196608edo: Difference between revisions

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[[File:Tetradecamu Approximation Quality.png|thumb|Approximation quality of smaller edos in tetradecamu, maximum relative error against edo from 1 to 16808. ]]

The main application of 196608edo is not as a compositional device, but as a technical tuning standard. If we adopt direct approximation, some JI intervals are indeed improved.

The main application of 196608edo is not as a compositional device, but as a technical tuning standard. If we adopt direct approximation, some JI intervals are indeed improved, which makes sense since we are only quantizing JI to the grid of this edo.

Another usage that is not commonly seen in other edos is to approximate smaller edos~~, since they are quantized into the grid of this edo~~. It cannot approximate any larger edos or any edos of the same order of magnitude. From the diagram we can observe the maximum relative errors of smallers edos are most linear with respect to the edo number. [[16808edo]], a notable zeta edo that is an order of magnitude below, is approximated with a ~4% maximum relative error.

Another usage that is not commonly seen in other edos is to approximate smaller edos. It cannot approximate any larger edos or any edos of the same order of magnitude. From the diagram we can observe the maximum relative errors of smallers edos are most linear with respect to the edo number. [[16808edo]], a notable zeta edo that is an order of magnitude below, is approximated with a ~4% maximum relative error.

=== Odd harmonics ===

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**[[49152edo]] (12mu tuning)

**[[98304edo]] (13mu tuning)

~~[[Category:Equal divisions of the octave|######]] ~~

@@ Line 8: / Line 8: @@
 [[File:Tetradecamu Approximation Quality.png|thumb|Approximation quality of smaller edos in tetradecamu, maximum relative error against edo from 1 to 16808. ]]
-The main application of 196608edo is not as a compositional device, but as a technical tuning standard. If we adopt direct approximation, some JI intervals are indeed improved.
+The main application of 196608edo is not as a compositional device, but as a technical tuning standard. If we adopt direct approximation, some JI intervals are indeed improved, which makes sense since we are only quantizing JI to the grid of this edo.
-Another usage that is not commonly seen in other edos is to approximate smaller edos, since they are quantized into the grid of this edo. It cannot approximate any larger edos or any edos of the same order of magnitude. From the diagram we can observe the maximum relative errors of smallers edos are most linear with respect to the edo number. [[16808edo]], a notable zeta edo that is an order of magnitude below, is approximated with a ~4% maximum relative error.
+Another usage that is not commonly seen in other edos is to approximate smaller edos. It cannot approximate any larger edos or any edos of the same order of magnitude. From the diagram we can observe the maximum relative errors of smallers edos are most linear with respect to the edo number. [[16808edo]], a notable zeta edo that is an order of magnitude below, is approximated with a ~4% maximum relative error.
 === Odd harmonics ===
@@ Line 325: / Line 325: @@
 **[[49152edo]] (12mu tuning)
 **[[98304edo]] (13mu tuning)
-[[Category:Equal divisions of the octave|######]] <!-- 6-digit number -->