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An ipa e n disco e y in Basque olk unes
DARRELL CONKLIN
Depa men o Compu e Science and A i icial In elligence
Uni e sidad del País Vasco UPV/EHU, San Sebas ián, Spain, and
IKERBASQUE, Basque Founda ion o Science, Bilbao, Spain
[email p o ec ed]
Abs ac
This pape p esen s a new pa e n disco e y me hod o labelled olk song co po a. The me hod disco e s
gene al pa e ns ha a e a e o e en en i ely absen in a co pus, and among hose he ones ha a e he mos gene al
o equen in he backg ound se . The me hod is applied o wo pa allel on ologies o a la ge co pus o Basque olk
unes.
1 In oduc ion
In ecen yea s he e has been a enewed in e es in olk song analysis, due o in e es in
cul u al he i age and ad ances in music in o ma ics me hods. The abili y o analyse music
con en o di e en p ope ies o songs such as place name, dance ype, une amily, onali y,
and social unc ion, is an impo an pa o he managemen and unde s anding o la ge co po a.
The objec i e o he p ojec Análisis Compu acional de la Música Folcló ica Vasca is he
de elopmen and applica ion o da a mining me hods o Basque song collec ions h ough
au oma ed pa e n disco e y and classi ica ion, using da a mining algo i hms o disco e
p edic i e models ha ela e musical con en and he class labels o songs. This p ojec will open
new pa hs in he s udy and analysis o essen ial elemen s o Basque music, suppo ing he s udy
o he
e olu ion and o igins o Basque melodies, and will lead o me hods o au oma ic classi ica ion
and analysis o Basque olk songs.
The Cancione o Vasco is a collec ion o Basque dance and song melodies, compiled by he
musicologis , compose , and p ies Pad e Donos ia in 1912 as pa o a compe i ion held by he
Basque go e nmen o ga he musical olklo e o he egion. Recen ly he en i e collec ion has
been compiled in ou olumes (de Riezu, 1996) and digi ised, a p ocess o e seen by he
Euskomedia Founda ion
1
(Usu bil, Spain) and he E esbil Founda ion
2
(Ren e ia, Spain).
Songs in he Cancione o Vasco con ain wo impo an ypes o in o ma ion: musical da a (in
MIDI o ma ) ha encodes he melody, and me ada a collec ed by Donos ia including he egion
o collec ion o he song, and i s gen e. In he Cancione o Vasco a o al o 24 dis inc gen es a e
e e enced, besides oponyms o ganised in le els o e i o io ( egion), municipio (municipali y),
and nucleo ( own).
Much esea ch o da e on pa e n disco e y in music has been conce ned wi h disco e ing
pa e ns ha a e equen , salien , o e - ep esen ed, e c. in an analysis piece o se o pieces. This
pape p esen s a me hod o disco e ing pa e ns ha by con as a e in equen , a e, and
unde - ep esen ed. Such pa e ns migh be used, o example, wi hin p edic i e classi ica ion,
whe e hei occu ence migh s ongly sugges agains membe ship in a class. The pa e n
disco e y me hod is applied wi h illus a ion o he Cancione o Vasco.
2. Me hods
This sec ion desc ibes he heo y leading o a new me hod o disco e ing unde - ep esen ed
1
www.euskomedia.o g
2
www.e esbil.com
An ipa e n disco e y in Basque olk unes
220
pa e ns in a co pus. The gene al me hods o subg oup disco e y a e p esen ed, ollowed by a
gene al me hod o applying subg oup disco e y o sequen ial pa e ns in music. I is hen
demons a ed how his me hod may be eadily modi ied o ind unde - a he han o e -
ep esen ed pa e ns in a co pus.
Figu e 1: The schema o subg oup disco e y, showing he majo egions o objec s in ol ed. The op pa o he
ou e box encloses he class o in e es (in music called he co pus), below his he backg ound ( he an ico pus). The
inne box con ains he objec s desc ibed by a pa e n, and he op pa o he inne box he subg oup desc ibed by a
disco e ed pa e n.
Table 1: Glossa y o No a ion.
2.1 Subg oup disco e y
Figu e 1 depic s he da a mining scena io known as subg oup disco e y, o al e na i ely supe ised
desc ip i e ule disco e y (No ak e al., 2009), a ela i ely ecen pa adigm o da a mining. Gi en an
analysis class, subg oup disco e y a emp s o disco e pa e ns p edic i e o he class no o
any possible example, bu only o a subse (subg oup) among hem co e ing as ew o he
objec s as possible. An ideal pa e n would ha e as i s ex ension all and only he examples. In
p ac ice his is no possible excep in pa e n desc ip ion languages ha pe mi disjunc ion
(whe e a i ial disjunc i e desc ip ion o all examples may be possible).
In con as o supe ised p edic i e me hods, subg oup disco e y mus he e o e ealise wo
asks: iden i y he in e es ing subg oups, hen (in ac , in pa allel) desc ibe hem wi h
comp ehensible pa e ns. Thus he me hod is a he same ime supe ised (using labelled da a)
and desc ip i e (no ha ing class p edic ion as he main objec i e).
In gene al, in he supe ised desc ip i e da a mining scena io, he pa e ns disco e ed may no
co e all examples, ha is, hey a e agnos ic abou making p edic ions o examples ha a e no
ma ched by he pa e n. The e o e he esul s o da a mining a e e alua ed acco ding o he
in e es o pa e ns (usually some s a is ical measu e o o e - ep esen a ion) a he han
classi ica ion accu acy in he case o supe ised p edic i e me hods.
2.2 Sequen ial pa e n mining in music
To ex end supe ised desc ip i e me hods owa ds music, Conklin (2010a) p esen ed he idea
o using dis inc i e sequen ial pa e ns o desc ibe subg oups. A sequen ial pa e n in music is a
sequence o ea u es o no es, o example, [+2,+1] is a sequence o melodic in e als ha
An ipa e n disco e y in Basque olk unes
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ma ches ( o example) he no e sequences o .
The e is a close connec ion wi h dis inc i e pa e n disco e y in music and gene se
en ichmen s udies in bioin o ma ics (Al-Shah ou e al., 2004). The e, genes o in e es (which
a e selec ed by he scien is , o example by being o e -exp essed in some expe imen ) a e
p obed wi h a ious gene on ology e ms o ind e ms ha a e o e ep esen ed wi hin he
selec ed se o in e es . The analogy o pa e n disco e y in music is ha pieces in a speci ied
class a e analogous o genes o in e es , and pa e ns a e analogous o gene on ology e ms.
Table 2: A con ingency able o a Basque olk une pa e n. The p- alue o he associa ion be ween P and is
0:0014.
Subg oup disco e y in oduces compu a ional complexi ies o music, because he space o
e ms (pa e ns) used o desc ibe subg oups is no ixed, as in he bioin o ma ics s udies, and
may be p ac ically in ini e and he e o e he sea ch o in e es ing pa e ns mus be handled
ca e ully. This applies e en when a simple ep esen a ion o conjunc ions o global piece
ea u es is used o desc ibe subg oups (Taminau e al., 2009). The MGDP (maximally gene al
dis inc i e pa e n) algo i hm (Conklin, 2010a) disco e s associa ions be ween pa e ns and
classes in an e icien way due o i s s uc u ing and p uning o he pa e n sea ch space. I uses
wo impo an concep s o manage he p oblem o a la ge pa e n space: hese a e dis inc i eness
and gene ali y.
To illus a e he concep o dis inc i eness, Table 2 shows a con ingency able o he melodic
in e al pa e n [-4,+2,+2] ha occu s in a subg oup o songs o he gen e wedding song. The
pa e n appea s in c (P)=5 o n =6 (83%) o wedding songs, bu only in c (P) = 365 o
n =1892 (19%) o songs om o he gen es. I can be said ha his pa e n is dis inc i e o
wedding songs, because i s ela i e equency in ha class is highe han in he backg ound. Any
pa e n wi h a ela i e p obabili y abo e a h eshold may be conside ed dis inc i e.
The Fishe ’s exac es , based on he cumula i e hype geome ic dis ibu ion (Falcon and
Gen leman, 2008), is used o u he quan i y he s a is ical signi icance o an associa ion
be ween a pa e n and a class. Re e ing o Figu e 1, he p- alue o an associa ion is he
p obabili y o laying he inne box, i.e. d awing a se o c (P)+c (P) pieces om he co pus o
n +n pieces, and inding c (P) o mo e membe s o he class . Lowe p- alues indica e mo e
su p ising associa ions. The unc ion is symme ic: he same p obabili y esul s om d awing n
pieces om he co pus and inding c (P) o mo e pieces con aining he pa e n P. In Figu e 2,
o example, he cumula i e hype geome ic dis ibu ion gi es he p obabili y o inding 5 o
mo e wedding songs in a sample o 370 pieces (o , symme ically, 5 o mo e pieces con aining
he pa e n [-4,+2,+2] in a sample o 6 pieces).
The concep o gene ali y o subsump ion is e y impo an o s uc u e he sea ch and
p esen a ion space o pa e ns. A pa e n is subsumed by ano he i all songs ha con ain he
pa e n also will con ain he o he ( o example, he pa e n [-4,+2,+2] is subsumed by he
pa e n [+2]). The MGDP algo i hm disco e s a se o pa e ns ha a e bo h dis inc i e and
An ipa e n disco e y in Basque olk unes
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among hose he mos gene al (no subsumed by any o he dis inc i e pa e n). Fo example, i
he pa e n [+2] is no dis inc i e i would no be epo ed. I he pa e n [-4,+2,+2] is
dis inc i e, hen no mo e speci ic pa e n (e.g., [4,+2,+2,+1]) would be epo ed, and in ac he
en i e sea ch space unde he pa e n [-4,+2,+2] need no be explo ed.
The MGDP algo i hm ope a es by i e a ion, se ing each class as he co pus , and se ing he
es o he pieces, i espec i e o hei classes, as he an ico pus (see Figu e 1). Pa e ns a e
ound wi hin a co pus by ee sea ch o e a speci ied pa e n space (e.g., melodic in e al
pa e ns, hy hmic pa e ns) and da a mining pa ame e s including a dis inc i eness h eshold.
S a is ics a e compu ed o each MGDP ound and he esul s so ed by inc easing p- alue. Fo
olk songs, he class a iable may be used o label any imaginable pa i ioning o he da a, o
example, by he gen e o a song, i s geog aphic a ea o collec ion (and/o o igin, i known), o i s
une amily. The algo i hm was applied wi h success o a co pus o C e an olk music (Conklin
and nagnos opoulou, 2011), which we e labeled wi h 5 oponymic and 11 gen e desc ip o s.
2.3 An ipa e ns
An an ipa e n (an ico pus pa e n) is a pa e n ha is absen o su p isingly a e wi hin a co pus
bu occu s equen ly in an an ico pus (i.e., is a gene al a he han a speci ic pa e n) . To
disco e such pa e ns i is emp ing o y o enume a e he space o pa e ns in he co pus om
mos speci ic (longes ) o gene al ( a he han gene al o speci ic), bu his s a egy is ine icien
because nea ly all concei able pa e ns will be in equen in a co pus. Fu he mo e, a weakness
o his s a egy is ha i canno disco e jumping pa e ns (Dong and Li, 1999): hose ha a e
comple ely absen in a co pus.
Table 3: An ipa e ns in he Cancione o Vasco. Top: o gen es; Bo om: o e i o ios.
An elegan solu ion is ound by no ing ha he e is a na u al symme y o pa e ns ha a e
o e - ep esen ed in an analysis class and hose unde - ep esen ed in he backg ound. In ac he
MGDP algo i hm can na u ally be used o disco e an ipa e ns by e e sing he oles o co pus
and an ico pus. Fu he mo e, he p- alue o an an ipa e n has a symme ic meaning: he
p obabili y ha i occu s he obse ed numbe o ewe imes in he co pus. The e o e, by
swi ching he ole o co pus and an ico pus, and modi ying he p- alue compu a ions o
compu e he le a he han igh ail o he cumula i e hype geome ic dis ibu ion, he MGDP
algo i hm may be used o disco e an ipa e ns.
3. Resul s
The 7 e i o ios and 24 gen es in he Cancione o Vasco we e used as label dimensions o he
disco e y o an ipa e ns. The e o e, o example, one e i o io (e.g., bizkaia) would be aken as
he co pus and he songs in o he e i o ies as he an ico pus , and he MGDP algo i hm
An ipa e n disco e y in Basque olk unes
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used o ind pa e ns unde - ep esen ed in he co pus. As desc ibed abo e, his is done by
e e sing he oles o he co pus and an ico pus, and inding pa e ns o e - ep esen ed in he
an ico pus.
Table 3 shows some examples o disco e ed an ipa e ns, de i ed om a ious di e en
classes ound wi hin he Cancione o Vasco. Some an ipa e ns o Table 3 a e su p ising om a
musicological sense, o example he eligiosa an ipa e n which occu s in 128 songs in he
an ico pus bu only in 2 songs in he co pus. The an ipa e n ep esen s a long scalic passage
(e.g., [G,A,G,F,E,D,C]). The simple an ipa e n [+9], ep esen ing a leap o a majo six h, occu s
in only 1 (o 86) na a i a songs, hough in 211 pieces in he an ico pus. The an ipa e n [+4,+3]
is a jumping pa e n (i occu s in none o he pieces in he bizkaia e i o y), bu despi e his he
p- alue (0.023) is no signi ican , e lec ing he ac ha he e a e only 21 pieces in he co pus,
making i s a is ically no so su p ising as some o he o he an ipa e ns. In e es ingly, he
wedding song pa e n [-4,+2,+2] illus a ed ea lie in Table 2 is a he same ime an an ipa e n
o he class es i a-sa i ica.
4. Conclusions
The esul s wi h an ipa e n disco e y a e p omising and se e al di ec ions o u u e wo k a e
planned.
The opic o using a collec ion o pa e ns o classi ica ion was e iewed by Conklin (2009).
Dis inc i e pa e ns may be used as boolean ea u es as inpu o s anda d ea u e ec o
classi ie s. In his sense, pa e n disco e y can be iewed as a ea u e gene a ion p oblem.
Dis inc i e an ipa e ns may s ongly sugges agains membe ship in a class.
Clea ly some way o isualise esul s a e necessa y, and o his pu pose i is planned o
einco po a e disco e ed pa e ns back in o a o mal on ology o classes and pa e ns, using a
desc ip ion logic o malism encoded in he web on ology language OWL, and a on ology
isualisa ion ool. An ipa e ns may be ep esen ed as desc ip ion logic concep s using a me hod
simila o ha desc ibed by Hi sh and Kudenko (1997).
Though his s udy has shown ha labels o olk songs may be used p oduc i ely in a pa e n
disco e y se ing, in gene al he labelling o olk songs always aises some ques ions. The
seman ics o geog aphic loca ion labels can be unclea and open o in e p e a ion. In he
Cancione o Vasco he labels e e o he place o collec ion o he une, which is no necessa ily
he same as he home a ea o he pe o me , o he a ea whe e he une was lea ned. The gen e
labels may ha e an ambiguous ela ion o song con en in cases whe e he same une is used o
di e en social unc ions (Sel idge-Field, 2006).
An ipa e ns, hose pa e ns ha a e a e wi hin an analysis co pus, a e a guably e en ha de o
in e p e han equen pa e ns. This is because one canno simply highligh he occu ences
wi hin a lis o pieces ha con ain he pa e n and inspec hei musical con ex . One can inspec
he ew a e example pieces o ob ious wide de ia ions om he s yle (o da a anomalies) bu
in cases whe e he an ipa e n has a ze o co pus coun e en his me hod canno be applied.
Fu u e explo a ions include he use o an ipa e ns o mo i ic analysis o single pieces
(Conklin, 2010b) and disco e y o an ipa e ns o e di e en ep esen a ions o songs, o
example a highe s uc u al le els o ph ases and sec ions.
Acknowledgmen s
The Fundación Euskomedia and Fundación E esbil a e g aciously hanked o pa icipa ing in
he p ojec and p o iding he Cancione o Vasco o s udy. This esea ch was pa ially suppo ed
by a g an Análisis Compu acional de la Música Folcló ica Vasca (2011-2012) om he Dipu ación
Fo al de Gipuzkoa, Spain. Thanks o K. Neuba h and he e iewe s o aluable commen s on
he manusc ip .
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