GREGORIAN MELODY, MODALITY, AND MEMORY:
SEGMENTING CHANT WITH BAYESIAN NONPARAMETRICS
Voj ˇ
ech Lanz Jan Hajiˇ
c j .
Cha les Uni e si y, Facul y o Ma hema ics and Physics
Ins i u e o Fo mal and Applied Linguis ics
{lanz,hajicj}@u al.m .cuni.cz
ABSTRACT
The idea ha G ego ian melodies a e cons uc ed om
some ocabula y o segmen s has long been a pa o chan
schola ship. This so-called “cen onisa ion” heo y has e-
cei ed much musicological c i icism, bu equen e-use
o ce ain melodic segmen s has been obse ed in chan
melodies, and he in ac able numbe o possible segmen-
a ions allowed he op ion ha some undisco e ed segmen-
a ion exis s ha will ye p o e he alue o cen onisa ion,
and ecen empi ical esul s ha e shown ha segmen a ions
can ou pe o m music- heo e ical ea u es in mode classi i-
ca ion. Inspi ed by he ac ha G ego ian chan was mem-
o ised, we sea ch o an op imal unsupe ised segmen-
a ion o chan melody using nes ed hie a chical Pi man-
Yo language models. The segmen a ion we ind achie es
s a e-o - he-a pe o mance in mode classi ica ion. Mod-
eling a monk memo ising he melodies om one li u gical
manusc ip , we hen ind empi ical e idence o he link
be ween mode classi ica ion and memo y e iciency, and
obse e mo e o mulaic a eas a he beginnings and ends
o melodies co esponding o he p ac ical ole o modal-
i y in pe o mance. Howe e , he esul ing segmen a ions
hemsel es indica e ha e en such a memo y-op imal seg-
men a ion is no wha is unde s ood as cen onisa ion.
1. INTRODUCTION
G ego ian chan , he li u gical monody o he La in chu ch,
has been a pilla o Eu opean musical iden i y since he
Ca olingian pe iod in he 8 h-9 h cen u y A.D. And ye
we ha e no cons uc i e heo y o chan melody like we
ha e e.g., onali y o classical composi ion. No good ex-
plana ion exis s o why G ego ian melodies should be he
way hey a e, o how o w i e a plausible one om sc a ch.
“They a e no mean o be composed a all” would be an
answe , had no G ego ian melodies been newly composed
o hea ily edi ed. Howe e , new chan s we e composed [1,
p. 463], o example, o new eas s [2]. Thus, he ques ion
emains: how is G ego ian melody s uc u ed?
© V. Lanz and J. Hajiˇ
c j .. Licensed unde a C ea i e Com-
mons A ibu ion 4.0 In e na ional License (CC BY 4.0). A ibu ion: V.
Lanz and J. Hajiˇ
c j ., “G ego ian melody, modali y, and memo y: Seg-
men ing chan wi h Bayesian nonpa ame ics”, in P oc. o he 26 h In .
Socie y o Music In o ma ion Re ie al Con ., Daejeon, Sou h Ko ea,
2025.
1.1 Modali y
The main heo e ical amewo k o G ego ian melody is
modali y, which classi ies melodies in o eigh basic modes
1–8, 1also known as he chu ch modes and oday mos
o en e e enced by hei G eek names: do ian, hypodo -
ian, ph ygian, e c. Modes a e p ima ily iden i ied by hei
inalis ( he inal no e, ypically d,e, , o g) and hei
ange (au hen ic o plagal). This “ heo e ical” de ini ion is
passed down om ea ly medie al sou ces h oughou he
Middle Ages [3,4, Ch. 1].
The medie al de ini ion o modes says li le abou how
G ego ian melody should be cons uc ed. Modali y in-
ol ed mo e han jus he beginnings, ends, and anges o
melodies: an e ol ing unde s anding o modali y [4, ch. 6]
led o e isions, mos no ably, he Cis e cian o de made
ex ensi e e isions based on hei no ion o modal “pu-
i y” [1, p. 610] [5, p. 72]. Tona ies 2[3, 6] show ha
he epe oi e o en di e ged om he “ heo e ical” de i-
ni ion. A leas 1 in 10 an iphons and esponso ies would
be misclassi ied using he “ heo e ical” ea u es [7]. Some
ona ies e en disag ee wi h each o he [8]. Mode, he e-
o e, goes beyond i s medie al de ini ion.
An a ac i e app oach o modali y is he idea ha
modes a e hidden “ ocabula ies” o cha ac e is ic melodic
segmen s. This ollows om obse a ions ha many
melodic ges u es a e e-used ac oss di e en melodies
[9–11]. Melodies wi hin a mode end o be simila [3, 12],
sugges ing hese segmen s may be speci ic o modes. Tex -
based and o he nai e segmen a ions o chan melodies
ha e been used o mode classi ica ion [7, 13], show-
ing p omising esul s on he Can usCo pus 0.2 da ase
[14, 15] and ou pe o ming “ heo e ical” app oaches, as
well as pi ch p o iles. Taken o he ex eme, he heo y o
“cen onisa ion” pos ula es en i e melodies a e cons uc ed
by conca ena ing mode-speci ic melodic segmen s [16,17].
Cen onisa ion has aced s ong c i icism in G ego ian
chan schola ship [1, 18, p. 74–75]; howe e , his la gely
conce ns i s aming as a delibe a e composi ional s a egy,
no he ecu ence o melodic ma e ial ac oss chan s [18].
1.2 Memo y
G ego ian chan was o iginally an o al adi ion [4,18,19],
equi ing monks o memo ise housands o melodies wi h-
1Lea ing aside ansposed modes e c.
2Manusc ip s ha explici ly o ganise melodies by mode.
638
ou exac pi ch no a ion o o e 300 yea s. The challenge
o memo isa ion led o he apid adop ion o s a no a ion,
in oduced by Guido o A ezzo in he 11 h cen u y as a
eaching aid [1,4, p. 388].
Memo y cons ain s, along wi h cul u al-e olu iona y
and in o ma ion- heo e ic p inciples, s ongly suppo he
eme gence o cen onisa ion in he melodies. O al ans-
mission is impe ec [20, 21], and melodies end o e ol e
owa d lowe en opy [22]. Since melodies we e a ely
w i en he same way wice [23, 24], despi e e o s o
p ese e hem [1, p. 611], hey changed du ing cen u ies
o o al ansmission be o e ge ing w i en down wi h ex-
ac pi ch no a ion. Gi en he memo isa ion demands on
singe s, cen onisa ion would be expec ed unde he Min-
imum Desc ip ion Leng h (MDL) p inciple. Suppo ing
his, a ecen s udy [21] ound ha o al ansmission led
o “using ewe building blocks (in e als, con ou s) ha
a e inc easingly eused and combined” o e ime, which
is exac ly he ype o s uc u e cen onisa ion e e s o.
Many monodic o al adi ions show cen onisa ion – o
example, A ab-Andalusian [25] and Byzan ine chan [26],
and high o mulaici y has been obse ed in Old Roman
[27, 28] and Bene en an chan [29]. Melodic o mulas ap-
pea in Hindus ani Ragas [30], and we a e ce ainly omi -
ing ens, i no hund eds, o o he such adi ions he e.
1.3 Ou line
Since es ing all segmen a ions is in ac able, i emains
possible ha some segmen a ion could e eal ha G ego-
ian chan is a “cen ona e” adi ion.
In Sec ion 3, we o malise chan memo isa ion as a
compu a ional segmen a ion p oblem, sea ching o an
“op imally cen onised” segmen a ion o chan by exploi -
ing he connec ion be ween he MDL p inciple [31, 32]
and Maximum a Pos e io i (MAP) es ima ion [33,34], and
“bo owing” he nonpa ame ic Bayesian Nes ed Hie a -
chical Pi man-Yo Language Model (NHPYLM) [35] o
segmen chan melody ins ead o na u al language.
A e b ie ly in oducing he da ase s we use (Sec-
ion 4), using mode classi ica ion as a p oxy o segmen a-
ion quali y [7, 13], we show ha he memo isa ion-based
me hod ou pe o ms exis ing segmen a ion baselines, bo h
on pi ch and in e al ep esen a ions (Sec ion 5).
Imi a ing a monk lea ning om one manusc ip (Sec-
ion 6), we ind ha e icien memo isa ion ela es o
modali y, hough i s in luence a ies ac oss melody pa s,
depending on how hey we e pe o med in li u gy
We also con ibu e a Cy hon implemen a ion o he NH-
PYLM model, and a class-condi ioned e sion he eo . 3
2. NHPYLM–RELATED WORK
In asks such as ocabula y induc ion, phoneme- o-wo d
mapping, and wo d segmen a ion o ex wi hou whi es-
pace (e.g., Manda in o Japanese), nonpa ame ic Bayesian
me hods a oid manual model selec ion by lea ning model
complexi y om he da a as pa o in e ence. In his
3A ailable a h ps://gi hub.com/lanz /nhpylm
con ex , he Hie a chical Pi man-Yo Language Model
(HPYLM) [35] was in oduced. I has been widely applied
o unsupe ised wo d segmen a ion, om speech ecogni-
ion [36, 37] o opic models [38]. Mochihashi e al. [39]
ex ended his app oach wi h he Nes ed HPYLM (NH-
PYLM), inco po a ing cha ac e -le el p io s om Cha ac-
e HPYLM.
NHPYLM has been adap ed o melody segmen a ion,
modelling mo i s in onal music [40]. The segmen a ion e-
sul s we e compa ed wi h he Gene a i e Theo y o Tonal
Music, demons a ing he e ec i eness o Bayesian non-
pa ame ic models o s uc u ed sequence lea ning, which
we ex end in he con ex o G ego ian chan .
3. MEMORY-EFFICIENT SEGMENTATION
E icien memo isa ion o he G ego ian melodies can be
o malised wi h he MDL p inciple [31, 32]: he bes code
H o da a Dis one ha minimises L(D|H) + L(H),
whe e L(D|H)is he leng h o he da a encoded using he
codebook H, and L(H)is he leng h o he codebook. The
MDL p inciple hus encou ages codebooks such ha he
mo e equen ly occu ing and he longe a subsequence,
he sho e code i ge s o minimise L(D|H), and i encou -
ages small codebooks ia he L(H) e m. Impo an ly o
in e ing memo y-e icen segmen a ions, choosing a hy-
po hesis using he MDL p inciple is equi alen o choos-
ing he MAP hypo hesis unde a Bayesian model [33],
whe e he p io p obabili y o a hypo hesis (co esponding
o L(H)) dec eases wi h i s leng h [34].
To ind an op imally memo y-e icien segmen a ion,
we need an unsupe ised segmen a ion model ha : (1) in-
e s he ocabula y, including i s size, since we wan he
ocabula y o chan segmen s o be a dependen a iable
ollowing om e icien memo isa ion; (2) can model he
sequen ial na u e o chan melody (as one sings one seg-
men a e he o he ); (3) has a p io ha p e e s smalle
segmen ocabula ies; and (4) has ac able in e ence and
MAP es ima ion. These condi ions a e ul illed by he
Nes ed Hie a chical Pi man-Yo Language Model (NH-
PYLM) [35].
3.1 An in ui ion on he NHPYLM
The Pi man-Yo p ocess (PY) is a nonpa ame ic Bayesian
model ha assigns p obabili ies o ca ego ical dis ibu ions
wi hou se ing he numbe o ca ego ies in ad ance [41].
The in ui ion behind PY s a s wi h he Chinese Res au-
an P ocess (CRP): 4 he ca ego ical dis ibu ions a e no -
malised cus ome coun s a ables se ing a di e en dish
each. The key p ope y o he CRP is ha he n- h cus-
ome chooses o si a a gi en able p opo ionally o how
many cus ome s a e al eady ea ing he e, wi h a pa ame-
e α ha lea es a (dec easing) chance α/(α+n−1) o
si ing a a new able. This gi es ise o a ich-ge - iche
beha iou , and a p io ha s ongly p e e s ewe ables –
in he case o language models, ewe ocabula y elemen s
and hus sho e hypo heses unde he MDL p inciple. PY
4Also: Di ichle P ocess.
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639
is a gene alisa ion o CRP ha p o ides mo e con ol o e
he ich-ge - iche beha iou , o be e model long- ail dis-
ibu ions such as hose ound in na u al languages [41]. 5
In sequence segmen a ion, PY inds he op imal o-
cabula y unde his ich-ge - iche pa adigm o e unig am
p obabili ies o he esul ing segmen s. In o de o model
he sequence o de ing wi h big ams P(si|si−1)o he in-
e ed segmen s, we mus add a “ es au an o es au an s”,
which models he p obabili y o ha ing he his o y si−1.
The “inne ” es au an hen models he condi ional p oba-
bili y o si, ia a ye ano he hie a chy o es au an s o e
he cha ac e n-g ams in si. This is, inally, he Nes ed Hi-
e a chical Pi man-Yo P ocess [35,39].
In ou case, he “inne ” HPYLM ope a es on ones,
while he “ou e ” ope a es on segmen s. The base dis i-
bu ion o he segmen -le el HPYLM is ob ained om he
one-le el HPYLM.
3.2 Segmen a ion P obabili y wi h NHPYLM
To compu e he p obabili y o a gi en segmen a ion o a
melody, we only need o e alua e he p obabili y o each
segmen in i s con ex unde he NHPYLM and mul iply
hem oge he . Fo a segmen sgi en a con ex h, he
“ou e ” (segmen -le el) model compu es he p obabili y
ecu si ely as:
p(s|h) = c(s|h)−d· hs
θ+c(h)+θ+d· h
θ+c(h)·p(s|h′),(1)
whe e c(s|h)is he numbe o cus ome s (segmen occu -
ences) o segmen swi h con ex h,c(h)is he o al num-
be o cus ome s wi h ha con ex , hs is he numbe o
ables se ing segmen sin con ex h, and his he o al
numbe o ables wi h con ex h. The discoun dand con-
cen a ion θa e hype pa ame e s o he Pi man-Yo p o-
cess. The e m p(s|h′) e e s o he p obabili y o segmen
swi h a sho e con ex h′. We use a big am model, so
he ini ial con ex halways consis s o a single p eceding
segmen , and h′is he emp y con ex .
When no sho e con ex emains, he base dis ibu ion
is he “inne ” one-le el model, which compu es he p ob-
abili y o a segmen composed o ones 1, . . . , kas:
p( 1. . . k) = Qk
i=1 p( i| 1. . . i−1)
p(k)·Po(k|λ),(2)
whe e p( i| 1. . . i−1)is he one-le el p obabili y com-
pu ed by ma ginalizing o e all possible con ex leng hs n:
p( |h) =
∞
X
n=0
p( |h, n)·p(n|h),(3)
He e, p( |h, n)is he p obabili y o one gi en one
con ex ha dep h n(i.e., he las n ones o he con ex
a e conside ed). This is compu ed using Equa ion 1, bu
applied a he one le el wi h a uni o m base dis ibu ion
5PY di e s om CRP by applying a cons an discoun o able coun s,
slowing he decay o he “densi y budge ” o new ables.
o e ones. The e m p(n|h)deno es he p obabili y ha
con ex hhas o de n.Po(k|λ)is he Poisson co ec ion
o p e en sho segmen s om being o e - a o ed [39].
Fu he ma hema ical de ails can be ound in he o iginal
o mula ions o he model [35,39].
The model is ained using blocked Gibbs sampling.
Ini ially, each melody is assigned a andom segmen a ion.
In each sampling s ep, a andomly selec ed segmen ed
melody is emo ed om he model, all i s possible seg-
men a ions a e e alua ed wi h eqs. (1)–(3) using he cu -
en s a e o he model, and a new segmen a ion is sam-
pled om hem. The model is hen upda ed wi h he newly
sampled segmen a ion. Du ing in e ence, op imal segmen-
a ion is compu ed using he Vi e bi algo i hm.
3.3 Mode-speci ic segmen a ion
Each mode may ha e i s own cha ac e is ic melodic uni s
and segmen a ion pa e ns [16, 17]. We ex end he NH-
PYLM model o accoun o his by aining sepa a e seg-
men a ion models o each mode, as hough one we e
lea ning he epe oi e in 8 sepa a e sub-co po a.
A in e ence ime (i.e., when analyzing new chan s), he
mode o a chan cis unknown. Howe e , we can use all
eigh mode-speci ic models (each es ima ing p(¯c|m), he
likelihood o he op imal segmen a ion ¯cunde mode m) o
de e mine he mos p obable mode m∗= a g maxmp(m|
c)gi en he melody c, using Bayes’ Theo em. 6We e e
o he combined model as NHPYLMClasses.
3.4 F om Melody Segmen s o Modes
Gi en he in e ac ion be ween mode, melodic simila i y,
and memo isa ion [13], mode classi ica ion based on in-
e ed segmen s can se e as a p oxy o segmen a ion
quali y. Howe e , aside om he NHPYLMClasses model,
his “amoun o in o ma ion e ained abou mode” mus be
ob ained in a sepa a e downs eam s ep.
To ensu e compa abili y wi h p e ious wo k, we adop
he same mode classi ica ion pipeline used in ea lie s ud-
ies o chan segmen a ion and modali y [7, 13]. Each
melody is ep esen ed as a bag-o -segmen s ec o . Al-
hough sequen ial in o ma ion is no explici ly encoded,
segmen s a e in e ed using a model ha conside s se-
quence con ex , so some in o ma ion abou o de is implic-
i ly p ese ed. TF-IDF weigh ing is applied o he ec o s.
Following se ings used in p e ious wo k on chan seg-
men a ion [7], only he 5000 mos equen segmen s a e
e ained, wi h o he s disca ded. The esul ing ec o ized
segmen a ions om he aining melodies a e hen used o
ain a Linea SVM classi ie o p edic chan modali y.
4. DATASETS
We use he Can usCo pus 0.2 da ase [15], de i ed om
he Can us Da abase [14], he mos ex ensi e digi al col-
lec ion o G ego ian chan s. We ocus on he wo mos
abundan gen es: an iphons and esponso ies. An iphons
6Ma hema ical and implemen a ion de ails a e a ailable a :
h ps://gi hub.com/lanz /chan -modali y-wi h-nhpylms
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640
Can usCo pus 0.2 da a Pi ches In e als
An . Res. An . Res.
Classical app oach 89.6 89.4 – –
4-g am 91.0 91.6 82.0 83.1
Syllables 89.3 93.5 72.9 89.3
Wo ds 90.1 90.2 83.9 87.2
NHPYLM 91.7 93.3 86.7 89.7
NHPYLM-Cl, no SVM 92.6 93.8 90.4 92.4
NHPYLM-Cl 92.7 93.9 90.2 92.4
O e lapping n-g ams, 1-7 93.8 94.8 90.4 92.8
Table 1: F1 sco es o a ious mode classi ica ion me hods
applied o all an iphon and esponso y melodies, encoded
as bo h sequences o pi ches and sequences o in e als.
S .de . ac oss he 5 spli s was be ween 0.001 and 0.005, so
di e ences o an F1-sco e o 1.0 is “sa e” a 1.96σ.
a e simple and sho e melodies, while esponso ies a e
mo e complex and longe . We apply he same p ep ocess-
ing s eps as used in p e ious wo k [7], keeping only com-
ple ely ansc ibed melodies wi h simple mode anno a ions
(1–8), and disca ding non-pi ch cha ac e s om Volpiano
encoding. C ucially, we also emo e di e en iae om an-
iphons [13]. A e he desc ibed il a ion p ocess [7, 13],
a o al o 13551 an iphons and 7031 esponso ies emain.
Because esponso ies a e longe (137.38 pi ches on a e -
age s. 53.97 o an iphons), he esponso y da ase is
longe , a 966k no es, wi h an iphons a 731k no es.
The Can usCo pus also con ains mul iple e sions o
he same melody i i is ound in mul iple ansc ibed
sou ces. Al hough hese a e almos ne e iden ical [23,24],
his s ill means closely ela ed melodies could end up in
bo h he es and aining se s. While we could ensu e his
does no happen using he Can usID mechanism [14], he
abundances o di e en melodies would s ill dis o esul s
i p esen in he es se , and dis o op imisa ion i p esen
in he aining se . We p opose using melodies om a sin-
gle sou ce. This esembles he si ua ion o any chan p ac-
i ione : hey would be expec ed o lea n hei local epe -
oi e. We chose he la ges a ailable manusc ip , D-KA
Aug. LX,7, wi h 1965 an iphons and 907 esponso ies.
5. MODE CLASSIFICATION EXPERIMENTS
In his sec ion, we desc ibe expe imen s on he Can usCo -
pus da ase . Bo h NHPYLM-based me hods a e con igu ed
wi h segmen leng hs anging om 1 o 7 ones using de-
aul hype pa ame e s: d0= 0.5; max. segmen leng h o
7; ini ial θ= 2.0 o inne hype pa ame e upda es [39];
Gamma p io s on bo h dand θwi h α= 1.0, β = 1.0; and
a Gamma p io o he Poison co ec ion pa ame e wi h
ini ial αλ= 6.0, βλ= 1.2.810% o he aining da a is
ese ed as a alida ion se o checking o con e gence
o NHPYLM-based models.
Because ela i e pi ch has g ea e saliency han absolu e
pi ch [42, p.56,p.100], in addi ion o pi ch sequences om
7h ps://can usda abase.o g/sou ce/123612
8See also Supplemen a y ma e ials – NHPYLM implemen a ion.
cleaned Can usCo pus melodies, we also use sequences o
in e als (which hus ha e a leng h o n−1).
Fo all expe imen s, we use a 7:3 ain- es spli o bo h
NHPYLM-based models and he SVM classi ie . In he
case o NHPYLM and NHPYLMClasses models, aining
da a is used o lea n he op imal p obabili y dis ibu ion,
and he esul ing segmen ed aining da a is hen used o
ain he SVM classi ie . (This is why he ain- es spli
is necessa y also o he unsupe ised me hods.) Du ing
e alua ion, he es se is i s segmen ed by he NHPYLM
models, a e which he SVM classi ie p edic s he modes.
5.1 E alua ion
We e alua e how well he p oposed segmen a ion me h-
ods e ain modal in o ma ion by using in e ed segmen s
as ea u es in a mode classi ica ion ask. This app oach
is musicologically jus i ied, gi en he ela ionship be ween
modali y and memo y [4,13, ch. 3], and has been used be-
o e [7]. We epo mic o-a e aged F1-sco es in Tables 1
and 2. Fo NHPYLMClasses, we also epo he model’s
“in e nal” classi ica ion pe o mance, i.e., accu acy based
on mode m∗= a g maxmp(m|c)selec ed du ing in e -
ence, alongside SVM esul s using he in e ed segmen s.
Baselines. P e ious wo k [7] segmen ed chan s using
n-g ams, neumes, syllables, o wo ds. We adop hei bes -
pe o ming segmen a ions as baselines: 4-g ams, syllables,
and wo ds. We also include he Classical app oach as a
baseline, which classi ies modes based on ini ial and inal
ones along wi h he melody ange [7].
Uppe bound. We do no know wha he maximum
achie able mode-classi ica ion pe o mance o e any seg-
men a ion is. The mode o which a melody belongs
may no be solely de e mined by he melody i sel : some
melodies a e assigned o di e en modes in di e en ona -
ies [8]. We a leas make a ough es ima e o he up-
pe bound o mode classi ica ion pe o mance ha can
be achie ed using a “dis ibu ional app oach” [7] and he
SVM classi ie as a easonable “in o ma ion ex ac ion”
black box. In his se ing, we use all possible o e lapping
n-g ams o leng hs 1 o 7 as ea u es. Thus, mo e in o ma-
ion is a ailable o he classi ie han o any segmen a ion
(wi h TF-IDF p ep ocessing o limi he e ec o many un-
in o ma i e ea u es). We e e o his app oach as O e -
lapping n-g ams, 1-7. Al eady o e lapping 4-g ams ou -
pe o med all p e ious esul s [13].
C oss- alida ion. Each expe imen was epea ed i e
imes wi h di e en andom seeds o a 70-30 andom spli
o e he en i e da ase . While he spli is no explici ly
s a i ied by mode, a e aging esul s o e mul iple andom
spli s helps mi iga e po en ial imbalances and ensu es mo e
obus pe o mance es ima es.
5.2 Resul s
Mode classi ica ion o Can usCo pus an iphons and e-
sponso ies is shown in Table 1. Two ep esen a ions a e
used: sequences o pi ches and sequences o in e als.
Ac oss all ou se ings, NHPYLMClasses ou pe -
o med all baselines, hough he syllable baseline on e-
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
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D-KA Aug. LX da a Pi ches In e als
(Single manusc ip ) An . Res. An . Res.
Classical app oach 85.5 81.9 – –
4-g am 82.1 77.8 70.7 64.5
Syllables 83.3 82.8 61.0 71.7
Wo ds 78.8 70.4 64.1 61.9
NHPYLM 86.0 83.6 73.3 72.6
NHPYLM-Cl, no SVM 85.3 84.0 80.2 78.6
NHPYLM-Cl 86.1 83.6 79.9 78.5
O e lapping n-g ams, 1-7 87.0 86.9 81.1 76.8
Table 2: Mode classi ica ion sco es o an iphon and e-
sponso y melodies om he manusc ip D-KA Aug. LX,
encoded bo h as sequences o pi ches and in e als.
sponso ies wi h absolu e pi ches comes close. No ably, he
SVM showed no imp o emen o e he model’s in e nal
p(m|c), in line wi h he heo y ha modes se e o o ganise
epe oi e also in memo y [4, ch. 3]. The base NHPYLM
model was sligh ly wo se, bu did ou pe o m all baselines
excep o syllables on esponso ies wi h absolu e pi ches
( hough again ba ely), u he sugges ing ha despi e ha -
ing mo e da a o es ima e a good ep esen a ion, condi ion-
ing on mode would ha e been a mo e e ec i e p inciple o
o ganising epe oi e in memo y. NHPYLMClasses also
comes e y close o he “uppe bound” o e lapping n-g am
pe o mance, sugges ing ha he e may no be much oom
o imp o emen on mode classi ica ion.
6. REMEMBERING A MANUSCRIPT
We now conside a compu a ional scena io inspi ed by a
monk needing o memo ise melodies o he li u gical en-
i onmen he belongs o. In ou case, his would be in la e
medie al Zwie al en, documen ed by he li u gical book D-
KA Aug. LX. Suppose he monk has al eady lea ned 70%
o he melodies ( aining se ): how di icul is i hen o
memo ise he emaining ones?
6.1 Mode classi ica ion in a single manusc ip
Table 2 shows ha segmen a ion based on NHPYLM-
Classes is again he mos accu a e model o mode classi-
ica ion and, on esponso ies wi h in e al ep esen a ions,
ou pe o ms he “chea ing” o e lapping n-g ams ea u es,
wi h i s in e nal mode classi ie pe o ming sligh ly be e
han an SVM on op o he esul ing segmen a ions.
The d op in pe o mance compa ed o expe imen s on
he ull Can usCo pus may ha e wo main easons: i s ,
i is a much smalle da ase , and second, only e y ew
Can us IDs ha e mul iple ins ances in one li u gical book,
so i elimina es issues wi h mul iple e sions o a melody
andomly assigned o bo h he aining and es se s. To
isola e hese in luences, we an wo sepa a e expe imen s:
(1) assigning all ins ances o a Can us ID only o one o
he ain/de / es se s; (2) uni o mly subsampling Can us-
Co pus o he size o D-KA Aug. LX. In expe imen (1),
3% o pe o mance was los , and in (2), 4%. This co -
esponds su p isingly well o he app oxima ely 7% d op
Pe plexi y on D-KA Aug. LX An iphons Resps.
NHPYLM—in e als 20.0 17.7
NHPYLMClasses—in e als 16.1 14.3
NHPYLM—pi ches 15.4 13.5
NHPYLMClasses—pi ches 11.8 9.9
Table 3: Pe plexi ies o PY-based segmen a ions on pi ch
and in e al melody encodings on D-KA Aug. LX.
o e all (wi h pi ch ep esen a ion). 9
6.2 Pe plexi y
We ha e so a been measu ing segmen a ion quali y in-
di ec ly, ia mode classi ica ion. Howe e , we can also
measu e i s memo isa ion e iciency di ec ly h ough pe -
plexi y, a common me ic in language modelling [43] ha
ollows di ec ly om Shannon’s coding heo em, and so
is a measu e o comp ession (lowe is be e ). In ui i ely,
i e lec s he model’s a e age unce ain y - he numbe o
equally likely choices i has a each s ep. I is de ined as:
pe plexi y(s1. . . sN) = 2−1
NPN
i=1 log2p(si|hi),
whe e siis he i- h segmen o he gi en segmen a ion and
hiis i s con ex .
Table 3 compa es he pe plexi y o he models. NH-
PYLMClasses leads o mo e e icien memo isa ion o
melody han he s anda d NHPYLM me hod. 10 In e es -
ingly, an iphons appea o be mo e challenging o e ec-
i e segmen a ion han esponso ies. This is qui e in line
wi h he di icul y in iden i ying melodic amilies in an-
iphons [3, 12], and con e sely he ac ha melodic o -
mulas we e i s desc ibed in esponso ies [1,44,45].
Addi ionally, pi ch ep esen a ion appea s easie o e-
membe compa ed o in e al ep esen a ion, e en hough
hei s a e space is la ge . This may be because in he in-
e al ep esen a ion, he same segmen can occu a di -
e en posi ions in he pi ch sys em ( -g- - equi alen o
d-e-d-d), so he condi ional en opy o i s con inua ion can-
no dec ease as much. I is also in line wi h pe o mance
p ac ice: singe s should ha e been always awa e o which
pi ch wi hin he sys em hey we e singing, as e idenced
by p e alen echniques such as he Guidonian hand [4,
ch. 6] [1, p.469] and solmisa ion [1, pp.467–468].
We ind a co ela ion be ween pe plexi y alues in Ta-
ble 3 and he co esponding mode classi ica ion sco es in
Table 2 o −0.77 (and o e −0.88 wi hin he gen es indi-
idually), o e ing ini ial empi ical suppo o he hypo h-
esised ela ionship be ween modali y and e icien memo-
isa ion, consis en wi h his o ical pe spec i es [13].
6.3 Modal Iden i y and Memo iza ion in Segmen s
Is modali y, o mulaici y, and hus “cen onisabili y” mo e
p ominen in some pa s o he melody han o he s, and
does i ela e o mode? This ques ion ela es o mode
9See gi hub.com/lanz /chan -modali y-wi h-nhpylms.
10 Though unde MDL one should penalize i o ha ing 8 ocabula ies
ins ead o a single sha ed one.
