What is that intended to mean?
Phrases such as that seem to me entirely inappropriate in this context.
Isn't that a different issue? You commented that ET wasn't technically possible when Beethoven was alive. Beethoven didn't use "mass-produced pianos" (though his pianos were considerably different from today's instruments). Temperament was extensively discussed in the 18th century. One of the musicians especially exercised by the issue was Rameau who clearly understood the idea of ET. Bach presumably understood temperament, though we don't know what he implied the the term 'well tempered' and by Beethoven's time ideas on temperament were fairly developed.
...and what is that?amezcua wrote: What was the technical reason it became possible ?...Eben Goresko mentions a reason why it was not possible earlier than the 20th century.
Pitch varies with the log of frequency and that knowledge provides a way of expressing the exact requirements for different temperaments. Certainly logarithms were invented much before Bach and their use was well established by his lifetime.amezcua wrote: It`s based on logarithms which were invented about 1600...Let`s agree that Bach did not invent logarithms at least.
There is no reasoning with a person like this. I leave you to it. It's a pity because a rational discussion of key colours would have been interesting.amezcua wrote: ↑Wed May 24, 2017 10:29 pmI asked what Eben Goresko meant about ET not being possible until the 20 th century . There was a question mark at the end of the sentence. Don`t assume it was a rhetorical question . I wanted to pin down what that reason was .Just a straight question seeking an answer .
Ironically, pianos are not tuned to ET, but to stretched tuning which starts from ET and is modified to account for the inharmonicity of piano strings. The end result is an S curve of deviations from ET with middle C being zero, lower-pitched keys being progressively flatter than ET, and higher-pitched keys progressively sharper (because overtones are sharper than multiples and the deviation is also frequency-dependent):amezcua wrote: ↑Fri May 26, 2017 8:46 pmI have been trying to find out when ET became firmly established so I read the history of piano tuning ( on the blind tuners forum ). That covered the "job" of tuning through the ages .It talked about the boom in piano sales in Victorian days but there was no mention of how the pianos were tuned so they must have thought dividing the scales evenly just made logical sense. One date given for ET establishment was 1780 . [...] That`s where standardisation would have started .
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