Musical tuning systems and our connection to G*d
Navah Tsiporah Verhoeven
Edited by Tsiporah Levine, and then again by Navah.
There is an important story to tell that I feel needs to be told and worked with, especially now. This world is undergoing a major transformation. Some call it 'Mashiach is coming soon', others call it 'New Age.' Most of the Western music (and the music of many other cultures as well) works with a tuning system that is systematically slightly out of tune. This tuning system has become so commonly accepted and used, and it is so much easier to use than most other tuning systems, that hardly anybody is conscious of this fact any more. And yet, this tuning system has a number of significant disadvantages for our energetic connection to G*d. These are not yet commonly recognized but this might be very important for the near future.
Although the matter is rather complex, my aim is to explain it in simple terms that will be accessible to everybody. I will most certainly need to over-simplify and I want to excuse myself for that in advance. If people are interested, more detailed explanations are available from the website as well as from their Just Intonation Primer, which can be ordered from the site. (I have sometimes used ideas and phrases from this booklet in my work.)
Sound is actually a vibration of air and this vibration has a certain frequency. It is measured in movements per second, called Hertz (Hz). Our story concerns the relation between different frequencies of sound. What causes two tones to sound 'nice' together has to do with the ratio between their frequencies. A 'ratio' has to do with the relation between two numbers:
For example, 100 and 200 relate to each other in the same way as 10 and 20, or 25 and 50, or 1 and 2 relate to each other. In all these cases the second number is twice as high as the first. In other words, these pairs of numbers have a ratio of 1:2. Similarly, 100 and 150, 10 and 15, and 4 and 6 all have a ratio of 2:3, since the first number is two-thirds of the second number.
The simpler the ratio between the frequencies of two tones, the more 'harmonious' is our experience of their combined sound. A simpler ratio is always characterized by lower numbers. For example, two tones with frequencies of 100 Hz and 200 Hz sound very nice together (ratio: 1:2) but 100 Hz and 113 Hz don't (ratio: 100:113, not divisible into lower numbers). Other examples of 'nice' ratios are: 120 -> 180 (ratio: 2:3) and 120 -> 160 (ratio: 3:4). We experience notes with a ratio of 1:2 as the same note on different octaves. In Western music we even give them the same name, for example C or A.
Now, if we want to make a scale within one octave, we encounter some problems, because we cannot simply add up and subtract frequencies to make nice steps between tones. For example: if we take the octave from 200 to 400 Hz, the number that would be in the middle between those frequencies would be 300 Hz. But this tone is not the tone that is right in the middle of our octave. The ratio of that tone compared to our starting tone is: 200 -> 300 = ratio 2:3. And the ratio between the tone in the 'middle' of the octave and the other end of our octave/scale is: 300 -> 400 = ratio 3:4.
tones: 200 ---- 300 ---- 400 Hz
ratios between them: 2:3 3:4
We have to use ratios and this makes it mathematically much more difficult. Using ratios we encounter problems that are not so easy to solve, especially if we want all the tones in our octave to sound nice and harmonious with each other (and therefore have simple ratios) while at the same time wanting 'pure' distances (intervals) between the starting tone of the octave and all the other tones. Another problem arises when we want to play another piece of music that uses a scale that starts on a completely different tone, especially if our musical instrument has only fixed tones, like a piano.
I will show one much-used ideal of a 'major' scale in pure tuning and then elaborate on one example in order to give you an idea of the problem. In Western music we have 12 possible notes in an octave, all on ½ note distances from each other. We are used to hearing mostly the so-called Major Scale. In this scale the octave has 7 notes and the distances between the notes are: 1 - 1 - ½ - 1 - 1 - 1 - ½
In our example the ratios of each note with the first note (also known as keynote) of the scale have been made as simple as possible:
Frequency (Hz) 120 135 150 160 180 200 225 240
Ratio with keynote 1:1 8:9 4:5 3:4 2:3 3:5 8:15 1:2
Now take a look at the first 3 notes. The distance between the first and the second note has a ratio of 8:9. Now we calculate the distance between the second and the third note: 135:150 = 9:10.
So now we have found two different ratios for a 'whole' note: 8: 9 and 9:10.
And only if we use both these different 'whole' notes can we come to a truly harmonious, 'pure' distance of 2 'whole' notes 'added up' (with a ratio of 4:5)!
Now here are shown the ratios of all the neighboring notes in the scale:
Frequency (Hz) 120 135 150 160 180 200 225 240
Ratio with keynote 1:1 8:9 4:5 3:4 2:3 3:5 8:15 1:2
Ratios with neighbors: 8:9 9:10 15:16 8:9 9:10 8:9 15:16
Now you can understand what our problem is with tuning an instrument like a piano in such a way that one can play all kinds of musical pieces that use different keynotes. Actually, if we would want to be able to play pieces on all the scales used in today's Western music, we would need several versions of every key on the piano.
