Harmonic Composition Lines.
This is something that has been floating around for centuries, discovered by Pythagoras, in fact. The following excerpts are from Juliette Aristides’ Classical Atelier Painting:
…Compositional schemes and their accompanying philosophies have come in different forms over the centuries….yet none has dominated the art worlds of the past so much (and none is as little known today) as the composition schemes based on harmonic proportion. This particular field of design owes its discovery to Pythagoras.
….legend has it that in 500 B.C.E, Pythagoras was walking past a blacksmiths’ shop when he noticed that each of the sounds emanating from the hammers hitting the anvil was different. He went into the shop to investigate and discovered that the different sounds were caused by the avarious sizes and weights of the hammer. This led to his discovery that number, e.g the size and weight of the hammer, creates a physical effect in space and time ( in this case a sound)..
Pythagoras wanted to further investigate this mysterious connection between number and physical reality as it is manifested through sound. To do so, he conducted experiments with musical strings of different lengths. Pythagoras found, like hammers, the shorter strings (smaller numbers) produced higher pitched sounds and vice versa. H ethen made a startling discovery. First, eh struck teh string, Then, ehile it was vibrating, he lightly touched his finger along teh string. In most places, this deadened the sound. Yet in a few places a remarkable physical phenomenon occurred- the clear and pleasing ringing of a musical tone. The new tones were created at the one half, two thirds and three quarters divisions of the string when measuring the string from right to left. When measuring the string from left to right, however, these tones are created at the one quarter, one third and one half divisions.
…these pleasing tones are called ‘harmonics’ or ‘musicial root harmonies’. They are the result of the sting taking a new physical form called a sinusoidal wave when it is pressed at the one half, two thirds and three quarter division points. We now refer to these key positions along the string as the ‘octave’, the ‘perfect fifth’ and the ‘perfect fourth’ respectively….
….Curiously, the same ratios that are pleasing to our ears provide pleasing intervals to our eyes. Throughout history, master artists have used the harmonic ratios discovered by pythagoras….
This site explains how to construct the armature. I used a rather simplified form of it-
and here is the original armature from Bouleau: