Introduction

In the modern, Western world, music surrounds us every day – in our cars, on radio and television, in movies, dance clubs, and on our stereo systems. And although we say we like this or that kind of music, and we just can’t stand that other kind stereo-systemof music, all the music we are generally talking about is exactly the same in one fundamental respect: it is played on instruments that are tuned to exactly the same pitches. (Pitch is the perceived highness or lowness of a tone or musical note.) Thus, if you are a piano player, it doesn’t matter if you’re playing rock, ragtime or Bach, all the notes you play (in fact, all the notes you can play) come from a single set of eighty-eight possible pitches (since there are eighty-eight keys on a piano). When a band or an orchestra “tunes up,” all the players insure that their respective instruments will play exactly the same pitches. In other words, when an instrument plays the note called A, it should produce the same pitch as all the other instruments playing an A.

But where did these all pitches come from in the first place? Are there other pitches that could be used, and if so, what would our music sound like? How would it be different if the strings inside a piano were tuned to different pitches? How would it feel? The thesis of this paper is that since all of our modern, Western music, whether acid rock or Chopin preludes, contains pitches that are disharmonious with one another (as I will explain shortly), the effect on us, the listeners, is also disharmonious. Since we hear with our entire bodies and not just our ears, we become physically immersed in the music we listen to in a very real way: our entire bodies are forced to resonate to the music we hear.

Whether music feels good to us or not depends on many things – tempo, loudness, genre, familiarity – but beneath all these lies harmony, the feeling evoked in our bodies by musical tones or pitches trio3played together or in sequence. The external effect of musical harmony or disharmony on us is profound, and if we don’t notice this, it is only because we have never heard truly harmonious music since it is almost never played today in Western countries. One reason is, most of our modern musical instruments cannot play exact harmonies in the first place, due to their designs. As we will see, every fixed pitch instrument – pianos, guitars, clarinets, and so forth – are tuned to pitches that are inherently disharmonious. And variable-pitched instruments – violins, trombones, fretless-basses, and the human voice – are played to duplicate these same pitches so they are not perceived to be “out of tune” with the other instruments. But what would it sound like – what would it feel like – if all of the notes were harmonious?

In our exploration of the effects of harmony, we will be looking at why Western music is tuned the way it is (and there are some good reasons), and also at other types of music with different tunings. Finally, we will concentrate on seven almost unknown tunings that are over 5000 years old that came from (as far as we know) ancient Mesopotamia –that area of the Middle East that is now Iraq, Kuwait and Iran. We will not be interested in exploring modern Arabic music at all, but instead we will apply tunings that predate all the modern cultures of this area to Western instruments and melodies so as to discover the effects of their perfect harmonies on health and altered states of consciousness. We will begin with a tuning used in early classical music up to the time of Bach called Just Intonation, then move on to the modern Equal Temperament tuning used today, and finally discuss the Mesopotamian tunings. Along the way we will touch on the blues, Indian raga music and the sitar in particular. Always our emphasis will be on feeling, how music effects us consciously and unconsciously.

It has been known from ancient times (from very ancient times, indeed) that music and mathematics are intimately related. We will discuss the mathematical aspects of the various tunings – again emphasizing feeling – but we will relegate all but the simplest fractions to another page so as not to get too sidetracked. (Although if you ever wondered why the frets on a guitar are spaced the way they are, here will be the answer. Remember logarithms?)

Octaves and Such

Okay, I need two minutes to talk about octaves and notes and things before getting to Just Intonation.

gpiano1If you strike Middle C on a piano, you hear a certain pitch. If you then strike the next C key higher up the keyboard, you hear a pitch with the same “quality” only higher. These two C notes define an octave, and this is the only interval between two notes on a piano (or any other instrument) that are exactly, perfectly in tune –they are perfectly harmonious. Likewise, if you pluck the first string on a guitar, you hear an E note. If you then hold down the string exactly halfway along its length – and there is a fret in exactly in this spot for just this purpose – you will sound another E one octave higher.

So what’s going on with these octaves? Is it just a coincidence that a string half as long produces a pitch exactly one octave higher than the original string? No. To keep matters simple (and to stay under my two minutes), I’ll just say that an octave is defined as the pitch difference between a plucked whole string and a half string with the same tension. In a piano, the string lengths, tensions and thickness’ are all balanced to produce octaves. When a piano tuner goes to work on your out-of-tune piano, the first thing he/she does is get the octaves right.

One way this is done (nowadays) is with a little electronic gadget that measures the frequency of a note. Whatever frequency Middle C is tuned to, the next C above it is tuned to a frequency exactly twice as large. This holds for any two notes that are one octave apart. But this is rather amazing: How can two notes that sound “the same” have numbers that are related by a factor of two? Why not 6 or 3.14 or something else? This is the first clue that music and mathematics are related. As we shall see, mathematics is indispensable for good musical vibes.