On melodical similarity in versions of a Swedish ... - Semantic Scholar

Dept. for Speech, Music and Hearing

Quarterly Progress and Status Report

On melodical similarity in versions of a Swedish folk-tune Sundberg, J.

journal: volume: number: year: pages:

STL-QPSR 16 2-3 1975 061-066

http://www.speech.kth.se/qpsr

61.

S T L - Q P S R 2-311975

B. ON MELODICAL SIMILARITY I N VERSIONS O F A SWEDISH FOLK- TUNE J. Sundberg Abstract

&

.

A set of different versions of the Swedish folk-tune "Fiskeskarsvisan" collected by Moberg i s studied a s r e g a r d s the question why they a r e felt to be melodically similar. The observations of common elements made in an analysis of the melodies a r e integrated into a rule system by means of which new versions of the folk-tune can be generated. The rule system shows that signaling the constituent structure i s important, and that melodical similarity s e e m s to be closely related to the marking of constituents and the prominence values of the notes.

i

STL-QPSR 2-3/1975 Introduction Variation, sequencing, thematical r e l a t i o n a s well a s m u s i c a l style a r e used to denote different d e g r e e s o r k i n d s of s i m i l a r i t y i n m u s i c t h e o r y , and m o s t of u s will a g r e e t h a t s i m i l a r i t y p l a y s a v e r y important r o l e i n composing and perceiving m u s i c .

The phenomenon of s i m i l a r i t y

s e e m s to be r e g a r d e d a s a self-evident psychological fact, which is experienced by a l l music-minded p e r s o n s .

Still, the phenomenon a s such

s e e m s to be weakly explored f r o m the side of m u s i c theory. rather remarkable.

This is

On the one hand, s i m i l a r i t y is a b a s i c phenomenon

i n m u s i c and we r e a d i l y recognize when and w h e r e i t a p p e a r s .

On t h e

other hand, we a r e not able to t e l l explicitely what conditions should be fulfilled i n o r d e r to evoke t h i s phenomenon, and consequently our understanding of this b a s i c phenomenon m u s t be s a i d to be r a t h e r poor. Moberg (1950) h a s collected a l a r g e number of folk-tunes which a c cording to h i m have a common origin. apparent melodical s i m i l a r i t y .

Moberg's support f o r t h i s i s their

Consequently, h i s m a t e r i a l m a y be useful

i n an investigation of what actually m a k e s two melodies sound s i m i l a r . The purpose of the p r e s e n t investigation i s to explore s o m e of the conditions that m u s t be fulfilled i f melodies shall be felt to be s i m i l a r .

These

conditions will be f o r m a l i z e d i n a r u l e s y s t e m which can be said to explicitely d e s c r i b e the s i m i l a r i t y observed i n the v e r s i o n s considered. The r u l e s y s t e m i s generative so that the type of s i m i l a r i t y which i t d e s c r i b e s can be d e m o n s t r a t e d by a s e t of generated v e r s i o n s of the

"Fiske s k a r svisan" . I

Data Fig. 111-B-I here.

shows the v e r s i o n s of the folk-song that will concern u s

They w e r e selected f r o m M o b e r g ' s m a t e r i a l on the c r i t e r i o n of

apparent melodical s i m i l a r i t y .

Ver sions with e x t r a b a r s i n s e r t e d , with

m a j o r changes i n the m e t e r , and s o on w e r e excluded. in F i g . 111-B- I

A l l the v e r s i o n s

have the function of a lullaby.

An a p p a r e n t common denominator of the songs is the p r e f e r e n c e i n half-notes a t the ends of the even-numbered b a r s .

Also, we note that

a l l melodies end on the fundamental of the tonic, and that a l l even-numb e r e d b a r s end on t h i s note o r on the fifth of the dominant. A c l o s e r a n a l y s i s of the songs r e v e a l s some additional common fea-

tures.

F i g . 111-B-2 gives a n overview of them.

Specific pitches, pitches

BAR NUMBER:

I

I

PITCH

2

1

I

3

I

I

1

I 1

1

INTERVAL re tolitwing

I I

I SING OF INTERVAL

IMPLlCATlON OF TONALITY

I

I

I

I

I I

a

I

I

i

I

5

4

I

I

I

!

I

r

I

I II

I

I

I

I

I

I

1

8

I

I

I

1

I

I

I

I

I

I

8

10

9

I 1 I

I

I

I

I

I

I

I

7

6

:

I

I I

I

I

I

I

.

I

I

I

I

I I

1

I

I

I

I

I

I

I

I

I I I I

I

I

I

I

I

1

I

I

Fig. 111-B-2. Occurrence of variour phenomena i n the melodies shown i n Fig. 111-B-I.

STL-QPSR 2-3/1975

63.

belonging to a specific chord, intervals between odd-number ed beats, and the direction of such intervals a r e invarbhLe in certain positions within the period.

Also, we see that the positions for these phenomena As was previously found to be the

form a regular pattern in the period.

case in some Swedish n u r s e r y tunes, the position within the period s e e m s to be an important factor even in this m a t e r i a l ( s e e Lindblom & Sundberg 1970). It s e e m s reasonable to interpret this segmentation a s an indica-

1

tion of a constituent structure. Rule svstem In order to account for these and other observations we need a generative rule system.

As t h e r e s e e m s to be good reasons for assuming

a constituent structure deciding which modifications that a r e allowed where, a mapping of the constituent structure and a generation of the

1

corresponding prominence contour a r e required. We propose that the melodies be regarded a s an 8-bar structure in which b a r s 5 and 6 a r e repeated once.

I

This a g r e e s with the observation

that, i n fact, b a r s 7 and 8 generally repeat b a r s 5 and 6 metrically and melodically, see Fig. 111-B- 1.

The transformation needed i s used so

often i n music that it h a s a special sign of i t s own,

1)

:

asymmetrical t r e e we obtain i s shown in Fig. I- B- 3.

:

1.

The slightly

I t depicts the

hierarchical o r d e r between the constituents: period, phrase, feet, and beat. Next step is to transform the t r e e diagram into a string of prominence values.

The derivation can be followed in Fig. 111- B-4.

i s exactly the same a s i n the case of the n u r s e r y tunes.

I

The procedure I I

Fir s t , each beat

i s assigned the prominence rank of 1 and each constituent i s embedded in l

a pair of parentheses.

Then, the innermost p a i r s of parentheses a r e

cyclically e r a s e d until1 all par entheses a r e eliminated.

Thereby, a s soon

a s two prominence ranks of 1 appear within the same parenthesis the leftmost o r rightmost has priority and r e t a i n s i t s prominence while a l l other prominence ranks f a l l one step.

Left priority i s applied a t the feet level,

and right priority on higher levels.

The final r e s u l t i s the prominence

contour shown in the bottom line of the figure.

This contour r e p r e s e n t s

the prominence relationships between the beats on a scale of integers where 1 i s the highest rank.

PE RlOD

PHRASE

SUBPHRASE

FEET

BEAT

Fig. m-B-3. Tree diagram illustrating the hierarchical order between the constituents of the melodies shown in Fig. 111-B-I .

64.

STL-QPSR 2-3/1975 The prominence ranks play a decisive role i n the rule system. r u l e system i s shown in Fig. I-B-5.

The

I t consists of two groups of r u l e s ,

one for tonality and melody, and one for the m e t e r . This i s r a t h e r natural,

The harmony i s rudimentary in this material.

since the song i s normally performed without any accompaniment. e v e r , certain r u l e s a r e followed.

How-

The introduction of the opening and

closing p h r a s e s and the beginning of the l a s t subphrase give chord notes of the tonic.

The end of each subphrase contains the fundamental of the

tonic o r the fifth of the dominant.

