source file: mills2.txt Date: Wed, 30 Oct 1996 06:39:55 -0800 Subject: Pentatonic source scale From: wauchope@AIC.NRL.Navy.Mil John Chalmers wrote: > Other interesting pentatonics are slendro-like septimal scales such as > 1/1 7/6 4/3 3/2 7/4 2/1 and neutral ones such as 1/1 11/9 4/3 3/2 > 11/6 2/1, etc. and their modes. If you take the 13-limit pentad 1/1--26/21--14/11--14/9--8/5 and duplicate it in four parallel 3/2's, i.e. 28/27--14/9---7/6-----7/4 104/63--26/21--13/7--39/28 4/3-----1/1---3/2----9/8 16/15----8/5----6/5---9/5 56/33---14/11--21/11--63/44 you get a fairly evenly spaced 20-tone scale that contains thirty-two different pentatonics of the form 1/1--X--4/3--3/2--(3/2)X--2/1 where "X" ranges from a minor second (giving you "descending" or koto-like pentatonics), through major seconds and then minor and major thirds (for "ascending" or gamelan-like pentatonics), including the two scales John mentions. This comes about because the pentad contains eight different major or neutral thirds, ranging from 11/9 (347c) to 84/65 (444c). Adding the 3/2's thus creates eight (each) major seconds, minor seconds, and minor thirds for a total of 32 values of "X". (Of the 32 six are just a few cents apart, so the number of really distinct pentatonics is 26.) The scale can be tempered and evened out a bit by using the corresponding tones from scales like 72-TET or 75-TET, which will give you just the 26 distinct pentatonics. Since twenty is a nice manageable source scale size for fixed-pitch instruments like guitar or metallophone, I thought this might be of interest. Ken Wauchope Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 30 Oct 1996 20:16 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA30288; Wed, 30 Oct 1996 16:02:50 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA04021 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id HAA14664; Wed, 30 Oct 1996 07:02:48 -0800 Date: Wed, 30 Oct 1996 07:02:48 -0800 Message-Id: <961030150106_71670.2576_HHB68-10@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu