source file: mills2.txt Date: Thu, 1 Feb 1996 15:56:58 -0800 From: "John H. Chalmers" From: mclaren Subject: melodic modes in 19 & 17 --- As mentioned some months ago, efforts to force-fit the 19 tone equal tempered scale into the melodic patterns familiar throughout Western music are doomed to failure. This, because there's nothing like a semitone in the 19-tone system. Since 19 is a member of the third-tone family of scales, this is obvious. Yet many notation schemes and suggested melodic modes depend on the mistaken idea that 19 has something that sounds or functions like a semitone. In actual musical practice, two 19-tone scale-steps do not sound anything like a semitone--the resulting interval, 126.315 cents, sounds a full quarter of a semitone larger than the semitone found in 12. Alternating this interval with the 3-step whole-tone in 19 produces a queasy effect that cannot be described as either "major" or "minor"--instead, the overall impression is that of a 7-out-of-48-tone mode which sounds distinctly out of tune. Since major and minor melodic modes do not exist as such in 19, this creates a substantial conflict. After all, major and minor *vertical* triads are easy to play in 19--but a major or minor melodic mode are not to be found. So what's the solution? The experience of the Southern California Microtonal Group has shown definitively that the concept of major and minor melodic modes must be abandoned in 19. To avoid producing a bizarre and queasy out-of-joint melody, 12-tone melodic paradigms must be thrown overboard and new forms used. Recently, Jeff Stayton recorded a duet with me in the 19-tone system. Stayton used one melodic mode, while Your Humble E-Mail Correspondent used another. Neither mode, however, had any point of contact whatever with 12--and as a result, the combination sounded entirely natural in 19. My melodic mode used ascending and descending subsets of the following: LssLssssLsL L = 3 scale-steps in 19, s = 1 scale-step in 19 This "super-mode" appeared as two different modes, one ascending, the other descending: ASCENDING: LssLsLLsL (intervals shown as number of 19-tone scale-steps) I.e., 1 4 5 6 9 10 12 15 16 (20=1) (scale degrees played: numbered from 1 to 19, with 20 = 1) DESCENDING: LsLsLsLsL (intervals shown as number of 19-tone scale-steps) I.e., 20=1 17 16 13 12 11 8 5 4 (20=1) (scale degrees played: numbered from 1 to 19, with 20 = 1) Variety was added by borrowing additional steps from the "super-mode" and adding them ornamentally to either the ascending or descending mode. Jeff Stayton's guitar accompaniment used an entirely different mode: (Descending) LsmssmsL where L = 3 scale-steps in 19 s = 1 scale-step in 19 m = 2 scale-steps in 19 I.e., 4 20=1 19 17 16 15 13 12 9 (scale degrees played: numbered from 1 to 19, with 20 = 1) Stayton varied his mode by substituting 2 single scale-steps for a 2-degree "m" step: thus he might play LsssssmsL instead of LsmssmsL, for example. The combination of these two melodic modes worked smoothly and sounded entirely natural in 19. However, they do NOT derive from any 12-tone or Pythagorean paradigm. More to the point, both of these modes use *more* than 7 tones. It has been my experience when improvising in or writing scores in 19 that more than 7 tones are required for a natural-sounding melodic mode. This should not come as a surprise. In 1956, Miller's paper "The Magic Number Seven, Plus or Minus Two" pointed out that the human cognitive system is capable of easily assimilating as few as 5 or as many as 9 "units." If each step of the melodic mode is thought of as a unit, this explains why 9-tone modes come so naturally to 19-- even though such modes use 2 more steps than the Pythagorean-based 12-tone melodic modes familiar from Western music theory, a 9-tone mode still fits comfortably the limits of the channel capacity of the human sensorium. (By contrast, serialism's 12 notes are too many.) Thus my experience indicates that at least 8 and usually 9 steps are needed to create a convincing and natural-sounding melodic mode in 19. On the other end of the perceptual scale, the 17-tone equal-tempered scale sounds best melodically when used with 5-step or 6-step modes: 1 6 4 1 5 (ascending: intervals in number of 19-tone scale-steps) I.e., 1 2 8 12 13 17 (18=1) or 1 6 1 4 4 1 (ascending: intervals in number of 17-tone scale-steps) I.e., 1 2 8 9 13 17 (18=1) (ascending: scale degrees played--numbered from 1 to 17, with 18 = 1) Not all xenharmonic equal temperaments require a complete rejection of 12-tone melodic modes. 22, 24, 27, 29, 31, 36 and so on all have familiar 7-note major and minor melodic modes. 19, however, does not. This startling contrast between the familiar-sounding major and minor triads available in 19 and the utterly alien-sounding melodic modes is one of the greatest resources of the 19 tone equal temperament. Composers who ignore this fact do so at the peril of producing awkward-sounding out-of-joint music that gives the impression of 12 badly mistuned. --mclaren ATDT *70, 633-4360 Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 2 Feb 1996 04:20 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id TAA26453; Thu, 1 Feb 1996 19:20:00 -0800 Date: Thu, 1 Feb 1996 19:20:00 -0800 Message-Id: <960201221740_412518206@emout10.mail.aol.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu