TheLipps–Meyer law, named forTheodor Lipps (1851–1914) andMax Friedrich Meyer (1873–1967), hypothesizes that the closure ofmelodic intervals is determined by "whether or not the end tone of the interval can be represented by the number two or apower of two",^[1] in the frequency ratio between notes (seeoctave).

"The 'Lipps–Meyer' Law predicts an 'effect of finality' for a melodic interval that ends on a tone which, in terms of an idealized frequency ratio, can be represented as a power of two."^[2]

Thus the interval order matters — aperfect fifth, for instance (C,G), ordered⟨C,G⟩, 2:3, gives an "effect of indicated continuation", while⟨G,C⟩, 3:2, gives an "effect of finality".

This is a measure ofinterval strength or stability and finality. Notice that it is similar to the more common measure of interval strength, which is determined by its approximation to a lower, stronger, or higher, weaker, position in the harmonic series.

The reason for the effect of finality of such interval ratios may be seen as follows. If${\displaystyle F=h_2/2^n}$ is the interval ratio in consideration, where${\displaystyle n}$ is a positive integer and${\displaystyle h_2}$ is the higher harmonic number of the ratio, then its interval insemitones can be determined by taking the base-2logarithm${\displaystyle I=12{\log }_2(h_2/2^n)=12{\log }_2(h_2)-12n}$. For example, a ratio of 3:2 gives${\displaystyle I\approx 7.02}$, about seven semitones, and a ratio of 4:3 gives${\displaystyle I\approx 4.98}$, about five semitones. The difference of these terms is theharmonic series representation of the interval in question (using harmonic numbers), whose bottom note${\displaystyle 12n}$ is a transposition of thetonic byn octaves. This suggests why descending interval ratios with denominator a power of two are final. A similar situation is seen if the term in the numerator is a power of two.^[3][4]

• Consonance and dissonance
• Intervals (music)

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