December 26, 2009
I was happily surprised to see this new video by Jonathan Glasier, demonstrating 19-tone equal temperament (19ET) on a synth keyboard using a TBX1 Tuning Box. He shows the box briefly at the beginning of the video.
Many tuning enthusiasts know about Jonathan's career, but since biographical facts are not listed in the video comments (Jonathan is not one to draw attention to himself) it might be useful to know that here we have someone who has done an awful lot in this field, and who is also a direct link to one of the most influential people in the history of tuning! Jonathan worked with Harry Partch in the 60's, as his personal assistant, and a member of his ensemble. He also founded the Interval journal in the 70's, and Sonic Arts Gallery in the 80's. He lives in San Diego where he performs microtonal music with his own ensemble.
He says early on if you're interested in the mathematics, that's not what his videos are about; he is showing practical keyboard related issues. This type of instruction is sorely needed, and it's great to see this kind of video being made, using an overhead camera so you can see what he's doing.
If you are more interested in the theory, I have some things about 19ET here and here. A list of the intervals of 19ET according to the H-System is:
(0) 1.0000000… 0.00¢ = 0Ç+0J = P.P1
(1) 1.0371550… 63.16 2¢ = 2Ç+1J = P.Sm2
(2) 1.0756905… 126.32¢ = 4Ç+2J = aa.Lm2
(3) 1.1156579… 189.47¢ = 6Ç+2J = a.SM2
(4) 1.1571102… 252.63¢ = 9Ç-2J = m.Sm3
(5) 1.2001027… 315.79¢ = 11Ç-1J = P.Lm3
(6) 1.2446925… 378.95¢ = 13Ç+0J = m.SM3
(7) 1.2909391… 442.11¢ = 15Ç+1J = a.LM3
(8) 1.3389041… 505.26¢ = 17Ç+1J = M.P4
(9) 1.3886511… 568.42¢ = 19Ç+2J = M.Na4
(10) 1.4402465… 631.58¢ = 22Ç-2J = m.La4
(11) 1.4937589… 694.74¢ = 24Ç-1J = m.P5
(12) 1.5492596… 757.89¢ = 26Ç-1J = d.Sm6
(13) 1.6068224… 821.05¢ = 28Ç+0J = M.Lm6
(14) 1.6665240… 884.21¢ = 30Ç+1J = P.SM6
(15) 1.7284437… 947.37¢ = 32Ç+2J = M.LM6
(16) 1.7926641… 1010.53¢ = 35Ç-2J = d.Lm7
(17) 1.8592707… 1073.68¢ = 37Ç-2J = dd.SM7
(18) 1.9283519… 1136.84¢ = 39Ç-1J = P.LM7
(19) 2.0000000… 1200.00¢ = 41Ç+0J = P.P8
Notice we have a Perfect Large Minor 3rd and its inversion a Perfect Small Major 6th. Thirds and sixths aren't normally thought of as intervals that can be Perfect, because they aren't called Perfect in 12ET. In the H-System, the term "Perfect", when it is placed at the start of the interval name (in abbreviation as a letter to the left of a dot), is referring to a "virtually beatless" sound produced by an interval in voices of harmonic timbre. Jonathan demonstrates these intervals in the video and calls them the "Perfect Minor 3rd" and "Perfect Major 6th". The H-System basically supports these names, further qualifying them with Large and Small, respectively, to clearly differentiate them from their 3-Limit siblings.
He also says in 19ET we don't have a Perfect 4th or Perfect 5th, and in terms of evaluating harmonic-timbre intervals for beatlessness, this is indeed true. In 19ET, the 4th and 5th both beat noticeably, the 4th being noticeably sharp and the 5th noticeably flat. The H-System names for these 19ET intervals are Major Perfect Fourth and Minor Perfect Fifth, indicating that they are 1 JND (Just Noticeable Difference) out of tune from their Perfect (beatless) harmonic versions.
Just to be clear, I had no idea that Jonathan was going to make these videos, I didn't ask him to point out TBX1 or talk about it at all, and I certainly didn't pay him to advertise for me! The fact he mentioned TBX1 was a really nice surprise. Thanks, Jonathan! He says that this is part 1 of 3, so I look forward to the next videos.
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