SCALE TYPES

Non 12-Tone Equal Tempered (Based on a mathematical factor)

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In this series, the listener is exposed to different types of equal-tempered scales.  Our western chromatic or 12-tone equal tempered scale is mathematically derived.  Non-12 equal tempered scales are also mathematically derived, but their number of notes per octave is different which results in audible distances/differences between neighboring notes, and this creates the character of the scale

Currently, there are four (non-12 equal) instruments that have been made:

5-tone equal, 7-tone equal, 8-tone equal, and 9-tone equal.

 

Common Details that Apply to All Instruments

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

Bars: African Padauk

Resonator: Poplar

Finish: Semi-gloss clear coat (waterbase)

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This instrument is available for rental from
LA Percussion Rentals

5-Tone Equal Tempered

CCBANTA Model: C311ET5 - 5 Tone Equal Marimba

Model C311-ET5 Specification

2-Octave / 5-tone equal-tempered scale

No. of Notes: 11

Dimensions: W: 30 x D: 14" x H:14-1/2"

Weight: 14.5lbs.

Scale Technical Definition: 5-Tone Equal

  • Octave determination: 5th root of 2 = a factor of 1.14869835

  • Number of notes per octave = 5

  • Number of cents per octave = 1200

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

Scale Character

5-Tone Equal has notes that relate to 12-Tone Equal.  Scale character can be heard when two note intervals with x no. of notes in between.

5-Tone Equal / Scale - Chris Banta
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5-Tone Equal / Scale in Unison Octaves - Chris Banta
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5-Tone Equal / Improv - Chris Banta
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5-Tone Equal / Composition - Chuck Jonkey
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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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This instrument is available for rental from
LA Percussion Rentals

7-Tone Equal Tempered

CCBANTA Model: C315ET7 - 7 Tone Equal Marimba

 Model C311-ET7 Specification

2-Octave / 7-tone equal-tempered scale

No. of Notes: 15

Dimensions: W: 40" x D: 14" x H: 14-1/2"

Weight: 18.5lbs.

Scale Technical Definition: 7-Tone Equal

  • Octave determination: 7th root of 2 = a factor of  1.1040895

  • Number of notes per octave = 7

  • Number of cents per octave = 1200

  • Number of cents between notes = 171.43 (1200/7)

Scale Character

7-Tone Equal has no notes that relate to 12-Tone Equal. Scale character can be heard when two note intervals with x no. of notes in between. 

7-Tone Equal / Scale - Chris Banta
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7-Tone Equal / Unison Octaves - Chris Banta
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7-Tone Equal / Improv - Chris Banta
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7-Tone Equal / Composition - Chuck Jonkey
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7-Tone Equal / Interval: 1 Bar Inbetween - Chris Banta
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7 Tone Equal / Interval: 4 Bars Inbetween - Chris Banta
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7-Tone Equal / Interval: 2 Bars inbetween - Chris Banta
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7 Tone Equal / Interval: 5 Bars Inbetween - Chris Banta
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7 Tone Equal / Interval: 3 Bars Inbetween - Chris Banta
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This instrument is available for rental from
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8-Tone Equal Tempered

CCBANTA-Model-C317-ET8-2web.jpg

Model C317-ET8 Specification

2-Octave / 8-tone equal-tempered scale

No. of Notes: 17

Dimensions: W: 44-1/2" x D: 14" x H: 14-1/2"

Weight: 19.5lbs.

Scale Technical Definition: 8-Tone Equal

  • Octave determination: 8th root of 2 = a factor of  1.090507733

  • Number of notes per octave = 8

  • Number of cents per octave = 1200

  • Number of cents between notes = 150 (1200/8)

 

Scale Character

The 8-tone equal is based on the 12-tone equal's minor 3rds or diminished scale which consists of four tones: C, D#, F#, and A or notes 1, 3, 5, and 7 (as shown in the photo above).  If we move up one step and only play notes 2, 4, 6, and 8, then the second diminished scale is revealed.  Both scales are demonstrated in the audio example -->.

When the 1, 3, 5, 7 and 2, 4, 6, 8 notes are combined in their numerical order as 1, 2, 3, 4, 5, 6, 7, 8, then the half-diminished equal scale is more easily understood as demonstrated in the first audio example above.

8-Tone Equal - Scale - Chris Banta
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8-Tone Scale - Unison Octaves - Chris Banta
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8-Tone Equal - Scale Unisons - Faster - Chris Banta
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8-Tone Equal - Ascending Pattern - Chris Banta
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8-Tone Equal - Improv - Chris Banta
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8-Tone Equal - Two Half-Diminished Scales - Chris Banta
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This instrument is available for rental from
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9-Tone Equal Tempered

CCBANTA-Model-C319-ET9-web.jpg

Model C319-ET9 Specification

2-Octave / 9-tone equal-tempered scale

No. of Notes: 19

Dimensions: W: 49-1/4" x D: 14" x H: 14-1/2"

Weight: 19.5lbs.

Scale Technical Definition: 9-Tone Equal

  • Octave determination: 9th root of 2 = a factor of  1.08005974

  • Number of notes per octave = 9

  • Number of cents per octave = 1200

  • Number of cents between notes = 133.333333 (1200/9)

Scale Character

The 9-tone equal is based on the 12-tone equal's major 3rds or augmented scale which consists of three tones: C, E, and G# or notes 1-4-7 (as shown in the photo above). This would be considered the first 3rd

 

Second 3rd: If we move up one step and only play notes 2, 5, 8, then the second augmented scale is revealed. 

 

Third 3rd: Finally, if we move up one more step and only play notes 3, 6, 9, then the third augmented scale is revealed. 

The top audio example is how the 9-tone scale sounds when these three groups are combined.

The two audio examples on the bottom provide the flavor of a two-note interval - one in the high octave, one in the low octave.

9-tone equal scale - Chris Banta
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9-tone equal octave scale - Chris Banta
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9-tone equal improv No. 1 - Chris Banta
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9-tone equal improv No. 2 - Chris Banta
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9-Tone Equal Aug Scale No 1 (Notes: 1-4-7) - Chris Banta
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9-Tone Equal Aug Scale No 2 (Notes 2-5-8) - Chris Banta
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9-Tone Equal Aug Scale No 3 (Notes 3-6-9) - Chris Banta
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9-tone two note interval-high octave - Chris Banta
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9-tone two note interval-low octave - Chris Banta
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​NOTE:

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)

12-2-3-4-6-SCALES-CHART.jpg

43-Tone Equal Tempered

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This instrument is available for rental from
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Harry Partch "Boo" Recreation (2017)

1-1/2-Octave / 43-tones per octave equal-tempered scale

No. of Notes: 64

Dimensions: W: 101" x H: 60.25" x D: 35"

Weight: TBD

Year of Construction: 2017

Client: John Schneider (Partch Ensemble)

Scale Technical Definition: 43-Tone Equal

  • Octave determination: 43rd root of 2 = a factor of 1.0162503

  • Number of notes per octave = 43

  • Number of cents per octave = 1200

  • Number of cents between notes = 27.9 (1200/43)

Boo-Improv1-2-players
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Boo-Improv1-2-players-Reverb
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Boo-Improv2-2-players
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Boo-Improv2-2-players-Reverb
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