EDO: Difference between revisions

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== Non-integer EDO ==

A non-integer ~~edo~~ can be defined as using a non-integer divisor to divide the octave. Typically, non-integer ~~edos~~ are understood as ''not'' containing the exact octave, so that they remain [[equal tuning]]s. All fractional EDOs are integer equal divisions of another integer interval. For example, (25/2)edo is equivalent to 25ed4. In general:

A non-integer EDO can be defined as using a non-integer divisor to divide the octave. Typically, non-integer EDOs are understood as ''not'' containing the exact octave, so that they remain [[equal tuning]]s. All fractional EDOs are integer equal divisions of another integer interval. For example, (25/2)edo is equivalent to 25ed4. In general:

<math>\displaystyle (p/q) \text{edo} = p \text{-ed} 2^q</math>

for integers ''p'' and ''q''. ~~Irrational~~ EDOs cannot be converted to integer equal divisions of another integer interval, so they are things of their own.

for integers ''p'' and ''q''. Many irrational EDOs cannot be converted to integer equal divisions of another integer interval, so they are things of their own.

Non-integer EDOs can be written in decimal form, such as 12.1edo. This is often meant to be approximate, used in the context of [[octave stretch]] of an integer EDO, rather than as a fractional EDO.

== Scale tree ==

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 == Non-integer EDO ==
-A non-integer edo can be defined as using a non-integer divisor to divide the octave. Typically, non-integer edos are understood as ''not'' containing the exact octave, so that they remain [[equal tuning]]s. All fractional EDOs are integer equal divisions of another integer interval. For example, (25/2)edo is equivalent to 25ed4. In general:
+A non-integer EDO can be defined as using a non-integer divisor to divide the octave. Typically, non-integer EDOs are understood as ''not'' containing the exact octave, so that they remain [[equal tuning]]s. All fractional EDOs are integer equal divisions of another integer interval. For example, (25/2)edo is equivalent to 25ed4. In general:
 <math>\displaystyle (p/q) \text{edo} = p \text{-ed} 2^q</math>
-for integers ''p'' and ''q''. Irrational EDOs cannot be converted to integer equal divisions of another integer interval, so they are things of their own.
+for integers ''p'' and ''q''. Many irrational EDOs cannot be converted to integer equal divisions of another integer interval, so they are things of their own.
 Non-integer EDOs can be written in decimal form, such as 12.1edo. This is often meant to be approximate, used in the context of [[octave stretch]] of an integer EDO, rather than as a fractional EDO.
 == Scale tree ==