Werckmeister temperament

Werckmeister temperament

Werckmeister temperament refers to any of the tuning systems described by Andreas Werckmeister in his writings [Andreas Werckmeister: Orgel-Probe (Frankfurt & Leipzig 1681), excerpts in Mark Lindley, "Stimmung und Temperatur", in "Hören, messen und rechnen in der frühen Neuzeit" pp. 109-331, Frieder Zaminer (ed.), vol. 6 of "Geschichte der Musiktheorie", Wissenschaftliche Buchgesellschaft (Darmstadt 1987).] [A. Werckmeister: Musicae mathematicae hodegus curiosus oder Richtiger Musicalischer Weg-Weiser (Quedlinburg 1686, Frankfurt & Leipzig 1687) ISBN 3-487-04080-8] [A. Werckmeister: Musicalische Temperatur (Quedlinburg 1691), reprint edited by Rudolf Rasch ISBN 90-70907-02-X] . The tuning systems are confusingly numbered in two different ways: the first refers to the order in which they were presented as "good temperaments" in Werckmeister's 1691 treatise, the second to their labelling on his monochord. The monochord labels start from III since just intonation is labelled I and quarter-comma meantone is labelled II.

The tunings I (III), II (IV) and III (V) were presented graphically by a cycle of fifths and a list of major thirds, giving the temperament of each in fractions of a comma. Werckmeister used the organbuilder's notation of ^ for a downwards tempered or narrowed interval and v for an upward tempered or widened one. (This appears counterintuitive - it is based on the use of a conical tuning tool which would reshape the ends of the pipes.) A pure fifths is simply a dash. Werckmeister was not explicit about whether the syntonic comma or Pythagorean comma was meant: the difference between them, the so-called schisma, is almost inaudible and he stated that it could be divided up among the fifths.

The last "Septenarius" tuning was not conceived in terms of fractions of a comma, despite some modern authors' attempts to approximate it by some such method. Instead, Werckmeister gave the string lengths on the monochord directly, and from that calculated how each fifth ought to be tempered.

Werckmeister I (III): "correct temperament" based on 1/4 comma divisions

This tuning uses mostly pure (perfect) fifths, as in Pythagorean tuning, but each of the fifths C-G, G-D, D-A and B-F# is made smaller, i.e. tempered by 1/4 comma. Werckmeister designated this tuning as particularly suited for playing chromatic music ("ficte"), which may have led to its popularity as a tuning for J.S. Bach's music in recent years.

Werckmeister IV (VI): the Septenarius tunings

This tuning is based on a division of the monochord length into 196 = 7 imes 7 imes 4 parts. The various notes are then defined by which 196-division one should place the bridge on in order to produce their pitches. The resulting scale has rational frequency relationships, so it is mathematically distinct from the irrational tempered values above; however in practice, both involve pure and impure sounding fifths. Werckmeister also gave a version where the total length is divided into 147 parts, which is simply a transposition of the intervals of the 196-tuning. He described the Septenarius as "an additional temperament which has nothing at all to do with the divisions of the comma, nevertheless in practice so correct that one can be really satisfied with it".

One apparent problem with these tunings is the value given to D (or A in the transposed version): Werckmeister writes it as 176. However this produces a musically bad effect because the fifth G-D would then be very flat (more than half a comma); the third Bb-D would be pure, but D-F# would be more than a comma too sharp - all of which contradict the rest of Werckmeister's writings on temperament. In the illustration of the monochord division, the number "176" is written one place too far to the right, where 175 should be. Therefore it is conceivable that the number 176 is a mistake for 175, which gives a musically much more consistent result. Both values are given in the table below.

In the tuning with D=175, the fifths C-G, G-D, D-A, B-F#, F#-C#, and Bb-F are tempered narrow, while the fifth G#-D# is tempered wider than pure; the other fifths are pure.

External sources

* [http://www.groenewald-berlin.de/Gliederung.html http://www.groenewald-berlin.de]
* [http://240edo.googlepages.com/equaldivisionsoflength(edl) 196-EDL & 1568-EDL and Septenarius tunings]

References


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Temperament inegal — Tempérament inégal Acoustique musicale Note de musique Harmonique Intervalle Consonance Cycle des quintes Gamme musicale Système tonal Échelle musicale Échelle diatonique Échelle chromatique Liste des g …   Wikipédia en Français

  • Tempérament inégal — Acoustique musicale Note de musique Harmonique Intervalle Consonance Cycle des quintes Gamme musicale Système tonal Échelle musicale Échelle diatonique Échelle chromatique Liste des gammes …   Wikipédia en Français

  • Temperament — Gammes et tempéraments Acoustique musicale Note de musique Harmonique Intervalle Consonance Cycle des quintes Gamme musicale Système tonal Échelle musicale Échelle diatonique Échelle chromatique Liste …   Wikipédia en Français

  • Well temperament — (also circular or circulating temperament) is a type of tempered tuning described in 20th century music theory. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach s famous composition, The Well Tempered …   Wikipedia

  • Andreas Werckmeister — (November 30, 1645 ndash; October 26, 1706) was an organist, music theorist, and composer of the Baroque era.Born in Benneckenstein, Germany, Werckmeister attended schools in Nordhausen and Quedlinburg. He received his musical training from his… …   Wikipedia

  • Musical temperament — In musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system. Most instruments in modern Western music are tuned in the equal temperament …   Wikipedia

  • Meantone temperament — is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a stack of perfect fifths, but in meantone, each fifth is narrow compared to the ratio 27/12:1 in 12 equal …   Wikipedia

  • Magic temperament — In microtonal music, Magic temperament is a regular temperament whose period is an octave and whose generator is an approximation to the 5/4 just major third. In 12 tone equal temperament, three major thirds add up to an octave, since it tempers… …   Wikipedia

  • Miracle temperament — In music, miracle temperament is a regular temperament discovered by George Secor which has as a generator an interval, called the secor, that serves as both the 15:14 and 16:15 semitones. Because 15:14 and 16:15 are equated, their ratio 225:224… …   Wikipedia

  • equal temperament — Music. the division of an octave into 12 equal semitones, as in the tuning of a piano. * * * ▪ music       in music, a tuning system in which the octave is divided into 12 semitones of equal size. Because it enables keyboard instruments (keyboard …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”