Re: Gis major key signature; Lily's key signature algorithm

[N. Andrew Walsh]

I agree, and we find even older semi-equal temperaments on instruments from ancient China that also make clear that theorists knew what those tunings were. But the first-hand accounts of theorists and composers (and prior to the 20th century, those two disciplines had a lot more overlap) was that equal temperament sounded bland and uninteresting, and that well temperaments (or any of the vast array of 19th-century meantone derivatives, not to mention the extended temperaments like the one used on the cembalo with 24 keys on which a young Mozart [!] was famous for improvising in the courts) were musically superior in every way. 

Musicians at the time certainly *knew* what equal temperament was, even if they couldn't reach it exactly, and the fact that almost none of them advocated for it on musical grounds tells you all you need to know about what the "old masters" thought of it. 

-A

On Thu, Feb 8, 2018 at 11:21 AM, Hans Åberg <address@hidden> wrote:

> On 8 Feb 2018, at 10:39, David Kastrup <address@hidden> wrote:
>
> "N. Andrew Walsh" <address@hidden> writes:
>
>> It is entirely acceptable to be a music hobbyist who enjoys a passing
>> familiarity with the classical tradition and is largely uninterested
>> in more … esoteric discussions of theory. It is absolutely *not* all
>> right to be spreading historical inaccuracies of this sort. The WTC is
>> extensively researched and discussed in musicological and historical
>> circles, sometimes heatedly, but the idea that Bach wrote it to prove
>> that Well Temperament sounded "awful" (or the much worse assertion,
>> that he wrote it to demonstrate *equal* temperament, a technological
>> and historical impossibility in the 18th century)
>
> Don't be silly.  Equal temperament most certainly is not
> "technologically impossible".  Tuners of organs and accordions versed in
> their art work by tuning a circle of fifths in a reference octave by
> getting the proper sequence of beatings corresponding to the desired
> temperament, then tune the other octaves in reference.

The first effective E12 tunings for piano arrived in the early 1900s—the idea was present in Ancient Greece, and something like it was used on lutes. A lot of tunings were studied using monochords, but they are too crude for the required fine tuning. So if equal temperament was technologically possible earlier, perhaps they did not see any point in it: a method to play equally harmonically bad in all keys.