Relative interval error: Difference between revisions

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</math>

Here is an example. The relative errors of 26edo in its 7-limit patent val is

Here is an example. The relative errors of 26edo in its 5-limit patent val is

<math>E_\text {r, 26} = \langle \begin{matrix} 0.00\% & -20.90\% & -37.01\% \end{matrix} ]</math>

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Another linearity is actually about the interval space {b}. This enables us to find the relative error of any ratio in a given tuning of an equal temperament.

Let us try finding the relative error of 6/5 in 19edo's patent val. We first find the errors of 2/1, 3/1 and 5/1 in 19edo are 0, -11.43% and -11.66%, respectively. Since 6/5 = (2/1)(3/1) / (5/1), its error is 0 + (-11.43%) - (-11.66%) = 0.23%. That shows 19edo has fairly flat fifths and major thirds, yet they cancel out when it comes to minor thirds and results in a very accurate approximation.

== See also ==

@@ Line 39: / Line 39: @@
 </math>
-Here is an example. The relative errors of 26edo in its 7-limit patent val is
+Here is an example. The relative errors of 26edo in its 5-limit patent val is
 <math>E_\text {r, 26} = \langle \begin{matrix} 0.00\% & -20.90\% & -37.01\% \end{matrix} ]</math>
@@ Line 60: / Line 60: @@
 Another linearity is actually about the interval space {b}. This enables us to find the relative error of any ratio in a given tuning of an equal temperament.
 Let us try finding the relative error of 6/5 in 19edo's patent val. We first find the errors of 2/1, 3/1 and 5/1 in 19edo are 0, -11.43% and -11.66%, respectively. Since 6/5 = (2/1)(3/1) / (5/1), its error is 0 + (-11.43%) - (-11.66%) = 0.23%. That shows 19edo has fairly flat fifths and major thirds, yet they cancel out when it comes to minor thirds and results in a very accurate approximation.
 == See also ==