Microtone

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The term microtone may have different meanings depending on the context in which it is used. Generally, it can mean any interval between two musical sounds that cannot be represented by an integer number of semitones, or, it can mean one one-millionth of a whole tone.

Practical Microtone Meaning

"Microtonal" music, in a broad sense, is any music composed and performed with any musical intervals outside of the set of those generally accepted in western music traditions. A microtonal interval, in generally speech, refers to such an interval, which cannot be broken down into standard western theoretical semitones. In more specific contexts, the meaning of this term might evaporate into that which is vaguely supported by other more specific or technical terms. Some music theorists with experience in xenharmonic music might tend to think of microtones as intervals smaller than semitones and therefore use a juxtaposed term, such as "macrotone" to describe an interval larger than a semitone but also not an integer number of semitones. Other music theorists within this field of study may avoid this distinction or avoid using the term to describe the field itself or the music or ideas used to compose the music therein. A literal definition has been constructed for use within a xenharmonic theoretical context, which is more intuitive, more specific, and of practical use (as a fine limit of precision).

Literal Microtone Meaning

The Microtone is an interval measure that can be considered as sufficiently precise for all thinkable musical and music-science purposes. Besides its high accuracy, it is of high neutrality since it favors neither twelve-tonality nor even the octave. Nevertheless its relevance for practical application in music is low due to the incompatibility with "human scale". Humans are not good at big numbers and have only limited pitch perception (the Just-noticeable difference (JND) is around 6 cents).

One actual microtone (1µt) would be defined as one millionth of the tone:

Some numerical impressions (laughter permitted)
Name Size Size (¢, 12 decimals) Size (in cents (¢), scientific notation)[1]
Tone (=9/8) 204¢ 203.910,001,730,775 2.03910001730774835488973465474759621023555E+2
Millitone 204m¢ 0.203,910,001,731 2.03910001730774835488973465474759621023555E-1
Microtone 204µ¢ 0.000,203,910,002 2.03910001730774835488973465474759621023555E-4
  1. The values were produced by High precision calculator.

The Microtone Challenge

A microtone is indeed a very small interval: 4,904 microtones make one cent, and 5,884,949 an octave.

Helmholtz had argued that pitches spaced less than 5 cents are generally not possible for a human to perceive as different, but the difference itself is easy to perceive as beats of constructive/destructive interference between the two slightly different waveforms.

However, two sounds different only by only 1µt produce a very slow beat; depending on the frequency one have to wait more or less to recognize it. The beat frequency is

  • at the upper limit of the hearing range (20 kHz) 7 minutes
  • in the range of the highest acoustic sensibility (4 kHz) 35 minutes
  • at the lower limit of the hearing range (16 Hz) 7 days

Given this, will it be ever possible to make a microtone experience at all?

According to Adam Neely, the slowest perceivable beat humans can generally distinguish is about 33 bpm. Therefore, the general lowest limit of human perception between tones is roughly 250 µt, or about 0.05 cents. A more practical approximation might be to take 33 bpm of interference beats at 4 kHz, which is about 0.25 cents, as a practical limit of perceived difference between two simultaneously performed tones. With that in mind, it seems that adjustments in tuning of practical music on the order of microtones is necessarily imperceptible even to the most veteran ears.

See also

External links