Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!linus!philabs!seismo!presby!burdvax!floyd From: floyd@burdvax.UUCP (Floyd Miller) Newsgroups: net.music Subject: Re: Scales Again Message-ID: <939@burdvax.UUCP> Date: Tue, 2-Aug-83 22:13:10 EDT Article-I.D.: burdvax.939 Posted: Tue Aug 2 22:13:10 1983 Date-Received: Thu, 4-Aug-83 23:51:55 EDT References: watdaisy.240 Lines: 46 I'm not an expert, but from a course I took years ago at Univ. of Mich. called "The Physics of Music", I remember some discussion on musical scales. The basis for most scales (especially the "western" 12 tone scale) is that human hearing is very sensitive to certain intervals (differences in pitch between two notes). This is pronounced when the two (or more) notes are heard sameoltimeously. Not only are these intervals easily distinguishable, but we are able to percieve when the tones are close to the interval (the "beating" effect). It seemed only natural to base a musical scale on these intervals since most people could hear them and they sounded "nice". (these intervals also happen to line up, more or less, on a logarithmic mathematical scale). I don't remember all the details (I could look it up in the handouts I saved) but the clearest interval is the octave (a 2:1 frequency ratio) and the western scale has been based on this for a long time. An early scale was based on the notes obtained by progressing at "fifth" intervals (ration of 3:2) and moving each note by a factor of two to bring it into the base octave. A scale of seven note resulted (the diatonic scale). THe problem with that scale (also called the Pythagorean scale) is that it ignores all the other natural intervals besides the octave and the fifth. Many of the notes are close to, but not at, these other intervals. The interval of a "third" is noticably "sour" as was demonstrated in one of the lectures. An alternative scale, called the "Just" scale was developed using the intervals of "octaves", "fifths" and "thirds" (5:4). Thus, the basic unit of the "Just" scale is the major triad, a combination of three notes whose frequencies are of the ratio 4:5:6 (containing the ratios of 5:4 & 3:2. The "just" scale still has a serious problem: the interval from D to A (asssuming the scale was based on C) is close to a perfect fifth but off by enough to really louse up any song that tries to build chords on various steps of the scale (most intersting music does). Temperament is the process of modifying a scale by small amounts to achieve a more even sounding scale. What is done to the "Just" scale is to spread the difference between the interval D to A and a real fifth over the entire scale to weaken its effect. Thus, the "Equal Tempered Scale" in which only 3 intervals are exactly at the mathematical and natural intervals, the octave, the fifth, and the fourth. That's all I have time to type now.