A distinguishing characteristic of the series of ratios which represent the consonant intervals within the compass of an octave is that it advances by the addition of 1 to both terms:  1:2, 2:3, 3:4, 4:5, and 5:6.  Such a series always approaches unity, just as, represented graphically by means of parallelograms, it tends toward a square.  Alberti in his book presents a design for a tower showing his idea for its general proportions.  It consists of six stories, in a sequence of orders.  The lowest story is a perfect cube and each of the other stories is 11-12ths of the story below, diminishing practically in the proportion of 8, 7, 6, 5, 4, 3, allowing in each case for the amount hidden by the projection of the cornice below; each order being accurate as regards column, entablature, etc.  It is of interest to compare this with Ruskin’s idea in his Seven Lamps, where he takes the case of a plant called Alisma Plantago, in which the various branches diminish in the proportion of 7, 6, 5, 4, 3, respectively, and so carry out the same idea; on which Ruskin observes that diminution in a building should be after the manner of Nature.

[Illustration 90:  ARCADE OF THE CANCELLERIA]

It would be a profitless task to formulate exact rules of architectural proportion based upon the laws of musical harmony.  The two arts are too different from each other for that, and moreover the last appeal must always be to the eye, and not to a mathematical formula, just as in music the last appeal is to the ear.  Laws there are, but they discover themselves to the artist as he proceeds, and are for the most part incommunicable.  Rules and formulae are useful and valuable not as a substitute for inspiration, but as a guide:  not as wings, but as a tail.  In this connection perhaps all that is necessary for the architectural designer to bear in mind is that important ratios of length and breadth, height and width, to be “musical” should be expressed by quantitively small numbers, and that if possible they should obey some simple law of numerical progression.  From this basic simplicity complexity will follow, but it will be an ordered and harmonious complexity, like that of a tree, or of a symphony.

[Illustration 91:  THE PALAZZO VERZI AT VERONA (LOWER PORTION ONLY).  A COMPOSITION FOUNDED ON THE EQUAL AND REGULAR DIVISION OF SPACE, AS MUSIC IS FOUNDED ON THE EQUAL AND REGULAR DIVISION OF TIME.]

[Illustration 92:  ARCHITECTURE AS RHYTHM.  A DIVISION OF SPACE CORRESPONDING TO 3/4 AND 4/4 TIME.]

In the same way that a musical composition implies the division of time into equal and regular beats, so a work of architecture should have for its basis some unit of space.  This unit should be nowhere too obvious and may be varied within certain limits, just as musical time is retarded or accelerated.  The underlying rhythm and symmetry will thus give value and distinction to such variation.  Vasari tells how Brunelleschi.  Bramante and Leonardo