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)rMrKrJ)rMrKr)rMr|r)rUrJr)rUrOr)rUrQr)rUrRr)rUrSr)rUrTr)rKrJr)r|rJrname)unisonmonad singleton)zinterval class 1z minor secondm2z half stepsemitone)zinterval class 2z major secondM2z whole stepz whole tone)zinterval class 3z minor thirdm3)zinterval class 4z major thirdM3)zinterval class 5zperfect fourthP4)tritonezdiminished fifthzaugmented fourth)zchromatic trimirror)zphrygian trichord)zminor trichord)zmajor-minor trichord)zincomplete major-seventh chord)ztritone-fourth)zwhole-tone trichord)zincomplete minor-seventh chord)!incomplete dominant-seventh chord)rzItalian augmented sixth chord)z(incomplete half-diminished seventh chord)zquartal trichord)zdiminished triad)z minor triad)z major triad)zaugmented triadzequal 3-part octave division)zchromatic tetramirrorBACH)zmajor-second tetracluster)zalternating tetramirror)zminor third tetracluster)zmajor third tetracluster)zperfect fourth tetramirror)zArabian tetramirror)zdouble-fourth tetramirror)zdouble tritone tetramirror)zminor tetramirror)zphrygian tetrachord)zlydian tetrachordzmajor tetrachord)zharmonic minor tetrachord)z!major-third diminished tetrachord)z"minor-second diminished tetrachord)z$perfect-fourth diminished tetrachord)zmajor-second minor tetrachord)zperfect-fourth major tetrachord)zall-interval tetrachord)zminor-second quartal tetrachord)ztritone quartal tetrachord)zmajor-minor tetramirror)zmajor-diminished tetrachord)zminor-diminished tetrachord)zminor-augmented tetrachord)zaugmented major tetrachord)zmajor seventh chord)zwhole-tone tetramirror)zmajor-second major tetrachord)zperfect-fourth minor tetrachord)zquartal tetramirror)zaugmented seventh chord)zMessiaen's truncated mode 6zFrench augmented sixth chord)zminor seventh chord)zhalf-diminished seventh chord)zdominant seventh chordzmajor minor seventh chordzGerman augmented sixth chordzSwiss augmented sixth chord)zdiminished seventh chordzequal 4-part octave division)zchromatic pentamirror)zmajor-second pentacluster)zminor-second major pentachord)zSpanish pentacluster)zblues pentacluster)zminor-third pentacluster)zmajor-third pentacluster)Asian pentaclusterquasi raga Megharanji)r)double pentaclusterzquasi raga Nabhomani)r)ztritone-symmetric pentamirror)ztritone-expanding pentachord)ztritone-contracting pentachord)zalternating pentachord)zcenter-cluster pentachord)zlocrian pentachord)zaugmented pentacluster)z'double-seconds triple-fourth pentachord)zasymmetric pentamirror)z!major-minor-diminished pentachord)z!major-minor diminished pentachord)zminor-major ninth chord)zRoma (Gypsy) pentachord)zJavanese pentachord)zBalinese pentachord)zBalinese Pelog pentatoniczquasi raga Bhupalazquasi raga Bibhas)zHirajoshi pentatonicIwatoSakurazquasi raga Saveri)zmajor-augmented ninth chordzSyrian pentatonicr)zLebanese pentachordzaugmented-minor chord)zPersian pentamirrorzquasi raga Ramkali)zdorian pentachordzminor pentachord)zmajor pentachord)zphrygian pentachord)zlydian pentachord)zdiminished-major ninth chord)zminor-diminished ninth chord)z diminished-augmented ninth chord)z augmented-diminished ninth chord)zmajor-ninth chord)zminor-ninth chord)augmented-sixth pentachord)zJavanese pentatonicr)zKumoi pentachord)enigmatic pentachord)rzaltered pentatonic)zdiminished minor-ninth chord)zflat-ninth pentachordzquasi raga Ranjaniraga)zNeapolitan pentachord)zwhole-tone pentachord)zdominant-ninthz major-minorzPrometheus pentamirrorzdominant pentatonic)zmajor pentatoniczblack-key scalezblues pentatonicslendrozquartal pentamirror)zmajor-seventh pentacluster)zminor-seventh pentacluster)zcenter-cluster pentamirror)zdiminished pentacluster)z(A all combinatorial (P6, I11, RI5, RI11)zchromatic hexamirrorzfirst-order all-combinatorial)combinatorial I (I11))combinatorial I (I1))combinatorial RI (RI6))zcombinatorial I (I3))zdouble cluster hexamirror)z-B all combinatorial (P3, P9, I5, R6, R12, R8)zMessiaen's mode 5zsecond-order all combinatorial)z!D all combinatorial (P6, I1, RI7))zalternating hexamirrorcombinatorial I (I7))zcombinatorial P (P6))zcombinatorial I (I5))rzquasi raga Megha)zall tri-chord hexachord)z'all tri-chord hexachord (inverted form))z@E all combinatorial (P2, P6, P10, I3, I7, R4, R8, RI1, RI5, RI9)zMessiaen's truncated mode 3z Genus tertiumzthird-order all combinatorial)combinatorial RI (RI8)zsuper-locrian hexamirror)zmelodic-minor hexachord)zlocrian hexachord)zminor hexachord)zphrygian hexamirrorr)rzpyramid hexachord)zdouble-phrygian hexachordr)zcombinatorial RI (RI9))Messiaen's truncated mode 2zminor-bitonal hexachordcombinatorial R (R6)combinatorial I (I1, I7))zStravinsky's Petrushka-chordrzmajor-bitonal hexachordrr)r)zGuidonian hexachordz!C all combinatorial (P6, I3, RI9)zmajor hexamirrorzquartal hexamirrorzfirst-order all combinatorial)zdorian hexachordzcombinatorial I (I6))zdominant-eleventhzlydian hexachordr)zScriabin's Mystic-chordzPrometheus hexachordr)zaugmented-eleventhzharmonic hexachordr)zwhole tone scalez6 equal part divisionzuF all-combinatorial (P1, P3, P5, P7, P9, P11, I1, I3, I5, I7, I9, I11, R2, R4, R6, R8, R10, RI2, RI4, RI6, RI8, RI10)zMessiaen's mode 1zsixth-order all combinatorial)combinatorial RI (RI4))zcombinatorial RI (RI3))z%complement of all tri-chord hexachord)z5complement of all-tri-chord hexachord (inverted form))zSchoenberg Anagram hexachord)zquasi raga Bauli)z blues scale)zcombinatorial RI (RI2))r zPrometheus Neapolitan mode)zcombinatorial RI (RI1))zchromatic heptamirror)zDebussy's heptatonic)zchromatic phrygian inverse)zGreek chromaticzchromatic mixolydianzchromatic dorianzquasi raga Pantuvaralizmela Kanakangi)zRoma (Gypsy) hepatonic)double harmonic scalezmajor Roma (Gypsy)zHungarian minorr zquasi raga Mayamdavagaula)ztritone major heptachord)zmystic heptachordzEnigmatic heptatonic)zmodified blues)zNeapolitan-minor mode)alternating heptachordzHungarian major mode)diminished scaler )zharmonic minor scalezharmonic minor collectionzSpanish Roma (Gypsy)z mela Kiravani)zharmonic major scale (inverted)z$harmonic minor collection (inverted)zmela Cakravanazquasi raga Ahir Bhairav)zNeapolitan-major modezleading-whole-tone mode)zmelodic minor ascending scalez jazz minorz augmented thirteenth heptamirrorzharmonic/super-locrian)z major scalezmajor diatonic heptachordznatural minor scalezdominant thirteenthlocrianphrygianz major inverse)zchromatic octamirror)zMessiaen's mode 4)zblues octatonic)zenigmatic octachord)zSpanish octatonic scale)Greekzquartal octachordzdiatonic octad)zMessiaen's mode 6)zSpanish phrygianblues)zoctatonic scalezMessiaen's mode 2zalternating octatonic scaler )zchromatic nonamirror)znonatonic blues)zdiminishing nonachord)zMessiaen's mode 3 Tsjerepnin)zchromatic decamirror)zmajor-minor mixed)zMessiaen's mode 7)zchromatic undecamirror) aggregate dodecachordztwelve-tone chromaticzchromatic scale dodecamirrorcU[[SS55;a[SUS35eUS:d U[U:a[SUS35e[UUSnUSS:aS/$SS/$) aw Return possible inversion values for any cardinality and Forte index >>> chord.tables.forteIndexToInversionsAvailable(3, 1) [0] >>> chord.tables.forteIndexToInversionsAvailable(3, 2) [-1, 1] >>> chord.tables.forteIndexToInversionsAvailable(3, 3) [-1, 1] >>> chord.tables.forteIndexToInversionsAvailable(3, 6) [0] >>> chord.tables.forteIndexToInversionsAvailable(3, 12) [0] rJr cardinality not validindex rOrr)listrr -maximumIndexNumberWithoutInversionEquivalencer)cardindexmorriss rforteIndexToInversionsAvailablers 4a $$"\$z#BCC qyEI$OO"VE7*#=>> 4[  "F ay1}s AwrcV[U5nUSnUSn[U5S:aUSnOSnU[[SS55;a[SUS35eUS:d U[U:a[S US35e[ X5nUbX4;a[S US35eUc SU;aSnOSnXU4$) a Check that an address is valid >>> chord.tables._validateAddress((3, 1, 0)) (3, 1, 0) >>> chord.tables._validateAddress((2, 3)) (2, 3, 0) >>> chord.tables._validateAddress((3, 12, None)) (3, 12, 0) >>> chord.tables._validateAddress((3, 12)) (3, 12, 0) >>> chord.tables._validateAddress((20, 1, 0)) Traceback (most recent call last): music21.chord.tables.ChordTablesException: cardinality 20 not valid >>> chord.tables._validateAddress((8, 3000, 0)) Traceback (most recent call last): music21.chord.tables.ChordTablesException: index 3000 not valid >>> chord.tables._validateAddress((8, 3, -30)) Traceback (most recent call last): music21.chord.tables.ChordTablesException: inversion -30 not valid rrJrQrONrrrrz inversion )rrrr rr)addressrrr inversionsAvailables r_validateAddressr"s27mG 1:D AJE 7|qAJ   4a $$"\$z#BCC qyEI$OO"VE7*#=>>9$F  /&I;j'IJ J # #II  ##rc>[U5upn[UX#4S$)a; Given a TN address, return the normal form transposed to start on 0. >>> chord.tables.addressToTransposedNormalForm((3, 1, 0)) (0, 1, 2) >>> chord.tables.addressToTransposedNormalForm((3, 11, -1)) (0, 4, 7) >>> chord.tables.addressToTransposedNormalForm((3, 11, 1)) (0, 3, 7) If the inversion in the address is omitted or None, then the default inversion is used: >>> chord.tables.addressToTransposedNormalForm((3, 11)) (0, 3, 7) >>> chord.tables.addressToTransposedNormalForm((3, 11, None)) (0, 3, 7) >>> chord.tables.addressToTransposedNormalForm((3, 1)) (0, 1, 2) rr"cardinalityToChordMembersr rrr s raddressToTransposedNormalFormr'#s+*.g6D $T *E+= >q AArcD[USS5upn[UX#4S$)a Given a TN address, return the prime form >>> chord.tables.addressToPrimeForm((3, 1, 0)) (0, 1, 2) Since we are talking about primeForm, inversion does not matter. These both return the minor triad. >>> chord.tables.addressToPrimeForm((3, 11, -1)) (0, 3, 7) >>> chord.tables.addressToPrimeForm((3, 11, 1)) (0, 3, 7) If inversion is omitted or None the default value is used: >>> chord.tables.addressToPrimeForm((3, 11)) (0, 3, 7) >>> chord.tables.addressToPrimeForm((3, 11, None)) (0, 3, 7) rrOr$r&s raddressToPrimeFormr)<s1..gal;D $T *E+= >q AArc>[U5upn[UX#4S$)a  Given a TN address, return the interval class vector as a 6-tuple >>> chord.tables.addressToIntervalVector((3, 1, 0)) (2, 1, 0, 0, 0, 0) >>> chord.tables.addressToIntervalVector((3, 11, -1)) (0, 0, 1, 1, 1, 0) >>> chord.tables.addressToIntervalVector((3, 11, 1)) (0, 0, 1, 1, 1, 0) Inversion can be omitted or None without causing an error (or, of course, changing the output) >>> chord.tables.addressToIntervalVector((4, 29)) (1, 1, 1, 1, 1, 1) >>> chord.tables.addressToIntervalVector((3, 11, None)) (0, 0, 1, 1, 1, 0) rOr$r&s raddressToIntervalVectorr+Ws+&.g6D $T *E+= >q AArc /n[U5n[U5S:wa [S5e[SS5HJn[ [ U5H1up4UcM USU:XdMUR [X#SS55 M3 ML U$)a Given a vector as a 6-tuple, return a list of ChordTableAddress namedtuples for all addresses that match that vector. >>> chord.tables.intervalVectorToAddress((7, 6, 5, 4, 4, 2)) [ChordTableAddress(cardinality=8, forteClass=1, inversion=None, pcOriginal=None)] >>> chord.tables.intervalVectorToAddress((12, 12, 12, 12, 12, 6)) [ChordTableAddress(cardinality=12, forteClass=1, inversion=None, pcOriginal=None)] Vector can also be a list: >>> chord.tables.intervalVectorToAddress([2, 2, 3, 1, 1, 1]) [ChordTableAddress(cardinality=5, forteClass=10, inversion=None, pcOriginal=None)] A value that matches nothing returns an empty set. >>> chord.tables.intervalVectorToAddress((2, 2, 3, 1, 1, 99)) [] In the case of Z-related pairs, such as the all-interval tetrachord, more than one address will be returned. >>> chord.tables.intervalVectorToAddress((1, 1, 1, 1, 1, 1)) [ChordTableAddress(cardinality=4, forteClass=15, inversion=None, pcOriginal=None), ChordTableAddress(cardinality=4, forteClass=29, inversion=None, pcOriginal=None)] If the vector does not have six elements, raises a ValueError: >>> chord.tables.intervalVectorToAddress([0, 2, 4]) Traceback (most recent call last): ValueError: Vector must have exactly six entries rTz$Vector must have exactly six entriesrJrN)tupler ValueErrorr enumeraterappendr)vectorpostrnumscs rintervalVectorToAddressr5nsD D 6]F 6{a?@@a  t-GCz!u -dtDE . Krc~[U5upn[UUSnUS:Xag[XS45n[/UQSP76$)a Given a TN address, return the ChordTableAddress of the Z-set if one exists. If none exists, returns None. >>> chord.tables.addressToZAddress((5, 12)) ChordTableAddress(cardinality=5, forteClass=36, inversion=1, pcOriginal=None) >>> chord.tables.addressToZAddress((5, 36, None)) ChordTableAddress(cardinality=5, forteClass=12, inversion=0, pcOriginal=None) >>> print(chord.tables.addressToZAddress([3, 11])) None >>> chord.tables.addressToZAddress((5, 37)) ChordTableAddress(cardinality=5, forteClass=17, inversion=0, pcOriginal=None) >>> chord.tables.addressToZAddress((8, 29)) ChordTableAddress(cardinality=8, forteClass=15, inversion=1, pcOriginal=None) rQrN)r"rr)r rrunused_inversionzzAddresss raddressToZAddressr:sR$%5W$=!D! d E1AAv#TdO4 1(1D11rcT[U5n[UnSU;a[US5$g)a Given a TN address, return one or more common names if available: >>> chord.tables.addressToCommonNames((3, 1, 0)) ['chromatic trimirror'] >>> major_address = chord.tables.ChordTableAddress(3, 11, -1, 2) >>> chord.tables.addressToCommonNames(major_address) ['major triad'] More than one name might be returned: >>> chord.tables.addressToCommonNames([7, 33]) ['Neapolitan-major mode', 'leading-whole-tone mode'] This system does not take into account spelling or inversion, so that the minor triad would give the same name. The `.commonName` property of the `chord.Chord` object itself takes into account non-post-tonal spellings. Note that names referring to ethnic stereotypes that are not in common usage will be removed in music21 v8 or at any time thereafter without a deprecation cycle. Those matching this description that are still in common use will be demoted to the end of the list of names and may still be removed in the future. rN)r"tnIndexToChordInfor)r refDicts raddressToCommonNamesr>s24w'G )G GFO$$rc[U5up#nSnUR5S:XaUS:XaSnOUS:XaSnO US:XaSnOSnUSUU3$) a Given an address, return the set-class name as a string. By default, A and B are appended to chords without inversional equivalence: >>> octachord_address = chord.tables.ChordTableAddress(8, 15, -1, 10) >>> chord.tables.addressToForteName(octachord_address) '8-15B' >>> chord.tables.addressToForteName((8, 15)) '8-15A' The augmented triad is invariant under inversion, so it gets no designation: >>> chord.tables.addressToForteName((3, 12)) '3-12' If classification is the string 'tni' then the "A" and "B" for inversions will be omitted. >>> chord.tables.addressToForteName((8, 15), 'tni') '8-15' >>> chord.tables.addressToForteName((5, 37)) '5-37' tnrBrJAr-)r"lower)r classificationrrr iStrs raddressToForteNamerHsh0.g6D D% ?D !^D !^DV1UGD6 ""rcURnSnSnU(d[S[U5S35e[U5nUS:Xa[SSSUS5$US:Xa[SSSS5$/n[ U5HnXSUSU-nUSnUV s/sH oU- S-PM nn UV s/sH n SU - S-PM n n U R 5 U V s/sHn U SU S- -S-PM n n [ U5[ U 5U4n URU 5 M Sn Sn [ S[[U55H`n[UUnUSn[XN5nUH;unnnUU:XaUnSU;aSnOSnUn Sn MBUU:XdM)UnSU;aSnOS nUn Sn M^ Mb U (d[S U35e[XBX=5$s sn fs sn fs sn f) a9 Utility method to return the address to the chord table; used by many Chord operations, such as `.primeForm`, `.normalOrder`, etc. Table addresses are a ChordTableAddress named-tuple giving the cardinality, the Forte-index-number, the inversion, and the original pitch class that matched (it may be arbitrary for a symmetrical chord like the diminished seventh chord). Inversion is either 0 (for symmetrical under inversion) or -1, 1 >>> c1 = chord.Chord(['c3']) >>> chord.tables.seekChordTablesAddress(c1) ChordTableAddress(cardinality=1, forteClass=1, inversion=0, pcOriginal=0) Here the only note that is missing is A-sharp/B-flat. >>> c1 = chord.Chord( ... ['c', 'c#', 'd', 'd#', 'e', 'f', 'f#', 'g', 'g#', 'a', 'b'] ... ) >>> chord.tables.seekChordTablesAddress(c1) ChordTableAddress(cardinality=11, forteClass=1, inversion=0, pcOriginal=11) The major chord is considered the inversion of the minor: >>> c1 = chord.Chord(['g', 'b', 'd']) >>> chord.tables.seekChordTablesAddress(c1) ChordTableAddress(cardinality=3, forteClass=11, inversion=-1, pcOriginal=7) >>> c1 = chord.Chord(['c', 'e-', 'g']) >>> chord.tables.seekChordTablesAddress(c1) ChordTableAddress(cardinality=3, forteClass=11, inversion=1, pcOriginal=0) Chords invariant under inversion give an inversion of 0. >>> c1 = chord.Chord(['c', 'c#', 'd#', 'e', 'f#', 'g#', 'a#']) >>> chord.tables.seekChordTablesAddress(c1) ChordTableAddress(cardinality=7, forteClass=34, inversion=0, pcOriginal=0) >>> c1 = chord.Chord(['c', 'c#', 'b']) >>> chord.tables.seekChordTablesAddress(c1) ChordTableAddress(cardinality=3, forteClass=1, inversion=0, pcOriginal=11) Zero-length chords raise a pitch exception: >>> c2 = chord.Chord() >>> chord.tables.seekChordTablesAddress(c2) Traceback (most recent call last): music21.chord.tables.ChordTablesException: cannot access chord tables address for Chord with 0 pitches NOTE: this was once a time-consuming operation, though it is now quite a bit faster than before (order of 100 microseconds). Nonetheless, it should only be run when necessary. Methods that call this should try (as chord.Chord does) to cache the result. OMIT_FROM_DOCS Can the last entry be found? >>> c_aug = chord.Chord(['c', 'f-', 'g#']) >>> chord.tables.seekChordTablesAddress(c_aug) ChordTableAddress(cardinality=3, forteClass=12, inversion=0, pcOriginal=0) rz2cannot access chord tables address for Chord with z pitchesrJr|NFTrz&cannot find a chord table address for ) orderedPitchClassesr rrrreverser-r0rr)cpcSetrr r candidatesrottestSettestSetOriginalPCx testSetInvertcandidateTuplematchmatchedPCOriginalindexCandidatedataLine dataLinePcsr! candidatecandidateInversioncandidateOriginalPCs rseekChordTablesAddressr]s@B  ! !E EI "@U H UW W u:D qy Aq%(33  Q1--JT{+a ,#AJ9@AA))R/A0781"q&B 8#01"/QrM!$445;"/ 1 .% *>@QR.) 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