Temperaments Of The Chorum 10 - Viscount Chorum 10 Dlx Bedienungshandbuch

Chorum 10 Dlx – Chorum S10 – Chorum 10
User Manual
The Pythagorean comma can be split in larger parts and divided among a few (less than 12) fifths.
This leads to other temperaments, such as the Werckmeister III, which spreads the comma in four,
equal parts, between C-G, G-D, D-A, and B-F#.
A very important interval in the history of tuning is the major third. A chain of four pure fifths
makes (3/2) 4 . A major third interval is represented by a 5/4 ratio. Therefore, rounding off, the
frequency of a major third, generated by Pythagorean fifths is 1,2656, while a natural major third is
1,2500. This surplus is called Syntonic comma.
A series of four fifths, each one reduced by ¼ of Syntonic comma, makes a perfect major third.
These fifths are called "meantone". If a temperament recovers only one syntonic comma, it still
needs to compensate the small difference between Pythagorean and syntonic comma. This
difference is called skisma. For example, the Kirnberger II temperament is based on the syntonic
comma. It spreads the comma equally between D-A and A-E and the skisma between F# and C#.
A series of three natural major thirds makes a frequency of (5/4) 3 . The difference between that and
the octave is called enharmonic comma.
When a temperament makes up for more than the Pythagorean comma, usually one fifth is much
wider than the rest and becomes unusable. It is called the wolf fifth.

7.4 TEMPERAMENTS OF THE CHORUM 10

In addition to equal temperament, with the
Chorum 10 you can play other temperaments
described below.
MEANTONE
This tuning is the prototype of all temperaments
based on fifths reduced by ¼ of syntonic comma.
This generates eight pure major thirds: Eb, Bb, F, C,
G, D, A, E. However, the other thirds are unsuable
(B, F#, G#). The fifths are defined as meantone
fifths: shorter than pure fifths but still sounding
well. Only one, G#, fills all the gap created by 11
others and becomes a wolf fifth. Tonalities with
little alterations sound very pleasant. Well
characterised chromatic scale. Move the wolf on C#
to use the G# key as Ab.
WERCKMEISTER III
Based on four fifths, each reduced by ¼ Pythagorean
comma – the others are pure. Creates three
Pythagorean major thirds on: C#, F#, G#. As the
number of alteration in the piece performed
increases, so does the harmonic tension.
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