Vals and tuning space: Difference between revisions
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<math>\displaystyle | <math>\displaystyle | ||
\left<31 \; \frac{49}{\log_2(3)} \; \frac{72}{\log_2(5)} \; \frac{87}{\log_2(7)}\right| | \left< 31 \; \frac{49}{\log_2(3)} \; \frac{72}{\log_2(5)} \; \frac{87}{\log_2(7)}\right| | ||
</math> | |||
which is approximately {{val| 31.000 30.916 31.009 30.990 }}. The standard Euclidean norm would then be the square root of the sum of squares of this vector, which is approximately sqrt (3838.694), or 61.957. To use the RMS we divide that by sqrt (4) = 2, giving 30.976 for the TE norm. Note that the TE norm for this val is approximately 31; any val closely approximating JI is expected to have the TE norm close to its division of the octave. | which is approximately {{val| 31.000 30.916 31.009 30.990 }}. The standard Euclidean norm would then be the square root of the sum of squares of this vector, which is approximately sqrt (3838.694), or 61.957. To use the RMS we divide that by sqrt (4) = 2, giving 30.976 for the TE norm. Note that the TE norm for this val is approximately 31; any val closely approximating JI is expected to have the TE norm close to its division of the octave. | ||