source file: mills2.txt Date: Mon, 17 Feb 1997 19:55:29 -0800 Subject: [Fwd: GhostTones ?] From: Gary Morrison Replying to Charles Lucy: > It seems that by taking steps of fourths and fifths, from a given pitch, > all "harmonics" (ghosttones?) can be mapped in a continuous series. > The interval between the fourth and the fifth is exactly [1200/(2*pi)> 190.9858 cents] . This interval Harrison called the "larger" interval. > I have used the term "Large"(L). Can you show us any specific evidence that this maps to partials of any pitch from any instrument instrument more accurately than integer multiples? Or is the closeness of the mapping not your main point? > It seems that notes, which are closer on the spiral of fifths and > fourths are more consonant than those which are a greater number of > steps apart.. Are you sure that "consonant" is the best choice of words here? Would you for example view a major second (two fifths apart) as more consonant than a major sixth (three fifths apart)? "Consonant" is probably a good term in one sense but not another: Since consonance REALLY means closeness to resolution to the tonic in a tonal system (despite its common but technically incorrect usage as more or less the opposite of "discordant"), closeness on the circle of fifths (spiral or whatever) is a pretty good measure of closeness to the tonic in a tonal system. But it's probably not a very good measure of consonance in thee sense of discord (for the reason I suggested above). Discord is another way in which a harmony can sound farther from resolution. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 18 Feb 1997 06:38 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10224; Tue, 18 Feb 1997 06:38:51 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA10221 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id VAA27152; Mon, 17 Feb 1997 21:37:15 -0800 Date: Mon, 17 Feb 1997 21:37:15 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu