Select Page

Chapter 5: Four 53-eq Realms

Next Page: 6/2 – Ancient China


The twelve keys of the piano are “twelve black and white bars in front of musical freedom.” –Harry Partch

I see four broad categories of music where the 53-eq template offers a tremendous range of musical possibilities.

Ancient Music, built on the pure ratios of just intonation, arose independently in most advanced cultures from around 3000 B.C. to 1500 A.D., and includes the European Church traditions and Early Music practice up to the Renaissance. Since almost all of the ancient scales are built off the second, third and fifth harmonics, the 53-eq template is ideally suited for bringing these ancient scales and musical traditions from all over the world back to life. We will be covering three hundred scales from these ancient cultures in Chapters 6-10. We’ll also take a brief glimpse into the musical ethos of the major cultures whose scales we are reawakening. We’ll even look at new ways to merge ancient scales and modern modulatory techniques in Chapters 12 and 13.

In Chapter 11, we’ll investigate the second major category, “Common Practice“ music, our Western European Classical tradition from around 1500-1900, which is also employed in pop and jazz music, and which gradually devolved from just intonation to meantone temperament to various other temperaments to 12-equal temperament by the 1800s. But even 12-eq temperament is strongly based on the principles of acoustics found in the pure overtonal ratios of the ancients. We’ll discover why it’s no easy task to “translate” 12-eq compositions from Bach to Strauss into 53-eq or pure just intonation. Some interesting compositional changes are necessary, especially with regards to musical commas that no longer exist in 53-eq. Everything will sound much more in-tune in 53-eq, but you will have to untangle a plethora of musical commas that give rich ambiguity to the 12-eq compositional fabric and suddenly become “confusingly unambiguous” in 53-eq. Most music theory books don’t spend too much time on the commas in 12-eq (or for that matter the meaning of the enharmonic notes), because they’ve all been smoothed over in 12-eq and are therefore inaudible. The Grove Dictionary of Music, for example, devotes only a short paragraph to the subject of commas. But to fully understand what the great 19th century masters were doing in their harmonic journeys, you must understand all the ambiguities built into their harmonic journeys. So I spend an inordinate amount of time talking about those commas and the challenges they present in translating 12-eq into 53-eq.

The other reason the commas are important is because a whole new set of commas emerge in 53-eq. These enharmonically-equivalent notes arise when the overtones come to within ten cents of each other, and one 53-eq note can represent either or both. The great 12-eq composers of the past can teach us a lot about how to move forward as we navigate the “New Commas” of 53-eq!

While most Baroque, Classical and Romantic-era composers exploited the 12-eq commas for expressive purposes, things change around 1900. By the time you get to Busoni and Scriabin, these composers railed against 12-eq and could hear the beauty of the natural harmonics. Their complex music will almost certainly sound more clear and forceful when not muddied up by the inherent dissonances of 12-eq, and the composers themselves claimed that their music would sound so much better if it were just tuned correctly! If a Scriabinist took his Mystic Chord and other dense harmonies and translated them into 53-eq, they would absolutely shimmer. Scriabin himself actually said this about his dense chords.

“Contemporary” Music of the 20th century often has no tonal center. We’ll dive deeper into atonality and dissonance in Chapter 15. One would think that 53-eq would strengthen one’s sense of tonality, and it usually does just that. But there are many ways to avoid the feeling of a tonal center. Guitarist Neil Haverstick, for example, has a 19-tone guitar and composed a 19-tone row in his “Spider Chimes” piece. Schoenberg would have had a field day with a 53-tone row! In addition, certain tone clusters can be created that have harmonic connections but nevertheless are not tonal in any traditional sense. While pure dodecaphonic music is technically untranscribable into 53-eq, the possibilities of atonal and jarring musical effects abound in 53-eq. In addition, other twentieth century composers liked to walk that edge between tonality and ambiguity. Since the 53-eq template allows for greater complexity because the “background noise” of superfluous dissonances are so greatly reduced, a contemporary composer will find that this sonic boundary between music and noise is farther out from the tonal center in 53-eq than it ever was in 12-eq. We will explore these post-20th century realms in Chapter 12.

The fourth and final very broad category of music is what I call “Music of the Future.” In Chapter 14, I show how the seventh harmonic (which is 39 cents flat of the interval of C to Bb) can be woven into our traditional tonal fabric seamlessly, and how “dissonant” intervals and tone clusters can actually be heard as harmonically related when the superfluous dissonances of 12-eq are removed. There are harmonic explorations never dreamed of by composers employing 12-eq music. New Agers and Minimalists could create music that is incredibly simple and harmonious. Jazz and blues musicians have already brought the seventh harmonic into their musical palette with deeply flatted thirds, sixths, sevenths and even sharped fourths. But it is also possible to use the seventh harmonic as a lever to swing you into a whole new harmonic territory rarely before explored. My ears find a 39-cent shift in the tonal center absolutely new and fascinating. As I mentioned in the “Contemporary Music” paragraph above, the exploration of sonic boundaries and the limits of the ear’s ability to take complex harmonic journeys will be so vastly widened that no one can predict what composers could do with this incredible new tool. The “black and white jailbars in front of musical freedom” Harry Partch referred to can finally come tumbling down!

If you would like to learn more about what is talked about in this chapter, you can buy the entire book, The Grand Unified Theory of Music, in pdf form for $25 with hundreds of embedded musical examples of scales and chords from all over the world.

A free introduction to what The Grand Unified Theory of Music offers is on this website and includes both text and a few musical examples from each webpage. If you would like to learn more about this chapter and the full contents of this entire e-book, you can buy The Grand Unified Theory of Music for $25, with hundreds of embedded musical examples of scales and chords from all over the world — and ideas for how to set up your computer system —


You’ll get a personalized password you can use to see the entire e-book. Inside the full book, you will also get a link to the complete pdf file of this e-book, which you can read on your Kindle or similar device. The links to the hundreds of mp3 sound files – the same ones you can hear on the website — will also be included. This is “Version 1.0” of The Grand Unified Theory of Music. Because it is an e-book, additions, corrections and improvements in the sound may be added at any time. The Grand Unified Theory of Music is Copyright © 2018 by Christopher Mohr. All rights reserved.

One person per password. Sharing this password with others is a violation of copyright. Do not allow others to use your password or link to the pdf file!

Next Page: 6/2 – Ancient China