# Reaction to Telegraph Article



## millionrainbows (Jun 23, 2012)

https://www.telegraph.co.uk/comment/personal-view/3617581/How-Beethoven-ruined-classical-music.html

As early as Bach's day, there was a general trend towards Equal Temperament, because of the desire to play in all 12 keys. Bach's "well-tempering" was an early attempt at this: all 12 keys sounded good, and there were no "wolf tones" or unbearable notes. 

Precise Equal Tempering was not achieved until about 1919, when electric frequency counters were invented. Before that, it was close, but not perfect, as piano tuners had to use stopwatches and count the "beating" of adjacent pitches.

So, you don't necessarily "hear" mathematics as you listen to music, but you need to be aware of how this all affected the direction of music.

However, I think that Dylan Evans still is flawed in his conflation of any mathematical truth with subjectivity/objectivity.

Although he died in 1918, just before "true" equal temperament had been achieved, Debussy was probably affected by the more-or-less equal tuning, because he used the whole-tone scale often; in more-equal temperaments, and especially in 'true' Equal Temperament, all those major seconds of the whole tone scale sound really good; they create an even sheen of sound, like an aura.

All of this movement towards ET is a movement towards chromaticism, and moves away from the original principles of tonality, where one key sounded almost perfect, with perfect fifths and thirds. 

But, alas, the Pythagoran-derived 12-note octave was flawed from the get-go; hence, all of the "mean-tone" tunings which arose in order to achieve better thirds and fifths. And this was before "all 12 keys" were desired. This was just to get a few closely-related keys to sound more consonant.

The Western system of 12 notes per octave would never achieve perfect consonant ratios, _and neither can ANY scale which spans and encloses one octave.

There is a simple mathematical reason for this impossibility: an octave is the ratio 1:2, and the other "perfect" intervals which constitute our triad, are the fifth, 2:3 (and its inversion, the fourth, 3:4), and the major third, 4:5.

None of these "just" ratios is compatible with the 1:2 octave, since "1" can't be divided evenly by 3 (in the 3:2 fifth, 3:4 in the fourth) or 5 (the "just" major third 4:5).

To "close the octave," the intervals must fit into the octave with no "leftover."

In light of this, there is a grain of truth in the overall thrust of Dylan Evans' Telegraph article, although I don't blame Beethoven, and don't praise Pythagoras, either. The system was flawed from "perfection" from the start. Inevitably, Equal temperament would draw music into a vortex of chromaticism, away from tonality's original principles and desires for perfect consonance.

I think Dylan Evans is flawed in his conflation of this mathematical truth with subjectivity/objectivity, the latter I think has more to do with social and historical factors._


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