Once I opened my eyes, once I took in the first deep breath in this marvellous play of colours and forms, once I began a part of this mysterious world. Much later, when I grew up, I slowly opened my eyes again and began to see another form of beauty: an astonishing beauty of mathematics behind most of aspects of this physical reality we have been born in. Now I consider this world to be not only beautiful, but also graceful in its crystalline mathematical background and I imperfectly try to share this worldview with people around me.
A circle of fifths represents a sequence of tones, each higher of one fifth (3:2) than the previous one. Frequency of each tone due to reference frequency of C is shown as a projection of linear harmonograph. Frequencies of all tones are achieved here by successive steps of fifths (3:2) up and octaves (2:1) down, accordingly all other derived intervals are then imperfect. This is a source of two aspects: firstly, curves of those intervals seems to be asymmetric and unordered at the beginning, however, during following evolution create a pattern of beauty and inner structure, secondly, the whole circle seems to transform itself into a spiral, while we are not reaching back the original tone, but a tone slightly higher (Pythagorean comma).
This canvas represents a spectrogram of the first movement of one of Béla Bartók’s best known compositions. Musical structure is built on the Fibonacci numbers sequence: 21 bars of exposition of melody, removal of violin mutes at bar 34 and the highest musical climax at bar 55, which is clearly visible as a strong vertical line, dividing the 89 bars long movement approximately in the golden ratio. This image can be read as a score: horizontal axis represents time pointing from first tone to the last one, vertical axis represents frequency from 0 to 20 000 Hz while colour describes sound intensity level at any point.