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Harmony

 

 

Definition (Reference books)
Components (Richard Neutra)
Components (György Doczi)

Beauty (Leon Battista Alberti)
Simmetry (Matila Ghyka)

Ratio (Geoffrey Broadbent)
Ratio (Matila Ghyka)

Proportion (Odd Brochmann)
Proportion (Richard Neutra)
Proportion (Matila Ghyka)
Proportion and the Golden Section (Paul Jacques Grillo)
Proportion and the Golden Section (Matila Ghyka)
Proportion and the Golden Section (György Doczi)

Melody and Rythm (Union of International Associations)
Melody and Rythm (Odd Brochmann)
Melody and Rythm (Richard Neutra)
Melody and Rythm (Paul Jacques Grillo)
Melody and Rythm (Matila Ghyka)
Melody and Rythm (György Doczi)
Melody and Rythm (C.H. Waddington)
Melody and Rythm (Steen Eiler Rasmussen)

Grace (The American Heritage Dictionary)
Grace (György Doczi)

Harmony and Conflict (Kenneth Boulding)
Harmony and Conflict (W.W. Spradlin & P.B. Porterfield)

Varia Quotations (Albert Einstein and Leopold Infeld)
Varia Quotations (Richard L. Shadrin)

 

 

Definition

[1983] The Shorter Oxford English Dictionary
"Harmony: 1. Combination or adaptation of parts, elements, or related things, so as to form a consistent and orderly whole; agreement, congruity. 3. Combination of parts or details with each other, so as to produce an aesthetically pleasing effect."

[1986 Second Edition] Union of International Associations eds., Encyclopedia of World Problems and Human Potential, K. G. Saur, München
"Harmony. 1. The arrangement of parts within a structure or system in pleasing relation to each other. 2. The degree of efficiency with which a particular system achieves its purpose. A norm of harmony is distinguished from a norm of equilibrium which refers to the degree of interrelatedness between an equilibrium system as a whole and whatever are taken to be its parts. 3. Combination into a consistent whole. 4. The science of the structure, relation, and progression of chords in homophonic composition." (KC0424)

[1964, First Edition 1931] Read, Herbert, The Meaning of Art, Penguin, Harmondsworth
"Harmony is the due observance of proportions." (p. 21)
"Harmony is the satisfaction of our sense of beauty." (p. 28)

[1978, First Edition 1954] Neutra, Richard, Survival through Design, Oxford University Press, New York
"Recurrence, unity of elements, and consistency really make for harmony." (p. 58)

[1994] Doczi, György, The Power of Limits, Shambhala, Boston & London
"By harmony we generally mean a fitting, orderly and pleasing joining of diversities, which in themselves may harbor many contrasts. In this sense, harmony is a dinergic relationship, in which different and often contrasting elements complement each other by joining. That such dinergic joining is at the heart of all harmonies is suggested by the origin of the world harmony, from the Greek harmos, to join." (p. 8)

 

Beauty

[1443-1452] Leon Battista Alberti, De Re Aedificatoria
"Beauty comes from concinnitas: that is, the successful combination of number, measure and form (numerus, finitioand collocatio).

 

Symmetry

[1977, first published 1946] Ghyka, Matila, The Geometry of Art and Life, Dover Publications, New York
"... 'symmetry' as defined by Greek and Roman architects as well as the Gothic Master Builders, and by the architects and painters of the Renaissance, from Leonardo to Palladio, is quite different from our modern term symmetry (identical disposition on either side of an axis or plane ‘of symmetry’). We cannot do better than give the definition of Vitruvius: ‘Symmetry resides in the correlation by measurement between the various elements of the plan, and between each of these elements and the whole ... As in the human body ... it proceeds from proportion - the proportion which the Greeks called analogia - (it achieves) consonance between every part and the whole ... This symmetry is regulated by the modulus, the standard of common measure (belonging to the work considered), which the Greeks called the number ... When every important part of the building is thus conveniently set in proportion by the right correlation between height and width, between width and depth, and when all these parts have also their place in the total symmetry of the building, we obtain eurhythmy." (Introduction p. X)
"For this notion of symmetry seen as correlating through the interplay of proportions the elements of the parts and of the whole, the Renaissance coined the suggestive words ‘commodulatio’ and ‘concinnitas’." (Introduction p. X)

Ratio

[1988, First Edition 1973] Broadbent, Geoffrey, Design in Architecture. Architecture and the Human Sciences, David Fulton Publishers, London
".. the numerical relation one quantity bears to another of the same kind." (p. 327)
"... ratio in the form of proportional canons has been one of the formative bases of architectural design ... ." (p. 327)
"The size and shape of a window are clearly matters of proportional ratios, so are the size and shape of a façade, a room, a plan. Classical, medieval and Renaissance design were largely matters of ratio; so for that matter are dimensional coordination and much systems building today." (p. 327)
"... ratios may be applied in many ways. In classical systems generally the proportional relationships between elements remain constant but the sizes of the elements change. A large Greek temple is merely a small Greek temple, identical in form but larger in size. In medieval systems, on the other hand, the sizes of elements stay fairly constant but the proportional relations change. A Gothic cathedral is larger than a Gothic church; it also has more parts." (pp. 327-328)

[1977, first published 1946] Ghyka, Matila, The Geometry of Art and Life, Dover Publications, New York
"The mental operation producing ‘ratio’ is the quantitative comparison between two things or aggregates belonging to the same kind or species."
"This comparison of which a ratio is the result is a particular case of judgement in general, of the typical operation performed by intelligence. Judgement consists of
(1) perceiving a functional relation or a hierarchy of values between two or several objects of knowledge;
(2) discerning the relation, making a comparison of values, qualitative or quantitative. When this comparison produces a definite measuring, a quantitative ‘weighing’, the result is a ratio." (p. 1)

 

Proportion

[1970] Brochmann, Odd, Good or Bad Design?, Studio Vista, London
"People very early paid attention to this need to provide the effect of a harmonious whole; particularly perhaps in the rules the ancient Greeks set up for building their temples, the dimensions and proportions of which were the product of one and the same basic measurement, the same module. This module was usually the diameter of the column at its base. Once this had been decided all the other measurements followed from it, however big or small the temple was to be." (p. 35)
"One theory launched by Pythagoras was that the proportion between the lengths of the strings of a harp which provides the harmony for the ear, also appears harmonious to the eye." (p. 36)

[1978, First Edition 1954] Neutra, Richard, Survival through Design, Oxford University Press, New York
"One of the fundamental concepts with which designers operate is proportion. Proportion seems independent of time and also of absolute size." (p. 173)

[1977, first published 1946] Ghyka, Matila, The Geometry of Art and Life, Dover Publications, New York
"The name of the geometrical proportion (a/b=c/d) was in Greek, and in Vitruvius, analogia; harmoniously ordered or rhythmically repeated proportions or ‘analogies’ introduced ‘symmetry’ and analogical recurrences in all consciously composed plans." (Introduction p. X)
"The notion of proportion is ... either confused with the notion of ratio ... or with the notion of a chain of characteristic ratios linked together by a modulus, a common sub-multiple." (p. 1)
"The notion of proportion follows immediately that of ratio. To quote Euclid ‘Proportion is the equality of two ratios’." (p. 2)
"If we have established two ratios a/b, c/d, between the two magnitudes (comparable objects or quantities) a and b on one side, and the two magnitude c and d on the other, the equality a/b=c/d (a is to b as c is to d) means that the four magnitudes a,b,c,d are connected by a proportion." (p. 2)
- discontinuous geometrical proportion : a,b,c,d are different
- continuous geometrical proportion : a,b,b,c (two numbers are identical) (a is to b as b is to c that is a/b=b/c or b2 = ac that is b=*ac) (p. 2)
"The Greeks had already noticed that three terms at least are necessary in order to express a proportion." (p. 3) "But it is impossible to combine satisfactorily two things without a third one: we must have between them a correlating link ... Such is the nature of proportion ..." (footnote p. 3)

 

Proportion and the Golden Section

[1975] Grillo, Paul Jacques, Form Function & Design, Dover, New York
"The Golden Section (f = 1,618...) : is the ratio between the diagonal and the side of the regular pentagon."

[1977, first published 1946] Ghyka, Matila, The Geometry of Art and Life, Dover Publications, New York
"... the ratio known as ‘Golden Section’ when [it] exists between the two parts of a whole ... it determines between the whole and its two parts a proportion such that ‘the ratio between the greater and the smaller part is equal to the ratio between the whole and the greater part’." "Luca Pacioli ...called it ‘The Divine Proportion’."
(p. 4)
"The golden section therefore imposes itself whenever we want by a new subdivision to make two equal consecutive parts or segments fit into a geometric progression, combining thus the threefold effect of equipartition, succession, continuous proportion; the use of the golden section being only a particular case of a more general rule, the recurrence of the same proportions in the elements of a whole." (Timerding in Ghyka, Matila p. 12)
"It is this property of producing, by simple additions, a succession of numbers in geometrical progression, or of similar shapes (what Sir D’Arcy Thompson called ‘gnomonic growth’) which explains the important role played by the Golden Section and the F series in the morphology of life and growth, especially in the human body and in botany." (p. 13)
"The Golden Section also plays a dominating part in the proportions of the human body, a fact which was probably recognized by the Greek sculptors, who liked to put into evidence a parallelism between the proportions of the ideal temple and of the human body (cf. Vitruvius) or even to trace an harmonious correspondence (a proportion or analogia , in fact) between the terms Universe-Temple-Man." (p. 16)

[1994] Doczi, György, The Power of Limits, Shambhala, Boston & London
"A : B = B : (A + B). This is the formula of the celebrated golden section , a uniquely reciprocal relationship between two unequal parts of a whole, in which the small part stands in the same proportion to the large part as the large part stands to the whole ." (p. 2)
"The golden section’s ratio is an irrational, infinite number which can only be approximated, yet such approximations are possible even within the limit of small whole numbers." (p. 13)
"... harmony [in folk art : pottery making] is created by a conscious or unconscious tendency to unite the diverse elements of the shape, through shared proportions, ranging from the 0.5 and 0.75 rates and gravitating ... around 0,618, these three proportions corresponding to basic musical root harmonies." (p. 22)

 

Melody and Rhythm

[1986, Second Edition] Union of International Associations eds., Encyclopedia of World Problems and Human Potential
Melody : "The logically organized expression of tonal scale, pitch, harmony, tempo, rhythm, etc., in a succession of sounds, single notes or chords, by one or more instruments or voices. Melodic structures are of variable length and range from leitmotifs to many lines or bars expressing development of a theme." (KC0822)

[1970] Brochmann, Odd, Good or Bad Design?, Studio Vista, London
"The concept of rhythm can manifest itself in all sorts of sequences, and not just as a repetition of dots and lines."
"Otherwise rhythm is best known in connection with pattern or ornament, the essence of which is repetition, and which is often used to link surfaces and lines to something which can be clearly registered, something on which you want the eye to rest." (p. 41)

[1978, First Edition 1954] Neutra, Richard, Survival through Design, Oxford University Press, New York
"It is also conceded that we have, for example, a consistent preference for rhythm, possibly reflecting rhythmic processes within our body, such as those of respiration and peristalsis, pulse and heartbeat. This rhythmical disposition is a factor on which any designer can count as a constant" (p. 182)

[1975] Grillo, Paul Jacques, Form Function & Design, Dover, New York
"Rhythm, or recurrence of a certain pattern of sounds, numbers, figures, colors, or movements, is so closely associated with life that it seems to be the very expression of life itself." (p.154)

[1977, first published 1946] Ghyka, Matila, The Geometry of Art and Life, Dover Publications, New York
"An old but correct definition of rhythm was: ‘Rhythm is in time what symmetry is in space’." (Introduction p. XI)
"The notions of periodicity and proportion, and their interplay, can be used for succession in time as well as for spatial associations. If periodicity (static like a regular beat, or dynamic) is the characteristic of rhythm in time and proportion the characteristic of what we may call rhythm or eurhythmy in space, it is obvious that in space, combinations of proportions can bring periodical reappearances of proportions and shapes, just as in a musical chord or in the successive notes or chords of a melody we may really perceive an interplay of proportions." (p. 6)
"Rhythm is produced by the dynamic action of Proportion on a uniform (static) beat or recurrence." (Footnote p. 6)

[1994] Doczi, György, The Power of Limits, Shambhala, Boston & London
"The essence of all vibrations and rhythm is sharing of diversities - weak and strong, in and out, up and down, back and forth, - at recurrent time and intervals. This holds as true for the tides of the ocean as for our heartbeat, for light, weight and sound as for patterns of plant growth." (p. 51)

[1951] Waddington, C.H. in Whyte, Lancelot Law (ed.) Aspects of Form, Lund Humphries
Whitehead wrote ("The Principles of Natural Knowledge" p. 198) "A rhythm involves a pattern, and to that extent is always self-identical. But no rhythm can be a mere pattern; for the rhythmic quality depends equally upon the differences involved in each exhibition of the pattern. The essence of rhythm is the fusion of sameness and novelty; so that the whole never loses the essential unity of the pattern, while the parts exhibit the contrast arising from the novelty of their detail." (p 46)

[1993, First published 1959] Rasmussen, Steen Eiler, Experiencing Architecture, The MIT Press, Cambridge Mass.
"It is well known that physical work become easier to perform when the motions involved are regularly alterned. A job that cannot be done at one stretch is easily accomplished when it is carried out in short, regular spurts so that the muscles have a chance to rest in between." "Such regular alternation to lighten work is called rhythm." (p. 134)

 

Grace

[1974] The American Heritage Dictionary
"Grace: 1) beauty or charm of movement, form, or proportion. 2) fitness or propriety."

[1994] Doczi, György, The Power of Limits, Shambhala, Boston & London
"Harmony and grace are born from the marriage of plenty and poverty as Plato told us in his Symposium." (p. 102)

 

Harmony and Conflict

[1962] Boulding, Kenneth, Conflict and Defence

"Conflict is discord, and the opposite of conflict is harmony; the words reveal the evaluational bias in the language and common experience. Discord may be necessary to make music interesting ... but its significance lies in the ability of the composer to resolve discord into some meaningful harmony ... The essence of the drama of conflict is likewise its resolution." (p. 25)

[1979] Spradlin, W.W. & Porterfield, P.B., Human Biosociology. From Cell to Culture, Springer-Verlag, New York
"The self is a working construct, a fluid base of reference we use in programming information. It must be constantly tuned to function in harmony with the information processed in all systems. When the data from an individual’s environment do not validate the patterns of behavior composing his self system, the individual may become anxious and exhibit various fight-flight patterns." (p. 57)

 

Varia Quotations

[1938] Einstein, Albert and Infeld, Leopold, The Evolution of Physics, Simon and Schuster, New York
"The simpler our picture of the external world and the more facts it embraces, the stronger it reflects in our mind the harmony of the universe." (p. 226)

[1992] Shadrin, Richard L., Design & Drawing, Davis Publications, Worcester, Massachusetts
"Each culture, in its own way, seeks harmony. Where a Western architect might talk about the golden mean (perfect mathematical proportion) an Eastern architect might instead speak of ‘feng shui’ (the harmonious placement of objects." (p. 15)

 

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