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Literature:Elements of Harmony: Difference between revisions
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'''Motivation for log''': Assume strings 1 and 2 have equal tension and thickness, and have lengths $L_1$ and $L_2$ respectively. Find a function $\log$ that, given the ratio between $L_1$ and $L_2$, measures the corresponding subjective difference in pitch, i.e. is an isomorphism from the multiplicative group of positive real numbers to the additive group of real numbers. | '''Motivation for log''': Assume strings 1 and 2 have equal tension and thickness, and have lengths $L_1$ and $L_2$ respectively. Find a function $\log$ that, given the ratio between $L_1$ and $L_2$, measures the corresponding subjective difference in pitch, i.e. is an isomorphism from the multiplicative group of positive real numbers to the additive group of real numbers. | ||