Relative cent: Difference between revisions
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Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo|41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat. | Measuring the error of an approximation of an interval in an edo in terms of relative cents gives the relative error, which so long as the corresponding val is used is additive. For instance, the fifth of 12edo is 1.995 cents flat, or -1.955 cents sharp, which is therefore also its error in relative cents. The fifth of [[41edo|41edo]] is 1.654 relative cents sharp. Thus for 53=41+12, the fifth is -1.955 + 1.654 = -0.301 relative cents sharp, and hence (-0.301)*(12/53) = -0.068 cents sharp, which is to say 0.068 cents flat. | ||
The problem of the relative cent, though, is that 3/2 is 58.496 percent of the octave, which means the relative goodness of 3/2 to it is very heavily dependent on which edo you divide by 100. But if you increase the divisor, the following situation emerges: | |||
{| class="wikitable" | |||
|+ | |||
!Divisor | |||
!3/2 | |||
|- | |||
|101 | |||
|59.081° | |||
|- | |||
|102 | |||
|59.666 | |||
|- | |||
|103 | |||
|60.251 | |||
|- | |||
|104 | |||
|60.836 | |||
|- | |||
|105 | |||
|61.421 | |||
|- | |||
|106 | |||
|62.006 | |||
|- | |||
|107 | |||
|62.591 | |||
|- | |||
|108 | |||
|63.176 | |||
|- | |||
|109 | |||
|63.761 | |||
|- | |||
|110 | |||
|64.346 | |||
|- | |||
|111 | |||
|64.931 | |||
|- | |||
|112 | |||
|''65.516'' | |||
|- | |||
|113 | |||
|66.101 | |||
|- | |||
|114 | |||
|66.686 | |||
|- | |||
|115 | |||
|67.271 | |||
|- | |||
|116 | |||
|67.856 | |||
|- | |||
|117 | |||
|68.441 | |||
|- | |||
|118 | |||
|69.026 | |||
|- | |||
|119 | |||
|69.6105 | |||
|- | |||
|120 | |||
|70.1955 | |||
|- | |||
|121 | |||
|70.7805 | |||
|- | |||
|122 | |||
|71.365 | |||
|- | |||
|123 | |||
|71.95 | |||
|- | |||
|124 | |||
|''72.535'' | |||
|- | |||
|125 | |||
|73.12 | |||
|- | |||
|126 | |||
|73.705 | |||
|- | |||
|127 | |||
|74.29 | |||
|- | |||
|128 | |||
|74.875 | |||
|} | |||
In other words, only each 12th divisor of the next 28 after 100 has the same problem as 100 does for use as the base of a relative cent. | |||
== Application for quantify approximation == | == Application for quantify approximation == | ||
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----- | ----- | ||
''...also the term [[centidegree|centidegree]] was suggested, but this seems to be used already as a unit for temperature.'' [[Category:approximation]] | ''...also the term [[centidegree|centidegree]] was suggested, but this seems to be used already as a unit for temperature.'' | ||
[[Category:approximation]] | |||
[[Category:interval_measure]] | [[Category:interval_measure]] | ||
[[Category:practical_help]] | [[Category:practical_help]] | ||