116 / The Japanese Society for Aesthetics

Aesthetics No.15 (2011)

Norman McLaren’s Animated Film Rythmetic as Temporal
Art
KURIHARA Utako
Seinan Gakuin University, Fukuoka

1. Introduction
Norman McLaren (1914–1987) was a Scottish-born Canadian experimental animator andfilm director known for his work in the National Film Board (Office National du Film) where heplayed a commanding role from 1941 to 1982.
Besides filming without a camera or microphone and using his scratch sound system,
McLaren’s aesthetic belief in animation is legendary: “What happens between each frame ismore important than what happens on each frame”[1] and “How it moved is more important
than what moved”[2]. The animated art, which he defined as “the art of manipulating theinvisible interstices that lie between the frames”[3], was not a spatial subject but a temporal
one for McLaren. Such notions are reflected in his own compositions for his animated films
Neighbours (1952), Rythmetic (1955), and Synchromy (1970). In particular, the titles of the last
two works suggest his intention to explore beyond the traditional notion of film art by combing
words like rhythm and arithmetic (to form “rythmetic”) or synchronicity and chrome (to form
“synchromy”). However, the artistic dimension of Rythmetic, on which he collaborated with
Evelyn Lambart (1914–1999), has not been fully evaluated unlike that of Synchromy, which isalways refered as his representative work. For instance, in a special issue of Séquence for
McLaren in 1975, Rythmetic was classified as a film not for "aesthetic pleasure" but for“information and education”[4] and Collins depicted this work as an arithmetic lecture orcommunicative stress management through image:
Following on the heels of a teaching assignment in India for UNESCO, this amusing nonverbal lecture on the subject of mathematics reveals McLaren's feelings about theinadequacies of communication between peoples of different cultures and languages. Aftertoying with several different ideas for making a truly international films, he settled on
Arabic numerals as probably the most understood method of communication, far more sothan any other alphabet. [5]However, if an average to above-average animator comes to grips with practical purposessuch as arithmetic education as a delegate of UNESCO, would he choose a simple presentationof redundant calculation as “1 - 1 = 0 = 0 = 0” for over 8 minutes?
In Rythmetic, we see mechanical actions and anthropomorphic gestures made by figuresand symbols of arithmetic operations, and we hear rhythmic music with clicks or scratchingsounds made by ink directly painted on the soundtrack. As far as the aspect of “what moved” isNorman McLaren’s Animated Film Rythmetic as Temporal Art

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concerned, it is certain that the image of bright figures against a dark background effectively
brings to mind the blackboard in the classroom, and that the process of filling the blackboard
with calculative figures is reminiscent of an arithmetic lecture. We could be struck with wonderat the well-regulated placement of the figures and symbols and numerous calculations on thewall-to-wall screen, in addition to the continuously moving and changing nature of theanimation. Moreover, the order of mathematical expressions and the disorder created by the
clashing and clanging of the figures and symbols are also noteworthy. But how did such an
educational—say, mediocre—movie could win seven awards at international film festivals?[6]In addition, the 8-minute 40-second-long Rythmetic is among McLaren’s longest animatedworks[7].
Now, we consider the aspect of “how it moved” in order to see how the redundant actions
in Rythmetic would be regarded as the imaginative manifestation of McLaren’s rich originality.

2. Basis of our analysis
In order to reveal how this long movie avoids mediocrity, this paper adopts a temporalperspective to analyze McLaren’s paper-cut animation in Rythmetic, the rhythm of the figures’appearance, and the order in which the screen is occupied. The basis of our analysis is the
depiction (originally in French) on the catalogue for the Office National du Film.[8]It contains the crazy dance of arithmetic elements. The figures behave like clowns: they
are evasive, and they shake and swing at a furious rhythm. But like the policemen, thesymbols “plus,” “minus,” or “equal” fight the arithmetic operations in the cause of justiceand order. [9]We now focus on the description “the crazy dance of arithmetic.” This expression indicatesthat the normativity and deviancy in Rythmetic are focused on arithmetic elements. However,
it is not obvious from this brief description that the arithmetic elements go mad or the clown’s
dance is brought to order by the policemen. In the subsequent chapters, we will explore howsuch order and deviancy raise aesthetic contentment. How this work captivates the audience
will be explained through a description of the synthetic process of dichotomy: arithmetic as the
symbol of order and dance as the symbol of playful disorder.
While the length of the work, including the credit roll, is 8 minutes and 40 seconds, thispaper analyzes the most important part: from 33-second mark, where the background of thetitle turns from red to royal blue and the arithmetic figures appear, to 8-minute 19-second mark,where the background returns from royal blue to red (henceforth abbreviated as 0:33–8:19).

3. Two aspects of the “crazy” dance
The crazy dance of figures and symbols in Rythmetic has two aspects: the mutation of the
figures themselves and their intervention of each other.
The figures’ mutation includes the expansion/contraction of figures 0, 2, and 3 and the118

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bending of figures 4, 5, and 7, as well as their rolling. Such mutation makes the figures
resemble a human body wrenching and scratching his or her head or back. That is why thecataloger of the Office National du Film personified the figures as clowns. To display such amutation, McLaren and Lambart manufactured a few hundred variations of each figure withwhite cardboard, ranging from 1.5 to 4 centimeters[10], although today, we can probably
accomplish this task using computer graphics.
Their intervention includes the figures crashing, chasing, and jumping, and a chainedemulation of the other’s action. In the fledging scene (0:57–1:07), shortly after the equal markfor the equality “1 + 1 + 1 + 1 + 1 = 5,” the same equal mark jumps across the formula “5 – 1” tobecome an equal mark for the new equality “5 – 1 = 4.” In this case, the equal mark only
mutates and migrates, but the viewer regards it as “edging into” the other set of figures. Whenthe three figures of 0 on the upper right act up, and especially when the figure 0 on therightmost larks up (3:01–3:12), the two bars of the equal mark in turn embark to skewer (3:12),
to clip (3:23), and to relegate (3:24) the frolicking figure 0. Such a round trip or mutation
between the order and deviation of the figures is the reason why the cataloger said, “But likethe policemen, the symbols “plus,” “minus,” or “equal” fight the arithmetic operations in thecause of justice and order.” Besides, in the middle scene (2:01–2:05), when figures 1, 2, and 3
appear taking the upper-right 0 as the starting point, the existing figure 3 on the right-handside of the equality “4 – 1 = 3” attacks the new figure 3 to replace it. Such a clash lets us imagine
that the figure 3 cries out, “Outta, outta my way!”
These appearances of the figures and symbols are chaotic; however, it can be comprehended by using an auxiliary line to divide the screen into seven sections from A to G (Fig. 1).
Furthermore, these acts are accompanied by varied sounds. According to McLaren’s
technical note[11], six kinds of sound materials were “painted” on the film’s soundtrack after
the visual production (Fig. 2). The nature of each sound depends on the size and shape of thepaints. A single line sounds like a click or impulsion (Figs. 2a, 2b, 2c, and 2d), and the pitchfrom a set of plural lines differs according to the spacing of lines while the volume is
proportional to the ratio of the width to the soundtrack (Figs. 2e and 2f). Moreover, when weclassify these sound marks according to the pitch and volume (Fig. 3), we see that McLarendesigned the sounds as they cover three sections with two kinds for each: loud high tone (Figs.
3a and 3e), quiet high tone (Figs. 3b and 3d), and quiet low tone (Figs. 3c and 3f), in order tomake the materials that make the minimal sound the most expressive. The avoidance of theloud low tone seems appropriate to the visual subtlety that the little figures and symbols
mutate and intervene on the wide screen.

4. Rhythm of motion and soundThe rhythm in Rythmetic has also two aspects: the visual rhythm of the motions and theauditory one of the sounds. Although the plus of the latter is fundamentally dependent on theformer, since every appearance of figures and symbols is accompanied by the auditory
rendition, the auditory rhythm itself is highly independent from that and more ornamental
than that.

Norman McLaren’s Animated Film Rythmetic as Temporal Art

Fig. 1The order of the fulfillment on the screen (Drawing by the author)

Fig. 2 Six kinds of the marks of the soundtrack on the roll of film
(Norman McLaren, Technical notes on Rythmetic, National Film Board, 1956/1984, p.1)

Fig. 3 The nature of the six marks on the sound(Drawing by the author)

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Fig. 4

Rhythm and tempo of the appearance of ﬁgures (Drawing by the author)

As for the visual rhythm, McLaren explains that “the motion of each symbol was taken as aunit of 5 frames, 10 frames, 15 frames, 20 frames, 30 frames, 40 frames, 60 frames”[12] on thegeneral basis of 24 frames for one second in an animated film. These units, whose ratio is 1, 2, 3,
4, 6, 8, 12, will be classified as binary rhythm and ternary rhythm. The basic pulse alternates
between = 96 and = 72 (Fig. 4a)—more specifically, “ = 48/= 96” in sections A to B (0:33–
1:35), “= 72” in sections B to D (1:35–3:27), and “= 96” in sections E and F, except a shortspan of “= 72” on the 5th and 6th lines, which starts from the figures 4 and 5 (4:56–5:40) (Fig.
4b). The basic pulse is difficult to find only in section G, where the behavior of the materials isthoroughly impersonated.
In the calculation scenes, visual binary rhythm of cyclic nature is chosen. The regularblows and the iambic rhythms effectively draw our attention to the shift in the tempi and thecorresponding design; the regular blow increases the speed, while the iambic rhythm
alternately slows down and speeds up: the tempo in regular blows from section A (,  = 48) tosection A' (,  = 96), or from section B' (,  = 72) to section C' (,  = 72), andto section F (, = 96); that of the iambic rhythm from section B ( || , = 96) tosection C ( | | ,  = 72), and its shift to section E ( ||, = 96). On the other hand,the visual ternary rhythm enters habitually when the calculations get off, so to speak, “dance.”
The triplet of 5 frames (), a certain type of the ternary rhythm, for the domino actions oneach line of section E emphasizes its liquidity.
Meanwhile, the auditory rhythm is composed purely as musical matter in the calculation
scenes; however, it is hugely dependent on visual contents in that it mimics them—calledNorman McLaren’s Animated Film Rythmetic as Temporal Art

Fig. 5

121

Visual rhythm and auditory rhythm (Drawing by the author)“Mickey Mousing”—in the dancing scenes. For instance, in the above scene featuring thenonsensical equality “0 = 0 = 0,” we can hear mimic and nonperiodic rap, whereas in the scenefeaturing the general equality “4 – 1 = 3,” the auditory rhythm is rich and it crescendos tomimic the transformation of the growing figure 0 (Fig. 5).

5. Creolization of calculation and dance
The lengths of elapsed time in each section vary widely and, as seen in Fig. 1, do notconform to rules. Incidentally, the average of elapsed time per one appearance of figure or
symbol is obtainable by using the number of the figures or symbols appearing in each section
as a denominator and the elapsed time in each section as a numerator (Fig. 6a). It indicates thelength of dance per one figure or symbol, since the appearance of a figure or symbol isequivalent to the process of calculation in the sections B, C, D, E, F, and G. Consequently, itsvalue is directly proportional to the disorder with the dance and inversely proportional to theorder with calculations of the figure or symbol. Their graphic representation (Fig. 6b) shows
the trend in which the calculation is emphasized in the intrados sections (A–D, 0:33–3:27) andthe dance is emphasized in the extrados sections (E–G, 3:28–8:19); the latter case results in theaesthetic satisfaction, while the former case results in educational satisfaction.
(a)
0:33-1:00
1:01-2:07 2:08-2:40 2:41-3:27 3:28-5:31 5:32-7:38 7:39-8:19
Time
Field
Number of theappeared figures
Time / Number ofthe figures

