Tristan, yet again

The discussion doesn't seem to have progressed very far. However, a
few issues have cropped up.

First, there do exist historical temperaments intermediate between
1/5 comma meantone and 12-ET - so if you reject one you are not
forced to take up the other. In fact, according to what I understand
of what is in Jorgensen for the early and mid-19th century in middle-
Europe, typical piano tuning methods combined some pure 5ths with
some mildly tempered ones which typically form some meantone series
with say 1/7 comma. The result was fairly close to ET but perhaps
noticeably different, and was often *called* equal.

(Copies of Jorgensen seem to be extremely hard to obtain on this side
of the Atlantic, by the way.)

Second, we can't assume what Wagner's intention was with respect to
if the chord was supposed to be 'nice' or 'nasty'. He certainly once
had a reputation for 'nasty' sounds. The Tristan chord was felt to be
not exactly nasty, but certainly disorienting.

Third, how far can orchestral tuning have deviated from the not-quite-
equal-tempered piano, when piano concertos were an extremely popular
genre and Liszt wrote many transcriptions of orchestral pieces?

Fourth, remember that Mahler said that the musical world *had*
discarded the distinctive features of earlier meantone tunings in
favour of ET: he was presumably referring to the later 19th century.
I cannot think he would say this if he had not been brought up with
equal or near-equal as the norm.

Last, and slightly tangentially, what about the augmented triad in
near-equal temperament? It is made up of three major 3rds each of
which is accepted to be a consonant interval, therefore it should be
a concord. But it is always treated in theory as a discord. I claim
that this is because it is unstable and ambiguous, being equally at
home in three different, mutually remote tonalities. This is part of
my argument about the Tristan chord, that it is properly at home in a
tonality of D sharp which is maximally remote from A.

~~~T~~~

>First, there do exist historical temperaments intermediate between
>1/5 comma meantone and 12-ET - so if you reject one you are not
>forced to take up the other. In fact, according to what I understand
>of what is in Jorgensen for the early and mid-19th century in middle-
>Europe, typical piano tuning methods combined some pure 5ths with
>some mildly tempered ones which typically form some meantone series
>with say 1/7 comma. The result was fairly close to ET but perhaps
>noticeably different, and was often *called* equal.

Yup. I would say they are "subtly different".

>Second, we can't assume what Wagner's intention was with respect to
>if the chord was supposed to be 'nice' or 'nasty'. He certainly once
>had a reputation for 'nasty' sounds. The Tristan chord was felt to be
>not exactly nasty, but certainly disorienting.

Yup.

>Third, how far can orchestral tuning have deviated from the not-quite-
>equal-tempered piano, when piano concertos were an extremely popular
>genre and Liszt wrote many transcriptions of orchestral pieces?

Pretty far, but not in a principled/septimal way.

-Carl