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The Measurement of Musical Tone. WILLIAM H. STUBBINS. PRESENT. METHODS and techniques for the measurement of sound per- mit the analysis of musical tone as.
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q = f ( z 1 , … , zN )
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1 1
marginal productof (^11) z f q z MP = ∂
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1
2 1
(^1) z
f z z z
AP = q = (^1 , )
z 2
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2 1 2 1 2
dz MP dz MP d z z
f dz z
f dq (^21) 1
2
1 q q MP
MP dz
MRTS =− dz = (^1) = (^0)
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i i
f z
f
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2 11 0 1
2 1
(^1) = ≤ ∂ =∂ ∂
∂ (^) f z
f z
MP^22 = 22 ≤ 0 ∂ =∂ ∂
∂ (^) f z
f z
MP 2 2
2
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f ( tz 1 , tz 2 ) = atz 1 + btz 2 = t ( az 1 + bz 2 ) = tf ( z 1 , z 2 )
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z 1
z 2
q 1 q^2 q^3
slope = -a/b
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z 1
z 2
q 1
q 2
q 3
q 3 /a
q 3 /b
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