Ancient Natural Harmony, Maqams and Just Intonation
Mouse Over Image Above to Play Short Informational Video
In ancient times musicians could develop skills in producing perfectly harmonious music. Modern physicists call the intervals between these perfectly tuned notes "just intonation" because the wavelengths of acoustic sound they produce fit together absolutely perfectly.
With the 17th century European invention of the complex machine called the "piano" the system of "equal temperment" was invented so that musicians could transpose melodies into all 12 notes in the octave. Unfortunately, in order to accomplish this, the scales of all 12 keys had to be compromised so that they all are slightly out-of-tune. The result: our modern musical sound fields are flooded with "equally tempered" intervals and we no longer grow up in musically harmonious environments. We don't even know what we are missing.
These are the out-of-tune equally-tempered intervals we listen to today:
This is what out-of-tune equally-tempered waveforms look like:
This is a simple recording of musical intervals of truly harmonious just-intonation:
This is what perfectly-tuned waveforms look like:
Dr. Robert Smith described the newly invented "equal temperment" in 1759 as: "that inharmonious system of 12 hemitones, which produces a harmony extemely coarse and disagreeable."
And here are the words of Hermann Helmholz from 1852: "When I go from my justly-intoned harmonium to a grand pianoforte, every note of the latter sounds false and disturbing.... On the organ, it is considered inevitable that, when the mixture stops are played in full chords, a hellish row must ensue, and organists have submitted to their fate. Now this is mainly due to equal temperament, because every chord furnishes at once both equallytempered and justly-intoned fifths and thirds, and the result is a restless blurred confusion of sounds."
Fortunately, the musicians in Egypt, Syria, and other parts of the indigenous Middle East, have preserved ancient systems of musical scales known as "maqamat" which have resisted the movements in Europe and America toward "equal tempered" music.
Cameron Powers has spent the last 35 years discovering and learning and mastering musical performance which traditionally employs these ancient "quartertone" intervals, sometimes learning musical pieces which may be as much as a thousand years old.
And yes, these ancient musical scales have flexibilities which allow the performance of "justly intonated" or perfectly-tuned music. It could also be said that musicians using these ancient scales also have the ability to use intervals which are not "justly intonated" and which produce dissonant vibrations similar to those found in modern "equally tempered" Western music. But there is a critical difference: the musician can be in control. He can perform perfectly harmonious intervals to create an ultimately soothing sound environment. Or he can deliberately introduce dissonance to put an edge or create "blues notes" for certain emotional moments induced by the use of these ancient modes.
Cameron Powers has written a "how-to book" for musicians called "Arabic Musical Scales: Basic Maqam Teachings with 2 CD's" which teaches a total of 45 different ancient scales. Having made numerous trips to study and perform in Egypt, Syria, Jordan, Iraq and Lebanon, Cameron suggests: "The emotional repertoire in these ancient lands is more complex than what we now live with here in America. The pressures exerted by our mono-lingual, competitively-driven, musically out-of-tune dualistic culture which sees everything in black and white simplistic terms has robbed us of the ancient complexity of human feelings. My Egyptian friends enjoy a richer fabric of emotional realities and they have the music to go along with all of it."
Truly harmonious music, seldom heard in the Western world today, does not even require the musician to invest his own personal emotional enthusiasm. The music alone creates a magnetic attraction and a healing energy field. The possibility for "egoless" music then arises.
Here is a short video clip which shows the differences both audially and visually:
Just Intonation vs. Equal Temperament
Here are some comments about just intonation by Kyle Gann:
"Just-intonation chords are much calmer, more passive; you literally have to slow down to listen to them. (As Terry Riley says, Western music is fast because it's not in tune.) I've learned to hear equal temperament music as a kind of aural caffeine, overly busy and nervous-making. If you're used to getting that kind of buzz from music, you feel the lack of it as a deprivation when it's not there. But do we need it? Most cultures use music for meditation, and ours may be the only culture that doesn't. With our tuning, we can't.
My teacher, Ben Johnston, was convinced that our tuning is responsible for much of our cultural psychology, the fact that we are so geared toward progress and action and violence and so little attuned to introspection, contentment, and acquiesence. Equal temperament could be described as the musical equivalent to eating a lot of red meat and processed sugars and watching violent action films. The music doesn't turn your attention inward, it makes you want to go out and work off your nervous energy on something.
On a more subtle level, after I've been immersed in just intonation for a couple of weeks, equal temperament music begins to sound insipid, bland, colorless. There are only eleven types of intervals available instead of the potential several dozen that exist in even the simplest just system, and you don't get gradations of different sizes of major third or major sixths the way you do in just tuning. On a piano in just intonation, moving from one tonic to another changes the whole interval makeup of the key, and you get a really specific, visceral feel for where you are on the pitch map. That feeling disappears in bland, all-keys-the-same equal temperament. As a composer, I enjoy having the option, if I'm going to use a minor third interval, of being able to choose among the 7/6, 6/5, 19/16, and 11/9 varieties, each with its own individual feeling.
Far beyond the mere theoretical purity, playing in just intonation for long periods sensitizes me to a myriad colors, and coming back to the equal tempered world is like seeing everything click back into black and white. It's a disappointing readjustment. Come to think of it, maybe you shouldn't try just intonation - you'll become unfit to live in the West, and have to move to India or Bali." (Or Egypt or Syria or Iraq...)
"Before the 20th century, European music had its own wonderful non-equal-tempered tunings, which unfortunately we've abandoned."
More Info from http://www.justintonation.net/:
Equal temperament was not adopted because it sounded better (it didn't then, and it still doesn't, despite 150 years of cultural conditioning) or because composers and theorists were unaware of Just Intonation. The adoption of twelve-tone equal temperament was strictly a matter of expediency. Equal temperament allowed eighteenth- and nineteenth-century composers to explore increasingly complex harmonies and abstruse modulations, but this benefit was short-lived. By the beginning of this century, all of the meaningful harmonic combinations in the equally-tempered scale had been thoroughly explored and exploited, and many composers believed that consonance, tonality, and even pitch had been exhausted as organizing principles. What was really exhausted was merely the limited resources of the tempered scale. By substituting 12 equally-spaced tones for a universe of subtle intervallic relationships, the composers and theorists of the 18th and 19th centuries effectively painted western music into a corner from which it has not yet succeeded in extricating itself.
"There are regions in the soul where only music can penetrate... The purpose of music is to connect us to, refine and develop our inner life." -- Zoltán Kodály, Hungarian composer
"The first experience of music is of your mother's voice-even just the way that mothers speak to children all over the world. In whatever language and whatever culture, mothers speak to children in highly inflected speech. 'Oooh, little one...' It's instinctive. There's something there. So the pitched speech, which is the beginning of music, modulates the relationship between the infant and the mother-as do the mother's gestures. There's this kind of song and dance which is the infant's first experience of human relationship. And it's all one thing. Song and dance and love are one thing. Which is why to me it's such a sorrow that, with the professionalization of music in this culture, so many people think, "I can't sing." Mothers are not singing to their babies now because the culture is telling them that they can't sing. And I have pleaded with some young mothers, please, sing to your babies. And some of them are doing it. But one young mother said, "No. I can't sing. I'm going to give him CDs of lullabies." So then music for that child doesn't mean love. It means something that comes from a machine." -- Gail Needleman
"You're singing different intervals just to tune the hearing, and the voices lock in on the vibration so that it's really a true, pure interval. Then the overtones start to ring out in the room and you've entered the world of forces. I can tell them until I'm blue in the face that these are properties of matter that we're talking about when we're talking about overtones. This is physics. This is how the universe is created. And then they hear it. The idea that their inner experience could actually be obeying the same laws as the planets in their orbits doesn't make any connection. But when they sing one note and hear the overtones that are there, that they couldn't hear before-that's a real experience.
And once in a while, one of the students will say, that was like meditation. So something is being received." -- Gail Needleman
"And the other thing I think is really important is how a sense of trust in one's own experience is really central for our life as a society. It's not only that those who rely on verification of truth from others are subject to demagoguery, it's that you can't have a participatory culture if it's composed of people who don't have any trust in their own experience." -- Gail Needleman
"What a shame that is. I mean I would love to be a fly on Pythagoras's wall. And of course for Pythagoras it was the discovery of the mathematical and physical principles of physics in music. And there was also the esoteric study in ancient Egypt, and healing. It was all one thing. The modern idea of the self-as a monad, in a way, a self-contained, separate unit is new. My sense is that the relationship between people was different then. I heard about a man talking to a woman from one of the Northwest coast tribes. He asked her to tell him something about herself. She said, 'My mother was so and so from the so and so clan, and my father was so and so.'
And the guy was like, 'Okay, that's nice, but tell me about yourself.' But she thought she had done that. That was who she was-not a separate entity. So we've certainly lost that. And music, the most communal of human activities or arts, becomes those billboards with the person with the iPod dancing to music that no one else can hear." -- Gail Needleman
"If a human being is a nexus of vibrations in a world of vibrations, and ancient teachings and modern science do agree on that, then why wouldn't vibration affect the whole organism?" -- Gail Needleman
"Equal temperament and the piano seem to go together. But our music was not born into the world in the shape of a piano. Nowadays more and more pianists are aware of alternative temperaments, and are asking for them. Modern piano technicians - many of whom have mathematical or engineering backgrounds just like their counterparts in earlier centuries - are trading temperament recipes by email and at meetings; programming them into their computerized tuners; writing about them in their magzines and newsletters; attending classes about historical tunings; listening to recordings of pianos tuned in alternative temperaments; and engaging in lively discussions and experiments. In short, temperament is once again on the move. A growing number of contemporary composers are deliberately incorporating alternative keyboard temperaments into their work." -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"We have tolerated complete harmonic impurity in our music for over a century in equal temperament..." -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"Consider the parts of an equally-tempered scale. Each note, as the scale ascends, vibrates faster than the note below it. How much faster it vibrates is a multiple of the vibrations of the previous note. For our equally tempered scale that amount is the twelfth root of two, and cannot be expressed as a whole number or a simple fraction. Therefore, in a sense, it is inexact, and in the same sense the intervals between notes are doomed to be forever parts, never wholes, never finished, but trailing their remainders on out and out into infinity in one of those awful curves that keeps approaching a line but never reaching it." -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"Just intonation, at one end of this new spectrum, contains a maximum of "pure" or rational intervals. Total purity is its standard, and while this is not possible on keyboard instruments, as we have seen, it is possible in singing and on unfretted stringed instruments, and can be squeezed out of many wind and fretted instruments with judicious use of finger and mouth. Therefore it is a system that can be realized in quite a lot of music. Equal temperament, at the other end of the spectrum, has almost none of its intervals "pure" or rational (the octave being the exception.)" -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"After equal temperament came along...then the notion of what "key" a piece was composed in became essentially meaningless." -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"Ironically, by increasing the number of chords we can play...we have decreased the kinds of chords we can play. Is there now only one Great Melody that all composers take snippings from?" -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"Gradually, in ensembles, it came to be that all the other instruments were expected to accommodate themselves to the way the piano was tuned, rather than a kind of general adjusting done by the many wiles and squiggles that music and musicians allow. The piano is definitely more "fixed" than the harpsichord and clavichord in terms of how hard it is to tune, and this is likely one of the cause behind the gradual dominance of equal temperament and the great reduction of intonational flexibility in our music." -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"The piano may have, as it evolved (fairly quickly) into a monster with iron in its heart, inspired a kind of technology-grip among composers and performers." -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"If exact consonance was no longer even wished for, then what - exactly - was a piano supposed to do?" -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
"In 1688 the first organ was tuned in accordance with Mersenne's formula for equal temperament...thus setting the Western stage for nearly three hundred years of music's 'golden age,' the classroom for the compete divorcement of the science of music from music theory, the concert hall for the benevolent fraud of equally-tempered modulation, the radios of x million American homes for a twenty-five-year siege by the industrialized harmony-armies of mediocrity..." -- Harry Partch
"The novice piano tuner is told that she must first "set a temperament" before doing anything else. This means she will begin in the center of the keyboard, tuning a single note of her choice (usually the middle C or the A just below it), tuning it purely to match a tuning fork. After that, she must tune a little "wheel" of intervals radiating out from that note - fifths, fourths and major thirds - so that each interval is a tiny bit out-of-tune. How much out-of-tune is the "rule" imposed by equal temperament, the keyboard tuning system that has been used on pianos for about 150 years (the piano is about 300 years old)." -- Anita T. Sullivan, The Seventh Dragon: The Riddle of Equal Temperament
Latest historical research indicates Bach did not compose in equal temperament.
Research by Bradley Lehman, 2004, continuing a doctoral project from 1993-4 in "modified meantone" tuning as applied to Bach's music. The interpretation is based on analysis of Bach's extant keyboard music, plus a historical study of tuning methods, plus (in 2004) the suspiciously irregular drawing on Bach's title page.
These loops have been deciphered to represent Bach's favorite "well-tempered" tuning which preserved individual characteristics for each key played upon his clavicord. Why, we must ask, would Bach have bothered to compose in all the different keys represented in his collection entitled "Well-Tempered Clavier" if he had been using equal temperament which renders all keys to sound exactly the same?
Bradley Lehman has video performances of Bach pieces performed both in equal temperament and also in the "Bach temperament" represented by Bach's own drawing above. He comments after creating these performances: "The Bach temperament sounds enough like equal to fool just about anybody, and yet...it brings both more intensity and more relaxation to the music. In any event, it encourages me as a player to bend the music more freely and naturally, investing it with more nuances, in reaction to the sound. It makes me listen more closely to melody and counterpoint, the way the musical lines interact with one another. Tonality "locks in" with a subtly different character and mood for every key (scale). Equal temperament, by contrast, goes on and on with a relatively bland inoffensiveness...being less than inspiring, and encouraging "run-on" uninflected performances. The performer has to work harder to make something special of the music. Why not tune instead with a subtle inequality, and let the intonation itself do part of the interpretive work?" -- Bradley Lehman - www.larips.com
I enjoyed reading about your work and your clear explanation of the true harmonic intervals in Arabic music. I have an appreciation for this quality of pure harmony, as well through building contemporary wind harps and I have found that listening to them over the years has sort of re-tuned my hearing so that I can appreciate the more eastern musical modes.
Thank you for bringing awareness to this beautiful music .
Ross Sterling Barrable
Now there is an urban legend developing about tuning A to 432 Hz instead of 440 Hz and about how those Nazis were trying to poison us by doing that...
Ben Martens: so are you saying that this article is not on the right track, and we could have a harmonically perfect scale that starts on 440?
Cameron Powers: Yes... We could be playing music in perfect harmony starting on our scales on any frequencies we choose... harmony is created when two notes have a relationship... so what is most important for satisfying our hunger for beautiful sacred music is that the pitches of different notes be related to each other in simple mathematical ratios so that their sound waves can nestle together... like two lovers whose vibes can intertwine...
unfortunately, when the equal-tempered music scale was created for music mass-production on the keyboard, these harmonious intervals were discarded... why? because in order to play in perfect harmony the pitches of all the notes in a music scale are dependent on their relationship to the beginning note in the scale: the "tonic" or "key"... so in order to be really in tune, all the pitches of each note in a scale will change depending on what key you are playing in...
musicians who are just singing or playing a fretless instrument like the cello will automatically feel and make tiny adjustments to be in tune in the key they are playing in... but pianos are very cumbersome... you can't stop and re-tune a piano every time you choose to play in a different key...
so the piano industry back in the mid-19th century became the Monsanto of the music world and sold hundreds of thousands of pianos to an ignorant public with instructions to just tune all the notes with equally spaced intervals: so-called equal temperament...
Just like the public still buys those hard red balls in the supermarket thinking that they are tomatoes, the public is still churning out out-of-tune music from keyboards and fretted stringed instruments and we have forgotten how to listen for perfect harmony as it is no longer relevant... until we explore ancient wisdom and bring back justly intonated perfect harmony we have walled ourselves off from sacred music...
As for whether an A is tuned at 440 or 432 Hz... it makes no difference if we drag the whole out-of-tune equal tempered system down one third of a half-step... there are 100 cents in an equal tempered half step... moving from 440 to 432 carries all the pitches 32 cents flatter... generally speaking, lower pitches are more soothing and higher pitches are more stimulating... so there is a tiny difference... but if we are looking for a way to re-claim the beauty of ancient sacred music then we must re-tune the intervals between our notes by returning to just intonation...