0edo: Difference between revisions

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'''0 equal division of the octave''' ('''0edo''') is the [[tuning system]] that contains a single note.

'''0 equal division of the octave''' ('''0edo''') is the [[tuning system]] that contains a single note or is not defined as an [[EDO|edo]].

== Theory ==

There are two ways to approach this idea.

Given that ''n''-edo means that you are dividing the octave into 1''/n'' equal divisions and that 1/0 is sometimes considered undefined, it would follow that 0edo would be similarly undefined and thus would comprise no sounds at all (or intervals from unison are undefined, so 1 note is there).

Given that ''n''-edo means that you are dividing the octave into 1''/n'' equal divisions and that 1/0 is sometimes considered undefined, it would follow that 0edo would be similarly undefined and thus would comprise no sounds at all (or intervals from unison are undefined, so 1 note is there). Or they are, but they are unequal (e. g. [[Well temperament|well temperaments]]) or not primarily compared to the octave (e. g. the former perfect ambitus of a mode was a ninth or a tenth).

The other way of looking at it is to see what happens as ''n'' gets smaller. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller you reach a point where you only have one note within an audible octave range and any other notes outside of this range. Taking this to its conclusion, and assuming you want 0edo to be defined, you would conclude that 0edo is just one note without any octaves.

@@ Line 1: / Line 1: @@
-'''0 equal division of the octave''' ('''0edo''') is the [[tuning system]] that contains a single note.
+'''0 equal division of the octave''' ('''0edo''') is the [[tuning system]] that contains a single note or is not defined as an [[EDO|edo]].
 == Theory ==
 There are two ways to approach this idea.
-Given that ''n''-edo means that you are dividing the octave into 1''/n'' equal divisions and that 1/0 is sometimes considered undefined, it would follow that 0edo would be similarly undefined and thus would comprise no sounds at all (or intervals from unison are undefined, so 1 note is there).
+Given that ''n''-edo means that you are dividing the octave into 1''/n'' equal divisions and that 1/0 is sometimes considered undefined, it would follow that 0edo would be similarly undefined and thus would comprise no sounds at all (or intervals from unison are undefined, so 1 note is there). Or they are, but they are unequal (e. g. [[Well temperament|well temperaments]]) or not primarily compared to the octave (e. g. the former perfect ambitus of a mode was a ninth or a tenth).
 The other way of looking at it is to see what happens as ''n'' gets smaller. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As ''n'' gets smaller you reach a point where you only have one note within an audible octave range and any other notes outside of this range. Taking this to its conclusion, and assuming you want 0edo to be defined, you would conclude that 0edo is just one note without any octaves.