Asked • 06/22/19

Natural vs tempered semi-tones?

I am reading "Fundamentals of Musical Composition" by Arnold Schoenberg. Chapter XI, page 99, states: > Chromaticism is difficult partly because the natural semi-tones differ in size from the tempered (a fact which causes choirs to get off pitch)I do not understand this sentence. What is the difference between natural and tempered semi-tones? What does this have to do with chromaticism, or choirs getting off pitch?

Alden J.

tutor
"Tempered" means "adjusted", and what is being adjusted are the "natural" pitches of the harmonic series. Singers are likely to be drawn to these natural pitches because they can feel them, physically. The "adjustment" that brings about the "tempered scale" results in a chromatic series of notes which are all the same interval. Look at this table: http://pages.mtu.edu/~suits/notefreqs.html If you take any two consecutive frequencies, say 55.0 and 58.27 and divide 55 by 58.27, the result is the same if you divide any other two consecutive frequencies, say 69.3/73.42. This shows that the ratio between any two semitones in the tempered scale will be the same.
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06/26/19

1 Expert Answer

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David W. answered • 06/26/19

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PhD in Music Composition with 5+ Years of Teaching Experience

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