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Melodic Sequence

If a_1, a_2, a_3, ... is an artistic sequence, then 1/a_1, 1/a_2, 1/a_3, ... is a melodic sequence. The recurrence relation obeyed by melodic series is

b_(i+3)=(b_ib_(i+2)^2)/(b_(i+1)^2)+(b_(i+2)^2)/(b_(i+1))-b_(i+2).

See also

Artistic Sequence

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References

Duffin, R. J. "On Seeing Progressions of Constant Cross Ratio." Amer. Math. Monthly 100, 38-47, 1993.

Referenced on Wolfram|Alpha

Melodic Sequence

Cite this as:

Weisstein, Eric W. "Melodic Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MelodicSequence.html

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