André Laporte once told me – to my surprise – that one cannot continue to deny tonality. This remarkable statement, especially for him, has always stayed with me. It summarizes well the actual situation of music in human life.
Sounds that contain a clear pitch and which are conceived either together or one after the other will get meaning for us only when the number of vibrations of these sounds form a ratio, which is expressible in whole numbers.
This knowledge, first described and developed by Pythagoras, has led to the creation of the modes and keys, but also to restrictions! If one would tune everything in perfect intervals, this would yield an impossible and useless set of sounds.
This is easy to prove: a perfect major third has a 5:4 ratio in Herz. If you stack three major thirds above each other however, you will not obtain a perfect octave (2:1 = 2) but a slightly smaller distance, namely
(5:4) x (5:4) x (5:4) = 125:64 = 1.953125
This ‘imperfection’ of nature (it seems the law of Gödel) was circumvented at the time of Bach by the tempered tuning (the ‘well temperament’ and the ‘equal temperament’) which makes every third slightly larger. A very handy trick that ensures we can play in all keys.
Since that time, nothing has changed really. There has been more experimenting with different scales but this has not lead to an outcome with any significance.
Lutoslawsky, with whom I had two long conversations, told me at the time he was working on his fourth symphony, that he had spent his whole life several hours a day to reflect upon the purely technical aspects of musical composition! The techniques he developed that way were applied in effective compositions only after about more or less 10 years. He also told me that he had invented another tonescale (or temperament) many years earlier and asked several engineers to calculate it. The result, he said, was horrendous and unusable. We, people, are chained to the well-tempered system!
In the 19th century the tonal center was self-evident. Both the vertical (chords) and the horizontal (the melody) in music possessed a tonal center, which could shift in the course of the composition, but was always present and recognizable. Both components became however more complex and sometimes ambiguous, first in the chords and later in the melody.
The famous ‘ Tristan’ chord can be explained and solved in different ways. The chord itself not expresses any tonality, and acquires meaning depending on what is coming next. If the continuation of the music has no clear tonal center either, then one evolves in the direction of ‘atonality’. This concept I do not like to use however, because I think there persists always a suggested tonal center (one or more). Also the (trained) listener will automatically create such a center, usually unconsciously. So there is at least a subjective tonality, which even can be different than the one meant by the composer.
Also the melody lines became more complex. Composers increasingly used key foreign notes and gradually all twelve notes were used within a melody. Schönberg has formalized this trend by introducing dodecaphony.
“Today I have discovered something which will assure the supremacy of German music for the next hundred years.” A remarkable statement of Schönberg himself …
It is known that Schoenberg did disapprove of the terminology ‘atonal’ in relation with his music. Dodecaphony is indeed not a synonym for atonality .
I often use dodecaphonic sequences or sequences that are bigger, but I definitely do not write ‘atonal’. I deal with tonality freely, and sometimes use several tonal centers simultaneously or write passages in which the tonality is not evident and most of the time suggested. I suspect that tonality has deep roots in human nature.
Robert Groslot 