source file: mills2.txt Date: Mon, 23 Sep 1996 10:36:08 -0700 Subject: Blackwood's Etudes; more on pitch spacin From: PAULE >Odd >structural artifacts like this in low-consistency tunings are features >of, for example, several of Easley Blackwood's 12 Microtonal Etudes, and >massively cool pieces I think they are. It's just a different path than >that which I am attempting to follow. Of the tunings Blackwood uses, 13, 14, 17, 20, and 21 are inconsistent within the 5-limit. I find the 14, 17, and 20-note pieces to be successful due to their melodic structures and good 3-limit harmonies. I find the 21-note piece intolerably sour (these days I just skip it), since neither the scale nor the harmony are in tune. The 13-note piece may be effective as a piece of atonality, though I've never been a fan of atonal music. The 17-tone piece is perhaps my favorite, and Blackwood aptly avoids tonicizing the major triad, as it would necessitate good 5-limit approximations. The minor triad only necessitates a good perfect fifth for its tonalness; although the out-of-tune thirds contribute just as much roughness to both chords, the effect on tonalness is far more pronounced in the major triad. In the major triad there is pronounced beating between the difference tones, the root, and the virtual pitch. So much for "dualistic" theories. I believe the minor triad in Pythagorean or 12-tET to be subtlely more tonal than the just minor triad. This is because the fundamental of 16:19:24 (cents: 0, 298, 702) is octave-equivalent to the root, while that of 10:12:15 (or, for that matter, 6:7:9 or the 17-tET m3) is not. My first impression on retuning a guitar major chord to just was "Ah, that sounds better," but retuning a guitar minor chord to just, I thought "Hmm, that really doesn't sit right." However, I learned to like the sound of the near-just minor triads in meantone tuning -- they are smoother. Perhaps the use of the Picardy third to tonicize minor keys in the days of meantone tuning died away because of the adoption of the more tonal near-16:19:24 minor triads. To summarize: retuning the third of a minor triad can alter its ratio-interpretation but will not have a large effect on consonance, while retuning the third of a major triad by the same amount may preserve its ratio-interpretation but will have a larger effect on consonance. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 25 Sep 1996 18:05 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA28139; Wed, 25 Sep 1996 18:05:29 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA26441 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA18123; Wed, 25 Sep 1996 09:05:17 -0700 Date: Wed, 25 Sep 1996 09:05:17 -0700 Message-Id: <9609251605.AA03701@arthaud.saclay.cea.fr> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu