0edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author spt3125 and made on 2017-07-22 19:05:56 UTC.
- The original revision id was 615831721.
- The revision comment was: added link (deorphaning)
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=Zero equal divisions of the octave= 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 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). 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. An example of a [[trivial temperaments|trivial temperament]], 0edo tempers out all commas and is consistent in all limits.
Original HTML content:
<html><head><title>0edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Zero equal divisions of the octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->Zero equal divisions of the octave</h1> <br /> There are two ways to approach this idea.<br /> <br /> Given that <em>n</em><em>-</em>edo means that you are dividing the octave into 1<em>/n</em> equal divisions and that 1/0 is 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).<br /> <br /> The other way of looking at it is to see what happens as <em>n</em> 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 <em>n</em> 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.<br /> <br /> An example of a <a class="wiki_link" href="/trivial%20temperaments">trivial temperament</a>, 0edo tempers out all commas and is consistent in all limits.</body></html>