The main function of these few r u l e s I

seems to be to establish the tonality of the song.

.

The prominence values play an important role in the assignment of other pitches a s well.

The notes a r e treated in an order determined by

their prominence ranks.

With the prominence rank of four the distance

to the following note of higher prominence i s decisive to the order of tone assignment.

The prominence rank of five i s determined in relation to the

following note of higher prominence.

I t may be observed that the r u l e s

1

f o r this prominence rank a r e applied cyclically and a r e ordered in such a way that smaller intervals will occur m o r e often than l a r g e r intervals. When the tone assignment i s completed, the meter may be modified.

I

N o modifications a r e tolerated in the bar containing prominence 1, and no insertion of prominence 6 i s allowed in the bar containing prominence Prominences 3 and 4 may be divided into two notesif i t i s a half-note.

2.

If so, the extra note approaches the following by a scale tone step in accordance with the adjacency principle o r i t simply repeats the preceding note.

Inversely, a sequence of two identical pitches, the f i r s t of which

has the prominence of 4 may m e r g e together to a half note.

Remaining

notes of prominences 4 and 5 may be divided into two eighth notes provided that this gives a sequence of scale tone steps with o r without one repeti-

I

tion.

Another allowed alternative i s that the extra note fills in a fifth inter-

val.

These r e s t r i c t i o n s a s r e g a r d s insertion of eighth notes a r e the main

reason why the meter i s modified after the melody in the case of the folksong.

I

This seems logical in view of the fact that the melody i s used for

different texts. Generation As was pointed out before, our r u l e system does not r e p r e s e n t m o r e than a m e r e hypothetical description of the melodical similarity between

TONALITY AND MELODY

p = 3 .

p = 4

+ VofD A:

/-

5q,

q = I

identical

q = 2

I identical

q = 3

B:

/-

q = I

545q,

C

ID = 0

identical

(ID ID = 0

ID identical identical}

chord note of

T

C

identical ID identical identical but delayed by 1

p = 5 Interval r e . following is

S, adjacency p r i n c i p l e ? S3 03 3, adjacency principle?

JI

3? 4, adjacency principle ? 4? 5, adjacency principle?

5.

METER

p

=$!if '} 4/,5

q

¶

3: p

-

second note =

r e . following, adj.

p6 if this gives a sequence 01 S

*

one R

Fig. 111-B-5. The r u l e system used for generating the v e r s i o n s of the folk-song shown in Fig. 111- B- 6. The notes constituting a chord a r e given by their step number (e. g. V denoting the fifth) and the tonic chord by T and the dominant chord by D. I r e f e r s to the interval r e . the n e a r e s t following note of equal o r higher prominence, and ID r e f e r s to the direction of such intervals. S = s c a l e tone step, R=repetition.

STL-QPSR 2-3/1975

66.

the difficulties in separating r u l e s that m i r r o r stylistic f e a t u r e s f r o m r u l e s associated with melodical similarity. I t a p p e a r s that m o r e r e s e a r c h on style c h a r a c t e r i s t i c s

- in terms

of generative theories

-

is needed be-

f o r e such a separation can be made. Acknowledgments This work was supported by the Bank of Sweden Tercentenary Foundation, Contract No. 67/48. References LINDBLOM, B. and SUNDBERG, J. (1970): "Towards a generative theory of melodyt1, Svensk Tidskrift for Musikfor skning (Swedish J. of ~ u s i c o l o g ~ 52, ) , pp. 71-88.

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MOBERG, C-A. ( 1950): "Tvd kapitel om svensk folkmusiktt, Svensk Tids k r i f t for Musikfor skning (Swedish J . of ~ u s i c o l o g y ) ,32, pp. 5- 49.

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RESTLE, I?. (1970): "Theory of s e r i a l pattern learning: Structural t r e e s t 1 , Psychological Review 77:6, pp. 48 1-495.

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