For Cam: Two JI progressions with 11/6 (mp3) that might port to 80-ed2 This article is dedicated to Cam Taylor and his wonderful creations in 80-ed2. Here are two progressions in JI, with links to mp3 files, involving an 11/6 middle or Zalzalian seventh which could also be realized in 80-ed2. The first progression, one of my favorites, has 11/6 as the highest voice of 6:7:9:11 (0-266.9-702.0-1049.4 cents), or 1/1-7/6-3/2-11/6, with the highest voice then descending by a 22:21 semitone to 7/4, for 12:14:18:21, which resolves to a 3:2 fifth. In the JI system used here, Zeta-24, this is played ..F*---E*----F*---E*---D* 11/6--7/4--11/6..7/4..14/9 ..D....................D* .3/2..................14/9 ..A*...................G* .7/6..................28/27 ..G....................G* .1/1..................28/27 In this version of the progression the 12:14;18:21 resolves by voices moving up a 28/27 thirdtone (63.0 cents) or down a 9/8 tone (203.9) cents. Now lets port this to 80-ed2, where an asterisk (*) raises a note by the 60-cent enharmonic diesis (equivalent to 28/27, and also to the Pythagorean comma in an interesting way): ..F*---E*----F*---E*---D* 1050..975..1050..975..765 ..D....................D* .705..................765 ..A*...................G* .270...................60 ..G....................G* ..0....................60 Here 80-ed2 gives a very reasonable facsimile of the JI version. The second progression was inspired by an idea of Joe Monzo for a sonority of 12:15:18:22, or 1/1-5/4-3/2-11/6 (0-386.3-702.0-1049.4 cents). A variant at which I arrived looked complicated as a harmonic series, 78:99:117:143, but is much simpler as an arithmetic series, 33:26:22:18 or 1/1-33/26-3/2-11/6 (0-412.7-702.0-1049.3 cents). Its like a 33/26 major third below 13:11:9. It was easy to develop a JI progression out of this much like the familiar first progression, going from 33:26:22:18 to 12:14:18:21 to a stable 3:2 fifth. .Eb*---D*---Eb*---D*---Db* 11/6--7/4--11/6..7/4..13/8 ..C....................Db* .3/2..................13/8 ..A----G*----A----G*...Gb* 33/26.7/6..33/26.7/6..13/12 ..F....................Gb* .1/1..................13/12 Here two voices form a kind of pedal on 1/1-3/2, and the other two oscillate between 33/26-7/6 (a motion of 99:91 or 145.9 cents) and 11/6-7/4 (the same 22:21 motion as in the first progression). The cadence from 12:14:18:21 to a fifth is here equable, with voices ascending by steps of 13:12 (138.6 cents) or descending by 14:13 (128.3 cents) in resolutions from a 7:6 third to a unison, and from the outer 7:4 minor seventh to 3:2. I dont know if this is correct jazz terminology, but the sonority with 11/6 seems to me like a tension leading to the more concordant 12:14:18:21, and then the stable and concordant fifth. In 80-ed2, the best approximation for 33/26 (412.7 cents) isnt so close at 420 cents, a nice 14/11 (417.5 cents), but the result should still be interesting, with a near-66:84:99:121 sonority (1/1-14/11-3/2-11/6, 0-417.5-702.0-1049.4 cents) at 0-420-705-1050 cents: .Eb*---D*---Eb*---D*---Db* 1050..975--1050..975...840 ..C....................Db* .705...................840 ..A----G*----A----G*...Gb* 420..270...420..270...135 ..F....................Gb* ..0....................135 My apologies if this is too much detail for some very short examples, but Im not sure if the harmony and counterpoint here has been documented elsewhere.
Posted on: Tue, 06 Jan 2015 04:21:29 +0000
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