source file: mills2.txt Date: Fri, 27 Dec 1996 08:43:02 -0800 Subject: Triadic or tetradic infill? From: Daniel Wolf <106232.3266@compuserve.com> Gary Morrison wrote: '' As for why there's a historical preference for using triadic rather than seventh-chord fills within an octave's span, I think that that's pretty much historical. Seventh chords, especially those with diminished fifths, have been regarded as dissonances that need to be resolved to triads. '' Yes, but this still begs the question of why this particular preference appeared and not others. I was trying to argue from first principles about the infill phenomenon using a spacing model, not an intonational model (for which Pythagorean and 5-limit just intonations would provide a familiar and convincing argument for western music through the early baroque). For later music, where sonorities akin to 4-5-6-7 become common place, it is striking how these are left in the _dissonant_ category and required to _resolve_. Even vernacular musics tend not to end on seventh chords. Either this is evidence of a deep conditioning from common practice music, or there is some other mechanism at work. Possibilities which spring immediately to mind include (1) a problem with ratios of seven (or their tolerable approximations), or (2) a spacing function (which I have called variously "compacting" or "optimizing"). Any other ideas? Another possiblity - and one purely from an intonational standpoint - is that the ET approximation is bad enough to shove the seventh into a _dissonant_ category and to demand resolution. In this case, however, the resolutions of seventh chords occuring in real, existing Just intoned musics - chorales or Barbershop quartets - retain the avoidance of sevenths in final chords (except for special effects). Is this just conditioning from the the familiar temperament? Does anyone know of a way to test this? (Unfortunately, music that I am familiar with using justly intoned seventh chords (Partch, Johnston, Young, Leedy, my own) is often highly ambiguous about the whole issue of _resolution_. I do detect some tendency to respect harmonic series spacing in the voice leading, but this is as yet more of an impression than an established statistical fact). Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 27 Dec 1996 19:19 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03727; Fri, 27 Dec 1996 19:21:56 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA03723 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA26411; Fri, 27 Dec 1996 10:21:53 -0800 Date: Fri, 27 Dec 1996 10:21:53 -0800 Message-Id: <199612271321_MC2-DEE-EFC5@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu