THE HISTORIC TUNING PROBLEM THE HISTORIC TUNING PROBLEMJust intonation refers to music in which the scale intervals are precisely tuned to the pure harmonics of the natural overtone series. Harmonics are exact, whole-number multiples of a fundamental frequency, and are a natural phenomenon of vibrating bodies. A string vibrating at a fundamental frequency of 100 cycles-per-second, also vibrates simultaneously at harmonic frequencies of 200, 300, 400, 500, etc. cycles-per-second. Historically, the notes of musical scales in all cultures were based on these pure harmonics.
The precise tuning of the musical scale relies on fractions, and cannot be accurately presented without them. Everyone knows that 1/2 equals one-half. Similarly, 3/2 is three-halves, and 5/4 is five-quarters. Pure harmonic tuning, known as just intonation, is based on these fractions and these relationships to each other. What we will discover is that singing or playing in just intonation requires slight shifts in pitch for any given note.
The first three notes of the scale (Do, Re, Me) beginning with the note "C" are: "C", "D", and "E". The second note, "D", is 9/8 times the frequency of the first note, and the third note, "E", is 5/4 times the frequency of the first. So, the frequencies of these three notes in the "C" scale are:
C 1/1 x 528 = 528 cycles per second
D 9/8 x 528 = 594 cycles per second
E 5/4 x 528 = 660 cycles per second
However, if we want to start our scale on the "D" note, we face the tuning problem head on:
D 1/1 x 594 = 594 cycles per second
E 9/8 x 594 = 668.25 cycles per second
The "E" in the scale of "C" is 660 cycles per second, whereas in the scale of "D" it is 668.25 cycles per second. As we can see from the above examples, in order to modulate in just intonation, all pitches must have the ability to move. This is not a problem for instruments such as the violin, trombone or the voice because the musician has direct control over the pitch of each note. For fixed tone instruments, however (piano, organ or guitar), this poses a huge problem because the musician has no control over the pitch of each note. Should the "E" be tuned to 660 or 668.25 cycles per second?
Music, the timeless international language, is being transformed by modern computer and signal processing technology. Justonic Tuning Inc. is contributing to this revolution with a solution to one of music's oldest challenges: precise harmonic intonation.
Ancient Chinese and Greek musicians discovered the natural harmonics, and the scales of all cultures were derived from those harmonics. They also discovered that fixed tone instruments cannot freely modulate to all musical keys when so tuned. In the middle ages musicians began tempering their keyboard and fretted instruments to allow for some modulation. Tempered intonation is not in tune with natural harmonics.
Keyboards and frets digitized musical intonation, dividing the natural continuum of tones into distinct points that were not meant to change. Skilled musicians loathed the aesthetic compromise. "The easiest (system) to sing," said Martin Mersenne in 1636, "is that which follows the natural harmonics." At that time, when Claudio Monteverdi introduced the dominant seventh chord, its dissonance was more sharply felt than it is today. When a modern, tempered orchestra plays Monteverdi, the contrast between true consonance and dissonance is obscured. Inversions, modulations, and other compositional resources have also been dulled by temperament.
In 1685, the year that Bach was born, Andreas Werckmeister applied mathematics to the problem and came up with the entirely contrived equal tempered scale, eventually adopted by piano makers. Bach, however, wrote for meantone and "well" temperament in which the thirds and fifths were sweet and pure in the "near" keys and became more out of tune in the "distant" keys. When played in equal temperament the full radiance of Bach harmony is compromised. Likewise, a Mozart vocal harmony was written to be sung in tune. A tempered version is still music, but it isn't what the composer intended, and it does not reveal the full genius behind the harmony.
Equal temperament was the final compromise, making all keys equally out of tune. Beethoven introduced the age of fast chord changes and modulations made simple by equal temperament. Strauss, Verdi, Brahms, Tchaikovsky, and others carried on this tradition, and there is no question that they wrote great music, but none could restore the harmonic integrity abandoned for the convenience of equal temperament.
The simultaneous achievement of both pure harmony and free modulation has long been the elusive Holy Grail of instrument makers. Nineteenth century keyboard designers built instruments with up to 53 digitals per octave to solve the problem, but these mechanical solutions proved too cumbersome to play, and instrument makers abandoned the search.
There is no way around it: For music to modulate freely, and for all intervals to remain in perfect harmonic relationship, the actual frequency of all notes must be flexible. Furthermore, to be practical, the changes must be instantaneous in real time. By using original software, computer memory, and signal processing innovations, Justonic Tuning Inc. has achieved an historic solution to this musical problem.
The patented Justonic innovations not only restore to music the lost harmonies of Monteverdi, Bach, and Mozart, but open up a whole new world of tonal possibilities for modern musicians. The Justonic method facilitates the use of international musical scales since most of these scales are based on pure harmonic intervals.
"Wean singers early from the piano. When the piano plays ... proper vertical intonation cannot be achieved." Harvard choral director Jameson Marvin.
The Justonic method not only solves this problem for choral directors, but makes the piano a source of correct intonation rather than a hindrance to correct intonation.
Pure harmonic intonation by Justonic will set a new standard in musical sound quality. You can see in these images of .WAV files how the smooth chords of just intonation compare to the rough chords of equal temperament.
Just Intonation C Major 9 Chord -- Vs -- Tempered C Major 9 Chord
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The medieval sacrifice of harmonic integrity for a dubious gain in simplicity has limited the ability of musicians to achieve the full power and delicacy of their art. Justonic Tuning Inc. believes that its methods and products will benefit the world of music by returning to composers and musicians their full and rightful pallet of tonal colors, the foundation of their art form.
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