12 & 24-Tone Precise Temperament Tuning for 432Hz (and 528Hz)

Reading Time: 3 minutesAugust 25, 2023

Precise Temperament Tuning for 432 Hz (and 528 HZ)

In recent years Robert E Grant explored and shared the direct relationships between mathematics, geometry, cosmology and music, something I have been blogging about as well on Roel’s World since 2013.

Robert’s announced of May 16, 2023 the Sexagesimal Time System being based on musical scales that are fully incorporated into the compass navigation system: The Musical Wave of Time. In June 25, 2021 Robert published his article Precise Temperament.

An intriguing concept that caught my attention and was placed on my ‘to-blog-about-list’. Now I finally got around to do so. Obviously I am not going to add all info he shared here, you could simply visit his website and watch his video instead.

But, for your convenience, a short introduction:

“In July 2020, I first posted regarding my discovery of ‘Precise Temperament Tuning’ a geometrical approach to music temperament replacing the Just Intonation’s Major Third interval (1.25 or 5/4) with 1.26. In this approach, the MINOR (3rd) interval FALLS (from 1.2 to 1.19) and the MAJOR (3rd) interval LIFTS (increasing from 1.25 to 1.26). By combining 1.26 as the Major Third and a perfect 1.5 (3/2) as the Perfect Fifth I found that a new and complete musical scale could be derived that might overcome some of the limitations of Equal Temperament Tuning and allow for a direct connection to all geometrical expression.” ~ Robert E Grant

“Both e (Euler #) and π inform the entire Scale and all their multiples appear as frequencies within the 432.081hz Precise Temperament and 528.099hz Precise Temperament Tuning Chromatic Scales and together form a 24-Note Quartertone Chromatic Scale!” ~ Robert E Grant

Sidenote: Robert Grant was not the first person creating a temperament that combines both 432Hz and 528Hz. Years ago Bo Constantinsen created a tuning concept called “The Sacred Sound Scale” that places 424Hz (“Ra-Tuning”), 432Hz, 440Hz and 444Hz + 528Hz within one tuning concept. The scale has 32+1 (33 – an interesting number) pure harmonic tones and the reference frequency of 256 Hz (Scientific Pitch). It comes from the Natural Ascending Series of Harmonics 32 to 64 of the 8 Hz Fundamental Tone, and represents its 6th double.

Facebook friend Toni Mazzotti created a Youtube video with a chord progression cycle in both Equal Tempereament, Precise Temperament Tuning and Just Intonation, just to let you hear the difference.

To my ears Precise Temperament Tuning sounds the most consonant and more pleasing then Equal Temperament and even then Just Intonation.

Toni shared an interesting looking tone-color circle created for the 24-Tone Precise Temperament Tuning, (the first of the two circles below).

I personally feel and think another tone-color combination is more natural and logical, as described in my article about sound and color. Another small change I made was replacing the ‘asterix’ (*) with more common used ‘accidentals’ for 24-tone musical notation. I thus added my personal variant (second circle) on the tone circle here as well.

Tony has a large collection of files (including .tun files) and graphics available for download at his website!

Now, regular visitors of Roel’s World might think: “Hey, what’s that? An article about 528Hz? Didn’t Roel write a pretty tough article about the 528Hz “Ancient Solfeggio Tone Frequencies” concept by Horowitz?”

Yes, and I still stand behind what I wrote about the “Ancient Solfeggio Tone Frequencies” concept by Horowitz”. His story and claims are still nonsense, that has not changed.

But, as I mentioned in the epilogue of that article, I do NOT proclaim that numbers such as 528 are without meaning, importance or value, perhaps even as tone frequencies for some people. BUT, I personally do not see how the “Ancient Solfeggio Frequencies” concept (as Horowitz proclaimed, the flawed math and the frequencies shared) could ever work in harmony within a proper 12-Tone musical interval system / temperament.

The Precise Temperament Tuning is a temperament I could not ignore! The 432-tuning section of my blog would simply not be complete without it. And it is a more practical tuning concept that The Sacred Sound Scale of Constantinsen.


– The website and youtubes of Robert E Grant (Precise Temperament)
– The website and youtube of Toni Mazzotti

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