Tuning and Temperaments
Tuning and Temperament in Music
Well Temperament - A Subtle but Certain Difference
by Frank French
Although Equal Temperament has long been accepted as standard for modern
keyboard instruments it was by no means standard during the 18th and 19th centuries
when the vast amount of keyboard literature still played today was written.
These centuries comprise the periods of Baroque, Classical and Romantic music
which is considered standard piano repertoire even in the 21st century.
While we seem to grow ever more distant from the times during which such
music was first created the desire by pianists to play the earlier music
is undiminished today. Baroque, Classic and Romantic music remain the steady
source of piano study for serious pianists throughout the world.
With the music we hear as the ultimate goal let it be noted that there is
a subtle but significant difference in the way the music sounds on keyboard
instruments when played in the temperaments used during the period of the
music's creation. I assert that these temperaments influenced choices and
decisions made by composers at the time of creation and can still exert an
influence on how the music is interpreted even today
The musical scale, specifically the diatonic scale in use from at least 1600
to 1900 had been derived from the earlier ecclesiastical or "church" modes
used during previous centuries. The origin of the scale was postulated by
Pythagoras in ancient times on the basis of mathematical subdivisions of
the string giving rise to the diatonic scale through the partial divisions
of the string by two, by three, by four and so forth The science of
acoustics was thus born.
The modes in use throughout the middle ages and renaissance are known to
us most familiarly by the white notes on the keyboard. The various modes
or "moods" result by moving the tonal center. Today students of music theory
become acquainted with the various modes by the following names based on
the starting or "tonic" note.
These modes were used in secular and sacred music for centuries and prescribed
rules for their came about as experimentation gave way to convention. It
was through trial and error that composers developed the science of counterpoint,
and rules for its use as well, as determined by what sounded pleasing to
The gradual introduction of the non-white keyboard notes probably came about
through the desire on the part of composers to search out new possibilities
for sounds and color in music. By the 17th century the church modes were
appearing in transposition making use of the black keys and soon the use
of sharps and flats became standard in coloring music. In was inevitable
that alterations would have to be made in the existing system of tuning keyboard
instruments in order to accommodate the newly-introduced tones and make best
use of the existing twelve tones within the octave. The Pythagorean tuning
system based on division the string and tuning through a circle of twelve
fifths, resulted in some very sour sounding intervals as one got farther
away from the key of C. These intervals ( sound resulting from space between
two given notes) were known as "wolf" tones. In order to eliminate these
wolf tones in became necessary to modify the way in which the various notes
within the octave were tuned.
Illustration: circle of fifths.
The modification of the tuning system became know as "tempering" the intervals
within the span of the octave.
Music was evolving, moving forward, but with its feet still planted firmly
in tradition. The Greek names given to the modes denote the obvious ancient
origin of the modes and resulting musical traditions in the West, which spanned
the course of close to two millennia. Tradition was still a strong force
in all musical minds in the 17th and 18th century and composers were sill
using "classical" models in opera with ancient Greek and Roman themes and
titles. This was no less true in more abstract symphonic music, for example
in Moazrt's late Jupiter Symphony in C major. The color of the modes and
traditional associations exerted a powerful influence on composers right
up until the 20th century. Modal color, or characteristic had become assimilated
into "tonal" characteristics as the system of major and minor scales and
Tonal characteristics, or "character of keys" became an unwritten doctrine
in the minds of composers. Conscious or unconscious choice of key for a musical
work at the outset provided clearly defined criteria for musical expression.
Tempering of notes within the octave smoothed out certain rough intervals
and gave a certain edge to other intervals as a result.
Modulation was another inevitable result of the introduction of the five
non-white keys. The coloring, or chromaticism inherent in the possibility
for using all twelve tones gave rise to new possibilities through the ingenious
use of counterpoint as practiced during the time of J. S. Bach (1685-1750),
and by all great composers subsequently. Yet the composers remained rooted
in the traditions that provided all the raw material for their creations.
It was during the time of Bach that various means of tuning keyboard instruments
were propounded and proposed by eminent music theorists, who were most intrigued
by the possibility of being able to play and express music in all twelve
tonalities. Musicians of all types were concerned with the seemingly unlimited
possibilities for modulation and expression while preserving the traditions
of the modes. In the minds of theorists and musical idealists The key of
C major would have its own mood or character as would the key of D minor.
Each tonality would have its own identity and new identities would be established
for the previously obscure keys, which could now be fully employed through
the use of temperament.
Sooner or later it would come to pass that a set of keyboard pieces in every
major and minor key would be created, and indeed such sets were created.
The most notable work of this period is J.S. Bach's Well-Tempered
Clavier, a set of 24 preludes and fugues, one in each major and minor
key first appearing in 1721 with a subsequent set of 24 preludes and fugues
coming out ten years later.
Here it is necessary to stress that a "well-tempered" scale is not the same
as an equal-tempered scale. Equal temperament standardized in the 20th century
is a theoretical proposition that the distance between all twelve tones is
mathematically the same, or that the octave is divided into twelve equal
parts. Well-temperament, is fundamentally an unequal division of the octave,
and derives from a more subjective view based in the individual characteristics
of each tonality. How this was accomplished and how it evolved has been amply
documented and explored by music scholars, the most notable among these today
being Owen Jorgensen, who has compiled an exhaustive study of historical
It suffices to say that well temperament as practiced during the time of
Bach was an empirical science based in the ancient concept of moods in music.
Its use exerted a powerful influence on conception and creation of musical
works, choice of tonalities, choice of intervals, and other practical decisions
on the part of composers. It follows that 18th and 19th century music
sounds best when heard in the temperaments in use used during the time
the work was created. In this way the re-creation of the music and
re-discovered ways of hearing the music will give rise to interpretative
possibilities that may have been lost to us over time.
The subtle but certain difference in musical shading achieved by unequal
temperaments, or in the case of Bach through the use of well-temperament
will bear proof that hearing is believing.
for further reading please see the
Owen Jorgensen on
to view temperaments in history see
Chart of Historical Temperaments