The music and audio industry currently uses the A = 440 Hz universal standard pitch tuning around the world. It wasn’t always this way. In fact, 440 Hz has been the standard for less than a hundred years, a drop in the bucket in terms of music history. The tuning of A = 432 Hz, also used throughout music history, is making quite a comeback these days, especially in the field of sound healing and meditation. Researchers, scientists and musicians are leading a growing movement to prove this tuning is best for heart-centered, therapeutic sound work.
This article briefly explains the history of tuning and some key points that support 432 Hz as the scientific tuning, by relating it to mathematical relationships, harmonic ratios and frequencies found in nature. Hopefully this will inspire some thoughtful discussions. There are some audio examples to compare tuning for critical listening and a brief explanation on how to compose in 432 Hz tuning in Logic.
A Brief History of Tunings
An article by John Stuart Reid called the ‘Concert Pitch Conflict’ provides a comprehensive history of tunings and I reference many of his findings here. Greek philosopher and mathematician, Pythagoras (570–495 BC), is often credited with identifying musical harmonic ratios related to scientific pitch and the birth of 432 Hz tuning with his instrument called the monochord. It is believed, however, that instruments built accordingly to harmonic ratios were used in Egypt and Greece well before this time. The earliest instruments were flutes and lyres, often used for therapeutic purposes. Hundreds of years later during the classical periods of western music, it was documented that composers like Mozart and Verdi used the 432 Hz tuning. Verdi believed it was a much better tuning for Operatic voices. In the late 19th and early 20th centuries, 432 Hz tuning was challenged by other countries like Germany, the US and Britain who all seemed to be using and experimenting with different tunings.
Pythagoras with his Monochord.
In the early 20th century, there was a need to make a universal pitch standard used by all for sake of instrument makers, composers and orchestras everywhere. Even though 432 Hz was fully supported by the French and Italian composers through most of the classical music periods, 440 Hz eventually became the universal pitch standard. German Physicist Johann Heinrich Scheibler invented a device called the Tonometer and did the first experiments with 440 Hz tuning in the mid 1800s. The Tonometer consisted of 54 tuning forks with a range of 220 Hz to 440 Hz spaced at 4 Hz intervals. His work became widely recognized and a conversation began about a standardized tuning.
After much debate, the US adopted 440 Hz as the standard in 1936. Europe soon followed with its adoption many years after it was first proposed on both continents. Even today, musicians believe that music played in 432 Hz tuning has a better audience response, has a calming effect and sounds more integrated overall.
It is still not entirely clear why 440 Hz was chosen. It seems the scientific experiments by Scheibler had a lot of influence on this choice as opposed to what tuning may have been more in line with the harmonic ratios and relationships found in nature. I can’t help but notice how the music of India and the rest of Asia were left out of this discussion entirely. It is a testament to their unique musical and healing traditions that are affecting us more and more today.
Mathematics, Nature and Frequency
The chart below shows how 432 Hz tuning is derived based on Pythagorean harmonic ratios. Multiples of 2 and 3 forms the basis of the chart, and the left column shows all the multiples of 2 as the note C. In the middle, you will see that A=432 Hz. Also of note is the number 108, used in many spiritual traditions as a unifying number. Mala prayer beads come in strands of 108 and in yogic traditions, 108 sun salutations are often practiced. The number 186624 in the blue box is 432 squared and is the frequency of the speed of light within hundredths of a decimal—very close! Also, every column corresponds to a note with each being a 5th apart. You will recognize this as the Circle of Fifths—the basis for music theory, or at least Western music theory.
Harmonic Ratio Chart: Nature’s Tuning – In line with 432 Hz http://www.michaelleehill.net/wp-content/uploads/2015/02/UntitlMost-Harmonious.jpg
The Earth’s vibration, which is the frequency measured from the earth’s crust to the ionosphere fluctuates around 8 Hz. 8 Hz falls at the bottom end of where our calm, functioning brainwave state called Alpha is, and is almost in Theta (4-7 Hz), where we receive deep relaxation and healing during our sleep cycle or in deep meditation. Multiples of this frequency bring us to C = 64, 128 & 256 Hz (middle C), where the notes become audible to the human ear and then to our reference pitch A = 432 Hz. Recently, astronomers at Stanford found the fundamental frequency of the sun to be 144 Hz. The 2nd Overtone or 3rd Harmonic of this fundamental pitch is 432 Hz (see chart). These are auspicious findings indeed and point to a system that is connected in many ways.
