source file: mills2.txt Date: Mon, 25 Nov 1996 16:14:16 -0800 Subject: RE: Paul Hindemith & the harmonic series From: PAULE Brian wrote, >since the perfect fifth >is 1/170 of an octave off from the harmonic-series >value in 19-tone equal temperament, Yasser >proscribed the use of that 19-tone interval. That is not why. Yasser thought the consonant chord in 19-equal had to be constructed as every other note in a 12-note scale in 22. The perfect fifth in 19-tone equal is closer to its harmonic series value that the approximations to the eleventh and thirteenth harmonics in Yasser's hexad. Since the hexad did not include the twelfth harmonic of the same fundamental, Yasser concluded that the "perfect fifth" would have to be treated as a dissonance. Of course this is backwards, but necessary for Yasser to preserve his numerological patterns. These patterns happen not to be consistent with each other when the details of Yasser's proposed "super-ultra-tonality" or 19-out-of-31 system are worked out. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 26 Nov 1996 01:13 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07624; Tue, 26 Nov 1996 01:15:15 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA07661 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id QAA14453; Mon, 25 Nov 1996 16:15:12 -0800 Date: Mon, 25 Nov 1996 16:15:12 -0800 Message-Id: <42961125222324/0005695065PK2EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu