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. | * 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): 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28 | * 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. - | ||
{| class="wikitable" | |||
|+Converging sequence and pattern | |||
! rowspan="2" |Ratio divided | |||
! colspan="3" |Number of divisions | |||
|- | |||
!Alpha | |||
!Beta | |||
!Gamma | |||
|- | |||
|3/1 | |||
|3 | |||
|5 | |||
|8 | |||
|- | |||
|2/1 | |||
|5 | |||
|7 | |||
|12 | |||
|- | |||
|5/3 | |||
|7 | |||
|9 | |||
|16 | |||
|- | |||
|3/2 | |||
|9 | |||
|11 | |||
|20 | |||
|- | |||
|7/5 | |||
|11 | |||
|13 | |||
|24 | |||
|- | |||
|4/3 | |||
|13 | |||
|15 | |||
|28 | |||
|} | |||
* 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. | * 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. | ||