27

67

32

46

123

126

40

A
framework

B-B'-B''

C-C'
intrados

D

E-E'

F
extrados

G

25

28

16

19

25

27

10

1.08

2.35

2.00

2.42

4.92

4.67

4.00

(b)

Fig. 6

The average elapsed time for each appearance of the figure or symbol (Drawing by the author)

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Our process observation in each section from A to G will be refined below by a descriptionof the calculation in the form of equality and a description of the salient features of dance (Fig.
7).
In section A, 16 figures are arrayed in argyle from lower left hem, lower right hem, upper
right hem, and upper left hem. At an instant, they are the visual framework of the work and thebase of calculation; therefore, this paper henceforth converts them to the form of An, where thesubscript n is the ordinal number. In section A' and on each line of section B, the figure of An is
reduced by one to form 4, 3, 2, 1. In section B', the figures and symbols of the repeatedmeaningless equality “0 = 0” are dancing. In section C, where all of the An values are 5, as thesubtracted values increase from 2 to 5, the calculated values decrease from 3 to 0, while thecalculated values shake from side to side and we see the chain-rolling of A5→A4→A3→A2→A1
in section C'. The calculations in section D, where all of the An values are 1, are slightly
elaborated: the subtractions of 1 are operated to derive the An values, once on A15, twice on A14,and thrice on A13, followed by the dancing of the figures and symbols, including the existingones at section B'—the shaking of the figure 0 and the skewering of 0 by the equal mark as havebeendescribed above.
In each line of section E, the operations go over the existing equalities in sections A, B, andD, adding 1 from the upper-left 0. While each formula definitely reaches equality, it has almost
no regularity as compared to the unexpected appearances and the decorative actions, such as
domino and joint bending, so that the calculative order and the dancing disorder seem to blend

Fig. 7The calculation on each section (Drawing by the author)

Norman McLaren’s Animated Film Rythmetic as Temporal Art

123

together. Although one might argue about going over the existing sections A, B, and D as areview function of the arithmetic lesson, it is not as detailed as that in Séquence and by Collins.
The calculation and the dancing blend together—in that, they are creolized—in section F as well.
There are certain things in common, such as the review of signs, the addition of irregular(unexpected) operations, and domino actions at the end of each line, also with three dissimilar
points to hold someone’s attention. First, the unheard of appearance of the figures 5, 6, 7, and 8
at the start of each line impresses a sense of extensity. Second, the hastening of appearances ofthe figures and symbols deprives the audience of the allowance to make a prediction of what
happens next. Third, the interference between signs forges ahead of other lines: figure 5 in thebottom-center bends its upper arm as if scrabbling at its heart and back, and it jumps to clash
with the minus symbol in the above line, and yet, its serif walks around to replace the serif of
figure 1 in the above line.
Section G, where there occurs almost no calculation, focuses entirely on dance. After the
addition of the redundant equality “= 0 = 0” to the equality “8 – 7 – 6 + 5 = 5 – 5 = 0”[13] on thebottom line, the figure 0 jumps to the right of figure 1 at the end of the line A4/A6 and of figure
2 at the end of line A3/A7, to build “10,” “20,” and “2000,” and then, the symbols “plus,”“minus,” and “equal” unite to fight and push away the figure 0. After the letters E, N, D, andfigure 0 fight over their places, the letters T, H, and E end the movie with a display of “THE
END.”
Here is temporal concision of each section in a small compass to elucidate the ingenious
plan of Rythmetic (Fig. 8). Section A, which is, at an instant, the base of calculation and thebase of visual design of the screen, is well ordered. The format of sections B, C, and D is thecalculating first half and the dancing second half (B', C', and D'). Meanwhile, sections E and F
are created by a harmonious combination of calculation and dance. Eventually, section G is fullof dance.

Fig. 8The calculation and the dance on each section (Drawing by the author)

6. Conclusion
While Rythmetic has been assumed simply as “an animated film for education” and “thecrazy dance of arithmetic”, we have scrutinized the designation of the arithmetic and the dance,
focusing on both the rhythm of motion and that of sounds. Our observation of their blending
process along the spreading of the figures and symbols has elucidated that the arithmetic andthe dance are differentiated in the intrados sections from A to D while they are fused together
in the extrados sections from E to G. In Rythmetic, the orderly enchantment and theornamental one are organized from confrontation to integration.
Appropriate to the name Rythmetic, the movie is embellished with a pattern-oriented

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manipulation of frames on film’s roll to achieve a visual rhythm, in keeping with a musicalinterpretation on the soundtrack of the film’s roll to achieve an auditory rhythm. The visual
pattern was a blow or iambic for the calculating scenes, and a mimic sound rendition was madefor the playful dancing scenes. The auditory rhythm is musically composed freely from thevisual contents, but accompanies them in the playful dancing scenes. Thereupon, we hearcyclic-patterned rhythm and playfully mimic rhythm separately in the first half of the work,
while confused in the second half.
Rythmetic is an invitation to the aesthetic confusion of order and disorder by figures andsymbols; and besides, it is a temporally designed artwork both in the visual and auditory
aspects, more so than an educational film or arithmetic lecture.

Notes[1] Giannalberto Bendazzi, Le Film d’animation. Pensée sauvage, 1985, p. 178.
[2] Donald McWilliams, “Norman McLaren: Hands-on Animation,” http://www.nfb.ca/playlists/
donald_mcwilliams/mclaren/, 2010.9.28.
[3] Maureen Furniss, Art in Motion: Animation Aesthetics, Libbey, 2004, p. 5.
[4] Originally written ‘plaisir esthétique’ and ‘information et enseignement,’ in “But des 53 films,”
Séquence, numéro special du Norman McLaren, 1975, p.138.
[5] Maynard Collins, Norman McLaren, Canadian Film Institute,1976, p. 47.
[6] First Prize of Abstract Films at Rapallo International Film Festival 1957; Diploma of Honour at
International Review of Specialized Cinematography Rome 1957; Silver Reel Award of AvantGarde and Experimental at Annual Golden Reel Film Festival (Film Council of America) 1957;
First Prize at Festival of Contemporary Arts (University of Illinois) 1957; Certificate of Merit atInternational Film Festival Durban 1956; Certificate of Merit at International Film Festival
Johannesburg 1956; Diploma of Merit at International Film Festival Edinburgh 1956; Silver Bear
Prize of Short Films at International Film Festival Berlin 1956.
[7] It is the second longest; the first is A Chairy Tale, collaborated with Ravi Shankar (1920- ), afamous Indian musician and composer who plays the plucked string instrument sitar, and Claude
Jutra (1930-1986), a Canadian actor and film director, in 1957.
[8] The English and French authors of the collection do not seem to be the same, since the English
depiction is totally different. “An animated film by Norman McLaren and Evelyn Lambart thatendows arithmetic with lively humor. The screen becomes a numerical free-for-all as digits meetin playful encounter, add and subtract, jostle, attack, and elude one another.” ‘Rythmetic,’ “OurCollection” of National Film Board of Canada, http://www.onf-nfb.gc.ca/eng/collection/film/?id=10570, 2010.9.28.
[9] The author’s translation originally written: “C’est la ronde folle de l’arithmétique. Les chiffres se
conduisent ici comme des clowns, se fuient, se bousculent, s’évitent, à un rythme endiablé. Mais,
comme des policiers, les signes « plus », « moins » ou « égal » veillent au bon ordre et à lajustesse des opérations d’arithmétique.” ‘Rythmetic,’ “Notre Collection” of Office national du film
du Canada, http://www.onf-nfb.gc.ca/fra/collection/film/?id=1247, 2010.9.28.
[10] A carton of cardboards is kept safe in La Cinémathèque québécoise in Montréal.
[11] Norman McLaren, Technical notes on Rythmetic, typed but unpublished, National Film Board,
1956/1984, p.1.
[12] Ibid., p. 2.
[13] The second figure 5 among three fives is A5.