On Reference Pitch and Intonation
The onset of the journey of the budding audio alchemist is rife with misinformation wrapped in catchy titles such as "440 vs 432 hz", "Solfeggio Tones", unfounded "Healing Frequencies", along with every kind of insane abstract intellectual justification for some unique dissonance of a mathematically unsound nature. It is my purpose to rend through these illusions mercilessly and leave only the clear, pure, and Just truth to remain
To begin with, much like in cymatics, where the geometric pattern observed is dependent on the resonant frequency of the vibrating plate, any given reference frequency cannot be "good" nor "bad", universally, only in the context of the geometry of the environment it is played within, it is possible to create context for any reference pitch, so one should experiment freely rather than pigeon-hole themselves into 432 or 440.
On to "Solfeggio Tones", to be brief, the effect is purely placebo, the arrangement of the numbers 1,4,7 2,5,8 and 3,6,9 into hz frequencies is totally arbitrary and only yields some harmonious results accidentally (ironically 396, 440, and 528 are part of a Justly tuned scale, although Horowitz, hack that he is, claims the A of C=528 is 444! Madness!) these numbers, however, do function as nodes, called Family Number Groups, in Marko Rodin's Vortex Based Maths (similar to the Enneagram), to give credit, I cannot possibly word this better than it has already been done here
Pure Tuning is as such: 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 9/5, 15/8, 2/1
Well, I wish it were that simple, there are plenty of cases where Pythagorean, 7-limit, or other intervals sound more perfect, it is impossible to affix a concrete and inalterable rule to a note position and have that work for everything, alas, such is the curse of fixed pitch instrumentation, for non-fixed-pitch instruments, such as voice or strings, these subtle changes can be accounted for intuitively and immediately, as the player or singer can instictively feel the resonant harmony and shift into place, for a guitar or piano however, there are only compromises...
FORTUNATELY WE EXIST IN A NEW AEON, THE INFORMATION AGE! Divorced from the constraints of the material realm, the digital synthesizer and sample library (provided adequate microtuning support) prove the process of microtonal tuning, modulation, and free experimentation effortless! See Scala