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
642
Figu e 1: Dis ibu ion o a e age segmen leng h (o ange;
alues igh ) and a e age segmen modal uniqueness (blue;
alues le ) ac oss ela i e posi ions in melodies. No e he
di e ence in segmen leng h scales – esponso ies a e mo e
o mulaic. The legend in he an iphon plo applies o bo h.
and pe o mance p ac ice. An an iphon was sung be o e
and a e a psalm, and psalms we e sung on one o jus
a ew simple psalm ones highly speci ic o indi idual
modes. So, i would ha e been app op ia e o he end
(1s an iphon pe o mance) and beginning (2nd an iphon
pe o mance) o ha e a “compa ible” melody a i s in e -
aces wi h he psalm one o which i was assigned (as e -
idenced, again, by ona ies). Fo he esponso ies, ins ead
o a psalm he e is a esponso y e se, which s ill has el-
a i ely ew melodies o each mode bu mo e han psalm
ones, and a e he e se o en only he second hal o he
esponso y ( he “ espond”) would be sung.
We plo he a e age segmen leng h in which a no e a a
gi en ela i e posi ion in he chan melody pa icipa es in
Figu e 1 (o ange). High a e age segmen leng h indica e
mo e o mulaic melodies. Fo an iphons, we see a small
spike in segmen leng h a bo h ends; o esponso ies, we
see a mo e p ominen spike a he end, co esponding well
o he espec i e pe o mance con ex s.
The a e age uniqueness o he disco e ed segmen s o
indi idual modes (Figu e 1, in blue) is no as s uc u ed.
Fo he an iphons, we see a spike in uniquess a he begin-
ning, which co esponds o singing he an iphon a e he
psalm, bu a he end o he an iphon (co esponding o he
s a o he psalm, and highes o mulaici y) modal unique-
ness d ops ye lowe . Howe e , psalm ones o some mode
pai s ha e an iden ical o nea -iden ical s a [1, p. 59–60],
so he pe o mance con ex makes unique o mulas less
likely.
Figu e 2: Compa ing segmen a ion pa e ns: (a) wo ou -
pu s o ou model—a ypical case and a a e , mo e “cen-
onised” one; (b) segmen a ion p oposed by Le y [17].
7. CONCLUSIONS
Building on he memo isa ion o G ego ian chan , we ake
an in o ma ion- heo e ic app oach and implemen NH-
PYLMs o unsupe ised melodic segmen a ion. The e-
sul ing segmen a ions achie e s a e-o - he-a mode classi-
ica ion on Can usCo pus 0.2, and in a “monk simula ion”
using D-KA Aug. LX, also e eal how pe o mance con-
ex s shape o mulaici y and modal iden i y.
The co ela ion en a i ely ound be ween pe plexi y, as
“ease o memo isa ion”, and mode classi ica ion F1-sco e
is ini ial empi ical e idence o he ela ionship be ween
melody segmen a ion and modali y, in acco dance wi h he
music-his o ical a gumen o his link [4, 7, 13]. Pilo
expe imen s wi h o he melody encodings 11 sugges his
holds ac oss condi ions, wa an ing u he s udy.
Memo y e iciency o baseline segmen a ions could be
app oxima ed wi h a big am language model wi h In e po-
la ed Knese -Ney smoo hing [46] ained on he op imal
segmen a ions. KN smoo hing is closely ela ed o he PY
p ocess [35]. Pilo esul s showed i s pe plexi y di e ed by
no mo e han 0.5 om NHPYLM’s on D-KA Aug. LX.
NHPYLMs can p o ide memo y-based segmen a ions
o o he epe oi es – bo h o de ec cen onisa ion whe e i
is musicologically known o exis [25,26,29], and o enable
in o ma ion- heo e ic compa isons wi h G ego ian chan .
Howe e , sui able da ase s a e needed i s .
Howe e , despi e all he easons o belie e G ego ian
chan could be cen onised, and despi e he empi ical in-
dica ions o a close ela ionship be ween segmen a ion,
memo y, and modali y, he disco e ed op imal segmen s
a e a om a con incing cen onisa ion o chan . Compa -
ing a ypical model ou pu , and an ou pu wi h maximum
o mulaici y, wi h cen onisa ion p oposed in chan schola -
ship in Figu e 2, we see ha he disco e ed segmen a ion
pa e ns a e a mo e agmen a y han wha has been p o-
posed o G ego ian chan [17] and wha is known om
Byzan ine o mulae [26]. 12 This opens he in iguing pos-
sibili y ha ins i u ional ules and p ac ices we e able o
signi ican ly coun e ac p ocesses inhe en in o al ans-
mission, making he e olu iona y p ocesses o G ego ian
chan di e en om o he musical adi ions. The mys e y
o cons uc ing G ego ian melodies emains un esol ed.
11 E.g., collapsing epea ed no es – see esul s in he Supplemen a ies.
12 Full segmen a ion esul s on D-KA Aug. LX a e a ailable in Supple-
men a y ma e ials.
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
643
8. ACKNOWLEDGMENTS
The au ho s a e suppo ed by he Social Sciences and Hu-
mani ies Resea ch Council o Canada by he g an no. 895-
2023-1002, Digi al Analysis o Chan T ansmission, and
by he SVV p ojec numbe 260 698. The second au-
ho addi ionally acknowledges he suppo by he p ojec
“Human-cen ed AI o a Sus ainable and Adap i e So-
cie y” ( eg. no.: CZ.02.01.01/00/23_025/0008691), co-
unded by he Eu opean Union. The compu ing in as-
uc u e is p o ided by he LINDAT/CLARIAH-CZ Re-
sea ch In as uc u e (h ps://linda .cz), suppo ed by he
Minis y o Educa ion, You h and Spo s o he Czech Re-
public (P ojec No. LM2023062).
9. ETHICS STATEMENT
This s udy did no in ol e human pa icipan s, pe sonal
da a, o sensi i e in o ma ion. All da a consis s o an-
sc ip ions o publicly a ailable his o ical sou ces. No con-
ce ns ela ed o p i acy, consen , o bias apply. We, how-
e e , no e ha we aim o con ibu e o he unde s anding o
chan wi hou ein o cing any cul u al o eligious biases;
ou wo k in no way implies ha G ego ian chan ha ing
di e en ansmission pa e ns would be a alue judgmen .
10. DATA AND CODE ACCESSIBILITY
The Can usCo pus 0.2 da ase [15] ha we
used is a ailable a : h ps://gi hub.com/
baco /can usco pus/ eleases/ ag/ 0.2
The NHPYLM model code is a ailable a :
h ps://gi hub.com/lanz /nhpylm. The
expe imen code, including mo e de ailed esul s, is
a ailable a : h ps://gi hub.com/lanz /
chan -modali y-wi h-nhpylms.
11. REFERENCES
[1] D. Hiley, Wes e n plainchan : a handbook. Ox o d,
Uni ed Kingdom: Cla endon P ess, 1993.
[2] R. Hallas, Two hymed o ices composed o he eas o
he Visi a ion o he Blessed Vi gin Ma y: compa a i e
s udy and c i ical edi ion. Bango Uni e si y (Uni ed
Kingdom), 2021.
[3] P. Me kley, “Tona ies and melodic amilies o
an iphons,” Jou nal o he Plainsong and Medi-
ae al Music Socie y, ol. 11, p. 13–24, Jan.
1988. [Online]. A ailable: h p://dx.doi.o g/10.1017/
S0143491800001136
[4] C. M. A kinson, The c i ical nexus: one-sys em, mode,
and no a ion in ea ly medie al music. Ox o d Uni e -
si y P ess, 2008.
[5] J. Glasenapp, To P ay wi hou Ceasing: A Diach onic
His o y o Cis e cian Chan in he Beaup é An-
iphone (Bal imo e, Wal e s A Museum, W. 759–
762). Columbia Uni e si y, 2020.
[6] M. Huglo, “Les onai es,” In en ai e, Analyse, Com-
pa aison. Pa is: Socié é ançaise de musicology, pp.
132–40, 1971.
[7] B. Co nelissen, W. H. Zuidema, and J. A. Bu goyne,
“Mode classi ica ion and na u al uni s in plainchan .”
in P oceedings o he 21s In . Socie y o Music In o -
ma ion Re ie al Con ., Mon eal, Canada, 2020, pp.
869–875.
[8] H. Mo i, Con lic ing modal assignmen s o o ice an-
iphons: A compa a i e s udy o se en Ge manic
sou ces. Na ional Lib a y o Canada= Biblio heque
na ionale du Canada, O awa, 2001.
[9] K. Helsen, “The use o melodic o mulas in espon-
so ies: cons ancy and a iabili y in he manusc ip a-
di ion,” Plainsong & Medie al Music, ol. 18, no. 1,
pp. 61–76, 2009.
[10] T. Ka p, Aspec s o o ali y and o mula i y in G ego-
ian chan . No hwes e n Uni e si y P ess, 1998.
[11] K. Helsen, M. Daley, and J. Schindle , “The s icky
i : Quan i ying he melodic iden i ies o medie al
modes,” Empi ical Musicology Re iew, ol. 16,
no. 2, p. 312–325, Ma . 2023. [Online]. A ailable:
h p://dx.doi.o g/10.18061/em . 16i2.7357
[12] F.-A. Ge ae , La Mélopée An ique dans le Chan de
l’Église La ine. Ad. Hos e, 1895.
[13] V. Lanz and J. Hajiˇ
c, “Tex bounda ies do no p o ide
a be e segmen a ion o g ego ian an iphons,” in P o-
ceedings o he 10 h In e na ional Con e ence on Dig-
i al Lib a ies o Musicology, 2023, pp. 72–76.
[14] D. Lacos e, “The Can us Da abase and Can us Index
Ne wo k,” in The Ox o d Handbook o Music and
Co pus S udies. Ox o d Uni e si y P ess, 2022.
[Online]. A ailable: h ps://doi.o g/10.1093/ox o dhb/
9780190945442.013.18
[15] B. Co nelissen, W. Zuidema, and J. A. Bu goyne,
“S udying la ge plainchan co po a using chan 21,” in
7 h In e na ional Con e ence on Digi al Lib a ies o
Musicology, 2020, pp. 40–44.
[16] P. Fe e i, Es e ica g ego iana: ossia, T a a o
delle o me musicali del can o g ego iano, se .
Es e ica g ego iana: ossia, T a a o delle o me
musicali del can o g ego iano. Pon i icio is i u o di
musica sac a, 1934, no. s . 1. [Online]. A ailable:
h ps://books.google.cz/books?id= OWCnQEACAAJ
[17] K. Le y, “The i alian neophy es’ chan s,” Jou nal o
he Ame ican Musicological Socie y, ol. 23, no. 2, pp.
181–227, 1970.
[18] L. T ei le , “Cen ona e" chan :" übles lickwe k" o " e
plu ibus unus?” Jou nal o he Ame ican Musicologi-
cal Socie y, ol. 28, no. 1, pp. 1–23, 1975.
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
644
[19] H. Hucke, “Towa d a new his o ical iew o g ego ian
chan ,” Jou nal o he Ame ican Musicological Socie y,
ol. 33, no. 3, pp. 437–467, 1980.
[20] D. Shanahan and J. Alb ech , “Examining he e ec o
o al ansmission on olksongs,” Music Pe cep ion: An
In e disciplina y Jou nal, ol. 36, no. 3, pp. 273–288,
2019.
[21] M. Anglada-To , P. M. Ha ison, and N. Jacoby,
“S udying he e ec o o al ansmission on melodic
s uc u e using online i e a ed singing expe imen s,”
bioRxi , pp. 2022–05, 2022.
[22] T. Popescu and M. Roh meie , “Co e p inciples
o melodic o ganisa ion eme ge om ansmission
chains wi h andom melodies,” E olu ion and Hu-
man Beha io , ol. 45, no. 6, p. 106619, 2024.
[Online]. A ailable: h ps://www.sciencedi ec .com/
science/a icle/pii/S1090513824000953
[23] D. J. F oge , “The c i ical edi ion o he oman g adual
by he monks o solesmes,” Jou nal o he Plainsong &
Mediae al Music Socie y, ol. 1, pp. 81–97, 1978.
[24] J. Hajiˇ
c j ., G. A. Ballen, K. H. Mühlo á, and
H. Vlho á-Wö ne , “Towa ds Building a Phylogeny o
G ego ian Chan Melodies,” in P oceedings o he 24 h
In e na ional Socie y o Music In o ma ion Re ie al
Con e ence. ISMIR, Dec. 2023, pp. 571–578.
[Online]. A ailable: h ps://doi.o g/10.5281/zenodo.
