Logharmonic series: Difference between revisions
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= matharmonic series = | = matharmonic series = | ||
The e-logharmonic series can be approximated by pitches taken from the mathematical harmonic series: | The e-logharmonic series can be approximated by pitches taken from the [[wikipedia:Harmonic_series_(mathematics)|mathematical harmonic series]] (as opposed to the musical harmonic series): | ||
1 | <math> | ||
\qquad H(1) = 1 \\ | |||
\qquad H(2) = \frac{3}{2} = 1 + \frac{1}{2} \\ | |||
\qquad H(3) = \frac{11}{6} = 1 + \frac{1}{2} + \frac{1}{3} \\ | |||
\qquad H(4) = \frac{25}{12} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} \\ | |||
\qquad … | |||
</math> | |||
We can call this approximating series the ''matharmonic series''. | |||
The difference between pitches of the e-logharmonic series and the matharmonic series approaches the [[wikipedia:Euler–Mascheroni_constant|Euler-Mascheroni constant]], <span><math>≈ 0.5772156649</math></span>, which represents the difference between the natural logarithm and the mathematical harmonic series. | |||