vrijdag 8 februari 2013


Vaguely I was aware of it, but I never realized it as precisely as described by Stuart Isacoff in The Octave. That the establishment of our tonal system – in which we modulate through all keys back and forward and in doing so produce the most beautiful musical constructions – is the result of a major battle, and that this battle proceeded along theological and philosophical lines. The story of that struggle can be read as a sound built version of a larger story. If you want: a liberation story that has interfaces with the emancipation of Western man from the tutelage of the Greek classics and the Christian church.

The story begins with ideas and with a problem. The ideas include the view – based on Pythagoras and Plato – that music is the reflection of a universe which is organized according to harmonious mathematical relationships. Music therefore must be composed of pure intervals such as the perfect fifth (3:2) and the perfect fourth (4:3).

The problem with this was that Pythagoras’s formulas left no space for some very popular harmonies: the major thirds, the minor thirds and their counterparts, the sixths. These intervals were so popular because they made music more intimate, more sensual and more expressive. But their use generated a lot of discussion, because according to opponents these intervals did not fit into the the world order as proclaimed by Pythagoras and the Church.

There were quite some solutions for this problem. They were found in the musical practice and consisted in more or less cheating as to the purity of the intervals. With stringed instruments this could be done because the musician has to pitch the tone himself and always can intonate slightly higher or lower. Singers could do so the same by constantly adapting their pitch to make the different intervals sound together as harmoniously as possible.

These were pragmatic solutions in which the problem was not calked and which did not challenge the guardians of the strict mathematical order. But these solutions were half-baked, because singers were accompanied by organs and there was music written for strings with harpsichord accompaniment. And with keyboard instruments such as organ and harpsichord one can not intonate while playing as it can be done with a voice or a string. Instruments must be tuned properly in advance, and when you want to play thirds on them then you have to consciously tune them differently than when only fifths and quarters are to be heard.

This technical feature left less room for pragmatism, the question of tuning had quite some theoretical aspects. That’s why it soon attracted the attention and the interference of more or less self-appointed guardians of the divinely established order. And these had fundamental objections against any infringement of the pure mathematical relationships.

Meanwhile blood was thicker than water and musicians tried all kinds of tunings on their  keyboards. Concessions were made as to the purity of the intervals for the sake of the possibility to unlimitedly interconnect a variety of fifths, fourths, thirds and octaves without the music getting terribly false.

The opponents were not amused. The 16th century music theorist Zarlino Gioseffo believed, like many others, that singers naturally sing pure intervals and that the new tunings threatened the world’s unity. He was offended when Vincenzo Galilei (father of Galileo Galilei) found that singers in practice go in one piece through different tunings because they are constantly looking for a beautiful harmony. Galilei reproached Zarlino that he fought for an illusion and that the music had to be completely freed from the tyranny of the inviolable numbers.

Rousseau also took position in the debate and he chose for his own variant of the cosmic order. Therein music figured as a primeval force that definitely had to be defended against the refined and therefore decadent experimental tunings. Even Newton, who in his physical work was brave enough to describe the world as it is rather than as it should be according to tradition, showed conservative here: “It is unworthy of philosophers to interfere with the pure proportions” he thought.

In particular, in the appeal which is made here to the sanctity of a divine natural order – against the praxis actually experienced or sought by people – a parallel can be drawn between what happened in the musical area and what in other areas is still happening. I am thinking of some representatives of the established order that label gay sexuality as unnatural and therefore as undesirable. Or of managers who barely pay attention to the actual undercurrents in their organization because their self-invented order leaves no room for them.

From this perspective one could call the musical struggle against the illusion of purity and pro  the multiplicity of lived practice an exemplary European project. And fortunately that struggle  ended well. In the late 17th  century the physicist Daniel Bernoulli was able to show that each tone produces overtones and that the series of overtones ‘above’ the basic tone of a string is much larger than originally thought. Isacoff: “These additional sounds are an endless expansion of the range with tones that are generally not harmonious. So all vibrating bodies float in a sea of dissonants. The idea that nature has a preference for pure harmonies was, it appeared, permanently expelled from the scene.”

Also see Order