Implementation of a Ten-Tone Equal Temperament System

Andrew Gula


Tracing back to the ancient Greeks, humans have always been interested in the “harmony” that music creates.  Throughout time, many composers like Du Fay, Monteverdi, and Schoenberg have strayed from traditional musical practices in the hope of developing a more expressive sound.  In this study, a system was created that is based on ten tones instead of twelve in an attempt to make a new expressive sound.

Music has endured many changes throughout the centuries.  As the world moves into the 21st century, is it possible that a new melodious sound is yet to be discovered?  Music we are currently familiar with is based on an equal temperament scale composed of twelve similar intervals.  Each note on a piano and its corresponding frequency can be used to represent x and y values.  Using the x and y values, a graph of the frequency spectrum of a piano can be generated, from which a formula can be derived.  Next, dividing the number twelve by ten and then adding the sums together yields the ten-tone system x values.  By substituting the new x values into the equation of the frequency spectrum, the frequencies for the notes of the ten-tone system can be found, conforming to new system of equal tone temperament.  Using a program called “Cycling ’74 MAX/MSP,” these new frequencies can be assigned to the notes on a keyboard, creating an instrument based on ten tones instead of twelve.  The resulting sound from the ten-tone instrument is very unique and yields intervals that the ear is not conditioned to hearing, excluding the fact that the notes are produced with a sine generator.

The research involves an interesting procedure that allows for further experimentation.  For example, this system can be applied to create intervals built on any other number imaginable, all of which all would be based a new equal temperament scale.  This study attempts to find a new direction for music by creating a system in which the notes in each octave are spread out over ten tones instead of twelve.  The limited attempts in this study were unsuccessful in creating a sound that was music to one’s ears.  However, with further experimentation, it is possible that this system could yield pleasing results. Though the system didn’t produce any satisfying results at the moment, it opened up a new procedure for the creation of a unique intervallic system.


Music, Composition, Acoustics

Full Text: Chromatic 12-Tone Scale The Decitone Chromatic Scale A Mary Had a Little Lamb Decitone PDF


  • There are currently no refbacks.