source file: mills2.txt Date: Mon, 10 Mar 1997 18:15:44 -0800 Subject: Miscellany From: John Chalmers RE ether: Whether Einstein or other theorists still needed the concept of the ether in 1920 is irrelevant to physics today. The concept is not needed for current theories. Einstein never accepted quantum mechanics in full and ignored the strong and weak nuclear forces in formulating his abortive unified field theory. He made essentially no contribution to physics after General Relativity. Re Rydberg states of H: Spectra of atoms more complex than hydrogen do not have these simple relations. However, other number series than n^2 (n 1, 2, 3 etc.) may be used for defining chords, scales and intervals. Fokker made use of the Fibonacci and Lucas series. Brian McLaren has proposed a number of other series. Erv Wilson has generated many too. Dominant 7th: While one might add the 8 to the 4:5:6:7, it is not mandatory and makes the chord unnecessarily dense. One might add the 9 to make a dom major 9th or 17 (8:10:12:14:17 as a minor 9th. The 10:12:14:17 part is Ellis's diminished 7th. Other chords such as 11:13:15:17 have been used too. Re Aristoxenos: I think Jonathan's suggestion that reluctance to extract the 5th root of 4/3 explains the failure of Greek theorists to interpret Aristo correctly is a wonderful piece of insight. I too was seduced by the octave... Paul E: I have constructed a number of positive systems with good Harmonic 7ths. Will post a few later when I have formatted them. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 11 Mar 1997 03:21 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01105; Tue, 11 Mar 1997 03:21:16 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01103 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id SAA16638; Mon, 10 Mar 1997 18:19:40 -0800 Date: Mon, 10 Mar 1997 18:19:40 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu