RE: 7:10 diminished fifths and other annoying dissonance s

Jerry wrote,

>Those "dissonant dominant sevenths" are
>only appropriate for the _keyboards_ of that period--not for strings and
>voices.

That may simply be a matter of taste -- if you've read Nowitzky's page, as I
suggested, and read the posts of many musicians on this list, and read
Mathieu's book, you'll know that many truly _prefer_ their dominant sevenths
less than perfectly blending.

>Elsewhere and earlier, you commented that singers today who intend to
>perform this period music in a stylistically correct manner emulate this
>sort of compromise tuning.

No I did not -- in fact, I believe that perfect singers would come close to
what a certain version of John deLaubenfels' dynamic tuning program does --
keep vertical chords in JI (except augmented triads, 6/9 chords, maybe
diminished sevenths . . .)

>To be sure, many of today's singers emulate equal-tempered keyboard tuning,
>largely because they "learn their notes" by means of a piano and also
>because music educators have failed to let them know there is a better way.
>In spite of this, many talented singers (and most string players)
>intuitively escape this nonsense and tune their pitches to each other
>instead of to a keyboard standard.

So, Jerry, what is your hypothesis on the "high third"?

>It only
>makes sense that when functional harmony emerged in Europe, those human
ears
>(given the chance) would gravitate to that same simple combination of
>pitches when the dominant chord is sounding. Can I prove it. Probably not.
>Do I believe it? Absolutely. (At least until someone provides reasonable
>evidence to the contrary.) Has anyone been to the seventeenth century
>lately?

Jerry, the same line of reasoning led many to argue (a few months back on
this list) that the ratios of 5 _had_ to be used for thirds and sixths in
early to middle Medieval times. I feel Margo Schulter and others made a
powerful case that the historical evidence indicates that these intervals
were compositionally used, and perceived, as _dissonant_. Dissonant ratios
are not ones whose ratios are perceived clearly. The only ratio-based guides
to their tuning would have been chains of relations by 2:3 or 3:4, operating
alongside certain cadential tendencies that may have biased major thirds and
sixths toward "expansion" and minor thirds and sixths toward "contraction".

Much as the thirds and sixths were unstable sonorities in early to late
Medieval times, the diminished fifth was an unstable sonority in Renaissance
through Classical times, and hence its tuning was likely inflenced quite
strongly by the 5:6|5:6 intervallic structure normally contained within it,
and also somewhat by the 3:4 relation existing between the "seventh of the
dominant" and the "tonic".

>In that sense, Fokker's interval names can be seen
>as "non functional" in that they fail to reflect the "common practice" that
>likely arose as a result of flexible tuning and Fokker, like others before
>him, appears to encase "common practice" in the coffin of keyboard
>limitations.

We need a historical reality check. Wolf, Schulter, et. al., did "common
practice," specifically the use of the tritone to define tonal keys, arise
as a result of flexible tuning or as a result of keyboards and lutes or some
combination of the two?