Anarchy, chaos and terror have had some historic impact on the arts of the 20th century. I have no doubt that the tendencies of an overly outdated or primitive culture or anti-culture should now be done away with. This is brought about by a music which is novel but aware of its natural fundamentals. They are deeply interwoven with the phenomenon of “harmonics“ (contained in the harmonic series). A harmonical approach re-establishes the precise distinction of musical sounds and their interrelations which were neglected in “atonality“ but are evidently rooted in human life and experience. This helps to achieve a new power of melodic and harmonic expression in connection with a meaningful configuration of rhythm and form - which can last not least resolve problems of transmission and understanding.

The purpose of music should not be depression or incapacitation but an uplifting and animating effect in the sense of real essential survival. Notwithstanding its possible range of influence I believe in the mission of a composer to give to a world of many afflictions and menaces a feeling of factual, i.e. spiritual liberation and truth. This can in its way contribute to better standards of living and happiness.
September 2001/August 2004


Music, as all of life, is based on vibrations. It is their relationship which makes life, as music, fascinating. These relations can always be expressed in numbers to be found in rhythms, chords and melodies - though not easily becoming obvious in the latter ones. Here applies the maxim by Leibniz that “music is a hidden calculative exercise of Soul“.

Its universal significance was already perceived in ancient times when music was seen in one range with astronomy, arithmetic, geometry and even psychology in a general scientific approach connected particularly with the name of Pythagoras. His research was based on the so-called monochord: an oblong wooden box over which a single string was passed. By dividing it into 2, 3, 4 and more parts one obtained higher notes compared to the whole string, which formed the beginning of a harmonic series. By multiplying the length of any of these fragments of the string one got lower notes and the beginning of a "subharmonic series". It was the customary already in earlier cultures to build such proportions on whole numbers which gave an impression of harmony also shown in architecture. In general there was the conviction that all of the cosmos was organized in numbers as Platon told in his late dialogue TIMAIOS, where he pointed out the importance of simple whole numbers including their products and powers.

I believe one can spot such attitude not only in our musical history but also in other cultures even if they appear as “primitive“. Ever and ever again one can notice such simple proportions which regulate rhythms and at least approximately musical pitches. In the field of harmony as the greatest achievement of western music I could observe an increasing relevance of prime numbers beyond five. At any rate there is the probability of natural laws connected to numbers, partly attested by modern science.

June 2007/July2009


Apart from no-recognition of natural laws in music there are long since tendencies of an inner restauration which more or less consciously takes account of numeric relationships. The harmonic series is omnipresent as soon as a certain pitch of sound can be recognized. Its sequence of vibrations is defined by whole numbers. 1:2:3:4:5 etc. means that each note vibrates that much more per second compared to the basic note = 1. We can experience this relation as harmony! The proportion 3:4:5 presents here for the first time a major chord which is far from being arbitrary and well esteemed for this simple relation. Other well-known chords can be derived from the harmonic series despite their diverging from the system of 12-tone ‘equal temperament’. When this numeric series starting from 1 is applied not to the frequency but to the wavelength of sound the proportion of 3:4:5 provides us the minor chord. Frequency as a phenomenon of time and wavelength as one of space show their reversed situation. In the subharmonic series the intervals of harmonics have changed their direction, they go down instead of upwards. The universal contrast of multiplication and division, better known in the field of rhythm, is expressed here; the minor gender as opposed to the major one becomes evident. Each newly introduced prime number as a partial tone creates another dimension, an extention of musical awareness!

November 2011

Peter Michael Braun

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