# what mathematical rules can we use to generate paradiddles? [closed]

What mathematical rules can we use to generate (single, double, triple) paradiddles? Perhaps even paradiddles with odd meters.

thanks! k

• Do you want "functions" or rules for generating patterns that would likely make music. – Randy Zeitman Aug 23 '19 at 16:13
• This is more like an invitation to brainstorm than a question. Can you explain in more detail what you're trying to achieve, and what you need help with? – Your Uncle Bob Aug 23 '19 at 23:03
• @ggcg and Your Uncle Bob Thanks, I will update the question. – tEdör Aug 24 '19 at 8:17
• Crowdsourcing software development, getting domain experts to work for free... How about hiring someone and paying for it? – piiperi Reinstate Monica Aug 24 '19 at 11:34
• @piiperi - How familiar are you with open source and websites like Github? (I end up consulting code stored in it and assembled by "domain experts [working] for free" quite a bit of the time.) – Dekkadeci Aug 24 '19 at 13:16

If you really want to go full math-rock, you could always put notes on the beats given by floor( sqrt(2) * n), for n = 1, 2, 3, ... This will generate notes on beats

1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, ...

``````X: 1
K: Cmaj
M:
L: 1/4
A A z A A z A A A z A A z A A A z A A z A
``````

Mathematically, it can be proven that this pattern will never precisely repeat itself. It will never have two rests back-to-back. On average, there will be a note on about 1/sqrt(2) ≈ 70% of the beats.

Similar non-repeating patterns could be generated by replacing sqrt(2) with any irrational number greater than 1. A rational number would cause a pattern that repeated itself eventually, effectively acting as a polyrhythm where the number of the notes in the faster tuplet is given by the denominator of the rational number.

• An amusing idea though you would have to listen for ever to differentiate an irrational value from a close rational approximation. Even if it has not repeated as the universe comes to an end, it might be rational. Conversely, it might have been repeating up to the end of the universe and be just about to do something different as it ends. – badjohn Aug 23 '19 at 18:27
• thanks @Michael Seifert. Very interesting, I will try to put this in the code and listen. – tEdör Aug 24 '19 at 7:58
• I think this method needs a separate way to introduce accents (another such beat generator for accents instead of notes?), but a beat generator derived from a mathematical seed sounds like a great idea! – Dekkadeci Aug 24 '19 at 13:21
• @Dekkadeci. Thanks, accents are also good to have, – tEdör Aug 24 '19 at 20:54
• @Michael Seifert. Is there a proper name for this 'full math-rock' equation? – tEdör Aug 24 '19 at 20:56