MARIMBAS
Non-12 Equal Tempered Scales
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.
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Currently, there are four (non-12 equal) instruments that are available: 5-tone equal, 7-tone equal, 8-tone equal, and 9-tone equal.
Basic 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)
Each instrument come with a pair of mallets.
5-Tone Equal Tempered
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.
Price: $385 (Plus packaging and shipping)
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Scale Technical Definition: 7-Tone Equal
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Octave determination: 5th root of 2 = a factor of 1.14869835
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Number of notes per octave = 5
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Number of cents per octave = 1200
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Number of cents between notes = 240 (1200/5)
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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.
7-Tone Equal Tempered
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.
Price: $525 (Plus packaging and shipping)
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Scale Technical Definition: 7-Tone Equal
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Octave determination: 7th root of 2 = a factor of 1.1040895
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Number of notes per octave = 7
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Number of cents per octave = 1200
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Number of cents between notes = 171.43 (1200/7)
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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.
8-Tone Equal Tempered
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.
Price: $595 (Plus packaging and shipping)
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Scale Technical Definition: 8-Tone Equal
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Octave determination: 8th root of 2 = a factor of 1.090507733
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Number of notes per octave = 8
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Number of cents per octave = 1200
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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 -->.
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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.
9-Tone Equal Tempered
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.
$665 (Plus packaging and shipping)
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Scale Technical Definition: 9-Tone Equal
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Octave determination: 9th root of 2 = a factor of 1.08005974
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Number of notes per octave = 9
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Number of cents per octave = 1200
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Number of cents between notes = 133.333333 (1200/9)
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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.
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The top audio example is how the 9-tone scale sounds when these three groups are combined.
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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.
On the Drawing Board - Other Non-12 Equal Tempered Scales
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Model: C321-ET10
(10-Tone Equal - two octaves: 10+10+1 = 21 notes x $35/note = $735) -
Model: C323-ET11
(11-Tone Equal - two octaves: 11+11+1 = 23 notes x $35/note = $805) -
Model: C327-ET13
(13-Tone Equal - two octaves: 13+13+1 = 27 notes x $35/note = $945)
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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:
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2-Tone Equal (based on the flatted 5th or Tritone) - C, F#, C
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3-Tone Equal (based on major 3rds) - C, E, G#, C
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4-Tone Equal (based on minor 3rds) - C, D#, F#, A, C
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6-Tone Equal (based on the 2nd or whole-tone steps) - C, D, E, F#, G#, A#, C
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12-Tone Equal (based on half-steps) - C, C#, D, D#, E, F, F#, G, G#, A, A#, B, CNote: A
A 12-Tone Equal "in-line" bar layout (having the accidentals incorporated in with the naturals) that visually demonstrates the above scales, is available as a Model: C325-ET12 (12+12+1 = 25 x $35/note = $875)