The magic of numbers
In medieval philosophy, music was included among the mathematical disciplines and its nobility was explained by the fact that it reflected the God-given laws in exactly the same way as the sciences of geometry and arithmetic. (The opposite of this “pure” art was usually instrumental music meant purely for entertainment.) An encounter with the music of the Middle Ages unveils many surprises: the speculative works of the master Josquin des Prez and his contemporaries, who ingeniously reflected the most varied and sophisticated games with numbers and proportions in their vocal compositions, boldly measure up to the current avant-garde works. They are marked with a similar boldness and intellectual charge and for all that they are still works, whose message heads directly to our hearts. At the same time, this highly refined music is sensuous and fragile.
The renaissance composition textbooks read like mathematical cookbooks and they describe the combinatory possibilities for various musical proportions (so-called intervals). The abstract world of numbers gave rise to a counter-reaction in the 16th century in the form of monody, which preferred individuality and emotional narration. As is often the case in human history, however, the pendulum suddenly swung back and we can still find many advocates of the “old” mathematical style in Bach’s period.
The numerical magic at the end of the baroque period lost its strength of a while, but the fascination with certain numbers remained and music continued to reflect the four elements, the four points of the compass or the last seven words of the Bible. Musical collections contained compositions in six or nine parts and the symbolism of the numbers 3 or 30, which were considered to be perfect numbers, continued to appear.
In 2012, Concentus Moraviae will seriously and playfully present the most important aspects of mathematics in music – speculative medieval works, the elaborate and elegant work of the first contrapuntalists, the works of the master of counterpoint Johann Sebastian Bach, the baroque coding of works in general bass numbers, but also our own play on numbers. Some of the concerts will include works from the same year or with the same opus numbers or everything in them will be linked to three …
The intention of all of these rules and games with numbers is to discover the sound rules which will also bring harmony to our souls via music.
Barbara Maria Willi, the dramaturge