File:1957Barbour strahle 3-13.svg
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Summary
| Description |
English: Diagram of a geometrical and fractional approximation of published by J. Murray Barbour in "A Geometrical approximation to the Roots of Numbers" (American Mathematical Monthly vol. 64, 1957. p.1-9) based on Daniel Stråhle's construction for determining string lengths in his musical tuning of 1743. The construction in blue shows Barbour's conditions relaxed according to Isaac J. Schoenberg's second footnote on page 7, where the line OA does not need to be perpendicular to QR.
In the original musical application m is a fraction with a denominator corresponding with the number of equal divisions of the line QR in order to obtain that number of steps in pitch of similar size between the longer string MR and shorter string MP. |
| Date | |
| Source | Own work |
| Author | Mireut |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 01:38, 14 November 2009 | | 750 × 875 (22 KB) | Mireut | {{Information |Description={{en|1=Diagram of a geometrical and fractional approximation of <math>\scriptstyle MP\times(\frac{MR}{MP})^m</math> published by J. Murray Barbour in "A Geometrical approximation to the Roots of Numbers" (''American Mathematical |
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