Temperament - Viscount Chorum 10 Dlx Bedienungshandbuch

Chorum 10 Dlx – Chorum S10 – Chorum 10

7.3 TEMPERAMENT

Tuning a fixed intonation instrument (e.g. organs) consists of creating a chain of twelve fifths,
properly crafted so that at the extremes the interval can be reduced, through division or
multiplication, to a perfect octave. A perfect fifth is achieved when two sounds have a frequency
ratio of 3:2. If from any sound we calculate twelve ascending perfect fifths, the sound obtained is
12
(3/2) . With 7 octaves instead, the result is a 27 frequency. If we compare these values we find that
(3/2) 12 is slightly higher than 2
12
(3/2) =129,7463 , while 2
comma. It can be defined as the surplus of twelve perfect fifth compared to seven octaves, both
starting from the same sound.
The picture is not in scale (otherwise the comma would be almost invisible) but it gives a graphical
understanding of the problem.
Now, dividing the Pythagorean comma in 12 equal parts, and subtracting this value to each pure
fifth, the result is a twelve-fifth chain, ending with the same value as seven octaves.
This is the Equal Temperament System (with the comma split in twelve parts).
7 . Rounding off after the fourth decimal, we find that:
7
= 128,0000. The ratio between these two value is called Pythagorean
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