Brief Overview of 12-Tone Equal Tempered


Our Western music system utilizes the mathematically-derived 12-tone equal tempered or chromatic system which yields 12-notes between the octaves.  There are familiar elements in this system:

  • A letter has been assigned to each of the 12 tones along with a system of sharps and flats (e.g. C, C#, D, D#, E, F, F#, G, G#, A, A#, and B) which is derived from the layout of the piano keyboard.   

  • White keys represent the naturals (C, D, E. F, G, A, B). 

  • Black keys represent the accidentals C#, D#, F#, G#, A#).

  • The equal-tempered construct means that the note-to-note relationship is such that a composition or song can be transposed and be equally performed in any of the twelve keys.  "Transposing" is the basic magic of the 12-tone equal system.

  • In 12-tone equal, the interval relationships (seconds, third, fourths, fifths, sixths, and sevenths) are always the same relationship regardless of the tonic key a song is composed in.


Scale Technical Definition: 12-Tone Equal Tempered

  • Octave determined by the 12th root of 2 factor = 1.059463

  • Number of notes per octave = 12

  • Number of cents per octave = 1200

  • Number of cents between notes = 100 (1200/12)


Brief Overview of Non-12-Equal


Non-12 equal tempered scales function the exact same way as 12-tone equal, but their number of notes per octave is different.  This leads to different audible distances between neighboring notes creating the character of the scale.  The 5-tone equal and 7-tone equal marimbas are representations of the non-12 system.   

Non-12 equal scales don't utilize letters for pitches, instead they use numbers.

  • ​Each marimba (below) has a two-octave range.

  • Their lowest or starting pitch is Tenor C (C3) - notated as "1".

  • Their middle (1) pitch is middle C (C4)

  • Their highest pitch is treble C (C5)

5-Tone Equal Tempered

Model C311-ET5

2-Octave / 5-tone equal-tempered scale

No. of Notes: 11

Range: Tenor C (C3) to Treble C (C5)

Bars: African Padauk

Resonator: Poplar

Finish: Semi-gloss clear coat, waterbase

Dimensions: 29 L x 16" D x 13-1/2" H

Weight: 17lbs.

Pair of yarn-wound mallets

$385 (Plus packaging and shipping)

Scale Technical Definition: 5-Tone Equal

  • Octave determined by the 5th root of 2 factor =  1.1486958

  • Number of notes per octave = 5

  • Number of cents per octave = 1200

  • Number of cents between notes = 240 (1200/5)

5-Tone Equal / Improv - Chris Banta
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5-Tone Equal / Scale - Chris Banta
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5-Tone Equal / Composition - Chuck Jonkey
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5-Tone Equal / Scale in Unison Octaves - Chris Banta
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Scale Character

Two note intervals with x no. of notes in between

5-Tone Equal / Interval: 1 Bar Inbetween - Chris Banta
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5-Tone Equal / Intervals: 2 Bars Inbetween - Chris Banta
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On the Drawing Board - Other Non-12 Equal Tempered Scales

The following scales are in design.  Once constructed, they will be posted to this website.

  • 8-Tone Equal (has 17 notes)

  • 9-Tone Equal (has 19 notes)

  • 10-Tone Equal (has 21 notes)

  • 11-Tone Equal (has 23 notes)

  • 13-Tone Equal (has 27 notes)

It is interesting to note that the 12-Tone Equal Tempered scale actually contains five equal-tempered scales within it.  This is easily determined because the number 12 can be equally divided in five ways, as follows:

  • 2-Tone Equal (based on the flatted 5th or Tritone) - C, F#, C

  • 3-Tone Equal (based on major 3rds) - C, E, G#, C

  • 4-Tone Equal (based on minor 3rds) - C, D#, F#, A, C

  • 6-Tone Equal (based on the 2nd or whole-tone steps) - C, D, E, F#, G#, A#, C

  • 12-Tone Equal (based on half-steps) - C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C