User:Contribution/Successive superparticular complementary pair: Difference between revisions

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+== Context ==
+Read this first: [[Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions]]
 == The Alpha-Beta-Gamma family ==
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-== The fact ==
+== The converging Alpha-Beta-Gamma sequence ==
+As a fact, for each <math>n\ge 2</math>, equal divisions of <math>R_n=\dfrac{n+1}{n-1}</math> where low errors appear for <math>S_n=\dfrac{n+1}{n}</math> and <math>B_n=\dfrac{n}{n-1}</math> forms a converging sequence and pattern, with the happy equal divisions of <math>R_n</math> being:
+* '''Alpha:''' <math>k_\alpha=2n-1</math>
+* '''Beta:''' <math>k_\beta=2n+1</math>
+* '''Gamma:''' <math>k_\gamma=4n=k_\alpha+k_\beta</math>
-As a fact, all Alpha scales are (s1 + s2)ED(a / b), all Beta scales are (s2 + s3)ED(a / b), and all Gamma scales are (s1 + s2 + s2 + s3)ED(a / b).
+In this sequence, the errors are lower and lower.
-{{todo|Why this pattern|inline=1|comment=Explain why low errors make this pattern appears.}}
+{{todo|Why this pattern|inline=1|comment=Explain why divisions of ratios where low errors appear for successive superparticular complementary pair make this pattern appears.}}
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