source file: mills2.txt Date: Thu, 15 Aug 1996 16:20:58 -0700 Subject: RE: classifying tunings (or not!) From: PAULE >It would be interesting to see how people think that tunings should be >classified (or not!). It would also be interested to know, how people that >include tunings as part of their teachings introduce them (and subdivide >them). This is how I would structure a 15-week course on tunings, meeting twice a week, with musical examples along the way. The course would be "hands on" with monochords and scalatrons for all. 1. Introduce the octave as an acoustical phenomenon 2. Introduce the 3-limit consonances and Pythagorean tunings 3. Pythagorean tunings as applied to pentatonic scales: Chinese Music 4. 7-ET representations of pentatonic scales allowing modulational freedom: Thai music 5. Pythagorean tunings as applied to the heptatonic scale: Organum 6. Discuss the pythagorean comma; introduce 12-ET representations of the heptatonic scale 7. Non-just non-equal-tempered scales: African and much other music 8. Introduce the 5-limit consonances 9. Schismatic tuning of late middle ages and medieval Arabic tuning as Pythagorean approximations to the 5-limit 10. Just intonation: Indian music (I've heard some santoor music where the intonation is very clearly just 5-limit). 11. Discuss the syntonic comma; introduce meantone temperament: Renaissance music 12. Equal-tempered versions of meantone -- 31, 19, is 12 good enough? 13. Circulating temperaments/well temperament: Bach and "key colors" 14. 12-TET becomes standard :( , Arabic music measured and played in "quarter-tones" 15. Equal tempered versions of just intonation: 53, 34, maybe compare 22-equal with 22 sruti of Indian music to show how JI structures are preserved 16. Atonality, set theory, Balzano and 20-TET and other numerological constructs. 17. Introduce the 7-limit consonances 18. Augmented sixth chords as meantone approximations to the 7-limit 19. Introduce the 9- and 11-limit consonances in JI: Partch, Johnston, etc. 20. Equal-tempered representations of higher consonances: Huygens, Fokker, and 31; Herf, Sims and 72, proposals of 41-tone and 171-tone equal temperaments 21. Inharmonic timbres, tunings to go with them: Gamelan music, modern explorations 22. Non-octave scales in history and modern non-octave tunings such as Pierce's 13 per 3:1 23-30. Creative ensemble projects Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 16 Aug 1996 12:15 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16260; Fri, 16 Aug 1996 12:15:54 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA16195 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id DAA15971; Fri, 16 Aug 1996 03:15:51 -0700 Date: Fri, 16 Aug 1996 03:15:51 -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