Why are there 12 notes? Why do some intervals sound more consonant than others? Why do major chords and minor chords have such different characters? Why are notes an octave apart given the same name? What does it actually mean to be “in tune”? To address these questions, we need to understand musical pitch in a new way.

 

My aim is to allow musicians to have a greater understanding of musical pitches than one gets from conventional music classes. I would like to see more composers explore alternative intonation. Music from other periods or cultures could be performed in a more authentic intonation. Singers and musicians will be more willing to adjust their pitch to where it actually sounds best, instead of tending to follow the piano or the electronic tuner. Instrument designers and builders will find ways to build more flexibility into new or existing instruments. And piano tuners will be more willing to break ranks and vary the way they tune pianos.

 

Musical pitch has always intrigued me. The question of where this system of notes originated was never answered adequately by music classes. I was fascinated to learn that historic tuning systems could actually sound more consonant than modern tuning. When I would have occasion to hear exotic music from the East, it was plain to me that some of the notes were “in the cracks”, somewhere between the notes on the piano.

 

This led me to eventually choose a career as a piano tuner, as well as leading me to compose music for unusual tuning systems. I’m excited by the world that opened up to me by tuning in different ways. However, it is frustrating how little other musicians seem to understand the subject. If I try to suggest to my piano tuning clients that they try a different temperament on their piano, they typically have no clue what I am talking about.

 

Others seem to know about alternative temperaments, but think of it as merely an archaic curiosity. People are reluctant to change the status quo, for fear that the music will sound “out of tune.” What is often not understood is everything we play is already out of tune in one way or another. All tunings involve some sort of compromise.

 

Alternative tunings are not limited to historic temperaments or Eastern music. For composers, writing music conceived of in a completely alien tuning system is too rarely considered. When it is done, it is often limited to “quarter tones,” overlaying extra notes onto our existing system rather than starting from scratch with a whole new tuning. This is definitely a way to make new music become something really new. It seems logical and inevitable to me that musical pitch will continue to evolve, just as it has throughout history.

 

Tuning can be a difficult subject to explain briefly. Musicians have their own language of music theory and music terminology. The terminology of the physics student or the mathematician may be foreign to the musician. Attempts to bridge this gap are often filled with off- putting math. I will attempt to make the underlying numerical relationships between musical notes accessible to musicians without equations or calculations. The occasional example using simple arithmetic will be presented, but it will be minimal.

 

While it will be helpful if the reader has a basic knowledge of music theory, I do include a crash course in music theory for non-musicians. Those with a basic knowledge may still find this interesting, as I try to explain the basics of music with a fresh perspective. The remainder of this book is outside the realm of a conventional music class. Whereas music theory takes the notes of the scale and their tuning as a given, I will be starting with a blank slate. An infinite number of possible notes can be used. Definitions of such familiar terms as “octave” will be different then given in a music class.

 

Tuning is a subject mostly understood by various specialists. Piano tuners understand beat rates and coinciding partials. Early music buffs know about various historical temperaments. Ethnomusicologists study intonations used by various cultures. Microtonal composers use a host of new or experimental tunings. Physics students know about vibrations and wavelengths.

 

The average musician has little understanding of any of these subjects. The notes of the 12 tone equal tempered scale are presented as though they are the only available system of tuning. The question of whether these particular pitches offer the best possible sound for a given piece of music is rarely considered.

 

In practice, musicians do deviate a great deal from precise equal temperament. Singers and most instruments have the ability to vary their pitch slightly, intuitively placing it where it sounds best. My hope is to allow musicians and singers to do so intentionally, and not let the pitch of the piano, of the electronic tuning device, to dictate what is supposedly “in tune”.

 

There are big obstacles to writing and playing music in new or experimental tunings. The instruments themselves are the first obstacles. The spacing of frets on a guitar or the tone holes on a woodwind are designed to facilitate 12 tones per octave. If one wanted, for example, 13 equally spaced notes per octave, most instruments would have to be modified. This is one reason that most microtonal musicians work with electronic instruments.

 

If one’s instrument is not locked into a specific pitch (for example a voice or violin), an even greater obstacle still exists. We lack the ear training to sing or play the more unfamiliar notes. When I first started exploring intervals such as the neutral third (half way between a major and minor third), I discovered that singers were hard pressed to find these pitches with their voice. One singer described having to sing a minor third and then tweak the note a little higher. Of course, a singer of Arabic music would have no such difficulty.

 

We lack the nomenclature to name the notes of an alien tuning system. Every tuning system requires its own unique terminology. This is obvious with a system of more than 12 notes per octave. It can even be a problem with fewer notes. For example, if we had ten equal steps per octave, or eleven? How would we even identify the notes?

 

These are not insurmountable obstacles. String Quartets have played music with 31 tones to the octave. Singers have learned to use 72 tones to the octave. Guitars have been refretted for 19 tones to the octave. Pianos have been retuned to Siamese and Javanese scales. The list goes on; I can only hope to scratch the surface.