source file: mills2.txt Date: Thu, 13 Feb 1997 14:10:19 -0800 Subject: Reply to Neil from Paul From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE Neil, If the harmonic series is really your model for tuning, but you want equal temperament, it seems odd that you concentrate on 19- and 34- (and have lauded 53-) equal. 19 consistently represents the harmonic series only through the 9th harmonic (though in your music, you tend to use the diatonic, rather than harmonic, dom7th), and 34 consistently represents the harmonic series only through the 5th harmonic. Equal tunings with similar accuracies to 19 and 34, but which represent the harmonic series consistently through the 11th harmonic, are 22 and 31, respectively. I assume that, not being a Harry Partch fan, you don't get anything out of ratios of 7, 9, and 11. That's fine. Maybe your model for tuning is the harmonic series only through the 5th harmonic (plus octave equivalence). That's fine too. Someone else's model may be the diatonic scale with no commas and smooth 5-limit triads, they would choose 19- or 31- or 50-tET. Someone else might like 5-limit triads and huge commas; 15-equal is for them. Someone else might like diatonic scales with thirds tuned 7:6 and 9:7; they would love 22. (I have other reasons for loving it.) Another person might like to combine two different diatonic scales, taking consonant triads from either and consonant 7-limit additions from the other. 26-equal is for them. Someone else might want to strecth as far up the harmonic series as possible; they could go all the way through the 15th harmonic quite accurately with 41. Then there are those who don't like equal temperament, or don't like simple ratios (i.e., they like dissonance), or both, or have other specific desiderata. As long as these goals are perceptibly beautiful, and not merely mathematically beautiful, they will gravitate towards some tuning over others. Equal temperament is great for transposition, for "punning," and fretted instruments, but some want no deviation from just ratios, while others want to control these deviations compositionally. I believe that dissonance can be beautiful, but as almost any tuning has plenty of dissonances available, I find it important to find tunings where this dissonance can be contrasted with consonance. However, others may wish to find simple pitch structures lacking in tonality of any sort; Blackwood as singled out 11-equal as "the most effective for random dissonance" -- far better than 12-tone serialism would be 11-tone serialism! I'm just rambling here, but the point is that if we declare a tuning "best," especially in some cross-cultural sense, we are going to make life pretty boring for future composers, and impossible for performers of traditional music around the world (if 12-equal hasn't already done so). As for magic and healing and Creatorship, these are things which presumably escape scientific inquiry anyway so we'd be better off not trying to analyze or prescribe frameworks for them. -Paul Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 13 Feb 1997 23:40 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05726; Thu, 13 Feb 1997 23:40:45 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA05719 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id OAA18425; Thu, 13 Feb 1997 14:38:16 -0800 Date: Thu, 13 Feb 1997 14:38:16 -0800 Message-Id: <3303AD1C.3148@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu