The ‘Vitruvian Man’
J.S.Bach – Art of Fugue No.1 (c.1740-50)
Leonardo tells us that this most famous of drawings is based on a statement in the Ten Books of Architecture by the ancient Roman architect, Marus Vitruvius Pollio:
If a man lies on his back with hands and feet outspread, and the centre of a circle is placed on his navel, his figure and toes will be touched by the circumference. Also....a square can be discovered as described by the figure. For if we measure from the sole of the foot to the top of the head, and apply the measure to the outstretched hands, the breadth will be found equal to the height.
Unsurprisingly a number of draftsmen had tried to illustrate Vitruvius’s formula, but they assumed that the circle and square should both be centered on the navel, which is not what Vitruvius actually said. The only convincing way to make the formula work is to assume that that the square is centered on the man’s genitals. Leonardo additionally shows that ‘If you open your legs so much as to decrease your height by 1/14 and spread and raise your arms so that your middle finger are on a level with the top of your head, you must know that the navel will be the center of a circle of which the outspread limbs touch the circumference; and the space between the legs will form an equilateral triangle’. Leonardo’s positioning of he fingers and toes is the only arrangement that works with the main circle.
The overall schema is geometrical, but the internal proportions are numerical. For example, “the face from the chin to the top of the forehead and the roots of the hair is a tenth part [of the body]; also the palm of the hand from the wrist to the top of the middle finger is as much; the head from the chin to the crown, an eighth part”. The many compass marks show that the internal music of the body is composed from measured intervals, not pentagons or the other geometrical figures that are often imposed on the image. The numerology is analogous to Pythagorean intervals in music.
Leonardo saw the proportional harmonies of human body and the proportional harmonies of music as originating from the fundamentals of God’s design. The proportional diminution of forms in linear perspective and the proportional diminution of ‘impetus’ in a moving body manifested the same rule of divine mathematics.
The pool of literature on numerology in Bach’s music is too deep to dip into here but the fugues in his iconic Art of Fugue are a study in form and balance: proportion and horizontal ‘argument’ in music from the most universal of composers.
Rebecca Lea - soprano
Clare Wilkinson - mezzo-soprano
Nicholas Mulroy - tenor
Charles Gibbs - bass