Music tuned to A=432Hz resonates with light and therefore the human light body. Music tuned to A=432Hz is healing, whereas music from the standard A=440Hz is not. However, it appears that some readers are confused between the concept of a standard tuning pitch and “temperament.”
Summary
The tuning pitch is a fixed pitch and is the starting point for the temperament and not the temperament itself. My suggestion for all music, and especially for healing, is to tune to the fixed pitch A=432Hz or C=256Hz and use equal temperament to tune the whole instrument.
While tuning to a specific pitch solves one problem – playing music out of tune with light – temperament solves a different problem.
The crux of the confusion
Part of the confusion arises when using the term, “Pythagorean tuning,” which is a tuning system based on the pure Pythagorean ratio for a pure fifth, 3:2. As I understand it, Pythagoras also championed the idea of using C=256Hz (analogous to A=432Hz) as the starting pitch for his tuning system. So, don’t confuse the starting pitch with the tuning system.
I see that some people have jumped into this A432 idea by using an app such as ClearTune or an electronic tuning device and set it to Pythagorean tuning and dismissed the results as unusable. That’s because you’re tuning to pure Pythagorean intervals, which is not what I’m advocating. This is especially true for guitar, which is equal tempered due to the placement of the frets. Tuning a guitar to anything other than equal temperament will yield unsatisfactory results. But you can tune the A string to 432Hz, and then tune the other strings relative to that in equal temperament and your guitar music will resonate with light.
What’s a temperament and do I really need one?
“Temperament” refers to the formula tuners use to tune pitches relative to the fixed tuning pitch. The term “temperament” refers both to the formula and the result but not to the fixed tuning pitch. When tuning a piano, harp or harpsichord, the tuner starts by tuning the reference pitch, and then tunes the temperament around the fixed reference pitch using octaves and fifths to tune all the pitches between middle C and the octave above, and also the pitches down to the F below middle C. This is called setting the temperament. When the tuner is satisfied that the temperament is correct, he or she then tunes the rest of the instrument using octaves, occasionally employing fourths and fifths for quality control.
What problem does a temperament solve?
The problem with Pythagorean tuning, or tuning to pure fifths, is that the results sound unmusical. In Pythagoras’ day, music was therapeutic, not an art or entertainment delivery system.
For music to be musical, the fifths must be narrowed, or tempered, from their pure 3:2 ratio. The formula that the tuner uses to narrow the fifth is called a temperament. (For the technical-minded, tuning to pure fifths is referred to as Pythagorean tuning and is technically not a temperament because the fifths are not tempered.)
Modern harmony is based on thirds and fifths. When you tune to pure fifths, the thirds sound bad. When you tune to pure thirds, the fifths sound bad. And interestingly, in either case, the octaves are out of tune, and this is completely unacceptable.
In order for harmony to evolve and be useful as an artistic musical expression, temperaments evolved to create compromises between the fifths and thirds and keep the octaves in pure 2:1 ratios. Without temperament, we wouldn’t have the beautiful harmonies that music is associated with. Temperament is the gateway to beautiful harmony, which is the gateway to the evolution of music and harmony through the centuries.
Equal temperament
Most instruments are designed to be equal tempered, such as guitar — due to the frets, and harp — due to the design of the disk-pedal mechanisms that change the pitch of the strings. Pianos can be tuned to other temperaments but that’s not very practical because it takes a long time to tune a piano and requires a professional to do it right. In the Baroque period, many temperaments evolved that were designed to be easy for the average musician, as only noblemen could afford a professional tuner.
There are two types of temperament, regular and irregular. A regular temperament modifies all of the fifths to exactly the same interval. Equal temperament is a type of regular temperament. Equal temperament is the current standard and has been since the early 19th Century. It was “discovered” around 1640 (or even earlier, depending on which source you refer to) as the ultimate tuning compromise but musicians didn’t use it much because they thought it was not musical.
An irregular temperament modifies the fifths differently to achieve different results. Bach’s “Well-Tempered Clavier” was written for an irregular temperament, such as the Werckmeister temperament. You can read about well-temperament here.
What temperament should I use?
The reality is that most instruments are designed to be in equal temperament, including piano, guitar and harp. Equal temperament is fine for healing. If you play the harp, you can experiment with other temperaments, such as preset temperaments that come with the Peterson VS-1 tuner, which I use, or the ClearTune app. I have a Lyon & Healey Troubadour that I keep tuned to Peterson’s meantone temperament, which appears to be some sort of irregular temperament. Then I play in only one key. I retune the harp to work with specific chakras. For example, C resonates with the heart chakra and is a nice place to stay for healing. The Key of F resonates with the third eye, so you meditation subjects should be more advanced and thoroughly grounded lest they float home. I don’t recommend floating as a spiritual practice. The Key of B-flat resonates with the root chakra, so that’s a good healing key too.
Sidebar: An illustration of tuning to pure fifths
A fifth is a standard tuning interval: C to G is a fifth (C-D-E-F-G), otherwise known as a Perfect Fifth. Going through the “circle of fifths” you tune all the pitches in the chromatic scale (all the black and white keys on a keyboard). Eventually you arrive back at the starting pitch, C an octave higher. If you tuned middle C to 256Hz, the C an octave above will be 519Hz, 7Hz higher an a pure 2:1 octave of 512Hz (256 x 2 = 512). In order for music to work, the octaves must be pure. This table illustrates the frequencies resulting from tuning to pure fifths, in a typical session of tuning a harpsichord:
| Action | Pitch in relation to Middle C | Frequency in Hz | The Math |
| Tune the reference pitch | Middle C | 256 | |
| Tune a pure 3:2 fifth above | G above Middle C | 384 | (256×3)/2=384 |
| Tune a pure 2:1 octave below | G below Middle C | 192 | 384/2=192 |
| Tune a pure fifth above | D above | 288 | |
| Tune a pure fifth above | A above | 432 | |
| Tune a pure octave below | A below | 216 | |
| Tune a pure fifth above | E above | 324 | |
| Tune a pure fifth above | B above | 486 | |
| Tune a pure octave below | B below | 243 | |
| Tune a pure fifth above | F# above | 364.5 | |
| Tune a pure octave below | F# below | 182.25 | |
| Tune a pure fifth above | C# above | 273.375 | |
| Tune a pure fifth above | G# above | 410.0625 | |
| Tune a pure octave below | G# below | 205.03125 | |
| Tune a pure fifth above | E# above | 307.54687 | |
| Tune a pure fifth above | A# above | 461.3203 | |
| Tune a pure octave below | A# below | 230.66015 | |
| Tune a pure fifth above | E# above | 345.9902 | |
| Tune a pure fifth above | B# (C) above | 518.9853 |
On a keyboard, B# is theoretically the same as C and is out of tune with our Middle C tuning pitch of C256. Equal temperament narrows each fifth by 1/12 of the 7Hz discrepancy.
Sidebar: An illustration of tuning to pure thirds
You could also tune to pure thirds (ratio 5:4) but have the other interesting problem that the resulting octave C is lower than 512Hz.
Now, let’s tune the three major third intervals in between C256 and C512 in “pure” thirds according to the Pythagorean ratio of 5:4 for a mathematically and musically pure interval, that is, it not only looks good on paper (the Pythagorean math) but sounds good too. So our three major third pitches are E, G# and B#, which is theoretically the same as C, so we end up where we started an octave higher at C512, if everything goes right. Now, you can do this by ear, tuning the thirds into that sweet spot where they sound best, but I can’t demonstrate that in writing, so I’ll take you through the math
| Action | Pitch | Frequency in Hz | The math |
| Tune the reference pitch | C | 256 | |
| Tune a pure major third up | E | 320 | (256×5)/4 = 320 |
| Tune a pure major third up | G# | 400 | (320×5)/4 = 400 |
| Tune a pure major third up | B# (C) | 500 | (400×5)/4 = 500 |
Again, we didn’t end up at 512Hz, a pure octave from where we started. So, tuning in pure intervals looks good on paper and worked for Pythagoras because music back then was therapeutic, not entertainment or art, but doesn’t really sound good when playing any music we’re conditioned to hearing, whether it be classical, rock, jazz, blues, and so on. In order to make music an art, the pitches have to be modified (tempered) from their pure state.
Speaking of Pythagorean tuning as therapeutic, it is interesting to note that it is believed that Pythagoras got all of his lofty ideas from the Therapeutea in Egypt, and not only brought them back to Greece, but was nice enough to write them down. I wonder if he’s embarrassed that he gets all the credit?
This entry was posted by Mark Brewer.