordL = analysis.neoRiemannian.L(noOctaveChord) >>> chordL.pitches (, , ) z-m2m2Tz:Cannot perform L on this chord: not a major or minor triad) isMajorTriadroot isMinorTriadfifthr _singlePitchTransform quarterLengthrraiseExceptiontransposeInterval changingPitchoutChords rLr.=suB ~~!     T ![\ \$Q=IH__H OrcUR5(aSnURnO6UR5(aSnURnOUSLa [S5eU$[ XU5nUR UlU$)ad P transforms a major or minor triad chord to its 'parallel': i.e. to the chord of the same diatonic name but opposite model. Example: A C major chord, under P, will return an C minor chord >>> c2 = chord.Chord('C4 E4 G4') >>> c3 = analysis.neoRiemannian.P(c2) >>> c3.pitches (, , ) See :func:`~music21.analysis.neoRiemannian.L` for further details about error handling. OMIT_FROM_DOCS >>> c3 = chord.Chord('C4 D4 E4') >>> analysis.neoRiemannian.P(c3) Traceback (most recent call last): music21.analysis.neoRiemannian.LRPException... z-A1A1Tz:Cannot perform P on this chord: not a Major or Minor triad)r#thirdr%r r'r(r)s rPr2nsr* ~~!     T ![\ \$Q=IH__H OrcUR5(aSnURnO:UR5(aSnUR5nOUSLa [ S5eU$[ XU5nUR UlU$)ag R transforms a major or minor triad to its relative, i.e. if major, to its relative minor and if minor, to its relative major. Example 1: A C major chord, under R, will return an A minor chord >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = analysis.neoRiemannian.R(c1) >>> c2.pitches (, , ) See :func:`~music21.analysis.neoRiemannian.L` for further details about error handling. OMIT_FROM_DOCS >>> c3 = chord.Chord('C4 D4 E4') >>> analysis.neoRiemannian.R(c3) Traceback (most recent call last): music21.analysis.neoRiemannian.LRPException... M2z-M2Tz:Cannot perform R on this chord: not a Major or Minor triad)r#r&r%r$r r'r(r)s rRr5st* ~~    ! T ![\ \$Q=IH__H Orc[R"U5n[R"U5n[[UR55H]nSURUlUR URUR :XdM@URURUSS9 M_ [R"UR5$)zp Performs a neoRiemannian transformation on c that involves transposing `changingPitch` by `transposeInterval`. FT)inPlace) rrrangelenrspellingIsInferredname transposerChord)rr+r,changingPitchCopyris rr'r's  m4}}QH 3x''( )16.  ! !X%5%5a%8%=%= =   Q  ) )*;T ) J* ;;x'' ((rc$URnUH~nUS:Xa[U5nURU:Xa gM(US:Xa[U5nURU:Xa gMMUS:Xa[U5nURU:Xa gMr[ US35e g)aV Tests if two chords are related by a single L, P, R transformation, and returns that transform if so (otherwise, False). >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = chord.Chord('B3 E4 G4') >>> analysis.neoRiemannian.isNeoR(c1, c2) 'L' >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = chord.Chord('C4 E-4 G4') >>> analysis.neoRiemannian.isNeoR(c1, c2) 'P' >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = chord.Chord('C4 E4 A4') >>> analysis.neoRiemannian.isNeoR(c1, c2) 'R' >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = chord.Chord('C-4 E-4 A-4') >>> analysis.neoRiemannian.isNeoR(c1, c2) False Option to limit to the search to only 1-2 transforms ('L', 'R', 'P', 'LR', 'LP', 'RP'). So: >>> c3 = chord.Chord('C4 E-4 G4') >>> analysis.neoRiemannian.isNeoR(c1, c3) 'P' ... but not if P is excluded ... >>> analysis.neoRiemannian.isNeoR(c1, c3, transforms='LR') False r.r5r23 is not a NeoRiemannian transformation (L, R, or P)F) normalOrderr.r5r2r )c1c2 transformsc2NOr?rs risNeoRrGsL >>D  8"A}}$% #X"A}}$% #X"A}}$%!$WXY Y rcp/SQnURnUH n[XS9nURU:XdMUs $ g)au Tests if there is a chromatic mediant relation between two chords and returns the type if so (otherwise, False). >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = chord.Chord('A-3 C4 E-4') >>> analysis.neoRiemannian.isChromaticMediant(c1, c2) 'LFM' >>> c3 = chord.Chord('C4 E4 G4') >>> c4 = chord.Chord('C-4 E-4 A-4') >>> analysis.neoRiemannian.isChromaticMediant(c3, c4) False UFMUSMLFMLSMtransformationF)rBchromaticMediants)rCrD transformListrF transform thisChords risChromaticMediantrTs?"1M >>D" %bC  D ( # rcUR5(d+UR5(dUSLa[SUS35eU$U(aUSSS2n/nUHnUS:Xa;[U5nU(a'UR [ R "U55 MBMDUS:Xa;[U5nU(a'UR [ R "U55 MMUS:Xa;[U5nU(a'UR [ R "U55 MM[US 35e U(a%U(dU$UVs/sHn[U5PM sn$U(dU$[U5$s snf) a LRP_combinations takes a major or minor triad, transforms it according to the list of L, R, and P transformations in the given transformationString, and returns the result in triad. Certain combinations, such as LPLPLP, are cyclical, and therefore will return a copy of the original chord if `simplifyEnharmonics` = `True` (see :func:`~music21.analysis.neoRiemannian.completeHexatonic`, below). `leftOrdered` allows a user to work with their preferred function notation (left or right orthography). By default, `leftOrdered` is False, so transformations progress towards the right. Thus, 'LPR' will start by transforming the chord by L, then P, then R. If `leftOrdered` is True, the operations work in the opposite direction (right to left), so 'LPR' indicates the result of the chord transformed by R, then P, then L. `simplifyEnharmonics` replaces multiple sharps and flats where they arise from combined transformations with the simpler enharmonic equivalent (e.g. C for D--). If simplifyEnharmonics is True, the resulting chord will be simplified to a collection of notes with at most 1 flat or 1 sharp, in their most common form. >>> c1 = chord.Chord('C4 E4 G4') >>> c2 = analysis.neoRiemannian.LRP_combinations(c1, 'LP') >>> c2 >>> c2b = analysis.neoRiemannian.LRP_combinations(c1, 'LP', leftOrdered=True) >>> c2b >>> c3 = chord.Chord('C4 E4 G4 C5 E5') >>> c4 = analysis.neoRiemannian.LRP_combinations(c3, 'RLP') >>> c4 >>> c5 = chord.Chord('B4 D#5 F#5') >>> c6 = analysis.neoRiemannian.LRP_combinations(c5, ... 'LPLPLP', leftOrdered=True, simplifyEnharmonics=True) >>> c6 >>> c5 = chord.Chord('C4 E4 G4') >>> c6 = analysis.neoRiemannian.LRP_combinations(c5, 'LPLPLP', leftOrdered=True) >>> c6 >>> c5 = chord.Chord('A-4 C4 E-5') >>> c6 = analysis.neoRiemannian.LRP_combinations(c5, 'LPLPLP') >>> c6 Optionally: return all chords creating by the given string in order. >>> c7 = chord.Chord('C4 E4 G4') >>> c8 = analysis.neoRiemannian.LRP_combinations( ... c7, 'LPLPLP', simplifyEnharmonics=True, eachOne=True) >>> c8 [, , , , , ] On that particular case of LPLPLP, see more in :func:`~music21.analysis.neoRiemannian.completeHexatonic`. Tz(Cannot perform transformations on chord z: not a major or minor triadNr.r5r2rA) r#r%r r.appendrrr5r2r ) rtransformationStringr* leftOrderedsimplifyEnharmonicseachOne chordListr?xs rLRP_combinationsr^sKT >>  ANN$4$4 T !:1#=YZ\ \3DbD9I ! 8!A  q!12 #X!A  q!12 #X!A  q!12!$WXY Y" " 4=>Iq'*I> >"H&q) ) ?s>E*cURS:XaZ/nUn[[[[[[/nUH.nU"U5nU(a [U5nUR U5 M0 U$USLa [ S5eg)a completeHexatonic returns the list of six triads generated by the operation PLPLPL. This six-part operation cycles between major and minor triads, ultimately returning to the input triad (or its enharmonic equivalent). This functions returns those six triads, ending with the original triad. `simplifyEnharmonics` is False, by default, giving double flats at the end. >>> c1 = chord.Chord('C4 E4 G4') >>> analysis.neoRiemannian.completeHexatonic(c1) [, , , , , ] `simplifyEnharmonics` can be set to True in order to avoid this. >>> c2 = chord.Chord('C4 E4 G4') >>> analysis.neoRiemannian.completeHexatonic(c2, simplifyEnharmonics=True) [, , , , , ] z3-11TzHCannot perform transformations on this chord: not a major or minor triadN) forteClassTnIr2r.r rWr )rrZr* hexatonicList lastChord operations operations rcompleteHexatonicres: &   Aq!Q' #I!),I"/ :   + $  T !Z\ \ "rcUR5nURn1SkS41SkS41SkS41SkS4/nUHupEX$;dM Us $ [S 5e) aX Returns a lowercase string representing the "hexatonic system" that the chord `c` belongs to as classified by Richard Cohn, "Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions," *Music Analysis*, 15.1 (1996), 9-40, at p. 17. Possible values are 'northern', 'western', 'eastern', or 'southern' >>> cMaj = chord.Chord('C E G') >>> analysis.neoRiemannian.hexatonicSystem(cMaj) 'northern' >>> gMin = chord.Chord('G B- D') >>> analysis.neoRiemannian.hexatonicSystem(gMin) 'western' Each chord in the :func:`~music21.analysis.neoRiemannian.completeHexatonic` of that chord is in the same hexatonic system, by definition or tautology. >>> for ch in analysis.neoRiemannian.completeHexatonic(cMaj): ... print(analysis.neoRiemannian.hexatonicSystem(ch)) northern northern northern northern northern northern Note that the classification looks only at the pitch class of the root of the chord. Seventh chords, diminished triads, etc. will also be classified. >>> dDom65 = chord.Chord('F#4 D5 A5 C6') >>> analysis.neoRiemannian.hexatonicSystem(dDom65) 'southern' >rnorthern> eastern> southern> westernz'Odd pitch class that is not in 0 to 11!)r$ pitchClassr )rr$rootPCmappingspcSetpoleNames rhexatonicSystemr{sfL 668D __FJ'I&Z(Y'H $ ?O$ @ AArc/SQnX;a[SU35eSnUS:XaSnOUS:XaSnOUS:XaS nUR5(aS nO#UR5(aS nO [S 5e[XUS 9n[ U5$)a Transforms a chord into the given chromatic mediant. Options: UFM = Upper Flat Mediant; USM = Upper Sharp Mediant; LFM = Lower Flat Mediant ; LSM = Lower Sharp Mediant; Each of these transformations is mode-preserving; involves root motion by a third; entails exactly one common-tone. >>> cMaj = chord.Chord('C5 E5 G5') >>> UFMcMaj = analysis.neoRiemannian.chromaticMediants(cMaj, transformation='UFM') >>> UFMcMaj.normalOrder [3, 7, 10] >>> USMcMaj = analysis.neoRiemannian.chromaticMediants(cMaj, transformation='USM') >>> USMcMaj.normalOrder [4, 8, 11] >>> LFMcMaj = analysis.neoRiemannian.chromaticMediants(cMaj, transformation='LFM') >>> [x.nameWithOctave for x in LFMcMaj.pitches] ['C5', 'E-5', 'A-5'] >>> LSMcMaj = analysis.neoRiemannian.chromaticMediants(cMaj, transformation='LSM') >>> [x.nameWithOctave for x in LSMcMaj.pitches] ['C#5', 'E5', 'A5'] Fine to call on a chord with multiple enharmonics, but will always simplify the output chromatic mediant. >>> cMajEnh = chord.Chord('D--5 F-5 A--5') >>> USM = analysis.neoRiemannian.chromaticMediants(cMaj, transformation='USM') >>> [x.nameWithOctave for x in USM.pitches] ['B4', 'E5', 'G#5'] >>> USM.normalOrder == USMcMaj.normalOrder True rIzTransformation must be one of PRrKLPrLPLrMRPTFChord must be major or minorrY) ValueErrorr%r#r^r )rrOoptionsrXLOs rrPrPsR+G$9'CDD# 5 # 5 #~~     788bAA q !!rcSS/nX;a[SU35eSnUR5(a US:XaSnO)UR5(a US:XaSnO [S5e[X5n[ U5$)a Transforms a chord into the upper or lower disjunct mediant. These transformations involve: root motion by a non-diatonic third; mode-change; no common-tones. >>> cMaj = chord.Chord('C5 E5 G5') >>> upr = analysis.neoRiemannian.disjunctMediants(cMaj, upperOrLower='upper') >>> [x.name for x in upr.pitches] ['B-', 'E-', 'G-'] >>> lwr = analysis.neoRiemannian.disjunctMediants(cMaj, upperOrLower='lower') >>> [x.name for x in lwr.pitches] ['B', 'D#', 'G#'] upperlowerzupperOrLower must be one of PRPPLPr)rr#r%r^r )r upperOrLowerrrXs rdisjunctMediantsr4s" G"7yABB ~~ 7 "#(    7 "#( 7881A q !!rc[USSS9$)a  Slide transform connecting major and minor triads with the third as the single common tone (i.e. with the major triad root a semi-tone below the minor). So: root motion by a semi-tone; mode-change; one common-tones. Slide is equivalent to 'LPR'. >>> cMaj = chord.Chord('C5 E5 G5') >>> slideUp = analysis.neoRiemannian.S(cMaj) >>> [x.name for x in slideUp.pitches] ['C#', 'E', 'G#'] >>> aMin = chord.Chord('A4 C5 E5') >>> slideDown = analysis.neoRiemannian.S(aMin) >>> [x.name for x in slideDown.pitches] ['A-', 'C', 'E-'] LPRFrZr^rs rSrXs( Au% @@rc[USSS9$)a The 'Neberverwandt' ('fifth-change') transform connects a minor triad with its major dominant, and so also a major triad with its minor sub-dominant, with one common tone in each case. This is equivalent to 'RLP'. >>> cMaj = chord.Chord('C5 E5 G5') >>> n1 = analysis.neoRiemannian.N(cMaj) >>> [x.name for x in n1.pitches] ['C', 'F', 'A-'] >>> aMin = chord.Chord('A4 C5 E5') >>> n2 = analysis.neoRiemannian.N(aMin) >>> [x.name for x in n2.pitches] ['G#', 'B', 'E'] RLPFrrrs rNrns& Au% @@rc8\rSrSrSrSrSrSrSrSr Sr g ) Testic[R"S5n[U5n[U5nUR [ U5S5 UR U[R5 UR [ U5S5 [R"S5n[R"U5n[S5Hn[U5nM UR URUR5 [R"S5n[R"U5n[S5Hn[U5nM UR URUR5 [R"S5n[R"U5n[S5Hn[U5nM UR URUR5 g)N C4 E-4 