Many solutions to this problem have been found over time in different cultures, and more solutions are still being found today. In the West, one solution has become very popular over the last few centuries. This solution has been applied on practically all instruments with fixed intervals between notes today. It's full official name is: 12-Tone Equal Temperament. I am not going to explain exactly how this solution works mathematically, but roughly one could say that all the distances between the 12 half notes in the Western octave have been made mathematically equal. This means that they are all slightly out of tune, when you consider their ratios with other notes, with the exception of the same note on two different octaves, which remains pure. Most people nowadays don't hear this, especially because they grew up with it and never heard anything played in a purer kind of tuning system.
12-Tone Equal Temperament solves a lot of tuning problems and is much simpler to work with, but it has significant disadvantages:
1. It is a limited and closed system of tones. Only the 12 half tones in the octave are used, nothing that lies in between.
2. The whole possibility of 'sliding' from one note to another has become almost totally impossible and out-of-use. (and therefore has even become disliked by most people). The use of 'sliding' notes can be very beneficial when music is used for healing purposes: it can help to connect energy centers and to stimulate and balance the flow of energy in our bodies and energy fields.
3. It is out of tune. If one hears some really pure intervals played, the aesthetic experience is unmistakable, even if you think of yourself as 'musically insensitive.' Words like 'clarity, purity, smoothness, stability' come readily to mind, and the 'normal' tempered tuning suddenly sounds rough, restless or muddy in comparison.
4. It tends to impair our ability to connect our consciousness to the higher dimensions. This is a disadvantage that has not yet been recognized and understood so much in the field of music composition, not even by composers who are nowadays developing 'Just Intonation.'
This fourth disadvantage begs closer examination:
When I was studying Indian classical music (a form of music that uses a very subtle, complicated and pure tuning system) my teachers used to tell the following story: A long time ago, way before this equal tempered tuning was invented in the West, some Chinese composers discovered it. But at the time the ruler of that country was highly developed spiritually and as soon as he heard about this tuning system he made a law that forbade the use of it! Why? He said: "If we are going to use this system on a large scale, we are going to lose our connection 'up' and we are soon going to live in a purely materialistic world!" Well, it seems that losing our connection up needed to happen anyway. Although the causal relationship between the spread of equal-tempered tuning (starting at the end of the 17th century) and the rise of materialism and the decrease of spirituality and religion cannot be proven, it is clear that the two have gone pretty much hand in hand in Western culture.
The idea that pure tuning is spiritually beneficial can actually be explained scientifically. Everything is made of vibrations with certain frequencies, and very high frequencies go into the higher dimensions.
Each note that we hear contains additional notes within it that are termed 'overtones' or 'harmonics'. The frequencies of these overtones are mainly multiples of the original note's frequency (for example, if the original note had a frequency of 100, its overtones would have frequencies of 200, 300, 400, etc.) The presence or absence of certain overtones and their relative strength or weakness determines the tone color or timbre of the pitch. That is why no two instruments sound alike. Together, these overtones create a frequency spiral up and up into frequencies that we cannot hear any more, and even higher until at a certain moment they move into the higher dimensions, all the way up to G-d. When an instrument produces sound that naturally has many very clear and loud overtones, this helps the listener to feel his or her own connection with the higher dimensions / G*d. And when two notes are 'in tune' with one another in the purest way possible with a simple frequency ratio, many of their overtones will be the same, such that they will be able to strengthen each other. This, in turn, also strengthens the experience of the 'line up to G-d.'
Now when you play music that mostly combines notes that are not exactly in tune with each other, very few of these overtones are produced, creating a 'flat' experience. The potential ability of using music as a ladder to higher consciousness is therefore heavily impaired. Of course, such a connection is still possible even without pure tuning. But when one grows up hearing music all around that actually helps one connect to the higher dimensions (i.e., G-d), unknowingly one gets used to having such a connection, at least on a subconscious level. And that is what our Western music has not been giving us for the last few centuries and what I would like to restore by developing new musical forms that are in some form of pure tuning, while at the same time being easily accessible to Western musicians.
As in many other non-Western cultures, in India a way has been found to make music using pure intervals. The basic principle is that every piece of music being played, uses the same 'basic note' or 'key-note' throughout the whole piece. This basic tone is being played continuously, on and on, on a string instrument named 'tanpura' (see under: What is a tanpura).