source file: mills2.txt Date: Wed, 12 Mar 1997 13:09:36 -0800 Subject: Re: Dominant 7th 4-5-6-7-8 ? From: Andrew Milne Daniel Wolf wrote: > The most striking characteristics of a dominant seventh chord within an > otherwise triadic environment are - for me - the density of the chord (a > triad contains three interval classes, a tetrad six) But a great deal of tonal music is *not* expressed just with triads, so I cannot agree with this statement. A major seventh or ninth or even thirteenth can function perfectly well as a stable tonic chord in tonal music. This proves that "dominant function" is not a result simply of the "density" of the chord. > and the appearance of a new (even ''xenharmonic'') interval. Well this interval is only perceived to be "xenharmonic" if it is played as 7/4, and I don't believe that "xenharmonicism" is a necessary condition for the dominant seventh to function as it does. > These features are enhancements of > the dominant/tonic voice leading relationship: root movement by fifth, and > stepwise ''resolution'' in the remaining voices. Root movement by a fifth is certainly a powerful and satisfying resolution of the dominant 7th chord, but it is not the only acceptable resolution. V7 resolves well to vi (minor) as well (i.e. up a major second), and the augmented sixth chord (e.g. g - b - d - e#) - which is another chord that I think would be incorrectly represented by a 4-5-6-7 tuning - resolves most effectively to a major or minor chord a *minor second* below. The stepwise resolution of the intervals making up the tritone in both these chords is, I believe, the *critical* factor which determines their resolution. > When a dominant seventh chord is > suspended for a classical cadenza, it suffers little when tuned as 4:5:6:7 > and indeed, the stability of the chord enhances its contrast with the tonic > triad. On the other hand, the suspension of a 16/9 (or 9/5) as the seventh > introduces a tone dissonant to the rest of the chord, but not foreign to > the scale. If a dominant 7th chord is suspended for a while, then I think a case can be made for a 4-5-6-7 tuning just to soften the dissonance, but then how does the soloist tune his fourth scale note? Does he tune it as 21/16 or as 4/3 which has a much more simple and conventional relationship to the tonic? Can a singer, for instance, really be expected to pitch the former interval accurately when the latter is so common and so well-defined. In my experience 21/16 expressed as a melodic interval sounds like an out-of-tune 4/3 (in the context of common-practice tonal music). > One often-raised objection to the septimal tuning is the narrow semitone > (21/20) voice leading from the seventh to the third of the tonic. I find > this line of argumentation more compelling, but the interval itself is not > difficult to sing - and if melodically ''strange'', it does maximize the > contrast function. "Strangely" enough :) I wouldn't cite this as an argument against using 4-5-6-7. I believe that it is the very complex ratio made between the third and seventh of the dominant seventh (45/32) and the third and augmented sixth of the augmented sixth chord (25/18) that makes the two notes making up these intervals so "restless". Substituting 4-5-6-7 gives the much simpler, and consonant, ratio of 7/5 for both. For these reasons, and the arguments above, I really think that using 4-5-6-7 in common-practice tonal music is not appropriate. Using this ratio in a xenharmonic music is of course a different matter! > Readers might have some fun investigating the traditional rule of thumb for > the relative density of the chords in V7 - I cadences: In four voices, if > the voice leading is correct, then one of the two chords has to be > incomplete (that is with a doubled pc). (Why this should be so I will leave > as a kind of ''Puzzler''). Unless, of course, the Dominant 7th is in first or third inversion. Andrew Milne Islington London Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 13 Mar 1997 00:03 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04939; Thu, 13 Mar 1997 00:03:11 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA04949 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id PAA15113; Wed, 12 Mar 1997 15:01:37 -0800 Date: Wed, 12 Mar 1997 15:01:37 -0800 Message-Id: <009B12C603AD96B3.6A55@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu