Microtonal Music - Traditional, Modern, Bizarre, and Beautiful

In our society, the Western musical system has become so dominant that it is often taken for granted.  The keys on the piano, the frets on a guitar, the holes and keys on woodwind instruments are all spaced certain distances apart to give exactly 12 notes per octave.

These intervals are even hard-coded into most computer software.  A lot of computer software, including MIDI and various synthesizers, are not easily capable of producing music at any pitch--they require complex manipulations and pitch-bending to produce sounds of different intervals.

Non-Western music does not always fit neatly into the 12 tone system that is the dominant one in our society.  Indian classical music, and the scales of Arab music, cannot be played within this system, because they have notes, scales, and musical intervals that cannot be meaningfully approximated in the 12 tone system without the essential character of the music being lost.

Typically, Arab music is played using quarter-tones, dividing the 12-tone system in half, effectively making it a 24-tone system.  Arab music uses the Oud, a guitar-like instrument without frets; because it is fretless, a musician can play any note, including the notes that don't fit into the frets on a Western guitar.

Nearby, the music of Byzantine chant uses an even more complex system, with intervals that don't even fit into a 24-tone division of the octave, including even finer divisions to be accurately represented.

The Sitar, used in Indian classical music, has adjustable frets that can be tuned to play different scales.  Each song will typically use a different set of notes with different intervals, many of which do not correspond neatly to the familiar intervals of Western music.  Indian classical music is a little trickier to approximate with any equal temperament.  For a full explanation I recommend Indian Classical Music: Tuning and Ragas, by Catherine Schmidt-Jones.

Most East Asian music centers around pentatonic scales, which can be well-represented in a 12 tone system.  But there are many caveats; some scales in Japanese traditional music include notes corresponding to the 7th harmonic, which cannot be accurately captured with a 12 tone scale.

In Western music, the building blocks of the scale are the whole step and half step.  Microtonal music though can have any number of other stepwise intervals.

Some that occur in various traditional musics include:

• Neutral step or 3/4 tone - This interval is roughly halfway between a whole step and half step, which is why it is sometimes called a 3/4 tone.  This interval occurs in Arab music, and intervals close to this width appear in the harmonic series as the difference between the 10th and 11th harmonics, and again the difference between the 11th and 12th harmonics.
• 2/3 Tone - This interval is narrower than the 3/4 tone but still wider than a half step.  It appears in many of the modes or scales in Byzantine chant.  In the harmonic series, this interval is similar in width to the difference between the 12th and 13th harmonics, and the difference between the 13th and 14th harmonics.
• Septimal whole tone - This interval is a little wider than a whole tone; it represents the difference between the 7th and 8th harmonics.  This interval occurs in any traditional music using the 7th harmonic, including Japanese music.

As you see, microtonal intervals do not need to be smaller than a half step.  When people think of microtonal music, they often think of quarter tones, which are half the size of a normal half step.  But microtonal music usually does not use such tiny intervals musically--instead it uses intervals within the typical range of sizes found in normal scales, but a little narrower or a little wider than what we are used to.

There is no single way to notate microtonal music.  Pictured above is a method, using semi-sharps and semi-flats, that can work well for some systems, including quarter tones and 31 tone equal temperament.  These two tunings are among the easiest of microtonal tunings to notate.

This method does not work for systems that distinguish between whole steps of different size, or that have more than 6 steps in between the two notes of a whole step.  Examples would be 22, 34, or 53 tone equal temperament.

Most Western music uses equal temperament, an equal division of the octave, for practical reasons.  Although equal temperament doesn't provide an exact match to the natural intervals, for certain numbers of divisions, the match is so close that it is hard to notice anything being off.

An overwhelming majority of Western classical, jazz, and pop music uses 12 tone equal temperament.  Any division of the octave into more than 12 equal steps (i.e. each step is smaller) is considered microtonal.  Here are some of the most notable microtonal equal temperaments:

• 19 tone - Probably the easiest and most popular of the equally tempered microtonal tunings, 19-ET is relatively easy to work with.  It can be imagined on a piano by dividing each white key into two notes.  People have also built guitars in this tuning.
• 22 tone - This tuning is interesting, but a little bit alien sounding.  It matches familiar intervals like fifths and thirds, but it has no whole tone, making scales a bit more complex!
• 31 tone - This is my personal favorite tuning to work with.  I encourage you to explore more about this particular tuning on my site 31et.com.
• 34 tone - This tuning allows you to play tonal western music.  I find it very challenging to work with because it has two distinct whole tones, one of which is wider than the other.
• 41 tone - This tuning adds a few more intervals beyond 31 tone; intonation on a few intervals is greatly improved.  Perfect fifths are highly in-tune, even more than in 12 tone music.  This tuning also distinguishes between the major and minor whole tone, meaning in a C-major scale, the interval between C and D is wider than the interval between D and E...this makes the system a bit more unwieldly and trickier to notate.
• 53 tone - This is a fine-tuning that goes beyond 41-tone, improving the matches to various natural intervals and harmonics, and adding an even greater array of intervals.  With very narrow steps and so many intervals though, I find this system a bit too much for me to wrap my mind around though.
• 72 tone - Who would use 72 tones?  Byzantine music, which has lived on in the liturgical chant of the Eastern Orthodox church.  Granted, this music doesn't use all 72 notes (that would be overwhelming), but the 72 tone framework provides a basis for theoretically understanding this music, which cannot be easily explained in terms of normal Western music theory.

Why these numbers?  It seems a bit random, but these numbers are actually a result of deep mathematical truths.  Why does it turn out that way?  I don't really know, but it just does.

After fiddling with numerous microtonal tunings I came to like 31-ET best of all.  I wrote an essay: Why 31 Tone Equal Temperament?  A quick summary:

• It plays both Western and Arab music gracefully.
• It's easy to notate in standard Western musical notation.
• It can be easily visualized on a piano keyboard.
• It closely matches most of the musical intervals up through the 11th harmonic.
• There is only one problematic interval that is out-of-tune or unusually difficult to hear or work with.  Most small tunings have much more.

Want to be convinced?  Listen for yourself!

Microtonal music does not need to sound alien or bizarre.  The fine-tuned intervals of microtonal music, instead of being used to play new and alien sounding intervals, can also be used to provide closer matches to the natural harmonics.

This results in music that has a clean and pure sound, sounding much more in-tune than music played in the 12-tone system we are used to.  This effect is particularly clear when listening to high-pitched instruments with a clear sound, like a flute.