Editing Periodic function (section)

==Calculating period==
Consider a real waveform consisting of superimposed frequencies, expressed in a set as ratios to a [[fundamental frequency]], f: F = {{frac|1|f}}{{nnbsp}}[f{{sub|1}} f{{sub|2}} f{{sub|3}} ... f{{sub|N}}] where all non-zero elements ≥1 and at least one of the elements of the set is 1. To find the period, T, first find the least common denominator of all the elements in the set. Period can be found as T = {{frac|LCD|f}}. Consider that for a simple sinusoid, T = {{frac|1|f}}. Therefore, the LCD can be seen as a periodicity multiplier.

* For set representing all notes of Western [[major scale]]: [1 {{frac|9|8}} {{frac|5|4}} {{frac|4|3}} {{frac|3|2}} {{frac|5|3}} {{frac|15|8}}] the LCD is 24 therefore T = {{frac|24|f}}.
* For set representing all notes of a major triad: [1 {{frac|5|4}} {{frac|3|2}}] the LCD is 4 therefore T = {{frac|4|f}}.
* For set representing all notes of a minor triad: [1 {{frac|6|5}} {{frac|3|2}}] the LCD is 10 therefore T = {{frac|10|f}}.

If no least common denominator exists, for instance if one of the above elements were irrational, then the wave would not be periodic.<ref>{{cite web |last=Summerson |first=Samantha R. |date=5 October 2009 |title=Periodicity, Real Fourier Series, and Fourier Transforms |url=https://www.ece.rice.edu/~srs1/files/Lec6.pdf |access-date=2018-03-24 |url-status=dead |archive-url=https://web.archive.org/web/20190825162000/https://www.ece.rice.edu/~srs1/files/Lec6.pdf |archive-date=2019-08-25}}</ref>