This blog is dedicated to the sublime instruments called nose flutes and which produce the most divine sound ever. We have chosen to discard all the native models from S. Pacific and Asia, for they need fingering to be played. We'll concentrate on "buccal cavity driven" nose flutes : the well patented and trademarked metal or plastic ones, plus, by a condemnable indulgence, some wooden craft or home-made productions.

Aug 18, 2011

Mathematics : how many colors ?

Everybody knows that you can pick your Humanatone among 8 colors : red, orange, yellow, green, blue, violet plus pink and bordeaux/purple.

But how many different colors for the german plastic Nasenflöte ? I do not know which is the maker (if someone knows it, please let me know!). It is mainly distributed by Gewa and Arnold Stölzel, and wear a swan as a logo :

So, how many colors for the "swan" nose flute ? These Nasenpfeifen are two colored. And there are 13 different colors : white, yellow, orange, red, bordeaux, purple, violet, blue, green plus 4 scarcer colors : pastel blue, pink, silver and gold.
The trick is that no swan flute has got its two parts by the same color.

The answer is (n x n) - n.
(13 x 13) - 13 gives the choice between 156 different flutes to the public !

Oh! For sure, with online shops, you are never able to choose the color...They generally say "Assorted colors, sorry, no choice".
So, how many flutes in average a compulsive collector has to buy to get the complete collection (according to a homogeneous distribution of colors...)?

The answer is n x ( Ln(n) + γ) where γ is the Euler-Mascheroni constant (~0,577).
That is 878 swan nose flutes !

Very interesting post, isn't it ?

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