G4z zzC4 E4 G4 C5 C5 G5rgzC4 E4 G4 C5 E5 G5) rr=r.r2 assertEqualstrassertIsInstancerrr8rr5)selfrDc2_Lc2_Pc5copyC5r?s r testNeoRiemannianTransformations%Test.testNeoRiemannianTransformationssD [[ %uu T$FG dEKK0 T$DE [[, -r"qA2B 4 [[, -r"qA2B 4 [[, -r"qA2B 4rc[R"S5n[US5nUR[ U5S5 [R"S5n[US5nUR[ U5S5 [R"S5n[USSS9nUR[ U5S 5 [R"S 5n[US5nUR[ U5S 5 [R"S 5n [U SS S9n UR X5 UR [5 [U SSS9 SSS5 [R"S5n UR [5 [U SSS9 SSS5 [R"S5n [U SSS9n UR[R"S5RU R5 g!,(df  N=f!,(df  N{=f)NC4 E4 G4r~zzC4 E4 G4 C5 E5rz%Trz' C-4 E-4 G-4z zB- D# F#F)r*zB# F G#B# E# G#zC# E G#) rr=r^rrassertIs assertRaisesr r)rrc5_Tc6c6_Tc7c7_Tc8c8_Td_sharp_min_misspelledd_sharp_min_transformedf_min_misspelled e_sharp_mine_sharp_min_transformeds rtestNeoRiemannianCombinations"Test.testNeoRiemannianCombinationss [[ $D) T$EF [[) *E* T$KL [[) *Dd; T$MN [[ 'D) T$FG!&Z!8"23I4BG#I ,F   | , 3T$ O-!;;y1   | , -tD I-kk*- "2;UY"Z Y/779P9X9XY- ,- ,s; G*: G;* G8; H cd[R"S5n[R"S5n[X5nURUS5 [R"S5n[X5nURUS5 [XSS9nUR U5 [R"S5n[X5nURUS 5 [R"S 5n[ X5n URU S 5 [R"S 5n [X5n [ X5n UR U 5 UR U 5 [R"S 5n [R"S5n[X5n[ X5nUR U5 URUS 5 g)NrzB3 E4 G4r.rr2LR)rEzC4 E4 A4r5z C4 E-4 A-4rLz C-4 E-4 A-4rz C-4 E--4 A--4)rr=rGr assertFalserT)rrCrDans1c3ans2c4ans3rans4rans5ans6rrans7ans8s r testIsNeoRTest.testIsNeoRsQ [[ $ [[ $b~ s# [[ %b~ s#b.  [[ $b~ s# [[ &!") u% [[ 'b~!")   [[ ' [[ )b~!")  u%rc4[R"S5n[R"S5n[USS9nURUR/SQ5 [USS9nURUR/SQ5 [USS9nURUR Vs/sHofR PM sn/S Q5 [US S9nURUR Vs/sHofR PM sn/S Q5 [US S 9nURUR Vs/sHofRPM sn/SQ5 [USS 9n URU R Vs/sHofR PM sn/SQ5 gs snfs snfs snfs snf)NC5 E5 G5z C#5 E#5 G#5rJrN)rrrsrprK)rgrhrtrL)C5zE-5zA-5rM)zC#5E5A5r)r)BEGr)rrr) rr=rPrrBrrrr;) rc9c9aUFMcMajUSMcMajLFMcMajr]LSMcMaj upChromatic downChromatics r testMediantsTest.testMediantssP [[ $kk-(#Bu= ,,j9#Bu= ,,j9#Bu= GOODOq**ODFZ[#Bu= GOODOq**ODFYZ&sA  +*=*=>*=Q&&*=>P(7C  M4I4IJ4Iq**4IJ+ -EE?Ks F"F $F&Fc[R"S5n[R"S5n[U5nURURVs/sHoDR PM sn/SQ5 [U5nURURVs/sHoDR PM sn/SQ5 [ U5nURURVs/sHoDR PM sn/SQ5 [ U5nURURVs/sHoDR PM sn/SQ5 gs snfs snfs snfs snf)NrzA4 C5 E5)zC#rG#)A-CzE-)rFr)rrr)rr=rrrr;r)rc10c11slideUpr] slideDownN1N2s rtestSnN Test.testSnNskk*%kk*%C& '//:/Q&&/:OP sV "**5*Q&&*57GH sV "**5*Q&&*57GH;=66sD:D?EE c8[[R"S55n[[R"/SQ55nURURUR5 URUR[R"S5R5 [R"S5n[ USSS9n[R"/SQ5n[ USSS9nUR URS R5 URHnURUR5 M URURUR5 URUR[R"S 5R5 g) NzC# E# G#)rjrkrhrzB D# F#r~Fr)rtrrrorz A# D# F##) r.rr=rrr^ assertTruer:r)rc_sharp_maj_named_transformed%c_sharp_maj_pitch_classes_transformed b_maj_namedb_maj_named_transformedb_maj_pitch_classesb_maj_pitch_classes_transformedrs rtestInstantiatingChordPCNumbers$Test.testInstantiatingChordPCNumberssI()%++j*A(B%01%++i2H0I- 6>>>FF H >FFZ088 :kk), "2;GL#N#kk*5*:;NPTOT+V' +33A6IIJ088A   Q11 29 0888@@ B 8@@[199 ;rr N) r r rrrrrrrrrr rrrrs$54Z@"&H-0I";rr__main__)T)LRP)TFFF)FT)rJ)r)"__doc__ __future__rrunittestmusic21rrmusic21.analysisrr Environment environLocalMusic21Exceptionr r r.r2r5r'rGrTr^rer{rPrrrTestCaser _DOC_ORDERr mainTestr rrrs #  (&&'?@  <00 2/b#J#J )8t@%)!&)." n*`*\X2Br>"@""HA,A._;8  _;Hq!Q6',)   z Tr