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HARMONIC EXPERIENCE by W.A. Mathieu. Inner Traditions Press. Available at bookstores and at

One of the most turbulent battlegrounds of the culture wars is the conflict over musical tuning. Since the time of Bach, European music has used a system of compromised pitch relationships called equal temperament, which makes it possible to modulate amongst several different keys. Classical European musicians often see this system as one of the great innovations of modern civilization, which made possible the transition from simple “folk” music to complex “classical” music. But some scholars of Indian music, such as Alain Danielou, have claimed that this tuning system is a form of decadence that deadens the ear, and that the profundities of Indian classical music prove that we need not sacrifice genuine tuning to create great art. Allaudin Mathieu, whose music is equally influenced by both Pran Nath’s vocals and Mozart’s piano compositions, is not willing to accept either of these extreme positions. His latest book, Harmonic Experience, might be described as a proposed resolution to this conflict, and that is how it will be described in this article. But this complex and multifaceted volume cannot be fully described by this or any other quick summary. It combines scholarship, music theory, psychoacoustics, spiritual development, and pedagogy into a 600-page theoretical system. And it interrelates Indian, European, and almost every other form of music in a way that respects and honors them all.
How can a book about harmony do justice to Indian music, which doesn’t use harmonies? The answer lies in the fact that all “single” melody notes, whether played by sarods or tubas, share a harmonic structure that distinguishes them from mere noises. Mathieu teaches us how to hear these harmonies that lurk within each single note. To some degree, Mathieu accepts Danielou’s assertion that our ears have been deadened by equal-tempered music, and Mathieu has over a thousand exercises to bring our experience of harmony back to life.

Some of the first exercises are derived from his studies with Pran Nath and G.S. Sachdev. Singing in unison with a single drone note may not seem particularly challenging—until you actually try to do it. Westerners are used to hearing voices with a vibrato that blurs over the tuning nuances that are essential for Indian music. In their first attempts to sing a vibrato-free tone, even professional musicians usually wobble and quaver. But once you learn to sing an accurate sa (tonic), it becomes easier to hear it as harmonically built up of overtones. Mathieu teaches you how to hear the tones of the scale as built up from those overtones. Harmonies are not first formed by assembling melody notes; instead, melodies arise as we gradually untangle the overtones from the first sa note.

The most noticeable overtone is the octave, and Mathieu shakes up our presuppositions by questioning this name for it. Why use a derivation of the Latin word for “eight,” thus assuming that there are always eight notes for the scale? There are numerous ragas that have five, six, or seven notes. The one undeniable physical fact about the so-called octave is that the upper note in that interval vibrates at exactly twice the frequency of the lower note. So Mathieu refers to it with the ratio 2:1, and uses the equivalent ratios for the fifth (3:2) and the major third (5:4). These are not the only terms that he uses for musical intervals. This book is pluralist, not reductionist, for Mathieu recognizes that the notes need to be renamed when they are described in different contexts. So, after warning us of the limitations of the seven-note system that labels the 2:1 ratio as an octave, he relies most frequently on a set of names that presupposes it: the Indian sargam system.

In the sargam system, the first overtone after the octave is called pa (the fifth), and the next new overtone (the major third) is called ga. All 12 notes of the scale can be derived from these two intervals in several different ways, each of which produces significantly different relationships between the ratios that define each note.

The exact pitches used by Indian music are produced by what Mathieu calls a ga-blooded system (see diagram). A “spine” of four pas is generated off the initial tonic sa, then a ga is placed above each pa, and a komal ga (minor third) is placed below each pa. Because the minor third is the major third upside down, the resulting network of relationships reveals how all 12 tones of the scale can be generated from sa, pa, and ga.

This network becomes the basis for Mathieu’s theory of musical relationships, for it provides a map of the possibility-space available for musical composition. When he introduces the modes, he has you trace each of them through this network, so you can experience how they are derived from the overtones. From there he fragments and recombines the modes, making comments about his own experience as a composer working with each of these possibilities. He then expands beyond this network in two diametrically opposed directions: towards other microtonal nuances, such as those used in medieval European music and blues, and then into the world of Western equal-tempered music, which accepts blurred tuning in exchange for the chance to modulate to many different keys.

Mathieu sees equal temperament as a bargain in which something is lost and something is gained. He refers to this transition with phrases of mock-horror, such as “entering Babylon,” or “leaping from Paradise.” Ultimately, however, he argues that there is no real conflict. He shows us how much of the impact of tempered music comes from the different ways in which each tonal modulation clashes with the purer tunings used by Indian music. And he shows us that the possibility-space of Indian music is too vast to ever be exhausted.

Teed Rockwell has studied Indian classical music with Ali Akbar Khan and other great Indian musicians. He is the first person to play Hindustani music on the Touchstyle Fretboard.