Background: Verdi Tuning
Music has been found in almost every culture since ancient times, and, as Confucius wrote, the nature of the compositions reflected the harmony (or disharmony) of the society. Since ancient Greece, it has been known that the musical scale is pivoted at Middle C=256 Hz, and the octave and other intervals are generated from there. When, as today, the concert A is at 440 Hz or higher, it shifts that Middle C and the other intervals upward, knocking the process of hearing and performing classical music "off kilter" and damaging singers' voices.
The well tempered musical scale we know today was not created by mathematical calculations - it was a scientific revolution! And it was based on the trained bel canto human singing voice. Johann Sebastian Bach (1685-1750) discovered the principle of generating the intervals of the scale from the intersection of the singularities of the six separate species of the human singing voice: soprano, alto (mezzo-soprano), contralto, tenor, baritone, bass. Bach's circle was steeped in the work of Johannes Kepler, whose book "Harmonies of the World" elaborates the relationship between the musical scale and the orbits of the planets.
Each voice species has a characteristic set of physiologically determined regions where the singer, in order to maintain a beautiful tone, must shift from one register (color) to another. For example, when C = 256 Hz, the soprano and tenor must shift from their middle to high register between F and F# . When the A is tuned at 440 Hz (or higher), the register shift, or passagio, will instead be at the F or below.
These natural, biological, vocal registers are audible as a kind of musical color, which are a critical (poetic) element of classical composition, adding a dimension to the polyphony heard in the mind.
Bach's discovery meant that he and his musical circle could write music in all 48 keys (12 major, minor and their inversions) and also modulate (move from one key to another) within the same piece of music, and still be in tune-- for the first time ever. Different keys had different-sized intervals, giving each key its own nuance or "color" recreating that very human quality in instruments, which is lost in the modern practice of "equal-tempering," where all half-notes have the same value. The "comma" (the part of the octave that is left over if only mathematically "pure" musical intervals are used) is distributed unequally throughout all of the keys. The "comma" is also the process of making slight adjustments in tuning up choral voices as they sing together.
The great classical composers after Bach mastered this physical-biological concept, and composed poetically with it, as if painting with this palette of musical color. The classical polyphony created by the combination of tuning the instruments "in color", and then bringing in the choir voices to sing the poetry, created the most powerful, natural uplift for the human mind. (...the Verdi Tuning.)
But as concert pitches were arbitrarily raised (and lowered) over the centuries, the poetic ideas and ironies in the masterpieces were being eliminated, until finally, the great classical composer and statesman, Giuseppe Verdi (1813 -1901) put his foot down. Verdi insisted that there be an actual government law, to match natural law, that the A=432 Hz be the pitch and absolutely no higher.
Thus, we offer now the Verdi Tuning Forks for music, tuning, and many other fields-- many in the medical, holistic and alternative medicine fields have joined the chorus of those who utilize our A432 Hz and C256 Hz in their work, Together with science teachers, physics labs, radar, sound, healing and wellness professionals, our satisfied customers attest to the importance of staying in tune, and that is the SWB 256 Tuning Forks perspective.
"Sing With Beauty" and help make the world a better and more harmonic place.
Feel free to email us at tuning@swb256 for special requests, questions or comments.
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A wonderful presentation on tempering is found here: (http://larouchepac.com/node/22852
A Digression on Music ~
Excerpted from various articles by the Schiller Institute and Mr. LaRouche
An important but often difficult concept for people to grasp, is that "the values of the well-tempered tones are not algebraically exact. They are singularities, each a small, but finite region of discontinuity within the extent of the octave-scale. The values are determined, not only by the fact that there must be the obvious coincidence of the tones among all scales; but, that each local interval must be peformed, as Furtwängler's referenced motto implies, from the standpoint of a musical memory of the composition as that unified process which is manifested as a completed process of continuous, coherent development, in the immediate "aftertaste" of its concluding tones. This must take into account avoidance of the "wolf-tone" potential in the vicinity of each register-shift, of each and all of the voice-species represented in well-tempered polyphony as a whole. The region of singularity, within which the enunciation of the well-tempered tone, may lie within the range defined by the application of each and all of the inversions imposed by the function of "time-reversal" in performing, according to that view of each interval as apprehended in the mirror of the perfected, whole composition being completed..."
(The seven octaves (each divided into twelve tones) of the Classical well-tempered system of polyphony, are physically determined singularities of physical space-time, and each tone is a force-free region of physical space-time, whose value (frequency), like Kepler?s values for the orbits of the planets in the Solar System, is determined by the characteristic properties of a quantized field underlying physical space-time.)
See the Video on Kepler and Tuning:
See the guide to the Harmonies of the World by Johannes Kepler:
B. Director( Fidelio article ) "What Mathematics Can Learn from Classical Music" http://www.schillerinstitute.org/fid_91-96/944_math_music.html
M. Rasmussen's "Bach, Mozart and the 'Musical Midwife'" http://www.schillerinstitute.org/music/m_rasmus_801.html
...And more to come...