source file: mills2.txt Date: Sat, 19 Oct 1996 16:57:16 -0700 Subject: Similarity of scales. From: brg@netcom.com (Bruce R. Gilson) We've seen a number of debates on whether 19-tET, or 22-tET, or whatever is "like" the old familiar 12-tET. I think in part it comes down to what you're looking at. I think that it would be improper for me to comment on the general impression of what a piece in some unusual scale sounds like, as I've never heard any full piece played in any temperaments other than 12 or 7 (At least, I _assume_ the background music I hear in some Thai restaurants is in 7-tET; I've been told that it is Thai traditional music, and I've read that that is in 7-tET. But I haven't done a frequency scan to make sure they weren't using Western instruments tuned to 12.) But I've played scales generated on computers. And to my ear, Blackwood's comment that a diatonic scale will sound "recognizable" if it follows the standard pattern of 2 large intervals, one small, three large, and one small seems correct. Now the only tempered scales that permit this are those with 5x + 2y tones, with x > y > 0. This means 12, 17, 19, 22, 24, 26, ... and certainly both 19 and 22 qualify. And in fact, if I play a 19-tET scale, with "whole steps" of 158 moc (I'm using moc consistently; if you need to convert to cents to visualize, multiply by 1.2) and "half steps" of 105 moc for my intervals, it sounds to my ear so much like a standard major scale that I'd never spot the difference unless I heard them played together. The fact that the "half step" is MUCH more than half the "whole step" is not obvious to my ears. (In fact, in the most common sort of JI scale, the "half steps" are 93 moc and the "whole steps" are a mixture of 152 and 170 moc. So the fact that the "whole step" is less than double the "half step" does make it somewhat "JI-like." But the point is that ALL these scales, 12-tET, 5-limit JI, 19-tET, etc., permit the construction of major [and minor] scales of the same pattern.) Now having said this, we can note that a 4:5:6 major triad is characterized by three intervals: 5/4 (322 moc), 6/5 (263 moc), and 3/2 (585 moc). And these are represented in 12-tET by 333, 250, and 583 moc, while in 19-tET they are 316, 263, and 579 moc. It is possible that some ears hearing the CHORD may get a different impression because the two thirds are closer to JI while the fifth is further from JI. I don't know. I can't program my computer to play the chords and I don't have a keyboard I can retune. But I think that melodically, from what I've said, assuming that most tunes consist of sequences from the diatonic scale up or down for large portions of their scope, 19, 12, or 22 will sound all about the same. (If you write a complex piece with much modulation, this may not be so. But a popular song, for example, played in 19 will not sound unusual to ANYONE's ear unless they have far better absolute sense of pitch than I have.) Bruce R. Gilson email: brg@netcom.com IRC: EZ-as-pi WWW: http://www.geocities.com/CapitolHill/3141 Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 20 Oct 1996 12:01 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04046; Sun, 20 Oct 1996 12:03:02 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA04054 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id DAA02819; Sun, 20 Oct 1996 03:02:59 -0700 Date: Sun, 20 Oct 1996 03:02:59 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu