Triangulharmonic series: Difference between revisions
Cmloegcmluin (talk | contribs) Created page with "The triangulharmonic series is a subset of the harmonic series: only the harmonics which are [https://en.wikipedia.org/wiki/Triangular_number triangular nu..." |
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<math>1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ...</math> | <math>1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ...</math> | ||
Essentially, first you skip 1 harmonic, then 2 harmonics, then 3, then 4, then 5, etc. So | Essentially, first you skip 1 harmonic, then 2 harmonics, then 3, then 4, then 5, etc. So its unreduced intervals are [[Generalized_superparticulars|superbiparticular]] ratios: <span><math>\frac{3}{1}, \frac{4}{2}, \frac{5}{3}, \frac{6}{4}...</math></span> | ||
The formula for the nth triangular number is <span><math>\frac{n^2 + n}{2}</math></span>. | The formula for the nth triangular number is <span><math>\frac{n^2 + n}{2}</math></span>. | ||
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The next occurrence is at 121278 and 242556, which produces a 204 note scale. This scale and beyond are decreasingly likely to be of much interest. | The next occurrence is at 121278 and 242556, which produces a 204 note scale. This scale and beyond are decreasingly likely to be of much interest. | ||
== References == | |||
<references /> | <references /> | ||
[[Category:Harmonic series]] | |||
[[Category:Xenharmonic series]] | |||