Fundamental frequency of the sun and its harmonic— http://scalarheartconnection.blogspot.com/2014/11/the-sun-is-singing-to-our-hearts.html
Music researchers have also tested traditional healing instruments, like Tibetan Bowls from Nepal, and found they are made in accordance with A = 432 Hz tuning. Instruments made for sound therapy do not have to conform to a universal pitch standard and are becoming more popular in sound therapy centers around the world. We can learn a lot from cultural traditions of instrument making, linked to techniques being passed down through generations.
A Note on Equal Temperament VS Pythagorean Temperament
We have to keep in mind that our universal tuning system is based on 12-tone Equal Temperament. Meaning, all the intervals or adjacent notes are spaced evenly from each other in order for all the octaves to sound the same. In true Pythagorean temperament, this would not be the case. Equal temperament is required for instruments like piano where notes cannot be bent. Voices and string instruments however, are able to bend notes and change tuning easier to achieve the subtle differences between the notes. Roel Hollander describes this in detail on his blog post, ‘Concert Pitch vs Tuning System’ (http://www.roelhollander.eu/en/432-tuning/concert-pitch-vs-tuning-system/). Roel explains that in order to obtain a true representation of 432 Hz then, one would have to compose not only in A = 432 Hz but in combination with Pythagorean Temperament or a close implementation of it like Just Intonation or Twelve True Fifths Tuning. I did some investigating myself using the Cleartune App for iOS, a handy tool that allows you to change tunings. In Pythagorean tuning, A=432Hz, C =128 Hz, 256 Hz and 512 Hz and G below A = 384 Hz (as examples). When set to Equal Temperament, all the A’s calibrate the same and the others are C=128.4Hz, 256.9Hz, 513.7Hz and G=384.9Hz. There is a difference between .4 – 1.7Hz on those particular notes, but it’s a small difference compared to composing in any other tuning. Plus, when using equal temperament, it’s possible to play in an ensemble, for example, without reinventing instruments.
Audio Examples by Torkom Ji
Torkom Ji, founder of Quantum Harmonix Sound Healing, has graciously provided Ask.Audio with 3 music examples in 432 Hz, 440 Hz and 444 Hz. Torkom facilitates sound healing sessions all over the Los Angeles area with his custom Korg Electribe. He is a master at creating deep, resonant soundscape journeys using just this instrument. It’s very different than what most sound healers are doing with acoustic instruments, but some would argue just as powerful. Listen to the examples below in headphones and through your monitors. Notice how the different tunings affect the entire range of frequencies you are hearing. The excerpt is from his track, Internal Eyes, originally composed in A = 432 Hz tuning.
MP3 Internal Eyes 432 Hz:
MP3 Internal Eyes 440 Hz:
MP3 Internal Eyes 444 Hz:
*From the Album Hieroglyph: https://torkom.bandcamp.com/album/hieroglyph-432hz
As you listen, ask yourself these questions:
- Does one sound more integrated than the other?
- Does one bring out a certain range of frequencies?
- Does one sound thinner than the others?
- Do you feel more relaxed with one, more agitated with another, or neutral to all?
Some people believe in specific answers to these questions, but the reality is, more research is needed in this area to convince the masses one way or another. Since there aren’t many online articles that actually provide solid listening examples for comparison, we at Ask.Audio hope to keep this conversation going by having our readers way in and share their experience.
Try it Out In Logic
Logic is a great DAW to try 432 Hz or another tuning in. There is a global tuning settings window located in the Project Settings menu. Setting the tuning here affects all the software instruments in Logic, excluding third-party instruments. The tuning ranges from 415.3 Hz (-100 cents) to 466.3 Hz (+100 cents) with 440 Hz as the current pitch standard. When setting the slider I noticed I could set it to 432.2 Hz or 431.9 Hz, but not right on 432 Hz. The reason being the slider works off of cent increments. So, if you pitch your recordings or individual parts down, you would lower the pitch by 31 or 32 cents to get close to 432 Hz. (Editor's note: You can enter -31.7 manually to change the tuning to exactly 432 Hz.) This is helpful if you are working in another DAW that doesn’t have global tuning or if you are trying to match the tuning of a third-party instrument part in Logic for example. The good news is you can compose in 432 Hz tuning with acoustic musicians in conjunction with software instruments pretty easily in Logic.
The Great 432 Hz Debate
With so much of the musical world (acoustic and electronic) operating at 440 Hz standard tuning today, it’s hard to imagine the shift to 432 Hz happening on a large scale quickly. But there is a growing movement underway fueled by the sound healing community, select ensembles, researchers and scientists that will keep bringing this issue to light and allow music makers and listeners to consider the power of this tuning and how it affects the mind, body and spirit.
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Addendum from the author (Lynda Arnold):
First of all, thank you readers for your thoughtful feedback and insight into this controversial topic. The following are some clarifications to the article to clarify a few points. I know there are many holes, but I’ve chosen a few to begin with here.
*In the opening paragraph, I mentioned explaining some ‘key points that support 432 Hz as the scientific tuning…’. In order to be fair to all our readers, I should have prefaced this article as an inquiry into some belief systems, philosophical approaches and creative practices surrounding the way and how of this tuning.
*Regarding the history of 432 Hz as it relates to Pythagoras, there is no concrete evidence that he used the reference pitch A=432 Hz with his work with harmonic ratios. The ‘Birth’ of A=432 Hz as concert pitch come about in the Classical era (’1800s) and you can read about this evolution in the article I reference called ‘The Curious Concert Pitch Conflict.’
*When I mentioned the Earth’s resonance, I was referring to the Schumann resonance which fluctuates as much as 5 Hz in either direction making it difficult to pinpoint it as directly and specifically correlated to 432 Hz. https://en.wikipedia.org/wiki/Schumann_resonances
*In regards to ancient instruments, like Tibetan Bowls, being tuned to the A=432 Hz, there is no concrete evidence that this was the case since in more ancient times, tuning was done by ear and passed down through generations. Jamie Buttruff has done some inquiry into the area and has video showing his particular Tibetan Bowls are tuned to A=432 Hz reference pitch. http://blisscodedsound.com . I would love to see more research on this topic, however, with other instruments too.
*I want to provide a listening link for the Sun’s frequency and correlating chart that I mention above. You can listen and use a tuner to check the frequency that they found. I found using Cleartune App that the tone fluctuated between 141–144 Hz— it’s a pretty dynamic tone. It’s important to note that researchers at Stanford calculated this by recording ‘acoustical pressure waves and sped them up approx. 42,000 times in order to produce a frequency that we can hear’. Here is the listen link and more information: http://solar-center.stanford.edu/singing/
*in my paragraph comparing Equal Temperament to other tunings, the term that fits best in the tittle and surrounding comparison is ‘Just Intonation’, not ‘Pythagorean Temperament’. ‘Just Intonation’ is the tuning that expresses the pure harmonic ratios.
Despite the lack of concrete, scientific proof (and proliferation of false information) on this matter of using A=432 Hz tuning (just intonation, equal temperament or otherwise) for therapeutic work, I am encouraged to see so many people willing to try it on their own with an open mind and reach their own conclusions based on individual experience. Some readers weren’t even aware that tunings other than 440 Hz even exist at all!
Maybe these experiments will serve as a vehicle for more research or just provide another color for artists to use in their sonic canvases. The world of music and sound is complex, with many dialects. Meaning, some people approach music in a more technical, precise way while others choose to play based on feeling alone, letting the muse be their guide. However we get to the truth in this matter, it’s clear that people love music and have a special and unique relationship to sound that should continue be respected, inspired and cultivated.
Articles, blogs and sites for further research; some with strong arguments for and against:
Concert Pitch Conflict:
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