Pianotech

Roshan Kakiya's Expanding/Contracting Temperament (ECT)



Number of Keys

Number of Keys = 88.

My ECT is designed for pianos that have a keyboard with 88 keys.



Number of Semitones

Number of Semitones = Number of Keys − 1 = 88 − 1 = 87.



Number of Spaces between Each Semitone

Number of Spaces between Each Semitone = Number of Semitones − 1 = 87 − 1 = 86.



Number of Spaces between Each Semitone for Expansion and Contraction

Number of Spaces between Each Semitone for Expansion and Contraction = Number of Spaces between Each Semitone / 2 = 86 / 2 = 43.



Widest Semitone

Widest Semitone = A0-A#0 and B7-C8 = Pure Fifth Equal Temperament Semitone = 1200 × log₂(3 / 2) / 7 = 100.279285838 cents.



Narrowest Semitone

Narrowest Semitone = E4-F4 = Pure Octave Equal Temperament Semitone = 1200 × log₂(2) / 12 = 100.000000000 cents.



Semitone Multiplier for Expansion and Semitone Divisor for Contraction

Semitone Multiplier for Expansion and Semitone Divisor for Contraction = (Widest Semitone / Narrowest Semitone)^{1 / Number of Spaces between Each Semitone for Expansion and Contraction} = (Pure Fifth Equal Temperament Semitone / Pure Octave Equal Temperament Semitone)^{1 / Number of Spaces between Each Semitone for Expansion and Contraction} = {[1200 × log₂(3 / 2) / 7] / [1200 × log₂(2) / 12]}^{1 / 43} = 1.000064862.



Size of Each Semitone

Cents

Frequencies

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Roshan Kakiya
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Attachment(s)

Roshan Kakiya's Expanding ∕ Contracting Temperament (ECT)...zip   107 KB 1 version