architectural thesis- music in architecture

ARCHITECTURAL THESIS - 2012

SALEM SCHOOL OF ARCHITECTURE

VINAYAKA MISSIONS UNIVERSITY SALEM

INTERNATIONAL RESIDENTIAL SCHOOL AT KOTTAYAM

SUBMITTED BY : SINOJ NARAYANAN, REG. NO: 380051012

GUIDE: PROF. AR SUBOTH THOMAS

INTERNATIONAL RESIDENTIAL SCHOOL THESIS REPORT

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VINAYAKA MISSIONS UNIVERSITY SALEM SCHOOL OF ARCHITECTURE

SALEM 636 308.

The dissertation entitled ___________________________________is submitted on _____________in partial fulfillment of the requirements for the Degree of Bachelor of Architecture, Vinayaka Missions University, Salem. Name of the student _________________________________ Registration No: _________________________________ Signature _________________________________ Guide Coordinator Dissertation committee Dean & Head of the Department External Examiner


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Acknowledgement

I take great pleasure in expressing my gratitude and sincere appreciation to the people whose constant guidance, support and inspiration rendered to me and went a long way in rearing this project along in its inference.

I would like to first thank my Thesis Guide and Director, Ar. Suboth Thomas for leading me in the right direction, providing me all the useful knowledge of the selected subject and guiding me in every aspect in conducting this dissertation work.

I appreciate the staff of all the places where the case studies where executed and people who were stupendously supportive for providing all the information required.

I discern the timely co-operation of the staff of the Salem School of Architecture. Also I would like to thanks to the respected professors of our college who have always guided me for achievement of this project.

I am ever grateful to my parents, who supported me throughout this dissertation giving me all the encouragement whenever required.

Lastly but not the least my special thanks goes out to all my favorite juniors for their intense support for my work and also to all my close friends for they have been my greatest strength.


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Abstract

School is a part of the education system which develops the social skills of a child in order to make them fit in the present highly advanced and complicated civilized world. They represent some of the most important part of the civic structure. They train and develop the child, enhance their skills and set them for their future. Everyone remembers more than half their childhood through memories of their school, no matter how the school designs is. The corridors, classrooms, the playground etc brings in memories that remain fresh to any adult. What if the school is further enhanced with design features? It would invariably transform the school atmosphere to an education haven bringing out the perfect character required for their survival, in short the perfect student as man is a student throughout his life. Learning everyday something new is what man is designed to do. One can never design a perfectly functional school without knowing the basics factors which is involved in its working. There are lots of elements which come to play from the back drops of the design which should help in the intellectual and physical growth of the child. Schools are the stepping ground for a child, where the tools required for their survival is provided, or rather attained by the children throughout his or her life at school. These tools equip them accordingly for the race of life in future. As such much care is required for the designing of a school because it should affect every factor; if it doesnt, the school is a failure.


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While at designing a school, the architect should take into consideration the little voices, as it is these people who will be the main users affected by the design. Children are extremely aware of their surroundings and they are superb observers; they are cognizant, perhaps more than an adult. If the designing is done reluctantly taking in the reasons and factors involved in the adult realm, students may get the impression that designing of the school is done in an unimportant manner. They are capable of pointing out the flaws in the design and hence begin the age old problem of oppression faced by these students. They have to either fit in or rebel out of the school system. All have to work along well smoothly like a well oiled machine, a perfect school creating the perfect student for this high tech world.

his thesis report progresses in a specific manner such that the special topics are taken into consideration in the beginning and going down further into detailed discussions from then. This is

done so, such that one is gives a proper understanding to how the design was evolved and what plays the design deciding factors.

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Contents: Pages:

1. Music and Architecture 9 1.1. The Starting Note 11 1.2. Creation 12 1.3. Harmony 17 1.4. Proportions 19

1.4.1. Proportions: the Creators Tool 21 1.4.2. Harmony in Nature 23 1.4.3. Divine Proportions 24 1.4.4. Phi in Music and Architecture 28

1.5. Pythagoras 31 1.6. Leon Battista Alberti 34 1.7. Andrea Palladio 38

1.7.1. Arithmetic Mean 39 1.7.2. Geometric Mean 39 1.7.3. Harmonic Mean 40

1.8. Le Corbusier 41 1.8.1. Le Modulor 43

1.9. Conclusion 46

2. Education, Man and Society 52 2.1. Different ranges of Human Experiences 54 2.2. The 25 Patterns 55 2.3. Interactions 56

2.3.1. Types of Interactions 56 2.3.2. Trends in teaching and Learning 57 2.3.3. The 18 Modalities 58


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2.4. Life between Classrooms: Applying Public Space Theory to learning Environment 60 2.4.1. Applying this theory to school design

2.4.1.1. Corridors 61 2.4.1.2. Classrooms and formal Learning

Spaces 62 2.4.1.3. Indoor public spaces in

school 63

3. International school 64 3.1. The Beginning and the Result 64 3.2. Programs of the International Baccalaureate Organization (IBO) 67 3.3. Syllabus 70 3.4. Requirements derived 70

4. Case study

4.1.1. Indus International School 71 4.1.2. Montfort Anglo-Indian Higher Secondary

School 80 4.1.3. Conclusion 87

4.2. Literature Case study 4.2.1. Pathways World School 89 4.2.2. Mercedes Benz International School 94 4.2.3. GEMS International School 98 4.2.4. Tiruvananthapuram International School 102 4.2.5. Conclusion 108

5. Rules and Regulations

5.1. Kerala Municipality Building Rules (KMBR) 109 5.2. Basic other standards 112 5.3. Basic school building conversion norms 116


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6. Project Brief

6.1. Need for the project 118 6.2. Feasibility 118 6.3. Aim 118 6.4. Objectives 118 6.5. Methodology 119 6.6. Site study 120

7. Design Brief 8. Design Sheets


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The relation between

music and architecture

is therefore a language

or method, a cultural

invention by men.

1. Music and Architecture: Ying and Yang

he question about the relation between music and architecture is a topic that is being analyzed since ancient periods to present day. Music and architecture

are in ones consciousness only related through manmade systems and within the conception of art (the abstract or the interpretation of reality) and not within conception of reality. The relation between music and architecture is therefore a language or method, a cultural invention by men. One could suggest that due to modernity where mankind is alienated from his reality, also representation has been alienated from reality. Such is the pace of the modern world that man lost his ability to perceive things more deeply, something that in

ancient days was done in a daily process. Questions rarely arise to why it happens, rather it happens, a pattern just continuing over and over. Music and architecture and their links have been studied, understood and applied into

practice since ages. From ancient Greeks Parthenon to modern day contemporary structure such as Stretto House by Steven Holl shows how the architect can bring in music into architecture and in turn create their own environment of harmony or stretto note as such in the case of above examples. Throughout history, many analogies have been made concerning music and architecture along the narrow

channels of interaction: number, rhythm, notation and proportion.1 As such the music should be understood as a metaphorical structure requiring translation into visual terms before becoming available to architecture. As seen further own, one will understand how music is to be applied into architecture through the metaphorical device of harmony as this shows the clearest bond between architecture and music. This thesis will divided into parts according to the level of understanding that is required for knowing the application of music into architecture. Though this topic is considerably vast taking in account every detail is considerably not possible. Even every attempt has been made to understand the usage of music into architecture. The part that has been given utmost understanding is the musical device of harmony applied into architecture and its importance it plays in the divine creation. Due to the reason as obvious being that this topic being a quite vast one, works of many who worked for understanding the proper relation music have with architecture is, omitted. But all importance have been given that one truly understands the relationship which music and architecture share, or rather said by the end of the this research part that both these art forms were born from the same mother. Topics that helped in understanding the properties that linked the two systems have been discussed accordingly. As such of reasons stated above, rather than going through the topics that lay scattered throughout the time line, here,

1 MARTIN, E. (Ed), Architecture as a Translation of Music, pg 57

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subjects have been chosen in a manner that one can gain an understanding in the mystical bond that lay in both fields of creation. Must be specially mentioned is that what lay ahead is the literature study required for one to understand the true power of music over architecture. First part consists of the understanding that is to be given to know the metaphorical understand the music in architecture through lingual analogy. By exploring the seam between music and architecture and its metaphorical representation within the built environment, new modes of formal translation and a new paradigm of musical space can be identified. As such a basic understanding is to be provided in order for the proper understanding of the relationships that they share. The study continues on to discussion on the topic of creation. The history of creation is given an understanding; the history in which man has been striving to attain natural beauty is made known. Platos works are taken for understanding about the creation through the topic of Divine Creation of God: The Universe. Further on the topic of creation in architecture and music is understood. How architecture and music share same bonds are noted and analyzed. These parts have to be understood by one, in order to gain the proper knowledge of the process that underlay in the process of creating an object of beauty. The next part consists of the study on harmony as harmony lays the best example in the understanding of the deep bond shared between architecture and music. Beginning Nature

and Her play of Harmony one is given an understanding to harmony played the basis in ancient world. The study continues on the importance of Proportions in creation. How a set of integers rule the creation process of leading to a harmonious environment is understood. Its importance and its part it has played in the forming harmonious properties of any work of art are well illustrated. By here one will understand how proportions play the major role in the linking of music into architecture. Analyzing historically many examples can be seen that applies harmonious proportions, though it varied during the stages it progress in. One by then can easily interpret the presence of proportions in process of creation. Also in order for understanding the beginnings of proportions is understood through the works of Pythagoras. Further on, for the understanding of working of proportions in creation, the works of greats such as Alberti, Palladio and le Corbusier is studied.


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Then and then only can one see the perfect

creation in being.

1.1 The Starting Note: Metaphorical understanding through Lingual analogy.

f one were to be asked about the relation between music and architecture the answer by any commoner would be none or at least not much, for the obvious reason of

fundamental differences in their systems such as architecture not implying notes or chords in the design or music not using columns or beams in their composition. Just due to this reason people would tend to dismiss all notions of similarities between these two interrelated grand creations. This lack in understanding this fact is because of the reason that one perceives it using their senses the way humans are tuned by nature to do. Plato, stating in his Timaeus that man has received these senses as a gift from God. Using mans senses as his parametric boundary without knowing the differences, one will not be able see the beauty that lay between the intermeshed relations between music and architecture. But if one were to be given a further insight, a brief introduction to the basics of the links in music and architecture, then he or she will begin to see the world in a different way, a world consisting of perfectly balanced order reigning over the chaos that lies hidden underneath. When speaking of music and its influence in architecture or vice versa, the lingual analogy is the key to understanding the phrase and hence the end results that these creations are

to be considered as a unique language which seeks to represent experiences in a particular way. Then and then only can one see the perfect creation in being. Further defined when applying the above concept, it leads to whole new change in perception, barriers and borders are lifted and a whole new picture comes in being. The similarity in the two forms of art is now made visible. The obvious differences only occur between the elements or medium which each use to represent experiences; for instance columns and beams in one case and notes and chords in the other. Either how, at the level of organization and function, of how

they do it and what they do, one can see the similarities. Representation of experience is the key idea. It represents a language of its own kind; as such that this is the reason for a language to exist; this is what it does. Thus in simple words, the difference between the systems whether music or architecture is a matter or material which they use to achieve the goals of the system: namely, representing particular experiences. The similarity between them is a matter of process involved rather than the medium or material they use.

As such it is to be always kept in mind that no matter what the creative form is there holds an important place for selection and combination of available elements from a given vocabulary, whether it be words, architectural forms, sounds, colors in order to represent a particular experience. As such one should understand by now that the difference lies in, architecture playing in the dimensions of space, while in music it plays with the marking of time in space. The

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architect and a music composer share the same basic rules during the space of creation. They visualize the creation in their own method, in which abstract, practical concepts are applied. These ideas are further developed, imperfect tones are removed and the grand picture is musicians are known to visualize their entire score as one beautiful picture which in the end unravels itself in completely different way. at last it gets almost finished in my head, so that I can see it as a while, even when its a long piece, at a single glance, like a fine painting or a beautiful statue. Mozart Throughout history, many analogies have been made concerning music and architecture along the narrow channels of interaction such as: number, rhythm, notation and proportion. Just as one note can affect an entire song, one object can affect a room or even an entire building. Both are equally as difficult to begin as they are to complete. With music and architectures web of intermeshed relation with one another, the tendency has been to perceive music as a metaphorical structure requiring translation into visual terms before becoming available to architecture. When stating about translation one has to understand the simple yet complex terms that state basis for all work of art. When an artist begins his work there are some catalyst that act together, a sense unknowingly working alongside each other in the mind of the artist, all for the end product Representation. Translation, association, conceptualization and interpretation is possibly as old as the either conscious or unconscious existence of mimesis which is the human representation of nature/reality; maybe the sole raison dtre

of art itself, the ticking heart lying underneath a painting, a musical score, a poem on even a building. Metaphorical mixing that as explained creates an analogy state in which the process actually goes a step beyond the basic understanding of the word metaphor. It pushes across the boundaries of imagination, creating new worlds, new possibilities, and new creations. Just to give a vague example, in the song by the name Shape of my heart by Sting one can quite easily understand how an artist can easily bring an imaginative world through the use of words. He deals the cards to find the answer The sacred geometry of chance The hidden law of probable outcome The numbers lead a dance I know that the spades are the swords of a soldier I know that the clubs are weapon of war I know that diamonds means money for this art But thats not the shape of my hearts As seen above, the metaphorical use of words brings the tense situation following a poker game along with other emotions playing together. 1.2 Creation

efore one understands the use of metaphor of music to be used in architecture one should understand about creation. What is creation; a question that can be B


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answered simply as the act of bringing something into being. Art can be defined through the terms of creation. Art can be described as the application of human creative skill by use of the imagination. Art can be used in creative terms to express a representation of oneself; it is there to convey a singular belief, of a single person or an entire society, through creation. Relating something to a dominant being to bring in an understanding is, as mentioned earlier, the oldest form of learning. As such one should understand that there is definitely no manner in which one can actually create a system of his own without understanding the basics of the language to be used. In the world of knowledge of man, as far as it extends, it can be seen his endeavor to replicate Nature as She is seen to the naked eye. Man in his strive for attaining the perfection in his work to recreate God in work of the Divine creation of the universe, has learnt about the attaining of principles and proportions that helped attain the harmonious order required in his creation. The world that God created is a living, intelligent organism that magnificently displays mathematical order and proportion.2 Plato describes about the perfection in which God created the earth saying that he wanted everything to become as much like himself as possibleso he took over all that was visibleand brought it from a state of disorder to one of order.3

2 PLATO, Timaeus, pg xiii 3 PADOVAN, R., Proportion: Science, Philosophy, Architecture, pg 105

Like the Divine Creation discussed in Timaeus, the elements required to create both music and architecture are already present; sound is already created by everything around, space is already present, it is up to one to define them by arranging their different elements. The creation, in Plato's sense is really the creation of order.4 Later in Timaeus, Plato discusses about the senses, stating that they are a gift that in some way help one become better

and slightly closer to the perfection of the creator. The senses are not instruments, but rather passages, through which external objects strike upon the mind. The eye is the aperture through which the stream of vision passes; the ear is the aperture through which the vibrations of sound pass.5 Plato continues to discuss that along with these gifts, comes the

4 PLATO, TIMAEUS, sec. 4 5 ibid


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ability to realize such things as musical sound, harmony and rhythm. They are there to increase the understanding of the world around and in turn open the window for new creations. By investigating the Timaeus, it can be interpreted that Plato believed the heavens to be perfect due to their inherent order and harmony created through their architecture; in turn they produce music in their perfection. Furthermore, it can be deduced that the humans are unlike the heavens and lacking in grace and through creation one attempts to bring him somewhat closer to its beauty. With the creation of something perfect, one can relate to the heavens harmonious proportions. Through Platos Timaeus it becomes apparent that his ideas of the universe imply its creation as a result of three parts; God (the creator), architecture (order) and music (harmony). When architecture was applied to space it created order from chaos. The order created results in a harmonious universe, creating music. These order created through the fusing proportions that bring the unequal equal. The part which Plato played in describing about the Divine Proportion, though didnt state it by name, will be later on discussed, as such of the reason that the role of Proportions is not yet to be investigated in this stage of research. Creation as such in terms of art can be argued as ones attempt to relate to the divine by imitating the initial creation of the cosmos by God. In The Beautiful Necessity, Bragdon argues that music and architecture are allied in creation; They alone of all the arts are purely creative, since in them is presented, not a likeness of some known idea, but

a thing-in-itself6. In Platos Republic, the topic of mimesis is introduced. The Greek word mimesis can be translated to mean representation, and yet a deeper understanding would reveal that Plato used it when discussing artistic creation to mean imitation.7 Through this understanding it becomes clear that all creation is in fact imitation, only the degree of imitation varies. Protagoras coined the phrase: Man is the measure of everything on Earth, which is said perhaps then due to the understanding that came during the pre-Socratic era that there is specific reasoning for the dimensions in nature, and in turn the understanding of the Divine Creation. Unlike the other arts, neither architecture nor music can exist without the artist, the art is not attempting to become a predefined object; it is using already existing laws and elements to become something new. It is clear that music and architecture are both arts that dont need to imitate things.8 Therefore, when considered in respect to the theories of mimesis, it would seem that they are the truest of all art forms and are pure in creation as they have no mimesis with which to concern themselves they do not imitate.9 Although this statement cannot be proven, it does become apparent that out of all of the arts, these are the most unique and 6 BRAGDON,C., The Beautiful Necessity: Seven Essays On Theosophy and Architecture, pg 15 7 PLATO, Republic, pg 335

8 CAPANNA,A., Iannis Xenakis- Architect of Light and Sound 9 WATERHOUSE, P., Music and Architecture, Music and Letters, pg 321-324

Unlike the

other arts,

neither

architecture

nor music

can exist

without the

artist


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creative. To be creative, is to bring ones imagination into being, and this can truly describe how one creates with regards to both music and architecture.10 While they are allied in their creativity, there is a unique difference between music and architecture, which sets their creation apart. Similarities exist in the creation of both; nevertheless it is the context of their creation, which sets them apart. This is discussed earlier in which the basic differences and similarities appear in their element and mode of approach towards representation. Architecture is the social art that touches all human beings at all levels of their existence everywhere and every day. This is the only creation that encompasses the four major realms of human endeavor: Humanities, Science, Art, and Technology.11 Architecture deals with making of physical space into usable space, i.e., creation an aura that is required to produce the perfect harmonious feeling required; which in turn sent an appealing nature and helps perceive it easily by the senses. Vitruvius has stated that Architecture is a science arising out of many other sciences and the architect to be adorned with many branches of study and varied kind of learning; and with these apply those works which are the result of other arts.12 10 ANTONIADES, A. C., Poetics of Architecture: Theory of Design, pg 13 11 COUNCIL OF ARCHITECTURE, Architectural Practice: Conditions of Engagement and Scale of Charges, Preface, pg 61; Document approved by the COA at its 40th meeting. 12 VITRUVIUS, THE TEN BOOKS OF ARCHITECTURE, Chapter II- Fundamentals of Architecture

Architects create their own atmosphere in their own concepts. The only change which it creates is knowledge gained by one when the architects influence of the concept in the design. This could be with recurring columns, of windows or through the theme that they create. Creativity is the essence of architecture and harmony an essential aim of architecture. Architecture that has been recognized as great, in historic pat as well in our own time, has been harmonious with nature and its immediate environment. These are the essential tenets of design which architects aspire to follow.13 Architecture is the art of ordering elements spatially, whereas music is the art of ordering tones, or sounds in a temporal relationship, resulting in a unique composition. Music has a

non-retrogressive basis as music is solely based temporally it can only be viewed with the linear progression of time.14 It is true that music can be played in reverse but in these instances the music would cease to be the original composition, becoming a unique piece of music and would

13 Ibid, pg 62 14 MATOSSIAN, N., Iannis Xenakis, p 56 and pp 172-173


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still be played linearly. On the other hand, architecture, being based spatially, can literally be viewed from many different perspectives, each creating a unique experience of the architecture, yet remain the same. This is the main distinction, which sets apart the experience of each art form. However, it is clear from the interwoven relationship between space and time, that the creation of both can be connected, albeit analogically.15 The understanding of the word metaphor and its transformation that takes place when it is used in the case of music into architecture or architecture into music is to be understood. Either way it is need to perceive it with the naked eye, to understand its meaning; a graphical representation to be exact. In the musical sense this is called as musical notation and it comes in many ways. For a composer to convey musical ideas to a performer or the audience, the development of notation was central.16 Notation helps in preserving the art, to later understood and played or used all over again. Present day standard music notation is based on a five-line staff. Pitch is shown by placement of notes on the staff (adapted by additional symbols called sharps and flats) and the fraction (4/4, 3/4, 6/8, etc.) shown at the beginning of a piece of music denotes the time signature.17

15 MARTIN,E., Architecture as a translation of music: Pamphlet Architecture No.16, pp 78-79 16 SHAW-MILLER, S., Thinking Through Construction: Notation-Composition-Event. The Architecture of Music, pg 38 17 KENNEDY, M., Concise Dictionary of Music, pg 519

This musical notation forms the structure, which binds the music and represents all aspects of a musical piece. at last it gets almost finished in my head, so that I can see it as a while, even when its a long piece, at a single glance, like a fine painting or a beautiful statue. Mozart

As such music is dreamed and created first in the visual realm before being actually played. Architecture too begins in embryo stage in the form of 2 dimensional graphical representations. The creation, investigation and preservation of architecture specifically rely on a standardized graphical notation. The architect, the creator that is, plays with the elements in the process of


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representation and translation, in order to reach their final goal. Same is the case as in music, where experimentation and playing plays the important part of perfecting the score. As such the musician too can use his own way own creating their representation form of the music; other techniques to show It is used in the experimental music(Figure 1), created and performed by musicians such as John Cage, which in many cases is difficult to transcribe in standard notation. Another example of this can be seen in the composition Metastasis (Figure 2), by Iannis Xenakis, which often appears more like a technical schematic than a musical score.

Till above, architecture and music have been discussed with respect to creation and its metaphorical applications. However, to fully understand their inherent bond, parallels in harmony must be investigated, as this presents the clearest connection between the two art forms. 1.3 Harmony Music can be separated into three parts; rhythm, melody and harmony. Although these are not the sole considerations during the creation of music, everything within music will be related to one of these three aspects. Rhythm can be described as the organization of music in respect to time; the regular occurrence of beat, which gives a sense of movement. Rhythm refers to any movement characterized by a patterned recurrence of elements or

motifs at regular or irregular intervals.18 These recurring elements are perceived using the senses, as stated by Plato, to understand the recurrence that follows as it proceeds. Rhythm incorporates the fundamental notion of repetition as a device to organize forms and spaces in architecture.19 Although rhythm can be found throughout architecture such as the rhythm of classical columns, the vaults of gothic churches and the progression of repetitive housing, it is not musical in entirety. Yet Rasumussen in Experiencing Architecture states architecture itself has no time dimension, no movement, and therefore cannot be rhythmic in the same way as music. As such rhythm does not a play a major part in the whole part of the design is not taken much into consideration. Melody is concerned with the progression and succession of notes, varying in pitch, which have a recognizable shape; therefore rhythm is an important in melody. Additionally, through its definition, melody is similar to harmony, yet has one distinctive difference; Melody is horizontal i.e. they are heard consecutively, whereas in harmony notes are sounded simultaneously. Architecture is viewed as a whole, therefore melody, is rarely transferred to architecture. In music, harmony is the use of simultaneous pitches (tones, notes), or chords. The study of harmony involves chords and their construction, chord progressions and the principles of connections that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect. Carl Dahlhaus says: harmony

18 CHING, Architecture: Form, Space and Order, pg 382 19 ibid pg 382


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The explanation of

the order and

harmony of Nature

was, for

Pythagoras, to be

found in the

science of numbers.

comprises not only the (vertical) structure of chords but also their (horizontal) movement. Like music as a whole, harmony is a process. As such harmony is taken into account for this discussion as seen above that harmony is viewed as a whole just as in the case of architecture. Before anything else, there was number, which was introduced into architectural theory during the medieval period. The clearest connection that can be made between music and architecture is that of mathematics, and this can be seen architecturally by the use of geometry. Geometry forms a large part of the creation of architecture; in the past geometry and architecture was once considered one and the same, with architecture symbolizing geometry in the built form. Research on the relationship between geometry and

music begins with the ancient understanding of the artes liberales". The seven artes liberales" in antiquity and the Middle Ages were grouped in the trivium" with grammar, rhetoric and logic whereas arithmetic, music, geometry and astronomy were brought together in the quadrivium". Architecture was assigned to practical arts (artes mechanicae"), where harmony

and proportion are applied to principles of creation. With new ideas of interdisciplinary of arts and sciences one should refer to this classical understanding. Pythagoras' ideas on harmony and proportion impressed the formation processes

in music and architecture over many centuries. Geometry was given the role of formalization and mediation of the relations between architecture and music. The explanation of the order and harmony of Nature was, for Pythagoras, to be found in the science of numbers. He speculated that harmonious sounds were emitted by the heavenly bodies as they described their celestial orbits. This is the harmony of the spheres a notion which Shakespeare found congenial (Merchant of Venice):

There's not the smallest orb which thou behold'st, But in his motion like an angel sings, Still quiring to the young-eyed cherubins. Music allowed for the translation of number and mathematics into art, through harmony. The simultaneous combination of these notes and the ensuing relationships of intervals and chords are known as musical harmonies. The development of harmony has subsequently resulted in a more philosophical conception of the term; by harmony we generally mean a fitting, orderly and pleasant joining of diversities, which in themselves may harbor many contrasts.20 It can also be perceived that everything in the universe is run according to perfect, meticulous harmony. Such perceptions of harmony have led it to be not solely used in music, but other arts as well.

20 DOCZI, G., The Power of Limits: Proportional Harmonies in Nature, Art and Architecture, pg 8


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Harmony is a state recognized by great philosophers as the immediate prerequisite of beauty. A compound is termed beautiful only when its parts are in harmonious combination. The world is called beautiful and its Creator is designated the Good because good perforce must act in conformity with its own nature; and good acting according to its own nature is harmony, because the good which it accomplishes is harmonious with the good which it is. Beauty, therefore, is harmony manifesting its own intrinsic nature in the world of form. As Keats says in his Ode on a Grecian Urn: Beauty is truth, truth beauty, that is all Ye know on earth, and all ye need to know. Exactly as said above, that is all one knows. What beauty is to man is nothing else the than the sense of pleasure he receives when seeing or hearing, whatever may be the medium. This beauty is nothing but the harmonious combination of an order applied on to a work, which in turn works its magic. Harmony in ancient world was considered to bring one closer to the Divine Perfection; Gods image. It can be understood from treaties of the past, how important it was to have that order, that harmonious relationship between its elements as it is the basic essence of creation. As seen, it is evident that man has used nature as his module. As such nature created in such exact proportion it is inevitable that man use those same proportions into his creations.

1.4 Proportions By now one must understand, just for a basic understand it is some proportions in mans creation that is used to create harmony. Since the basis for this study consists of the use of music as a metaphor in architecture through the musical device of harmony, the area of research that falls under the category of understanding harmony in music is avoided and the topic of harmony in architecture is given rather importance. But in order for one to complete understand the working of harmony in architecture some guidance is to be provided which has to do with music too. Thus in the human body there is a kind of symmetrical harmony between fore arm, foot, palm, finger, and other small parts; and so it is with perfect buildings.21 Vitruvius here is definitively talking about the harmonious proportions in which nature applies. How harmonious proportions came into being is to be understood first. These musical harmonies are a key factor in the metaphor of music in architecture they account for much of musics influence in architectural design. Although they may seem indirectly related, by the use of proportions in architecture it is possible to visualize musical harmonies.

21 VITRUVIUS, THE TEN BOOKS OF ARCHITECTURE, Chapter II- Fundamentals of Architecture


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Mathematically derived

proportion is a confidence

trick [Smithson and Smithson

1970: 94].

These proportions were considered sacred in ancient Greek construction and were considered to be elementary in their design since the concept of attaining harmony in the structure was considered crucial in the design. They brought these properties of harmonies in their construction through simple harmonic proportions: octaves, fifths and fourths for example. Thus they created architectural marvels which even stand today, in which the elements were made in harmony with each other. Everything that falls in the design phase: the plan, elevations, the roofing, even to the minute details of carving on the columns was created in according to this rule. Later on these principles were analyzed by Pythagoras and ended finding the harmonious proportions that plays in music. Here too these simple proportions were taken as Pythagoras as the module. For Pythagoras beauty was associated with the ratios of small integers. Much later on, by Renaissance Age great Humanists wrote treaties on the importance of bringing harmonious proportions into a building. Humanist such as Alberti and Palladio devised their own methods of arriving to their harmonious proportions. The use of musical harmonies is highlighted with the harmonious proportions of Alberti and Palladio used in architectural designs and that same numbers that enchant our ears, also delight our eyes. 22

22 ALBERTI, L., B., op.cit., p 196, cited MORRIS, Toby E., Musical Analogies in Architecture, The Structurist, pg 67

Alberti took influence from both Pythagoras and Plato to define the acceptable proportions of a building, and where these proportions should be taken from. Musical harmonies can used in architectural design and that the same numbers that enchant our ears, also delight our eyes.23 Palladio worked on the same concept of the proportions too, but made his own variations to the proportions. Palladio seems to be the first Renaissance architect to apply the Vitruvian concept of symmetry: that is, to relate the corresponding measures of several interconnected spaces.24 Much later on example of marvel to be mentioned would be the creation of The Modular by the genius Le Corbusier.

Although the Modular was actually not created by all sense of creation, it proved to be a way of Representation, the ultimate attempt of man to create the perfect order. Le Corbusier just brought order into the jumbled set of architectural construction proportions and unified them into the Modular using the rules laid by Ancient World. His Modular was constructed on the basis of Golden Proportions and other rules written in the past, as such it created the necessary harmony which is to be

23 ALBERTI, L., B., op.cit., pg 196, cited MORRIS, Toby E., Musical Analogies in Architecture, The Structurist, pg 67 24 PADOVAN, R., pg 234


20

formed as by nature. It is later on discussed to on how Le Corbusier applied these proportions for his creation of The Modular. As such seen from above discussions the importance of Proportions is understood through the terms of architecture. As of now this study will continue in a progression based on the further understanding of how Proportions can be incorporated into the design. Hence, the topics covered will have the necessary progression and will have to obviously begin with Gods Ultimate Creation: Nature in which He has brought in the Perfect order, the order in which represented His Image. It further continues on Pythagoras and his discovery of the harmonious proportions in music. Also the use of proportions in the works of Alberti and Palladio is explained as the study progresses. 1.4.1 Proportions: The Creators Tool What one must understand is that, underlying any creation that required perfection, proportions played a great role in creating that perfection, a naturally formed pattern which creates harmony on its own. Harmonies in music are same as that used in architecture as both share the same rules in proportions. As such it will be these proportions that all importance will be given for in this thesis. These proportions play the role of linking architecture to music to incorporate the harmony that is required. These harmonious elements work along to create the pleasing effect for the eyes just as music does for ears.

"We are now to treat of the Figure: By Figure I understand a certain mutual Correspondence of those several Lines, by which the Proportions are measured, whereof one is the Length, the other is the Breadth, and the other is Height.

"The Rule of these Proportions is best gathered from those Things in which we find Nature herself to be most complete and admirable; and indeed I am every day more and more convinced of the Truth of Pythagoras's Saying, that Nature is sure to act consistently, and with a constant Analogy in all her Operations:

"From whence I conclude that the same Numbers, by means of which the Agreement of Sounds affects our Ears with Delight, are the very same which please our Eyes and Mind. We shall therefore borrow all our Rules for the Finishing our Proportions, from the Musicians, who are the greatest Masters of this Sort of Numbers, and from those Things wherein Nature shows herself most excellent and complete." Leon Battista Alberti.

In his ten books On the Art of Building, Alberti discussed all aspects of architecture specifically, architectural proportion, Alberti presents a mathematically coherent theory of proportion, one that owes to the Pythagorean and Platonic theory of cosmic harmony.25 Having thus made a single whole of these three, he went on to make appropriate subdivisions, each containing a mixture of the Same, and Different, and Existence. He began the division as follows. He first marked off a section of the whole, and then another twice the size of the first; next a third, half as much again as the second and three times the first, a fourth twice the size of the second, a

25 PADOVAN, R., op.cit., p 220


21

fifth three times the third, a sixth eight times the first, a seventh twenty-seven times the first." Plato, Timaeus. In the Timaeus, Plato gives the first vivid description about all that exists is ultimately on single being; the one God and the Multiplicity of all things. He believed that God created man in his image and used certain proportions in bringing in Beauty in His creation. According to Platos quote as seen above, he describes about how the proportions are formed. The soul as Plato stated was divided into harmonious appropriate subdivisions summarized in the Lamda which Pythagoras used for summing up the existence of harmony. The Roman statesman, philosopher and mathematician, Boethius (480-524 A.D.) explained that the soul and the body are subject to the same laws of proportion that govern music and the cosmos itself. The belief of many during the past, a past that includes greats such as Pythagoras, Alberti, believed in the cosmic music of the universes. They believed that since these heavenly bodies where harmonious in their own way as they were the perfect creation of God as such the music of the cosmos is produced, that perfect harmonious music that cannot be perceived by our senses. Yes, they can be perceived, they have been heard by man in the past. Pythagoras taught that each of the seven planets produced by its orbit a particular note according to its distance from the still centre which was the Earth. The distance in each case was like the subdivisions of the string referred to above. This is what was called Musica Mundana, which is usually translated as Music of the Spheres. The sound produced is so exquisite

and rarified that our ordinary ears are unable to hear it. It is the Cosmic Music which, according to Philo of Alexandria, Moses had heard when he received the Tablets on Mount Sinai, and which St Augustine believed men hear on the point of death, revealing to them the highest reality of the Cosmos. In the Pythagorean concept of the music of the spheres, the interval between the earth and the sphere of the fixed stars was considered to be a diapason (1/2) -the most perfect harmonic interval. The following arrangement is most generally accepted for the musical intervals of the planets between the earth and the sphere of the fixed stars: From the sphere of the earth to the sphere of the moon; one tone; from the sphere of the moon to that of Mercury, one half-tone; from Mercury to Venus, one-half; from Venus to


22

the sun, one and one-half tones; from the sun to Mars, one tone; from Mars to Jupiter, one-half tone; from Jupiter to Saturn, one-half tone; from Saturn to the fixed stars, one-half tone. The sum of these intervals equals the six whole tones of the octave. What from the works of the past its evident of the presence of work of proportions which play in bringing order to a creation. As seen, Nature too follows this pattern of proportion which lays rules for Her creations to be born. This proportion is evident in Her work and has been Mans greatest tool for his creation. It is up to these measurements that man looked upon for his module when creation began by man. These proportions as by nature created harmony among itself as the cosmic design as such the creations of man were harmonious in nature. The harmony of what Plato called as "one visible living being, containing within itself all living beings of the same natural order". 1.4.2 Harmony in Nature The creative method of Nature is a topic that has spilled ink over the centuries, about how it happens and its specifics. Throughout history, many great people have pondered, worked out and understood this sensitive matter. The Ancients....did in their Works propose to themselves chiefly the Imitation of Nature, as the greatest Artist at all Manner of Compositions," Leon Battista Alberti. Throughout nature, an underlying pattern seems to connect all forms. When investigated we discover perfection, an incredible

order that can leave one in awe of the world around us.26 Harmonies can be found throughout most objects, be them natural or manmade, like an imposed musical structure on the physical world. Many examples of this can be found in Gyrgy Doczis The Power of Limits: Proportional Harmonies in Nature, Art and Architecture, the simplest of which are the harmonies and musical

progressions found in the growth pattern of leaves (Figure 6) and in snowflakes (figure 7). The relationship found in this natural creation indicates that the same dinergic harmonies that delight our eyes in the shape of leaves and flowers also enchant our ears in the chords and melodies of

music.27 It is intriguing that harmonious patterns are not solely concentrated to just the formation of leaves, but other objects in nature, such as shells and even the proportions of the human form. Spirals found in shells, such as those discussed by Doczi, are defined by logarithmic patterns, which abide by the Golden sections proportions. It is astounding how organic growth can create such harmonious forms in all examples.

26 DOCZI, G., op.cit., pg i 27 ibid pg 13


23

A straight

line is said to

have been cut

into extreme

and mean

ratio when,

as the whole

line is to the

greater

segment, so

is the greater

to the lesser.

The harmonious proportions of the human body have been discussed greatly, by such people as the first know architect, Vitruvius and Leonardo da Vinci. These harmonic proportions; Divine Proportions, governs the physical form, define the parameters of any architecture made for human kind. Nature by far has excelled herself as the Divine creators perfection. Creating the pattern required for Her to make her unique world, She has chosen a perfect proportion for Her Replication. This proportion is unchanged, through the spam of time unknown, it continues to recreated, ever unknowingly, ever beautiful.

hen speaking of nature proportions, the topic of Divine proportions should be talked about. One should be given a proper insight about the Divine

Proportions, in order for the proper understanding of the division that lays foundation for the creation for life. 1.4.3 Divine Proportions: The concept of Divine Proportions division appeared more than 2400 years ago as evidenced in art and architecture. It is possible that the magical golden ratio divisions of parts are rather closely associated with the notion of beauty in pleasing, harmonious proportions expressed in different areas of knowledge Divine Proportion is also known as the Golden Ratio, Golden Section, Golden Mean and the mean of Phidias.

Although not identifying it as the Golden Ratio, Euclid of Alexandria (325-265 B.C) defined the proportion in his Book VI of the Elements: A straight line is said to have been cut into extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. The properties of golden ratio were mentioned in the works of ancients Greeks such as Pythagoras and Euclid, the Italian mathematician Leonardo of Pisa (1170 or 1180-1250), and the Renaissance mathematician J. Kepler (1571-1630) and Humanists such as Alberti has incorporated them into his designs. In 1509, L. Pacioli published the book De Divina Proportione in which he bought in new emphasis on the golden ratio, in which he illustrated the golden ratio as applied to human faces. G. Cardano (1545) mentioned about the golden ratio in his book Ars Magna and J. Kepler found the golden ratios presence in the Fibonacci sequence and it was Kepler who called it as Divine Proportion. M. Ohm (1835) gave the first known use of the term Golden Section and J. Sulley (1875) first used the term Golden Ratio in English with G. Chrystal (1898) using it first in mathematical context.

The ratio is given the Greek symbol (Phi) in honor of the great Greek sculptor Phidias who made extensive use of the

W

Greater

Lesser


24

ratio when designing buildings such as the Parthenon and the Propylaea on the Acropolis in ancient Athens. Though was

known then to mathematicians as Tau the Greek for the cut or the section, it wasnt until the early 20th century that the American mathematician M. Barrwas suggested the name phi the first Greek letter in the name of the Greek Phidias.

There is only one point that makes the golden section; this point is called the Golden Section Point. Dividing a segment into two parts in mean and extreme proportion, so that the smaller part is to the larger part as the larger is to the entire segment, yields the so called Golden

section and the ratio

designated

as , is known as the golden number. The ratio

is the reciprocal of . This number has many fascinating qualities and the ancient Greeks considered the regular pentagon which includes a number of 'golden ratio' relationships, as a holy symbol. The ratio of the golden section has to do with the Fibonacci Series. The Fibonacci series is a series of numbers in which the sum of the previous two numbers equals the following number. The Fibonacci series is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.. As the series goes on (as the numbers get larger), the ratio of each two adjacent numbers approximates to the golden section.

shows up throughout nature. Recall the famous drawing by Da Vinci showing man within the circle and the Golden Ratios in the human body, and more recently, Le Corbusier's

The Modular. For example, the finger bones are in ratio to each other, and the position of features on the human face

follow . The major 6th harmony interval in music is in ratio to the octave.

In the figure the point B divides the line AC of length 1 in the extreme and median ratio. Such that

AB: BC= =1.618 The Golden Ratio, divides a line at a point such that the smaller part relates to the greater as the greater relates to the whole: the ratio of the lengths of the two sides is equal to the ratio of the longer side to the sum of the two sides. As such according to the rule the above line of length 1 and the larger sub segment being then,

=

Thus is the solution of the equation:


25

Through the above formulae value of is gained as 1.61803 as the positive value and 0.61803 as the negative, the latter

being called as , as being the negative reciprocal of It is interesting to note that the golden proportions have influences in mathematics too. The astounding Fibonacci Sequence (named after the 13th century mathematician Leonardo of Pisa who introduced the concept to Western culture): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377is both additive, as each number is the sum of the previous two, and multiplicative, as each number approximates the previous number multiplied by the Golden Section. The ratio becomes more accurate as the numbers increase, forever closing in on the divine limit.28 i.e. as the number increases to higher limits towards infinity it is then that one reach closer to the value of as 1.6180340, the exact value to seven decimal places. So how a line can be divided into its golden section is shown diagrammatically alongside.

In the figure, the line AC of length a is divided by the point B at a pot that AB:AC=AB:BC. A rectangle which is in the ratio of the length to width is equal to 1. 618

28 Dr. Scott Olsen, Ph.D., The Golden Section: Natures Greatest Secret, pg. 10

approximately, is called a golden rectang1e The construction of the golden rectangle is a simple matter. The side BC of a square ABCD is bisected. With that point say E as center, an arc from point D is drawn cutting BC produced in G. Draw GF perpendicular to AB meeting AD produced in G. Then AFGB is the golden rectangle. The proof is equally simple. Let BC= 2 units of length. Then ED = EG= 5 units BG/GF = (BE + EC)/ GF = (1 + 5)/2= 1.618034 BG is divided by C in the golden section. C is sometimes called the "golden cut." It is associated with the idea of the "mean proportional ": BC is the mean proportional of BG and CG:

=

, i.e. BC2

For the subdivision of a Golden Rectangle, a rectangle of a certain property is taken into consideration. The rectangle should be as such that if a square is cut off from it the remaining rectangle should be similar to the original rectangle.


26

For better understanding this example is taken. Let a rectangle of length 1 and width x. A square of side-length x is cut off, there remains a rectangle of length x. As seen, the Golden Rectangle when cut using the Golden cut on it, then the end result is another Golden rectangle, this process is inexhaustible. For the further division of the Golden Rectangle, the figure aside gives the further explanation.

The end result being:

Figure below shows a logarithmic spiral superimposed on a coiled Golden Rectangle. This study shows the -ratio sectioning of the Golden Rectangle with short side squares and the diagonals of the original seed Golden Rectangle and the diagonal of the first -sectioned Golden Rectangle. Note that the two diagonals intersect at a point called the "Eye of God," the origin of the logarithmic spiral.


27

1.4.4 Phi in Music and Architecture The part phi plays in music is something needs to be explained in detail. As such one must have understood the perfect harmony phi creates in application. Its arranges, or rather said, creates an order in the proportioning laws, a perfect module; Natures Tool. Again musical intervals play along with the phi to create the necessary magic in creation. The musical intervals as stated earlier was experimented by Pythagoras. H.E Huntley in The Divine Proportions explains about the Divine proportions and relations it have with music through the use the musical interval major sixth, which according to him had the perfect relation with the Golden Cut. He offers an explanation by beginning the explanation by the psychological effect of the Golden Rectangle. The Golden Rectangle according to Huntley had a positive effect on the aural nerve just as a harmonious tone would for the ears. When one sees a Golden Rectangle the time interval the eyes take to relate the adjacent length of the rectangle is what links the two together.

However complex physiologically the act of seeing an object may be, the estimation by the eye of the relative lengths of the two adjacent sides of the rectangle is ultimately reducible to the instinctive measurement of the relative duration of two time intervals.29 The ratio of time taken for the line of vision to swing between two adjacent sides is registered instinctively by mans internal clock. The experience gained by man in the past makes him realize and come to an

29 HUNTLEY,H.E, The Divine Proportion: A Study in Mathematical Beauty, pg 52

analysis about the ratio of the length of the sides and conclude it to be a square or a rectangle. For example, its the past gained knowledge of one to understand a figure is a square through the two time intervals taken to analyze the sides.

Hence by now, one can answer the question of why the Golden Rectangle has an aesthetic appeal of its own. Its the time interval taken to analyze by the aural nerves of these harmonious proportional sides, that brings the soothing sensation same as the case of these harmonious intervals in music.

Pythagoras noted the interesting fact that the musical intervals which are most consonant30 are reducible to the ratio of small integers:

INTERVAL FREQUENCY RATIO Unison 1:1 Octave 2:1 Major Third 5:4 Major Six 8:5

As explained earlier there is exist a process of registering the harmonious proportion by the brain bringing a calming aural effect. Hence, when the ear hears an octave and the eye beholds a rectangle which is equivalent to a double square. 30 Harmonious blending of the tones of certain musical intervals was that an absence of "beats" between their harmonics resulted in consonance. The sound emitted by two notes such as those separated by a semitone is a dissonance: such an interval is rich in beats between interfering harmonics, a discord obnoxious to the ear.- Helmholtz


28

Parthenon,

designed by

Phidias, was

dedicated to the

Goddess

Athena,

therefore being

of utmost

importance.

But it is in accord with observation and experiment that the musical interval which gives the greatest satisfaction to the greatest number is the major sixth, frequency ratio 8:5, approximately. This corresponds to the pleasure experienced in seeing the golden rectangle, the adjacent sides of which are in the ratio- :1, which is approximately equal to 8:5.31

So for Huntley, the ratio- 8:5 create the most harmonious environment. This is explained by him due to the perfect proportion which brings in the concept of harmony, and hence eventually Beauty in Representation.

The work of Phi as said earlier was crucial in Ancient Greek designs. This fascinating relationship was a major part of Greek designing. The Golden Cut played an important part in the proportioning of their building. The Parthenon by Phidias is a striking example for the magnificent work of art.

ow to understand the work of Golden Proportion in ancient Greek architecture is explained.

Rather said, the previous line can be rephrased in a matter suiting this thesis to as: The part Proportion played in ancient Greek Architecture.

31 HUNTLEY,H.E, The Divine Proportion: A Study in Mathematical Beauty, pg 55

Parthenon, designed by Phidias, was dedicated to the Goddess Athena, therefore being of utmost importance. Buildings on the Acropolis in ancient Athens such as Parthenon and the Propylaea were constructed by Phideas as a monument to Greek Goddess Athena. Here one can see the work of musical proportions in the construction. The front columns of the Parthenon with their seven spaces embody the 3:4 ratiosthe corresponding musical harmony of the fourth-diatessaron(and the) fifth-diapente harmonies. This clearly shows a consideration of Pythagorean theories about harmony and their beauty when translated into visual forms. The Parthenons plan corresponds to two reciprocal golden rectangles, thus echoing the diapente harmony. The naos or celle of the temple and the treasury or virgins chamber in the Parthenon is in golden proportion32 The role Golden Proportions played in the construction of Parthenon is as explained below. If the Parthenon is inscribed inside a rectangle the so formed rectangle is a Golden Rectangle of ratio of side- 1:. Furthermore, the Parthenon has been constructed using the intervals considered to be harmonious to the ancient Greeks: fourth, fifth and octave respectively. The use of proportions is quite evident in every element in the Parthenon, even from the column spacing to the placing of the pediment. The plan being derived from the elevation too is attained using the Golden Proportion. The following pictures will provide an explanation to how the proportions where used in designing of the Parthenon. Only

32 DOCZI, G., op.cit., pg 110

N


29

basic dimensions where analyzed in the elevation which provided the result of the use of diapente as the proportion rule.

Many have investigated the Parthenon, resulting in different interpretations of its proportions. It is clear that some alterations have been required in the musical interpretation of the proportions for both of these buildings and this can also be true for the investigation for many other musical buildings. Obviously, some margin of error must be allowed for the construction of the buildings during times where any competent degree of accuracy was impossible in comparison to contemporary standards. What the end result of such analysis is the unconventional truth of existence the harmonious intervals in the construction of the ancient Greeks. As such it can be stated that the Greeks and Romans must have considered musical harmonies to a high regard as they were used in the design of their most significant buildings.


30

.Pythagoras

as it is he who

raised the art to

its true dignity

by

demonstrating

its

mathematical

foundation.

s of till above what has been discussed is the part proportions played in the ancient world and its understanding in the creation of Nature. As such, it is

seen that proportions got its own natural way bringing an order into its elements. Whatever be the proportion, there exists then an order, even if the case of unharmonious intervals, even if they play in accord there exist a pattern between their unharmonious tones creating their own music or in any other sense work of art.

Above, it is stated that harmonious intervals play a role in creation of beauty. In order for one to know how the understanding of harmony began in music, a small diversion here is required. Pythagoras and his discovery in music is to be understood. For understanding the principles behind the concepts of harmony and its role its play in the creation, one must begin with Pythagoras as it is he who raised the art to its true dignity by demonstrating its mathematical foundation. It is he who simplified the harmonious proportions in music.

1.5 Pythagoras (570-480 BC) The term harmony originated from the Greek word harmos, which can be translated to mean, to join. At the time of Pythagoras music was very rudimentary, to the point where there was no understanding of musical harmony. However, this changed with Pythagoras, who was concerned with the

nature of musical intervals; that is, with the sound of two different notes played in succession. 33 According to Pythagoras all things and principles of being can be grasped by integers and mathematical regularities. Thus he also expressed harmony by using relations on integers. He found that musical intervals are reached by the division of a string as well as the relations between the numbers of sound oscillations. All harmonic proportions are express able by the numbers of Tetraktys34; in the four directions north, south, east, west and the four elements water, fire, air and earth. Having first learned the divine theory of music from the priests of the various Mysteries into which he had been accepted, Pythagoras pondered for several years upon the laws governing consonance and dissonance. Pythagoras experimented with musical tone with the use of the monochord. Pythagorass mind, alive to possibilities, came upon a very simple theorem that had cosmic value. The legend is that Pythagoras, while walking past a blacksmiths shop, heard different pitches being emitted from the striking of the anvils. Pythagoras first realized complete musical harmony when noticing a musical relationship between the tones created by the striking of five blacksmiths hammers. Four of the five hammers seemed to create tones, which sounded harmoniously, while one did not.

33

VALENS, E. G., The Number of Things: Pythagoras, Geometry and Humming Strings, pg 149 34 The integers 1, 2, 3 and 4

A


31

or in

short the

whole

concept of

harmony

according

to

Pythagora

s rested of

these

intervals.

What must have gone through his mind was the variation in pitches was possibly created by the different weights of the hammers. Then he recreated the whole incident by hanging weights on to chords; twelve, nine, eight and six respectively (different weights corresponded to the sizes of the braziers' hammers). Number (in this case amount of weight) seemed to govern musical tone. Pythagoras thereupon discovered that the first and fourth strings when sounded together produced the harmonic interval of the octave, for doubling the weight had the same effect as halving the string. The tension of the first string being twice that of the fourth string, their ratio was said to be 2:1, or duple. By similar experimentation he ascertained that the first and third string produced the harmony of the diapente, or the interval of the fifth. The tension of the first string being half again as much as that of the third string, their ratio was said to be 3:2, or sesquialter. Likewise the second and fourth strings, having the same ratio as the first and third strings, yielded a diapente harmony. Continuing his investigation, Pythagoras discovered

that the first and second strings produced the harmony of the diatessaron or the interval of the third; and the tension of the first string being a third greater than that of the second string, their ratio was said to be 4:3, or sesquitercian. The third and fourth strings, having the same ratio as the first and second strings, produced another harmony of the diatessaron. Pythagoras investigated the number series 6, 8, 9 and 12 and was able to devise a clear relationship known as musical harmonies.35 According to Iamblichus, the second and third strings had the ratio of 8:9, or epogdoan. Pythagoras studied on these intervals or proportions he discovered as he taught at his school about these same intervals but here these intervals where about the stars and earth (as discussed earlier), or in short the whole concept of harmony according to Pythagoras rested of these intervals. From this point Pythagoras began to experiment and investigate different musical intervals and the effect of playing different notes simultaneously. The sound experiments were developed by Pythagoras using his monochord"36, a simple instrument with one string tightened over a resonance box. What he gained in understanding in this experiment is about the proportions which act in the play of pitch, the same proportions that

35

VALENS, E. G., The Number of Things: Pythagoras, Geometry and Humming Strings, pg 154 36 A single stringed instrument with a moveable bridge


32

The end results to his experiments were that the length of a string is

directly related to its pitch.

formed the sacred symbol of the Pythagoreans. By halving the string one get the octave (1:2). The proportion 2:3 stands for a fifth and 3:4 for a fourth. The proportion 4:5 for the major third was not included as a harmonic interval in the Pythagorean system. Later on, in the Renaissance the Tetraktys" was enlarged by Zarlino (1558), so that the major and minor third (4:5 and 5:6), the second, and

the sixth were also included as consonant proportions.

The end results to his experiments were that the length of a string is directly related to its pitch. Pythagoras confirmed his observation that any musical tone will be raised one octave whenever the string producing the tone is reduced in length by one-half.37 Pythagoras realized that when two strings are plucked together, the most harmonious sound will be created when the two strings are equal, or when one is plucked at , 2/3, or of the others length.38

37

VALENS, E. G., The Number of Things: Pythagoras, Geometry and Humming Strings, pg 149 38 DOCZI, G., op.cit., pg 8

He began then constructing the musical intervals for a perfect fourth and a perfect fifth mathematically, as they were the most perfect (Figure 5). Pythagoras experimented with the perfect fifth interval as he could construct this relationship using only four numbers, the same four numbers that make up the triangular number ten.39 The discovery of the number ten within the structure of the fifth interval compelled Pythagoras to continue his investigation of the relationships between musical notes, which eventually led to his discovery of musical harmony.

Moreover, Pythagoreans often referred to the harmony of the universe through its architecture of musical spheres,

describing their orbits through the harmonic principles discovered by Pythagoras. They

maintained that the universe sings and that the fast planets like Mercury sing in a higher voice than do the slow ones.40 It is clear that for the Pythagoreans the architecture of the universe, geometric forms and musical harmony were all

39 ibid pg 151 40 VALENS, E. G., op.cit., pg 147


33

intricately related in the harmony of the cosmos. Hence as usual, the eventual quest of Pythagoras was to find that harmony that rang in Gods Creation.

y this end one can put forth the argument that musical intervals play a major part in the harmonizing of music. The bringing in of harmony through the

proportioning as understood is due to its pitch being in relation to the length of the string. Pitch as in the sense required, the time interval as Huntley stated. This harmony, according to Pythagoras could be converted into mere integers. And it is these integers that played the catalytic role for the future development to come in architecture, when order was bought into chaos, when the world was keen to know about harmonious elements in structures. The musical harmonies, which have previously been discussed, are a key factor in the metaphor of music in architecture they account for much of musics influence in architectural design. Although they may seem indirectly related, by the use of proportions in architecture it is possible to visualize musical harmonies. In order to illustrate the theories of architectural harmony, the theories of harmony in art and architecture of Humanists, such as Leon Battista Alberti and Andre Palladio will be discussed. As it is Humanists greats such as Alberti and Palladio who brought the play of proportions in buildings.

1.6 Leon Battista Alberti During the fifteenth century, an emphasis began to be placed on the work of artists; music, arithmetic, geometry and astronomy, made up the Quadrivium and were known as the liberal arts.41 Together with the Trivium (Grammar, Rhetoric and Logic), they were promoted in the middle ages as vital for the education of the human being. This resulted in the elevation of theory, due to creation being considered inferior. But this in turn created a spirit of learning that developed at the end of The Middle Ages. During the period the focus of many intellectuals began to include practice as well as theory, through the translation of texts by the old masters, such as Socrates and Plato. This resulted in the realization of work by Humanist greats such as Alberti. As provided in Proportion: Science, Philosophy, Architecture, Alberti explains that For us, the outline is a certain correspondence between the lines that define dimensions;

41 WITTKOWER, R., Architectural Principles in the Age of Humanism, 4th ed., p 117

B


34

It is Alberti

who first

directly

attributed

musical

harmonies to

beauty in

architecture,

since stated by

Plato and

Pythagoras.

one dimension being length, another breadth, and the third heightI affirm again with Pythagoras: it is absolutely certain that Nature is wholly consistentThe very same numbers that cause sounds to have concinnitas, pleasing to the ears, can also fill the eyes and mind with wondrous delight. From musicians therefore or from those objects in which Nature has displayed some evident and noble quality, the whole method of outlining is derived.42 It is Alberti who first directly attributed musical harmonies to beauty in architecture, since stated by Plato and Pythagoras. Before this insight by Alberti, the application of musical theory to architecture had all but vanished, and without the belief in harmony, there was just number. However, with Albertis discussions, the use of music in architecture had been revitalized, drawing upon the harmonies discussed in Platos Timaeus to issue new considerations for the use of proportion and harmony in architectural design.43 This was caused by a belief that the same relationships which determine musical intervals also determine the movements of stars and, through astrological influences, affect the events on Earth.44 As such as seen similar to Pythagoras, Alberti believed in Cosmic Music, the

42 ALBERTI, L., B., On the Art of Building in Ten Books, p 196, cited in PADOVAN, op.cit., p 220 43 MALLGRAVE, H., F., op.cit., p 34 44 MITROVIC, B., Andrea Palladio's Villa Cornaro in Piombino Dese,

Harmonious Music of the Cosmos. He believed in the existence of harmonious proportions in the work of beauty. As such Alberti ended up creating harmonious proportions between the elements of the room through linking them to the musical harmonious ratios. Alberti began his investigation into harmony with the translation of musical harmonies into architectural proportions; he uses these proportions to define the areas of horizontal spaces, grouping them into short,

medium or long. Alberti composes these areas much like a musician would; in fact Alberti attempts to compose allratios out of the simple ratios 3:2, 4:3 and 2:1 in musical terms, the basic Pythagorean harmonies: fifth, fourth and octave. 45 What it resulted in was the amazing harmony attained between the different

45 PADOVAN, R., op.cit., p 221


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dimensions of a surface with its individual constituents. Alberti would only use ratios that could be broken up into the consonant intervals of the musical scale, the cosmic validity of which was not doubted.46 Alberti continued to use this technique in definition of three dimensional spaces and this technique influenced many of his contemporaries The following will describe about how Alberti used the musical intervals to create a relation for rooms proportioning. Alberti develops the relationship between the proportions of numbers and the measuring of areas. Methodically, he lists three types of area; short, middle, and long. The shortest of all is the square, and in this category of short areas he includes: sesquialteria, or fifths, or diapente, and sesquitertia, or fourths, or diatessaron.

These three Proportions therefore, which so called simple, are," he says, "proper for the smaller Platforms."

46 WITTKOWER, R., op.cit., pp 101-2, cited in PADOVAN, R., Op cit, p 221

Then he lists three further Proportions "Proper for middling Platforms": First the Double, which he says is best; second, the Sesqialtera Doubled; And third, the Sesquitertian Doubled.

The first is straight forward, The second is found by taking a square, finding its fifth or sesquialtera, and extending the area by that amount, and then, in turn, extending that area by its fifth. "Thus the Length will exceed the Breadth by a double Proportion plus one Tone more" The third Proportion is found by doing the same with the square and its Fourth. "Here the longer Line contains the shorter twice, excluding one Tone of that shorter Line."


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For his category of "long" areas he lists three: Double Sesquialtera, Double Sesqitertia, and Quadruple. So these are Albertis proportions: Short- 1:1, 2:3, 3:4 Middle- 2:4. 4:9, 9:16 Long- 1:3, 3:8, 1:4 During the time of Alberti music had a

particular attraction for artists because it had always been considered a mathematical science and in his work, Alberti was striving towards the creation of harmony within architectural design.47 A famous name that can be used as an example would be Leonardo da Vinci. He became highly interested in Albertis theories, and this can be viewed in his fascination in perspective; for both, music and painting convey harmonies; music does it by its chords and painting by its proportions.48

47 WITTKOWER, R., Architectural Principles in the Age of Humanism, 4th ed., p 117 48 WITTKOWER, R., Architectural Principles in the Age of Humanism, 4th ed., p 118

Musical intervals and linear perspective are subject to the same numerical ratios, for objects of equal size placed so as to recede at regular intervals diminish in harmonic progression. 49This clearly shows the influence Albertis theories on musical harmony in architecture had on Leonardo. Furthermore the Vitruvian Man, done by Leonardo, is the genuine proof to the argument that proportions have been worked on and studied by him. It is to be understood, the general trend that staged during the Golden Renaissance Age is being displayed, where the artisans realized their potential in reaching closer to their goal of perfect creations.

49 ibid pg 118


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.and it is this demand

for the right ratio which is

at the centre

architectural thesis- music in architecture

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