Equal-step tuning: Difference between revisions

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* For each pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math>, there exists a ratio <math>{a}/{b}</math> such that <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> are <math>{a}/{b}</math> complementary; it is observed that <math>a−b=1</math> or <math>a−b=2</math>. In other words, for each ratio <math>a/b</math> where <math>a−b=1</math> or <math>a−b=2</math>, there exists a pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> that are <math>{a}/{b}</math> complementary.

* We can observe a converging sequence and pattern for low errors ~~(Alpha, Beta, Gamma)~~: 3, 5, 8; then 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; etc. -

* We can observe a converging sequence and pattern for divisions of the ratio <math>{a}/{b}</math> where low errors appears for <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math>: 3, 5, 8; then 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; etc. -

{| class="wikitable"

|+Converging sequence and pattern

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* We can describe the pattern as follow: Alpha division = 3 + index * 2; Beta division = 5 + index * 2; Gamma division = Alpha division + Beta division

* Alpha types flatten the smaller interval and sharpen the larger; Beta types do the reverse; Gamma types again flatten the smaller and sharpen the larger.

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 * For each pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math>, there exists a ratio <math>{a}/{b}</math> such that <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> are <math>{a}/{b}</math> complementary; it is observed that <math>a−b=1</math> or <math>a−b=2</math>. In other words, for each ratio <math>a/b</math> where <math>a−b=1</math> or <math>a−b=2</math>, there exists a pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> that are <math>{a}/{b}</math> complementary.
-* We can observe a converging sequence and pattern for low errors (Alpha, Beta, Gamma): 3, 5, 8; then 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; etc. -
+* We can observe a converging sequence and pattern for divisions of the ratio <math>{a}/{b}</math> where low errors appears for <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math>: 3, 5, 8; then 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; etc. -
 {| class="wikitable"
 |+Converging sequence and pattern
@@ Line 307: / Line 308: @@
 |28
 |}
+* We can describe the pattern as follow: Alpha division = 3 + index * 2; Beta division = 5 + index * 2; Gamma division = Alpha division + Beta division
 * Alpha types flatten the smaller interval and sharpen the larger; Beta types do the reverse; Gamma types again flatten the smaller and sharpen the larger.