Bach's tuning (was: re: TD 411 -- Reply to John deLauben fels on dissonance...)

I wrote,

>>Though I would agree (perhaps strongly) with Margo, it should be pointed
out
>>that there is no record of Bach ever mentioning a subtly graduated scale
of
>>tension among the keys. Although quantitative studies of the WTC appear to
>>reveal that its composition was indeed informed by such a tuning,

Carl Lumma wrote,

>I've read this in several places, but can't remember any convincing
>examples.

The studies to this effect assumed that a fixed set of 12 pitches applied to
all the pieces, optimized the tuning of consonant intervals weighted by
frequency and duration, and came out with some kind of irregular
well-temperament that favored the "easy" keys.

>I am more inclined to accept Everett Hafner's thesis, that the
>tuning wrench was to be used before each piece. Two points on Hafner's
>article:

>1. He suggests that if the WTC was performed by order of 5ths rather than
>number it would support his thesis, but the WTC was not meant to be
>performed as a whole at all, and almost certainly was not during Bach's
>lifetime.

>2. The second book is much less forgiving than the first as far a staying
>within the consonant areas of one 12-tone meantone key. And what was Bach
>to do at the organ -- his organ book is the most chromatic of all his
output.

It sounds like you're not agreeing with Hafner at all. Why are you inclined
to accept his thesis, then?

>Some points of interest here: 1. Was the composition then so tailored to
>the specific key of irregular temperament?

I don't believe it was tailored at all, let alone "so tailored".

>>All we know for sure is that, once he had adopted the premise of a closed
12
>>tone temperament, Bach instructed that the major thirds be tuned sharp in
>>order to achieve that end.

>Bach is definitely on record for preferring closed temperament. There's
>even a story relayed by Bosanquet of Bach playing in the worst keys on a
>meantone organ when its builder was around, to annoy him.

Exactly. However, let's not forget that Bach had a long career as a
composer, and through the early part of that career, his music was
restricted to the ordinary meantone gamut of pitches; and only when his
music became more abstract and keyboard-oriented did he modulate so much
that a closed temperament became necessary.