source file: mills2.txt Date: Sat, 31 Aug 1996 09:28:44 -0700 Subject: Re: Seventh Tuning From: Gary Morrison <71670.2576@compuserve.com> > 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