10340442
[25] T. Nu all, M. Ga cía Casado, V. Núñez Ta i a,
R. Ca o Repe o, and X. Se a, “Con ibu ing o new
musicological heo ies wi h compu a ional me hods:
he case o cen oniza ion in A ab-Andalusian music,”
in 20 h Con e ence o he In e na ional Socie y o Mu-
sic In o ma ion Re ie al (ISMIR 2019): 2019 No 4-
8; Del , The Ne he lands.[Canada]: ISMIR; 2019. p.
223-8. In e na ional Socie y o Music In o ma ion
Re ie al (ISMIR), 2019.
[26] E. Wellesz, “Wo ds and music in byzan ine li u gy,”
The Musical Qua e ly, ol. 33, no. 3, pp. 297–310,
1947.
[27] T. H. Connolly, “In oi s and a che ypes: Some a -
chaisms o he old oman chan ,” Jou nal o he Ame i-
can Musicological Socie y, ol. 25, no. 2, pp. 157–174,
1972.
[28] J. Dye , “T opis sempe a ian ibus: Composi ional
s a egies in he o e o ies o old oman chan ,” Ea ly
Music His o y, ol. 17, pp. 1–60, 1998.
[29] M. Huglo, “The old bene en an chan ,” S udia Musi-
cologica Academiae Scien ia um Hunga icae, ol. 27,
no. Fasc. 1/4, pp. 83–95, 1985.
[30] S. Chak abo y, S. Tewa i, A. Rahman, M. Jamal,
A. Lipi, A. Chak abo y, A. Nanda, and P. Shukla,
Hindus ani classical music: a his o ical and compu-
a ional s udy. Sanc um Books, 2021.
[31] J. Rissanen, S ochas ic complexi y in s a is ical in-
qui y. Wo ld scien i ic, 1998, ol. 15.
[32] P. D. G ünwald, The minimum desc ip ion leng h p in-
ciple. MIT p ess, 2007.
[33] A. R. Ba on and T. M. Co e , “Minimum complexi y
densi y es ima ion,” IEEE ansac ions on in o ma ion
heo y, ol. 37, no. 4, pp. 1034–1054, 1991.
[34] S. Goldwa e , T. L. G i i hs, and M. Johnson, “A
bayesian amewo k o wo d segmen a ion: Ex-
plo ing he e ec s o con ex ,” Cogni ion, ol.
112, no. 1, pp. 21–54, 2009. [Online]. A ail-
able: h ps://www.sciencedi ec .com/science/a icle/
pii/S0010027709000675
[35] Y. W. Teh, “A bayesian in e p e a ion o in e pola ed
knese -ney,” School o Compu ing, Na ional Uni e -
si y o Singapo e, Technical Repo TRA2/06, 2006.
[36] O. Wal e , R. Haeb-Umbach, S. Chaudhu i, and B. Raj,
“Unsupe ised wo d disco e y om phone ic inpu us-
ing nes ed pi man-yo language modeling,” in ICRA
Wo kshop on Au onomous Lea ning, 2013.
[37] R. Takeda, K. Koma ani, and A. I. Rudnicky, “Wo d
segmen a ion om phoneme sequences based on
pi man-yo semi-ma ko model exploi ing subwo d in-
o ma ion,” in 2018 IEEE Spoken Language Technol-
ogy Wo kshop (SLT). IEEE, 2018, pp. 763–770.
[38] T. A aki, T. Nakamu a, T. Nagai, S. Nagasaka,
T. Taniguchi, and N. Iwahashi, “Online lea ning o
concep s and wo ds using mul imodal lda and hie a -
chical pi man-yo language model,” in 2012 IEEE/RSJ
In e na ional Con e ence on In elligen Robo s and
Sys ems. IEEE, 2012, pp. 1623–1630.
[39] D. Mochihashi, T. Yamada, and N. Ueda, “Bayesian
unsupe ised wo d segmen a ion wi h nes ed Pi man-
Yo language modeling,” in P oceedings o he
Join Con e ence o he 47 h Annual Mee ing o
he ACL and he 4 h In e na ional Join Con e ence
on Na u al Language P ocessing o he AFNLP.
Sun ec, Singapo e: Associa ion o Compu a ional
Linguis ics, Aug. 2009, pp. 100–108. [Online].
A ailable: h ps://aclan hology.o g/P09-1012
[40] S. Sawada, K. Yoshii, and K. Hi a a, “Unsupe ised
melody segmen a ion based on a nes ed Pi man-
Yo language model,” in P oceedings o he 1s
Wo kshop on NLP o Music and Audio (NLP4MusA),
S. O amas, L. Espinosa-Anke, E. Epu e, R. Jones,
M. So do, M. Quad ana, and K. Wa anabe, Eds.
Online: Associa ion o Compu a ional Linguis ics,
16 Oc . 2020, pp. 59–63. [Online]. A ailable:
h ps://aclan hology.o g/2020.nlp4musa-1.12/
[41] J. Pi man and M. Yo , “The wo-pa ame e
poisson-di ichle dis ibu ion de i ed om a s a-
ble subo dina o ,” The Annals o P obabili y,
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
645
ol. 25, no. 2, Ap . 1997. [Online]. A ailable:
h p://dx.doi.o g/10.1214/aop/1024404422
[42] S. Hallam, I. C oss, and M. Thau , Eds., The ox o d
handbook o music psychology, 2nd ed., se . Ox o d
Lib a y o Psychology. London, England: Ox o d
Uni e si y P ess, Dec. 2017.
[43] F. Jelinek, “Sel -o ganized language modeling o
speech ecogni ion,” Readings in speech ecogni ion,
pp. 450–506, 1990.
[44] W. H. F e e, An iphonale Sa isbu iense: a ep oduc-
ion in acsimile o a manusc ip o he 13 h cen u y,
wi h a disse a ion and analy ical index. G egg P ess
Limi ed, 1901.
[45] K. E. Helsen, “The g ea esponso ies o he di ine o -
ice: aspec s o s uc u e and ansmission,” Ph.D. dis-
se a ion, 2008.
[46] H. Ney, U. Essen, and R. Knese , “On s uc u ing
p obabilis ic dependences in s ochas ic language
modelling,” Compu e Speech & Language, ol. 8,
no. 1, p. 1–38, Jan. 1994. [Online]. A ailable:
h p://dx.doi.o g/10.1006/csla.1994.1001
P oceedings o he 26 h ISMIR Con e ence, Daejeon, Ko ea, Sep embe 21-25, 2025
646
