source file: mills2.txt Date: Wed, 19 Feb 1997 00:35:27 -0800 Subject: Re: Classifying Tunings From: Matt Nathan TONY SALINAS wrote: > > I can see two clear groups of tunings: > > A) The ones using fractions as ratios > > B) The ones using roots to determine the ratio It's interesting to note the the ones using roots still use ratios as the interval for which a root is found. Most often, the ratio for which roots are found is 2:1, but not always. I think there are more categories. What about equal temperaments of transcendental numbers (the most abundant numbers), which are neither ratios nor roots of ratios? What about "modulated equal temperaments"? These would be pitch sets which are sort of like equal temperaments but which vary in step size along the "scale" according to a given curve. For example, using a sine curve, the widths would cycle from narrow to wide and back again as you move up the "scale". I think either a slanted line or a log scale applied to a modulated equal temperament would produce an harmonic series. What about sets of "found" pitches--pitches which are determined randomly or from some natural data (like stock prices). I read a neat post in the archives, but lost it again, which described how someone would find the most comfortable finger positions for a wood flute before drilling the holes. That determined the pitch set for the instrument, for which music was then composed. There are conceivably as many pitch set categories as there are categories of numbers and number sets. I suspect, as John Starret here wrote, that "...we may be hardwired for mathematical understanding of all that we can understand mathematically, and that may spill over into musical understanding...". I think we can perceive different qualities in pitch sets derived by different mathematical means, given that the instrument has good enough resolution to distinguish them and that the actual pitch differences are large enough to fall above the threshold of perception. Matt Nathan Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 19 Feb 1997 10:15 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA11275; Wed, 19 Feb 1997 10:15:04 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA11272 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id BAA05320; Wed, 19 Feb 1997 01:13:21 -0800 Date: Wed, 19 Feb 1997 01:13:21 -0800 Message-Id: <330AC216.1551@ix.netcom.com> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu