Along with constant extensive teaching activity at two professional music universities in Moscow, aimed at developing the creative potential of the students on the basis of mathematical music, S. Filatov-Beckman continued to actively engage in the scientific research in the field of his discovery. The purpose of this work was to obtain more and more new geophysical data. This expressed the mathematical component of the scientist's activity.
Mathematical music as a new means of developing compositional skills
The Sixth Essay
At the same time, another component continued to develop - the musical component of the scientist’s work on the creation of mathematical music. It consisted in converting geophysical data, as already mentioned above, into a computer sound line. The work on the creation of mathematical music was carried out in several aspects: the creation of monorhythmic polyphony, the melodicization of fragments, the obtainment of polyrhythmic polyphony possessing genre features, etc.
A very important aspect of the scientist's work was the following: continuing to divide the received lines into fragments and combine them into polyphony, S. Filatov-Beckman attached great importance to the search for their brightest and most original computer sound. The researcher and his sound engineering students, conducting experiments in sound recording studios, searched for and found a variety of computer timbre sounds, they conducted searches in the field of registers, from the ultra-low to the ultra-high, performed all kinds of experiments in the fields of tempo, articulation, loudness dynamics, types of movement - from smooth, progressive to swift, sharp, characterized by large register gaps and generating spatial plans, planes, volumes.
Thus, mathematical music developed not only in the direction of melody and genre of the musical fragments, up to the creation of independent pieces by the students. At the same time, S. Filatov-Beckman himself attached great importance to the search for the original timbre colors of his sound lines and the polyphony of various types arising therefrom.
We offer for listening a number of musical tracks obtained as a result of these timbre searches. Selected examples of polyphony (the author's archive contains a much larger number of them) demonstrate the most diverse sounds, which, of course, are not recorded in musical notation.
Track 1
Track 2
Track 3
Track 4
Track 5
Track 6
Track 7
Track 8
Track 9
Track 10
Getting acquainted with these tracks, you can hear the bell beats and their movement along the scale, slow and fast ringing on the ostinato bass. But the loud-sounding piano clusters in different registers of the instrument resemble, as it were, a concert sound.
Quiet slow overflows are amazing, as if sounding in the «underwater kingdom» or in space. They are replaced by divergent or convergent piano scales that cross space.
In another example, we hear bell lines entering one after another - as if some kind of chime has begun, which then subsides and disappears...
And again there is a contrast - a mass of ringing bells is replaced by monophonic phrases of different timbres, phrases that sound on the ostinato bass and lead to a sudden loud finale. And in the following example, the rapidly ascending passages of the piano paint a picture of a virtuoso performance.
The same is heard in another example: ringing bells, combined with a dull bass, create a voluminous sound. They are contrasted by a variety of computer sonorities, and the pointillistic fabric at a fast pace brings a new contrast. In another example, the slowly rising wave in thirds and seconds again contrasts with the previous examples.
The resulting monophonic and polyphonic tracks possess sufficient brightness. At numerous conferences where the scientist demonstrated this material, the participants repeatedly expressed to Sergey Anatolyevich their true interest in the phenomenon called «mathematical music». These compositions were used by the students in school productions, in amateur performances and had a noticeable success with the audience. S. Filatov-Beckman, who himself visited such events, mentions this in his notes.
Among the listeners and participants of the conferences there were people of different specialties, including theater directors, who, with the author’s permission, used the scientist’s tracks in their productions.