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Tonal Resonance Manifesto
The Most Important thing we can do to heal our society is to restore true harmonic resonance to our instruments!!!!
A not-so-long time ago in a planet not-so-far away, tonal resonance was abandoned in Europe in favor of being able to quickly retune an entire orchestra.
Harmonic Resonance is extremely simple. As every physicist knows, energies are harmonic when they vibrate in simple multiples of eachother. For example, this is harmonic:
In the simplest terms imaginable, harmonics occur when energies vibrate in simple patterns relative to each other. This causes the waves (frequencies) to Reinforce each other at regular intervals, and the overall quality of the wave to repeat rhythmically, which creates pleasing overtones and smoothly integrated sounds.
By contrast, energies that do not vibrate in simple multiples of eachother tend to erratically interfere with eachother, creating disharmony and tones that we experience as less pleasant.
We need to return harmonic resonance to our musical instruments!
When European orchestras changed the scale from a harmonic scale to the current Western scale, they did so by retuning notes so that every note was 2^(1/12th) times the frequency of the prior note on the scale. Feel free to check this: A = 440 Hz, A# = 440*2^1/12 = 466.2 Hz, B = 466.2*2^1/12=493.7 Hz, etc…
Unfortunately, that means that NONE of the notes in the Western scale are truly harmonic with eachother (except for one octave intervals, where the note is harmonious with itself on the new octave) . This is really very unfortunate & musicians wind up learning all kinds of tricks & rules (thirds, fifths, etc) to find notes that sound close to (but are not actually) harmonious with each other.
By comparison, this is how notes were originally determined: There was a Base note (For example A = 432Hz)… hold on! We’ll get to why it’s not 440 Hz in a minute… & every note was equal to that note + 1/12th the base frequency. So for example:
| A = A + 0/12A | = 432 Hz |
| A# = A + 1/12A | = 468 Hz |
| B = A + 2/12A | = 504 Hz |
| C = A + 3/12A | = 540 Hz |
| C# = A + 4/12A | = 576 Hz |
| D = A + 5/12A | = 612 Hz |
| D# = A + 6/12A | = 648 Hz |
| E = A + 7/12A | = 684 Hz |
| F = A + 8/12A | = 720 Hz |
| F# = A + 9/12A | = 756 Hz |
| G = A + 10/12A | = 792 Hz |
| G# = A + 11/12A | = 828 Hz |
| A = A + 12/12A | = 864 Hz |
But why 12 notes? Why not 13 or 5 or 17? Well it turns out in fact that there are at least two very good reasons to have 12 notes in a scale:
- 12 has lots of prime factors, so any notes that involve those
prime factors will harmonize within that many wavelengths and
sound good together. For example: 0, 3, 6, 9 & 12 (or any
subset thereof) should all sound good together because their waves
will match up harmonically in < 4 cycles (wavelengths):
Similarly, 0, 4, 8 & 12 (or any subset thereof) will sound good together, harmonizing within 3 wavelengths. 0, 2, 3, 6 & 12 will also sound good together, although a slight dynamic tension will exist between 2 & 3 who will require a full 12 cycles to match up. You could probably create a pretty amazing instrument just using the 0, 2, 3, 4, 5, 6, 8, 9, 10, 12 tones from this scale, which would create the following potential harmonics: {0, 2, 4, 6, 8, 10, 12}, {0, 3, 6, 9, 12}, {0, 4, 8, 12}, {0, 5, 10}. For added tension potentials add #1, 7, & 11 back in: they'll still all harmonize with each other within 12 cycles. - Why 12? Oh yeah! Well as it turns out, most average human ears
only pick up as harmonic tones that synchronize within 13 cycles
of eachother. So of all the numbers < 13, 12 is the one
with the most prime factors and hence the most potential harmonic
arrangements within a single scale. But you could just as
easily do scales with 5, 6, 7 or 24 notes (& historically many
cultures have): Just adjust the Denominator in your multiplier to
get the right frequencies. For example, for a 5 note scale:
All of these frequencies harmonize (realign) with eachother within 5 wavelengths of the dominant tone, (intrinsically: because of how they were constructed) and so will all sound good together…A = A + 0/5A 440 Hz A# = A + 1/5A 528 Hz B = A + 2/5A 616 Hz C = A + 3/5A 704 Hz C# = A + 4/5A 792 Hz D = A + 5/5A 880 Hz
Okay, so wait a second: I just switched back to 440 Hz. Why? Well, because Harmonics is all about waves overlapping within a reasonable number of wavelengths, which is (as we have seen above) all about Prime Factors. And now we get to talk about the fundamental problem with using 440 Hz as the Base Tone upon which your whole scale is constructed(!)
440 = 11*4*10 = 11*2*2*2*5
Okay, so right off the bat, you can see that the prime factors are not harmonic. In fact, this is probably one of the least harmonic numbers that the ear & mind could withstand before screaming "Foul!" and rejecting it right off the bat as unpleasant. There is something positively eerie about it, so would it surprise you to learn that it was established by Hitler’s Minister of Propaganda? (Now there was a man with a knack for manipulating the populace to do all sorts of crazy sh*t)
There is a much, much better way, which is to return to the worldwide historical base tuning of 432 Hz. First of all, check out the prime factorization:
432 = 2 * 2 * 2 * 2 * 3 * 3 * 3
Wow! How many Harmonic Subsets can be derived from those prime factors?
| 1 | 3 | 9 | 27 |
| 2 | 6 | 18 | 54 |
| 4 | 12 | 36 | 108 |
| 8 | 24 | 72 | 216 |
| 16 | 48 | 144 | 432 |
That’s a pretty rich field! And probably explains why our ancestors intuitively (through the power of their hearts and ears versus the power of electronic devices and deceived brains) tuned all sorts of instruments worldwide ranging from Native American Flutes to Tibetan singing Bowls to this base frequency, which we now measure as 432 Hz.
And Hz is not an arbitrary scale… It stands for Cycles per Second, where there are (by definition of a second), 60 seconds in a minute, 60 minutes in an hour, & 24 hours in a day, so Hz are intrinsically calibrated and related to earth time within the solar system. The prime factorization of 60*60*24 is also harmonically resonant with 432, so there is a validity to this number within the context of human time on this planet.
I could get into all sorts of theory about Base Tones here, including using it to resonate with systems in the body, energy centers, Kung, or other planets in the solar system. For that, I recommend a book called the Cosmic Octave. But meanwhile, I have a gift for you to play with in your personal quest for harmonic resonance in a disharmonious society. This is a Harmonic Calculator: simply input the frequency that you want to use as your base tone, how many notes you want to define in an "octave" (perhaps better called an Interval), and it will spit out the exact frequencies in Hz that you want to tune your instruments to. I am also going to post a SongTree style blog where you can upload your musical results. Please be sure to tag them with your Base Tone & notes per interval so we can propagate beauty as it is discovered. As Elon Musk said when he publicized all of Tessla’s engineering plans: "If we're all in a [sinking] ship together... and we have a great design for a bucket, then... we should probably... share the bucket design".
Have fun!
♥
SHAKTI DANCE
