Image:Music Scale Comparison.png
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The file is a graph which compares harmonic ratios used in music to mathematical progrossions. The graph is created in an Excel file and the data for the graph calculated in the program from mathematical expressions and established harmonic ratios. A table of data goes along with the graph and identifies the notes, decimal value and harmonic ratio. A brief description discusses how harmonic ratios are related to linear mathematical progression rather than the geometric progression (Equal Tempered Scale). The geometric progression closely compares, however, to the double linear progression. The blank cells in the table are intentionally left blank because they are the same as the octave sequence shown but part of the previous or subsequent octave. The decimal value and decimal slope continuously progress.
| Name | Octave Note | Note Step | Linear Step | Decimal Value | Decimal Slope | Harmonic Ratio |
|---|---|---|---|---|---|---|
| 0 6 | 0.875 | 0.0625 | ||||
| 1 | 0.9375 | |||||
| C | 1 | 0 | 2 | 1 | 1:1 | |
| C-sharp | 2 | 1 | 3 | 1.0625 | 17:16 | |
| D | 3 | 2 | 4 | 1.125 | 9:8 | |
| D-sharp | 4 | 3 | 5 | 1.1875 | 19:16 | |
| E | 5 | 4 | 0 6 | 1.25 | 0.08333 | 5:4 |
| F | 6 | 5 | 1 | 1.3333 | 4:3 | |
| F-sharp | 7 | 6 | 2 | 1.4167 | 17:12 | |
| G | 8 | 7 | 3 | 1.5 | 3:2 | |
| G-sharp | 9 | 8 | 4 | 1.5833 | 19:12 | |
| A | 10 | 9 | 5 | 1.6667 | 5:3 | |
| A-sharp | 11 | 10 | 0 6 | 1.75 | 0.125 | 7:4 |
| B | 12 | 11 | 1 | 1.875 | 15:8 | |
| C' | 13 | 12 | 2 | 2 | 2:1 | |
| 3 | 2.125 | |||||
| 4 | 2.25 | |||||
| 5 | 2.375 | |||||
| 0 6 | 2.5 | 0.16667 |
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| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 19:29, 22 June 2005 | 578×577 (8 KB) | David Harty (Talk | contribs) | (The file is a graph which compares harmonic ratios used in music to mathematical progrossions. The graph is created in an Excel file and the data for the graph calculated in the program from mathematical expressions and established harmonic ratios.) |
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