4:5:6:7

My favorite recent quotes from the tuning list
regarding 7-limit from

Bob Valentine:
...
Why is 7-limit tuning any less legitimate than playing
a meantone
piece in 12-et, as a matter of principle?
-----------
JdL
...
Why are past masters relegated to some kind of holy
shrine, in which their works must never be touched, in
some people's
eyes? IMHO, the best way to honor someone is to take
bits of their
work and reconstitute them in new ways. When old
works become museum
pieces, they become brittle and eventually lost. This
is not honoring,
this is killing.

I do hope that faithful renditions of old works remain
in our ears, as
a point of comparison if nothing else.
-----------

With that great intro, now my 2.5 cents...

I became a real partisan for the use of 4:5:6:7
dominant sevenths about as soon as I could tune them
up with my Kurzweil and Clavette some 8 years ago.

We should remember the context in which past revered
musical theorists didn't find the harmonic 7th useful.
Most of them did not live at a time in which the
chromatically available harmonies and melodies in the
commonly used tunings had all been well-explored (as
is now the case with 12-ET), and they could not often
easily build instruments (or train choirs) for
reasonably easy >12-ET performance--practicality was
certainly a big factor

While it's fair to say that one can't easily
substitute this sonority for the dominant seventh
chords in most common practice music without
adjustments, this DOES NOT mean that we can't make NEW
pieces that sound as euphonious as music that period
using JIs or >12-ETs that represent them well.

As suggested by JdL, those of us on this list with
strong common practice harmony skills should also
consider 'desecrating' the 'holy writ of the musical
Masters' by taking some of those works, whether by
Monteverdi or Wagner or whomever else, moving 'em to
say 22-ET, and making musically appropriate
adjustments and corrections to create an aesthetically
satisfying transcription of the original into another
tuning domain.

Amongst the adjustments I make in musical context with
22-ET:

Descending major scales: from major scale degree 3,
the 5:4 match (7/22), I continue with 10:9 (3/22), not
9:8 (4/22).
Ascending: reverse the rule: 9:8 in place of 10:9
(the major scale here can be conceived of as "melodic
major")

My ears have no problem with melodic motion in 22-ET
that puts the minor 7th above the dominant, followed
by the harmonic 7th. You can even resolve from the
harmonic 7th with further hyperchromatic voice-leading
through the 9/7 (8/22) to the 5/4 (7/22).

We can also distinguish the top tone of the
minor-minor 7th chord from the top tone of the
4:5:6:7--in 22-ET these are 1/22 apart. Rich grounds
for investigation with jazzy styles.

-------------
Some recent quotes of Paul E. that deserve response:

>>...No one even conceived of music as a
set of "chord progressions" like we do today. Listen
to Victoria. What's the "chord progression"?

One way or the other, Victoria must have carefully
chosen his harmonies, even if German 19-century
harmonic theory was not known. We can hear 'chord
progression' because the music can fairly be heard
that way--just as we might label Martin Luther's
theology as Protestantism although perhaps no one in
1525 would understand that concept. Most Western music
is inextricably harmonic-melodic, or
melodic-harmonic--something like the way light can be
seen today by physicists as waves, or photons--but it
really is something of both, as well as being the kind
of brightness that we know as physical creatures with
sense organs.

>>...The meaning of the V7 chord is primarily
_melodic_ ("linear"), rather
than harmonic. The notes of the diminished fifth
always resolved in
contrary motion to a tonic third.

Even in common practice music the V7 frequently
resolves to a vi, and if reinterpreted as an augmented
7th it obviously resolves outward. (The moment of
reinterpretation obviously being as one hears the
resolution of what was first heard as a V7.)

Of course the "dominant seventh" chord is also the
basic harmony of the blues, and is generally the
'triad' of swing and later jazz. Although of course in
most of those functions, it's not a dominant seventh,
but a major-minor 7th chord.

I think you've taken too seriously the Schenkerian
ideology handed down in most US college music
departments today. If these analyses really revealed
so much about the structure of the masterworks from
which they're derived, why aren't we hearing new works
of brilliant tonal music from such theorists who after
all have unveiled 'everything' about, say, Beethoven's
5th? There is some value to Schenkerian theory, but
there is insufficient consideration of the interaction
of short and large-scale rhythm, orchestration,
dynamics, melodic shapes, the dramatic development of
tonal music: the surprises vs. the 'continuing', etc.
I found it quite interesting to look at 16th & 20th
century pieces in a Schenkerian way--music which
supposedly shouldn't be analyzed with his concepts.

-------------
Also: I don't find the conception of n-limit useful.
I'm not very interested in 7-denominator intervals
like say 10/7 or 25/49, while I find 7:4, 7:5, 7:6
really intriguing for the extension of common practice
harmony into >12 ETs.
==============
I look forward to all thoughtful critiques, and hope
to show you the fruits of my theorizations with more
music live and on the web in the near future.

Soundly yours,
Harold

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