3.2 Tuning and Temperament 07

3.2 Tuning and - Tuning and Temper ament An over view Review of Pythagor ean tuning • Based on str ing lengths • Octave r elationship is always

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Unformatted text preview: Tuning and Temper ament An over view Review of Pythagor ean tuning • Based on str ing lengths • Octave r elationship is always 2:1 • Fifth r elationship is 3:2 • “pur e” or “just” inter vals have no beats Building a Pythagor ean scale…. • Star t with C = f =1 • C to G is a fifth; G = 3/2 • G to D is a fifth; D = 3/2 · 3/2 = 9/4; dr op the octave and it becomes 9/8 • D to A is a fifth; A = 9/8 · 3/2 = 27/16 • A to E is a fifth; E = 27/16 · 3/2 = 81/32; dr op the octave and it becomes The pr oblem… • C to E inter val (Pythagor ean thir d) is 81/64 - this r atio is too wide • Pur e thir d inter val is 5/4, or 80/64 • Using A=440 H z as a base note: (80/64) A=440, C# =550 (81/64) A=440, C#=556.875 • The small differ ence 80/81 is called the syntonic comma Another pr oblem of inter nal consistency… • Star t with C and use 3/2 r atio to calculate the fifth (G), then go up another fifth, and continue until 12 fifths ar e built up • You “should” get back to wher e you star ted - but you don’t!...
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This note was uploaded on 07/24/2011 for the course MUS 3930 taught by Professor Bindell during the Fall '07 term at University of Central Florida.

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3.2 Tuning and - Tuning and Temper ament An over view Review of Pythagor ean tuning • Based on str ing lengths • Octave r elationship is always

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