Re: [Harp-L] Questions re: blue notes and micro-tonality






Please may I re-quote from "The Craft Of Musical Composition" by Paul Hindermith first published in 1937;

 

< If we were to ask an intelligent musician, who knew his métier and who had a certain theoretical knowledge, what tones he would choose from among the audible range, what series he would con­sider the most natural, the simplest, and the most practical raw material for composition, he would undoubtedly reply after a mo­ment's thought that we must mean a scale, for without a scale no ordered music would be conceivable. 

He would be thinking of the major and minor scales, which provide an inexhaustible supply of tones for all possible harmonic combinations, and according to which all melodies known to him can be classified. He would be forgetting, however, that our ancestors made use of other scales, and that even today peoples of other cultures use scales that often have little similarity to ours. 

Even the simplest musical activity, uninfluenced by education or experience-the song of the savage, or the first attempts to draw tones out of a hollow bone or a reed pipe-must make use of some interval-progressions which are based fundamentally-on a series of adjacent tones. The primitive musician, giving direct expression to his mood, will at first not be interested in the exact distance of one tone from another. Not until considerable experience has broadened his knowledge and raised the level of his desires will he feel the need of bringing order into the luxuriant tonal wilderness.>

 

Later on he considers different sized thirds as derived from the overtone series and here comes the crunch when we try to consider the limits of so called 'just' intonation:

 

<.we may examine a little more closely the thirds that exist in the lower part of the overtone series. Within the first 11 overtones alone there are five different sizes of thirds: 

 

the major 4:5, the minor 5:6, the under-sized 6:7, the over-sized 7:9, and the one which is between major and minor, 9:11. To these we may add the Pythagorean third, which we can easily calculate,  and which is between 4:5 and 7:9 in size. 

The ear not only hears all these as thirds; it permits itself to be hood­ winked still further by this beautiful but characterless interval.

 If we play on the violin or other appropriate instrument a third that is as small as it can be without being a second, and if we then slide the upper tone up to the upper boundary of the third, just below the point where it would become a fourth, we cannot say just where

the change from a minor third to a major third takes place..>

 

Food for thought, n'est pas?



another source of information is ;

A beginner's guide to temperament Stephann Bicknel 



 http://www.users.dircon.co.uk/~oneskull/3.6.04.htm Piporg-l



hope this helps



Mox





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