## Harmonic Design and Efficient Manufacture

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I have always been fascinated by the harmonic series, to wit:

1/1, 1/2, 1/3, 1/4………..1/n

It turns up all the time in nature, and thus in calculus, where it is involved in some very beautiful mathematical series. Of course it turns up in music, where all harmonics are integer values (where the harmonic series got its name) and these numbers have been studied since the ancient Greeks, and perhaps before.

Lately I have been considering the construction of simple structures using pvc pipe, for instance I constructed a nice pvc microphone stand for my street music rig, it is light and stable and cost me about 15 bucks @ ace hardware. Plus it breaks down into small pieces.

Another thing I would like to construct are small shelters, like for instance a very small greenhouse structure ( a few feet tall) to maybe a shelter that is human sized or even event sized.

Now pvc pipe comes standard in 10 foot lengths so it is helpful to keep that in mind when designing your contraptions. But lets say you design something that requires a piece of pvc that is 4’7″ long. Well you cut that off a 10 foot piece twice and you are left with a 10 inch piece. Scrap, unless you can find a use for a small piece.

But if you think and design harmonically.

If you leave the pvc uncut you have a 10 foot section’

If you cut it in half you have 2 five foot sections

If you cut it equally in three you have 3 three foot 4 inch sections

If you cut it equally in four you have 4 2 foot 6 inch sections

If you cut it equally in five you have 5 2 foot (24 in) sections.

If you cut it equally in six you have 6 one foot 8 inch (20 in.) sections.

& etc.

So if you think harmonically (essentially fitting your design to harmonic nature, not the other way around) , and you are designing a structure that wants roughly 8 ft. ceilings, well maybe you would couple a half with a third, you would get 8 ft. 4 in ceiling, but you would have no waste. Every inch of your raw pvc would be used. If you did it the traditional way you might cut 4 five ft. sections from two pieces and four 3 ft. sections two others , but you would have 2 x 1 ft. waste. Or you could cut four eight ft. sections from four poles but you would have four 2 ft. sections of potential waste. Maybe you could cleverly design a use for these wastes or maybe not, but now you see the idea behind harmonic design.

The principle of harmonic design can be extended to other manufacturing processes that require division of a raw input.

Basically your use of the raw input is granular, and the smallest grain is the smallest division that you use in your production. At the completion of the cycle everything is used. No waste.

Smart readers will understand. Enough said.

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