source file: mills2.txt Date: Mon, 19 May 1997 03:20:35 +0200 Subject: Re: ratios in JI From: rtomes@kcbbs.gen.nz (Ray Tomes) Pieter Smit wrote: >Would the 'natural' scale then be in the ratios > 1, 9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2 > for the scale CDEFGA(B-flat)Bc ? Do I get this right? What would >this scale be called, and how would it sound ? Pieter, I missed your question but saw some other replies. When you use the word "natural" I have some very definite opionions about this. If you go to my WWW pages (URL below) you can get the long version which I think you might enjoy given the questions you are thinking about. While there is some validity to what you have done in your post, it is not the complete story. In practice if you just take frequencies 1, 2, 3, 4, 5, etc and work out the notes by transposing back to one octave then you have assumed that the ratio of 2 (the octave transpose) is more important than all other ratios. That is actually true, but the ratios 3, 5, 7 etc are successively less important. Therefore the ratios of 11 and 13 are rather seldom really found in music and your 11/8 is more likely to be 21/16 but is generally really 4/3. >What would the scale be called > 1, 9/8, 5/4, 4/3, 3/2, ......., where the fourth is tuned as a >perfect fifth below ? Would this be the JI scale? Yes. The JI scale is 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2. The next two most common notes that can be added to the JI scale are 7/6 and 7/4 for Eb* and Bb* if the above scale is C. I like to express this by eliminating the denominator as: 24 27 (28) 30 32 36 40 (42) 45 48. [* What is the correct notation for this? Is it Mi-flat and Ti-flat?] In nature the ratios of 2, 3, 5, 7, 11, 13, ... tend to occur with a commonness of about 100, 42, 17, 10, 5, 4, ... so that when we have numbers with just one ratio of 5 present we can expect 2 or 3 ratios of 3 and about 6 ratios of 2 and a ratio of 7 would then have about a 60% chance of being present. -- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 19 May 1997 05:13 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05308; Mon, 19 May 1997 05:13:13 +0200 Date: Mon, 19 May 1997 05:13:13 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05305 Received: (qmail 17017 invoked from network); 19 May 1997 03:13:09 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 19 May 1997 03:13:09 -0000 Message-Id: <970518231103_-2068291672@emout07.mail.aol.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu