User:Frostburn/Theory From First Principles: Difference between revisions
Remove personal reminder. |
→Adding Geometry: Elucidate the behaviour of scalar multiples of the projective origin. |
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<math>\mathrm{freq}(\overrightarrow{\frac{p}{q} Hz}) = \frac{p}{q} Hz</math> . | <math>\mathrm{freq}(\overrightarrow{\frac{p}{q} Hz}) = \frac{p}{q} Hz</math> . | ||
Care must be taken when the multiplier of the projective origin is not 1. e.g. Let's consider 1.5 Hz which is a perfect fifth above 1 Hz. It's represented as <math>e_0 - e_2 + e_3</math>. | |||
If some other calculation gave us the result <math>2 e_0 - e_2 + e_3</math> it wouldn't represent 1.5Hz it's | |||
<math>\mathrm{freq}(2 e_0 - e_2 + e_3) = 1.5 Hz^2 \sim \sqrt{\frac{3}{2}} Hz \approx 1.22 Hz</math> | |||
instead. | |||
== Expanding geometry == | == Expanding geometry == | ||