Seventh Tuning

> If it is tuned "in frequency ratios of 4x:5x:6x:7x where x=some fundamental
> frequency," then it is consonant. If it is tuned according to a diatonic
> scale with six consonant triads, it is dissonant.

Gosh, I personally think that the picture is FAR from being that simple. But
maybe your point was to make a very general statement about those two chords in
isolation, that is, out of any particular musical context. If so, then I
suppose I'd agree to a fair extent anyway.

But speaking in realistic musical contexts for dominant seventh chords - the
most common clearly being an authentic cadence, I have repeatedly tested, and
demonstrated to others, authentic cadences where the dominant seventh chord is
tuned 4:5:6:7. Neither I, nor any of the people to whom I've demonstrated it,
have found it to be an unsatisfying resolution. That, by definition, makes
4:5:6:7 a dissonance (the starting point of a harmonic resolution).

Now understand that I don't doubt for a moment that tuning the seventh
sharper produces a MORE satisfying resolution. But 7:4 provides a completely
satisfying resolution to my ears, and many others'.

I suspect that that's in part because the melodic movement of the flatted
scale-degree 4 down to scale-degree 3 is shorter. That seems to make the
contrapuntal movement of that voice feel more inevitable. I suspect that
audiences, confronted with a smaller melodic movement, are prone to respond with
a greater sense that, "ah yes, how could that resolution possibly go
otherwise?".

I've found that I can intensify that effect by making BOTH tendency tones
resolve by shorter melodic steps. Try this one sometime: For the dominant
seventh, use 4:6:7 with an added third tuned to 9:7 instead of 5:4. That
provides a dominant seventh chord (or at least a functional equivalent in
12-tone contexts) that is easily as dissonant a 4:5:6 with a sharper leading
tone than 7:4. To my ears at least, the resolution of that
sharp-leading-tone/flat-subdominant chord is more satisfying than a 4:5:6 with
an added seventh at 9:5 or 16:9. I haven't played this on many other people
though.

Now these observations are of less interest in a musical context where the
individual chords are rarely less harmonically tense than seventh chords, as is
often the case in some styles of Jazz, for example. That is to say, in
environments where you rarely play a major chord (or minor for that matter)
without the seventh.


Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 31 Aug 1996 19:17 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10670; Sat, 31 Aug 1996 19:18:46 +0200
Received: from eartha.mills.edu by ns (smtpxd); id XA10709
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id KAA29430; Sat, 31 Aug 1996 10:18:43 -0700
Date: Sat, 31 Aug 1996 10:18:43 -0700
Message-Id: <3045ECDC.6602@interlinx.qc.ca>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu