User:Frostburn/Theory From First Principles: Difference between revisions
m Minor wording changes. |
→On units: Make it clearer that there's no "cent" for the tritave in this system. |
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As we have <math>e^2 = e_2 / w_2^2 = \hat{i} / w_2</math>; A reciprocal cent can now be expressed as <math>¢^{-1} = 1200 e^2 = 100 d^{-1} \hat{i}</math> or 100 reciprocal demitones in the <math>\hat{i}</math> direction. | As we have <math>e^2 = e_2 / w_2^2 = \hat{i} / w_2</math>; A reciprocal cent can now be expressed as <math>¢^{-1} = 1200 e^2 = 100 d^{-1} \hat{i}</math> or 100 reciprocal demitones in the <math>\hat{i}</math> direction. | ||
To be perfectly clear about the nature of these objects: There is no "cent" associated with primes besides 2. The closest we can get is: | |||
<math>\overrightarrow{3} \cdot \mathsf{JIP} / \log(2) * 1200 ¢ \approx 1901.955 ¢</math> | |||
Where we had to ''a)'' violate linear indepence over <math>\mathbb{Q}</math> ''b)'' remove "twoness" by dividing by the logarithm ''c)'' explicitly add the units to "twist" the answer into the requisitioned direction. | |||
== Clifford algebra nonsense == | == Clifford algebra nonsense == | ||