source file: mills3.txt Date: Thu, 16 Oct 1997 22:32:17 +0200 Subject: RE: how about 22et vs 19et ? From: "Paul H. Erlich" Neil Haverstick did a nice job talking about 19et. That's partially because the existing musical terminology makes sense in 19et. Which means, essentially, that traditional ways of composing and performing music work in 19et. When 12et was adopted, 19et was a viable, known alternative (Salinas, Costeley) but 12et won out for convenience's sake. In 19et, most Renaissance, Baroque, and some classical music will sound great. But, as Neil points out, the diatonic b7ths are unbelievably far from forming nice 7-limit tetrads, so dominant sevenths (and arguably half-diminished sevenths) sound better in 12et than in 19et. What Neil doesn't point out, and what I would recommend he explore in his playing, is that using the #6th instead of the b7th leads to a much better set of septimal intervals. For example, in 12et, playing a B and an F together is ambiguous as to whether the root is G or C#. In 19et, the root is much more clearly C#, while a B and an E# will evoke a root of G. It sounds to me like Neil, when playing a blues in G or D, is sticking to the diatonic F in some places where an E# might be much more consonant. I very often hear blues or pop music which, if transposed to the key of D, uses a septimal E# over the G (IV) chord, and slightly less often I hear the #6 over the I chord. Weighing against the acoustical superiority of the #6th is the familiarity and symmetry of the traditional diatonic scale, and the fact that 19et's 7-limit intervals often deviate from JI in the opposite direction than 12et's approximations of the same intervals, leading to a very strong initial "that's out-of-tune" reaction. 31et is just like 19et but more so (i.e., 7-limit intervals based on the augmented sixth chord are nearly just; those based on the diatonic b7 are worse than 12et but not as bad as the same in 19et.) It also has great 11-limit approximations. 22et is completely non-traditional. The fact that the product of four perfect fifths does not approximate a 5:1 ratio throws a wrench into the works. You have to scrap the usual notions about how to tune the guitar, scales, chords, and keys (not to mention repertoire!), or at least retreat to a much more bare-bones set of definitions in order to build an understanding of the tuning back up. You can read my paper on John Starrett's web site to see at least one approach. 34et is non-traditional as well, but the inequality between major and minor whole tones is much less noticeable than in 22et, and making a "comma" adjustment, often necessary when trying to force traditional chord progressions into non-traditional tunings, is more disturbing when the adjustment is as large as 1/22 octave. So 22et forces you to abandon much of what you have learned about how music works. It has much better 7-limit approximations than 19et, and will even get you as close to the 11-limit as Harry Partch's own voice could (max. error 20.1 cents). 34et is not consistent beyond the 5-limit. 15et and 27et are also nice, non-traditional tunings. 26et is "traditonal" in a sense but turns 12et's deviations from 5-limit JI upside-down. 26et's leading tone of 138 cents (3/26 oct) is certainly unusual-sounding, and it can even sound better to use a harmonically false leading tone to get a more familiar interval of resolution (92 cents or 2/26 oct). But 26et has a nice way of introducing 7-limit harmony (two diatonic scales tuned a half-octave apart will each contain the 7-limit completion of all of the other's 5-limit triads!) and is even consistent through the 13-limit. Finally, 29et is worth considering since it is consistent all the way through the 15-limit. If you want to get really non-traditional, try 24.6063et, which gives you great approximations of all ratios of odd numbers through 13, but forget about even numbers! As for fingering, it does help if you already have calloused fingers, otherwise your finger will just mash over several frets and probably dampen the string's vibrations somewhat. You need to get some hardened part of your fingertip (or side) to press the string down between two frets, and that can be a lot easier on an electric guitar, since the tension and action are lower. Don't expect to be able to pull off your usual set of flashy licks and tricks without a long period of slowly re-training your fingers. SMTPOriginator: tuning@eartha.mills.edu From: jpff@maths.bath.ac.uk Subject: Re: Music Notation Software & Synth query PostedDate: 17-10-97 13:37:38 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 17-10-97 13:36:58-17-10-97 13:36:59,17-10-97 12:37:41-17-10-97 12:37:42 DeliveredDate: 17-10-97 12:37:42 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256533.003FCB6B; Fri, 17 Oct 1997 13:36:48 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA19672; Fri, 17 Oct 1997 13:37:38 +0200 Date: Fri, 17 Oct 1997 13:37:38 +0200 Message-Id: <9710171137.AA19672@ns.ezh.nl> Received: from ella.mills.edu by ns (smtpxd); id XA19680 Received: (qmail 21221 invoked from network); 17 Oct 1997 04:37:21 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 17 Oct 1997 04:37:21 -0700 Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu