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Beethoven brazenly exploited the power of this 12-tone system. His music is filled with speed, spirit, energy, and drama. The roughness of equal
temperament is somewhat masked with this style of music, particularly with fast moving chords, and Beethoven made the most of it, producing effects no one before him had ever attempted.
However, Owen Jorgensen, authority on historical tunings, points out that
“for every gain in temperament history, there has been a corresponding loss.”50
Temperament is a compromise of harmonic purity, sacrificing the full power and delicacy of the pure harmonic proportions for simplicity in construction and play of keyboard and fretted instruments. Musicians of the 19th century knew this.
he keyboard, its particular temperaments, and the standardization of the diatonic and equal-semitone chromatic scales gave something very valuable to western music, namely simplicity and ease of play. Music is boundless, so by organizing some intervals, making them all comfortably accessible, and making modulation unrestricted, the modern keyboard helped musicians sort out the vast potential of music into a manageable system.
Today, most musicians grow up and are trained from inside the equal tempered paradigm, and may be only marginally aware that there is such a thing as a pure harmonic interval that is distinct from a tempered interval, or that there are infinite scale choices beyond our diatonic and chromatic default choices.
Jorgensen points out that pure equal temperament was not practiced on pianos before 1885. However, quasi equal temperament was used, and the intention was to achieve equal temperament within the limits of available technology. In fact, since tuning equal temperament by ear, by counting the beats of the mistuned intervals, had not yet been developed, tuners of equal temperament in the 19th century relied on devices such as the tuning fork tonometer invented by Johann Heinrich Scheibler in 1835. When speaking of equal temperament in the
19th century, we are speaking of quasi-equal temperament.
The J. G. Pleyel piano factory was established in Paris in 1808. Alfred James Hipkins introduced equal temperament to the James Broadwood piano factory in England in 1846, although James Broadwood himself had introduced the idea as early as 1811.51 Broadwood introduced the importance of the striking place on the piano string, a parameter that influences the tone since the striking point may dampen certain harmonics of the string. Broadwood’s solution was to strike the string somewhere between one-seventh and one-ninth of the length. This had the effect of dampening the seventh harmonic which clashes with the minor sevenths of equal temperament. In 1852 the Exeter Hall organ was tuned to equal temperament, and two years later English organ makers Gray & Davidson and Walker & Willis made equal tempered organs. The Henry Steinway & Sons piano factory was established in New York in 1853, and Baldwin Piano & Organ company was founded a decade later.
François Fétis introduced the term “tonality” in 1835 to describe the principle of musical intervals having a relationship to a fundamental, and he noted that the music of different cultures and scale styles placed different emphasis on this tonality. Fétis also pointed out that the ear can grow accustomed to almost any
tuning system, and he tells a story that emphasizes how far habitual hearing can lead one away from the harmonic proportional intervals.
Fétis was the teacher of the young composer Nicolas Jacques Lemmens.
Lemmens had been born in the village of Zoerle-Parwijs, the district of Campine, in the Belgian province of Limbourg, on a frozen January morning in 1823. As a youth he learned music on a harpsichord that was badly out of tune due to the harsh weather of the region and the fact that no tuner lived in this rural district.
Nearby was the abbey of Everbode, and there the organ was also mistuned and broken. An organ builder was summoned to repair the Everbode organ, and by chance this man stopped to visit the Lemmens family. Young Nicolas performed for the guest, and when the tuner heard the dreadful state of the instrument, he offered to tune it.
Later in life Lemmens recounted the story for his teacher Fétis. He told how, when the instrument was first tuned, he experienced “the most disagreeable sensations.”52 Growing up with no other musical reference, his ear had adapted to the arbitrary intervals of the mistuned harpsichord, and it took him a long time to feel comfortable with the intervals of the tuned instrument. Nicolas Lemmens later became one of the great organ masters of his time, a teacher at the Brussels Conservatory, and composer of symphonies, choral works, and keyboard pieces.
He was certainly a musician of considerable skill, with a good ear, and yet as a youth his ear had completely adapted to an entirely arbitrary tuning. The story reminds us that our certainty about what tuning system we prefer can be biased simply by our habitual way of hearing, a good reminder for 20th century musicians who have grown up with equal temperament.
Many music theorists and musicians of the 19th century contributed to the counter-current in the evolution of tuning. Equal temperament was establishing itself, but by no means exclusively. In 1812 the Glover sisters in Norwich, England devised the “movable doh” system for teaching singing, using “doh” as the keytone, and teaching the diatonic major relationships to this fundamental as
“re, mi, fa, sol, la, and ti.” They were so successful in teaching young children to
One advantage to young singers using the Sol-fa system is that all songs in all keys use the same symbol to express a given interval. That is, the interval of a third from the tonic is “mi.” Since this never changes, a student more easily makes the association between the sound of the harmonic or melodic interval and the symbol. Curwen advanced the system as a purely just intonation system with the help of instrument builder Perronet Thompson who, in 1864, built an “enharmonic organ” with 40 tones to the octave on three ranks of digitals.
sing that their system was later introduced into the English schools. Thirty years later the minister John Curwen visited the school where Sarah Glover was teaching the system, then known as the “sol-fa system of singing.” He was so impressed that he joined with the Glover sisters to form the Society of Tonic Sol-faists, and he later published the singing system as Singing for Schools and Congregations.
By 1862 there were some 150,000 sol-faists in England. The movement also spread to the continent.
Advances were also made in the understanding of acoustics. Michael Faraday advanced the theory of resonance, the phenomenon of one vibrating body setting a second vibrating body in motion. Jean Baptiste Fourier described
complex wave forms as additions of simpler waves. Today, the “Fourier
Transform” allows additive synthesizers to create complex musical timbres from sets of simple oscillations.
French scientist Jules Lissajous (1822-1880), hooked a large pendulum to his ceiling. Vincenzo Galilei’s son Galileo had earlier determined that a swinging pendulum keeps perfect time. Lissajous surmised that sound was some kind of a waveform in the air, and he imagined that sound had regular beats like those of the swinging pendulum. To the pendulum he attached a bag in which he made a small hole, in the bag he placed sand, and under the pendulum he placed a long scroll of paper. He set the pendulum swinging in one direction, and pulled the paper across its path in a perpendicular direction. The pendulum, he thought, represented the vibration of sound, and the moving paper represented its movement through the air. Through the small hole in the bag the sand spilled back and forth across the
paper, but as the paper moved the sand formed a wavy line, a line we now call a
“sine wave.” Lissajous predicted that this was the visual image of a single frequency of sound. He was correct, of course, but his theory was not confirmed until the invention of the oscilloscope in the early 20th century.
More impressively, however, Lissajous conducted a more elaborate
experiment entirely in his mind. He imagined that two sound waves would interfere with each other, and would therefore create more unusual wave forms. He
imagined that two imaginary pendulums swinging at different rates could swing across each other’s path, and he imagined the resulting images they might make with sand on the paper below. With this thought experiment, Lissajous predicted that two tones in perfect harmony would create certain well-defined patterns.
Again he was correct, and later proven so by oscilloscope images. Each harmonic interval has its own unique signature interference pattern, and these we now call
“Lissajous curves.”
Just as the wave of equal temperament was about to wash over the music world, German scientist Hermann Helmholtz, began his studies of acoustics.
Helmholtz was a great general scientist, unfettered by specialization. Between 1845 and 1894 he wrote over a hundred definitive papers and books on the conservation of energy, propagation of nerve impulses, the theory of complex colors, a review of Goethe's scientific work, optics, muscle movement, weather, electrodynamics, magnetism, the sensation of hearing, the physics of sound, and aesthetics of music. Music was his passion, he was an accomplished musician, and his instrument of choice was a harmonium tuned to just intonation.
He began his study of acoustics in 1852 and wrote On the Nature of Human sense perception. He built a "vibrating microscope" using a piece of glass that oscillated in one direction and a tuning fork that oscillated in the
perpendicular direction, connected both to sources of pure tone, and found the geometric patterns of sound predicted by Lissajous. He published On combination tones in 1856, followed by On Musical temperament, and On the motion of the strings of a violin. He reviewed the work of every music theorist from Pythagoras
to Neidhardt and Lissajous, and was arguably the most knowledgeable person in human history on the complete physics, physiology and aesthetics of sound. His magnum opus on the subject, On the Sensations of Tone, was published in 1862, is still in print, and has been translated into every modern language.
The design for Henry Poole's 100-tone per octave organ was published in 1867, but was never built. Similar designs by other researchers, including Helmholtz, proved too cumbersome to be practical for musicians. (From
Helmholtz/Ellis, 1885)
After exhaustive accounts of the physics and physiology of sound, and the mathematics of harmony, Helmholtz at last engaged the historical dialogue of intonation theory and aesthetics. "There is nothing in the nature of music itself to determine the pitch of the tonic of any composition," states Helmholtz. "[It is]
necessary for musicians to have free command over the pitch of the tonic. For singers these transpositions offer no difficulties ... But the matter becomes much more difficult for musical instruments ... [that] only possess tones of certain definite degrees of pitch,"53 the keyboards and fretted instruments.
"The justly-intoned chords," said Helmholtz, "... possess a full and saturated harmoniousness; they flow on, with a full stream, calm and smooth, without tremor or beat. Equally-tempered or Pythagorean chords sound beside them rough, dull, trembling, restless. The difference is so marked that every one, whether he is musically cultivated or not, observes it at once."54 He pointed out that chord inversions, modulations, the contrast between consonance and dissonance, and contrast between major and minor chords "are much more decided and conspicuous" in just tuning. Therefore the effect of these musical techniques becomes "much more expressive." On the other hand "when the intonation of consonant chords ceased to be perfect ... the differences between their various inversions and positions were, as a consequence, nearly obliterated."
"In a consonant triad every tone is equally sensitive to false intonation,"
Helmholtz observed, "... and the bad effect of the tempered triads depends especially on the imperfect Thirds." He outlined the four species of beats heard in a tempered major triad due to impure intervals, and remarked that they were
"always quite audible," and that they "strike the ear as a marked roughness ... The beats arising from the Thirds ... are decidedly disturbing in the middle positions, even in quick time, and essentially injure the calmness of the triad." Helmholtz, the scientist and musician, at once appreciated both the technical and aesthetic nature of pure sound. "When I go from my justly-intoned harmonium," he observed, "to a grand pianoforte, every note of the latter sounds false and disturbing."
Helmholtz lamented that "these are unpleasant symptoms for the further development of art. The mechanism of instruments and attention to their convenience, threaten to lord it over the natural requirements of the ear, and to destroy once more the principle upon which modern musical art is founded." In conclusion he said that "after all, I do not know that it was so necessary to
sacrifice correctness of intonation to the convenience of musical instruments. As soon as violinists have resolved to play every scale in just intonation, which can scarcely occasion any difficulty, the other orchestral instruments will have to suit themselves to the correct intonation of the violins. Horns and trumpets have already naturally just intonation."
A solution to the problem, in other words, was not out of reach. Helmholtz and others in the late 19th century proposed solutions. Henry Poole built a just intonation pipe organ, and designed (but never built) a keyboard of 100 tones per octave. Perronet Thompson’s 40-notes-per-octave organ included a device for correcting the changes caused by temperature on intonation. He claimed to have taught a blind organist to play the instrument in six days “thereby settling the question of the practicability of just intonation on keyed instruments.” Colin Brown at Andersonian University in Glasgow designed a 40-tones-per-octave voice harmonium, and built three such instruments. One of these was later played by 20th century composer Harry Partch who found it “easy to play and its intervals and triads a delight to the ear.”55 R.H.M. Bosanquet applied the 53-tone division to an enharmonic organ, and founded a company with T.A. Jennings to offer custom built organs with up to 84 tones per octave. These inventions were not complete solutions, and they posed problems of construction and play, but they held promise. Nevertheless, when Helmholtz died in 1894 the general acceptance of equal temperament slowed further research. The secrets of harmony had become visible, but the science of building instruments to play pure harmony faltered as equal temperament dominated western music.