The Mesopotamian Tunings

Several years ago, I ran across seven tunings (or modes) in a computer program called The World Music Menu written by Steven Nachmanovitch. They were grouped together under the heading “Mesopotamian,” and were found by Lou Harrison on a Old Babylonian cuneiform tablet in the British Museum. This program, when connected to an electronic synthesizer, would automatically retune it to any of several dozen tunings Steven had collected from around the world. In fact, without designing custom instruments that can be tuned to play different scales, only an electronic synth can play all these scales.

(I recently found a recording of Lou Harrison talking about the Mesopotamian tunings in a 27 minute radio interview broadcast on KPFA in Berkeley, California in 1971. It is on the radiOM.org site. You’ll have to register on the site, but it’s free and they don’t bother you. Lou plays the tunings on a recreation of a Sumerian harp, and demonstrates one way of retuning it from one mode to the next. Hats off to the radiOM folks for preserving old bits of arcana like this!)

I had taken my keyboard to Sedona to visit some friends. Before leaving home, I had programmed the keyboard to reproduce these seven tunings. Once there, I began improvising, a few minutes on each tuning in no particular order. We were doing an informal therapy session on a friend, when suddenly she began to experience a sharp pain in her right leg. I stopped playing after a few minutes, the pain was dealt with, and we began to discuss what had happened.

It seemed that the music had evoked an emotional childhood memory, constellated in that person’s leg. Everyone was surprised that simple music, played only for a short time could be so evocative. I played through the seven scales later that day and the next, and we were careful to notice what mental, physical and emotional reactions everyone felt. Each tuning seemed to evoke something, but that something was different for each person.

When I returned home a few days later, I again looked at the mathematical ratios of the tunings. I discovered that there was a natural order of the scales that was different than that printed in the computer manual. I was able to perform for several more people and then several groups of people during the next few weeks. In most of the cases, I asked those present to be aware of what they were experiencing while the music was playing. There were similarities and differences. No two people had the same experience, or even the same type of experience. However, without exception, their experiences came to an end precisely the same time I finished the last piece.

I had decided that the tunings should be played in spiral fashion. That is, I played an improvised composition in each of the seven tunings in the order I had discovered, then played through the tunings in the reverse order, ending where I had begun with the first tunings. This made thirteen pieces, played in the order 1-2-3-4-5-6-7-6-5-4-3-2-1. Each time I played, the entire cycle took about an hour.

Once I had recorded the music, I began doing journey work with people individually which I called Sonic Repatterning Therapy or SRT. For the most part, this consisted of some initial energy balancing as the recorded music got underway, then a period of silence to let the music open an internal journey for the client, and finally a series of questions to the client, such as, “What are you experiencing now?” and “What do you see now?”

My conclusions at that point were that the particular harmonies in these tunings, played in a certain order, relax the body, the mind, and indeed the whole self, in such a way that the inner Self can be heard, or at least sensed. These sensations are variously visual, auditory, even kinesthetic. It is also relatively easy for the therapist to be an escort for the client; in other words, the therapist can share and even anticipate the experiences the client is having, and thereby act as a guide and assistant to help the client understand the experience.

There is one other common thread I have witnessed: in nearly every case, whatever specific experience was evoked in the listeners, it related to some past or present event in the person’s life, or illuminated some choice the person was in the process of making for the future. Several people described the experience as similar to being shown an inner movie or a series of scenes that helped them understand and often release a past experience so they could get on with their lives.

The Mesopotamian Tuning Ratios

The seven Mesopotamian octave tunings as I found them are shown in Table 6. As you can see, each of the seven notes in the scale are represented by a fraction – a ratio of two integers that result in ascending numbers between one and two. Each tuning has a different set of ratios, which give it a characteristic sound and “feel”.

For several years I just composed music in these tunings, without being overly concerned with where these particular fractions came from. I also just took it for granted that there were only seven notes in each tuning, and restricted myself essentially to playing only the white notes on the keyboard. This restricted the harmonic complexity of the music – which was my goal, although the music was still rich and varied.

As an aside, the process of retuning my electronic keyboard (a Kurzweil 2500S) turned out to be fairly simple, after I developed some basic mathematical formulas for doing so. (These formulas are apparently well-known, but I didn’t have access to them at the time.) The problem was that the Kurzweil only knew about Equal Temperament semitones, which could be adjusted by cents, whereas I was starting with a sequence of fractional ratios. How to convert ratios to cents, that I could then program onto the keyboard?

Skipping over the derivation, given any ratio, the corresponding value in cents is given by (cover your eyes if you don’t dig logarithms)

centsformula

So, for example, using a ratio of 3/2 or 1.500 yields 701.9 cents. From Figure 2, the fifth, which is G, corresponds to 700 cents in the ET tuning. To produce an exact fifth, the G needs to be raised by 1.9 rounded to 2 cents – an easy adjustment on the Kurzweil. In this way, I programmed each of the seven tunings and stored them for easy recall.

It is also possible to adjust the entire keyboard either sharper or flatter. The zero adjustment corresponds to the concert pitch (at least here in the U.S.) of A below middle C of 440 Hertz, meaning that all instruments in the orchestra are tuned to this one pitch, so that the violin in the third chair is in tune with the piano and the clarinets. This seemed quite arbitrary to me. In fact, in France, the tuning is set to A 435, and has varied in different places over recent decades. As I was attempting to recreate the original effects of these tunings (without, of course, having any idea of what kind of instruments the ancient Sumerians used), I wanted to at least get the “concert” pitch right.

But what in the world, literally, could I use as a reference pitch? The Sumerian civilization is the oldest anywhere on Earth we have any detailed record of; it was in full flower by at least 3500 BC. What could possibly be contemporary with them? At first I settled on the following, possibly apocryphal story: I had heard that many years ago, the musician and composer Paul Winter had gone into the Great Pyramid in Egypt and had struck the stone “sarcophagus” in the King’s Chamber and measured the frequency at which it resonated. The result was 440 Hz, the same as the modern-day concert tuning. This was as good as I was going to get, I thought, since depending on whose dating you believe, the Pyramid was nearly as old or even older than the Sumerians. So I left the master tuning page on the Kurzweil as it was originally set, and played the music based at A 440.

It was not until much later that I discovered that the motions of the Earth have certain frequencies associated with them. For example, the 24 hour day, the sidereal year and the precessional year all have associated frequencies. (There are also frequencies associated with the moon, the other planets and the sun.) I will discuss this more fully in a later section. Suffice it to say here that this discovery caused me to adjust the keyboard to produce these frequencies in my music.

Early on in my exploration of these tunings, I asked myself how the seven tunings are related to each other. First of all, the different fractions appeared, usually, in several of the tunings, so there seemed to be some underlying pattern. One thing I noticed was that each fractional numerator and denominator was a power of 2 or 3. For example, in Qablitum, 256 is 2^8 (2 raised to the 8th power) and 243 is 3^5. Further on, 1024 is 2^10 and 729 is 3^6. This discovery was rather amazing. I had wondered why the Sumerian tunings were just these fractions; why not, say, the Just Intonation fractions, or some others? Here was a hint, although I didn’t understand it. Two and three are prime numbers; all the fractions in all seven tunings are powers of these two prime numbers. Was this important at all? Not being a believer in coincidences, especially numeric ones, I thought it was important in some way.

When I got to Nis gabri, I found the number 721 which is neither a power of 2 or 3. Since it was the only such number in all seven tunings, I assumed it was a misprint, and subsequently used 729 instead. This adjustment was corroborated in what I next found.

Since all the tunings were comprised of a common set of fractions, I wanted to find out if and how they might be related. I had assigned each tuning a musical key. When the keyboard was tuned to Nis gabri, for example, I played in the key of G; for Ishartum I played in A. I had made these assignments based on how the music sounded and felt. But what would happen, I asked, if I transposed one of the tunings into a different key? I started with Ishartum. I could derive a new tuning in B by taking the second note of the scale in A, which is B, and making its ratio 1/1 instead of 256/243. By doing this eight times, I would have a new scale that ran from B to the next B one octave above it. To convert 256/243 to 1/1 you multiply it by its reciprocal, 243/256. So I multiplied each fraction in the Ishartum tuning by 243/256, and arbitrarily tacked 2/1 to the end to complete the octave.

To my surprise, the result was the exact ratios of the Nis gabri tuning! What was going on here? I next took Embulum and multiplied its ratios by 8/9. I got Ishartum. I found that each of the tunings could be turned into one of the other tunings. There was some king of reciprocality among the tunings. It would be two years before I discovered why this was so.