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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: 51




Quote 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)