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What is Harmonic Tuning?

Harmonic tuning is when you tune your musical instrument to notes that are Harmonically Resonant with eachother. Resonance is when sounds (which are basicaly waves of energy traveling through the air) have wave-lengths that reinforce eachother at regular intervals to create pleasing overtones.

How is that different from regular Tuning?

Ever since the Industrial Revolution (when the world got really excited about efficiency), Western Orchestras have been using "Equal Temperament" tuning, which - oddly enough - is intrinsically DISHARMONIC.

We have become so used to it that most people don't even notice it at this point. After all, most of us grew up with it and have never known anything different.

However, because it is essentially disharmonic, the notes do not reinforce eachother^*, which means that much of the power that music has to vibrate physical objects resonantly (and thereby physically change/alter/organize them) is lacking from Western-tuned instruments. There's still power to music, but it's mostly the power of emotion and lyrics - the physical power of true harmony is dissipated by the chaos intrinsic to the disharmony of the notes that make up the current Western scale.

Explain Harmony again...

Okay, from a Math & Physics perspective, Harmony is when sound waves reinforce eachother at regular intervals, like this:

So that's pretty simple, right?

Harmonic Sound Waves: Example #2

In the first example, the second wave was twice as long as the first. But Harmony occurs whenever waves are simple fractional multiples of eachother. So here's another example where wave A is 3/4 as long as wave B:

Harmonic Sound Waves: Example #3

Okay you adorable little freak! Here's a Harmonic wave generator for you to play with... go have fun...

So what are Non-Harmonic notes?

Pretty simple: non-harmonic notes are notes where the wavelengths do not line up at regular intervals, so no pattern of reinforcement (aka pleasing overtones) ever emerges between the notes (well, not within a reasonable amount of time). It turns out that human ears are actually pretty picky about that: if the sound waves do not harmonize with eachother within about 13-17 wavelengths, average human ears will not register the sound as being harmonic. In fact that's one of the reasons scales typically have 12 notes (there are some cultural variations on that, but more on that later...)

I thought you said Western music is non-harmonic

Yeah, that's right, it currently is.

It didn't used to be though: Until the late 1800's, Western notes were harmoniously tuned & many cultures worldwide still use harmonic tuning. So every note in an octave was ¹/₁₂(A) higher than the previous one where A was the root tone of the octave. So for example, if A was 108Hz, and there were 12 notes in the scale, each note in the Octave would be ¹⁰⁸/₁₂ = 9Hz higher than the previous one. Thus, a typical octave would look like this:

See? Each note was 9Hz higher than the previous one (in that octave). Harmonious and easy right? Well, the only problem is that the same rules apply to the next octave: The new A is 216 Hz, so each note in its octave is ²¹⁶/₁₂ = 18 Hz higher than the previous note. so the new octave looks like this:

This is still all very well and good except for one little problem: In the 1800s, music was the biggest, most powerful form of mass entertainment (remember, television hadn't been invented yet) and there were all these fantastic composers writing epic music in different keys (to evoke different moods). There were also a lot of big-production opera houses performing these pieces. The problem came when you had to switch keys. If you wanted to switch from one key to another, you had to retune the entire orchestra.

At some point some misguided genius said "Hey! This is a real pain in the butt. Let's just 'fix' it

Before you think I'm making this up, here's the table of frequencies that result from his math, using 440Hz as the base frequency:

If you compare this to an actual table of current Western tuning, you will unfortunately find that this is really how modern day "even temperament" tuning is accomplished, which is the standard tuning for all Western instruments today.

Okay, so what's the problem with that?

The problem is that those notes are intrinsically non-harmonic to eachother. Harmony is determined by wavelengths being simple ratios of eachother. These numbers are not simple fractional ratios of eachother. In fact, since they are based on 2^^(1/12), which is an irrational number, the wavelengths will never realign precisely / harmonize with eachother. This is SHOCKING! And it means that all of modern Western Tuning in fundamentally disharmonic.

Harmonic, Shmarmonic, Why Should I Care?

Sound waves are waves of energy moving through the air. They have the power to physically affect matter. The difference between a Harmonic set of Waves and a non-harmonic set of waves is like the difference between a laser and a nerf gun. The former is highly focused, the latter loses a lot of its power to effect change in the chaos of dissonance.

We are so used to nonharmonic tuning that we have never known what it's like to experience the real thing. The power of music is known to be great. Historically, one of the most sacred duties of priests worldwide was the creation of large harmonic instruments such as church bells, gongs, and horns whose tonal resonances were constructed to harmonize entire villages. The priests were not only in charge of their construction, but also their maintenance, and it was said that when the instrument would go out of tune, the entire village would become disharmonious. Right now, all of Western music is disharmonious and people in America listen to it constantly. Is it any wonder that our society is suffering from so many problems and inflicting such harm on the earth as a whole? The single greatest thing we can do to heal ourselves & our relationship with the earth is to bring our notes & our music back into Harmonic tuning...

This is a Harmonic Calculator

This Harmonic Calculator is my gift to the musicians and instrument makers of the world. With it you can choose a base frequency (any you like, although there are many good reasons to choose 432 Hz - see Manifesto), the number of notes you want to generate in each Interval (octave), and how many Octaves you would like to see. Hit "submit" and it will instantly Calculate frequencies that you can tune your instrument to to make it harmonic. There are Advanced options for Pythagorean tuning and showing nearby Western notes. The Results table tells you how quickly the wavelengths Harmonize with eachother, and if you click on one of those numbers, it will generate a precise graphic showing that harmonic. Have fun, play around, but be Care-full, because once you go Harmonic, you are playing with real Power.