7:10 diminished fifths and other annoying dissonances

During a nice quiet discussion of acoustic "tritones," I was suggesting
that:

>> ...7:10 fits the partial series (of C) as Bb _up_ to
>>E--an augmented fourth in a dominant seventh chord belonging to the key of
>>F. In the C dominant seventh chord "acoustically" tuned, the Bb is closer to
>>the E below--a diminished fifth.

And inserted an attempt (lame as it is) at humor.

>>What's that you say? Common practice is not the only music system in
>>existence? Well, I'll be hornswaggled! You mean some composers could care
>>less about acoustic reality and four hundred years of practice? I'll be
>>damned.

Paul Erlich, ever ready to rescue from the pits of error, galloped into the
room and with one mighty swath of his blade announced that...

> Your "four hundred years of music practice" is a myth.

Now, the main point of my "humorous" paragraph had to do with acoustic
reality and the "four hundred years of practice" was included to give it a
kind of "ka-bum."

The valuable substance of Paul's contribution quickly follows, however, and
points out some historical practices which he believes scuttles any
possibility that persons practicing music during the four hundred years in
question had ears.

> In the meantone era,
> roughly 1480-1780, diminished fifths were tuned closer to 7:10 and augmented
> fourths were tuned closer to 5:7, making dominant seventh chords very
> dissonant by modern standards. But these dissonant dominant sevenths are
> highly appropriate for the music of that period.

Meantone tuning was an inadequate "stopgap" temperament used to tune
_keyboard instruments. Why would string players and singers from any era
settle for such ugliness when just a slight wiggle of a finger or vocal
chord produced stunning loveliness? Those "dissonant dominant sevenths" are
only appropriate for the _keyboards_ of that period--not for strings and
voices.

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. This makes no sense to me, so I choose not to
believe that pitch-sensitive singers in the periods in question would have
done so. Perhaps when they sang with meantone-tuned organs, they had little
choice. But certainly not when singing a cappella.

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.

Now, to diminished fifths, etc. The 5:7 interval appears in a non-functional
manner in many ethnic traditions--most prominently in Indian vocal lines and
in Georgian choral music. This interval invariably occurs between pitches
corresponding to the fifth and seventh partials of a sustained root. 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?

*****

Later in that discussion, I speculated:

>>It might be
>>considered that during Fokker's productive years, the principle of tonality
>>was being seriously challenged by Schoenberg and friends. It seems likely
>>that his use of these interval terms were intentionally "nonfunctional."
>
> On the contrary, Fokker kept all the features of meantone tuning intact, and
> remember, meantone is the tuning in which functional harmony was born.

It is no coincidence, I think, that the violin and functional harmony
emerged at roughly the same time. String players and the composers who wrote
for them must have delighted in the kaleidoscopic chromatic freedom provided
by these instruments--the dynamic well-tuned "tritone" flinging the tonality
in every conceivable direction. The ultra chromatic music written during the
Baroque period (particularly slow movements) argues _very loudly_ that the
players were enjoying true diminished fifths and augmented fourths and
clearly hearing the difference.

Why would Fokker--indeed, why would anyone--avoid such musical excitement in
favor of compromise? The answer, it would seem, is to accommodate
fixed-pitch instruments. 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.

I gotta get some sleep. Thanks again, Paul, for getting my juices going.

Respectfully,

Jerry

From: Gerald Eskelin >

> Meantone tuning was an inadequate "stopgap" temperament used to tune
> _keyboard instruments. Why would string players and singers from any era
> settle for such ugliness when just a slight wiggle of a finger or vocal
> chord produced stunning loveliness? Those "dissonant dominant sevenths"
are
> only appropriate for the _keyboards_ of that period--not for strings and
> voices.
>

Meantone is far from ugly or inadequate. Standard meantone tuning is based
on a chain of triads with pure major thirds, and the coincidental appearance
of good representations of septimal intervals among the augmenteds is also
useful. (Douglas Leedy's article on meantone in _Perspectives of New Music_
is worth reading; he is a musician who really begins from a vocal
standpoint).

> 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. This makes no sense to me, so I choose not to
> believe that pitch-sensitive singers in the periods in question would have
> done so. Perhaps when they sang with meantone-tuned organs, they had
little
> choice. But certainly not when singing a cappella.
>

But in the high Baroque (H�ndel, Bach) and classical eras (Mozart, Haydn)
there is very little a cappella repertoire if any. Vocal, including choral,
music was inevitably with instruments, and as a minimum that means a
continuo group, and that inevitably means tempered.

[Gerald Eskelin:]
>This makes no sense to me, so I choose not to believe that
pitch-sensitive singers in the periods in question would have done so.
Perhaps when they sang with meantone-tuned organs, they had little
choice. But certainly not when singing a cappella.

[Daniel Wolf:]
>But in the high Baroque (H�ndel, Bach) and classical eras (Mozart,
Haydn) there is very little a cappella repertoire if any. Vocal,
including choral, music was inevitably with instruments, and as a
minimum that means a continuo group, and that inevitably means
tempered.

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

[Paul Erlich:]
>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.

I've mentioned this example in this context (or one very similar to
it) before, but I don't remember whether anyone offered a more
historically educated opinion as to whether it was on or off the
mark - I can't vouch for the validity of the claim as I have no idea,
however, I do know that Joseph Yasser in his _A THEORY OF EVOLVING
TONALITY_ (p. 193) explicitly cites the a cappella music of the
Russian church (which he said did not use the V. 4:5:6:7) to contest
the claim that anything other than the 7/4 in the dominant seventh is
due to the influence of tempering.

Dan