Werckmeister temperament refers to any of the tuning systems described by Andreas Werckmeister in his writings ^[1] and ^[2]. The tuning systems are confusingly numbered in two different ways. In music, there are two common meanings for tuning: Tuning practice The act of tuning an instrument or voice. ... Andreas Werckmeister (November 30, 1645 – October 26, 1706) was a musician and music theorist of the Baroque era. ...

Werckmeister I (III): multiple-division just intonation

Werckmeister I is based on the Pythagorean tuning, but the Pythagorean comma is divided into four equal parts, and each of the fifths C-G, G-D, D-A and H-F# are made smaller by 1/4 comma. All other fifths are perfect. Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. ... When one ascends by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, one eventually reaches a note around seven octaves above the note one started on, which, when lowered to the same octave as the starting point, is 23. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ...

The cent is a logarithmic unit of measure used for musical intervals. ...

Werckmeister II (IV): meantone tuning

In Werckmeister II are the fifths C-G, D-A, E-B, F#-C#, and Bb-F are diminished by 1/3 Pythagorean comma, and the fifths G#-D# and Eb-Bb are enlarged by 1/3 comma. The other fifths ae perfect. When one ascends by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, one eventually reaches a note around seven octaves above the note one started on, which, when lowered to the same octave as the starting point, is 23. ...

Werckmeister III (V): well tempered tuning

In Werckmeister III are the fifths D-A, A-E, F#-C#, C#-G#, and F-C are diminished by 1/4 Pythagorean comma, and the fifth G#-D# is enlarged by 1/4 comma. The other fifths ae perfect. When one ascends by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, one eventually reaches a note around seven octaves above the note one started on, which, when lowered to the same octave as the starting point, is 23. ...

Werckmeister IV (VI): the septenarius tunings

In Werckmeister IV are the fifths C-G, Bb-F, and B-F# diminished by 1/7 Pythagorean comma, F#-C# by 2/7 comma and G-D by 4/7 comma. D-A, G#-D# are enlarged by 1/7 comma. The other fifths are perfect.

The cent is a logarithmic unit of measure used for musical intervals. ...

External sources

• http://www.groenewald-berlin.de

References

1. ^ Andreas Werckmeister: Musicae mathematicae hodegus curiosus oder Richtiger Musicalischer Weg-Weiser - Frankfurt und Leipzig 1687 ISBN 3-487-04080-8
2. ^ Andreas Werckmeister: MUSICALISCHE TEMPERATUR (Quedlinburg 1691) edited by Rudolf Rasch ISBN 90-70907-02-X