Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site decwrl.UUCP Path: utzoo!watmath!clyde!floyd!harpo!decvax!decwrl!rhea!marvin!isbell From: isbell@marvin.DEC (Chris Isbell ) Newsgroups: net.music Subject: Tempered scales Message-ID: <6082@decwrl.UUCP> Date: Wed, 7-Mar-84 03:49:28 EST Article-I.D.: decwrl.6082 Posted: Wed Mar 7 03:49:28 1984 Date-Received: Thu, 8-Mar-84 07:41:42 EST Organization: DEC Engineering Network Lines: 51Quote from seismo!tiberio: >Is there any need for a discussion on the virtues of untempered scales >(as played by woodwinds, they go flatter in the higher octaves) verses >tempered scales (played by ugg pianos, they go sharper). > >learn to play a flute! The classic work on this subject is by Hermann Helmholtz, On the Sensation of Tone. There is a translation published by Dover in paperback. It is heavy going, but worth it if you are interested in the subject. In general modern woodwind instruments are tuned to the equal tempered scale, the same at modern keyboard instruments. Early woodwind instruments (recorders, capped reeds etc.) give the player much greater control of the pitch. I can vary the pitch of a note by about a semitone each side of normal on most of my capped reed instruments. In general flutes (fipple and transverse) tend to be sharp in the higher registers when played by unskilled players (just listen to a class of school children playing recorders!). If you wish to go flat in the upper registers, take up a reed instrument or a member of the violin family. The greater variation in pitch of early woodwind instruments has two effects. Firstly, an inexperienced early music consort is usually out of tune. Secondly, a good consort will play in non-equal temperament - usually just intonation. This means that the pitch of some notes of the scale change in pitch as the music changes key. The reason for having different temperaments is complex, but briefly, I is a result of the fact that roots of two are irrational numbers. The octave, which is the most basic musical interval is a frequency ratio of 2:1. Any attempt to divide the octave into a finite number of equal frequency ratios will result in intervals which are based on roots of two. If the octave is not divided into equal ratios, than certain keys will be out of tune. However, the musical intervals which are pleasing to the ear are simple frequency ratios such as 2:3 (fifth), 3:4 (fourth), 4:5 (major third) etc. Any deviation from simple ratios will cause interference between the two sound sources which, if the deviation is small, results in a beating sensation. The modern equal tempered scale has a frequency ratio between semitones of the twelfth root of two. This means that certain intervals are out of tune. In particular, the major third is too wide. My subjective feeling is that this produces a harsh edge to the music which I find unpleasant. Chris Isbell. (...decwrl!rhea!marvin!isbell)