1/0: Difference between revisions

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:''Not to be confused with 1\0, the first step of [[0edo]], another undefined interval.''

:''Not to be confused with 1\0, the first step of [[Single-pitch tuning|0edo]], another undefined interval.''

'''1/0''', the '''singularitone''', is a degenerate "interval" with an undefined numeric value. As a ratio, it can be taken to refer to the distance between any [[note]] and the note with a frequency of 0 Hz (equivalent to silence or a DC offset in Fourier Transform parlance), or with an infinite frequency (which does not exist).

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For example, you could take a descending 1/0 from 440 Hz to 0 Hz, and then an ascending 1/0 from 0 Hz to 660 Hz, seemingly implying that a [[3/2|perfect fifth]] is the same as a [[unison]]. This problem is solved by declaring that 1/0 cannot be used to make any mathematical statements, leaving it mathematically undefined. However, it can be represented as a [[ratio]] between any number and 0.

=== Absurdities ===

* 1/0 is [[S-expression|S1]], and as a result defines a self-referential temperament which tempers 1/0 out, yet at the same time equates it to the octave while simultaneously splitting it in two.

== In scale building ==

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 {{Wikipedia| Division by zero }}
-:''Not to be confused with 1\0, the first step of [[0edo]], another undefined interval.''
+:''Not to be confused with 1\0, the first step of [[Single-pitch tuning|0edo]], another undefined interval.''
 '''1/0''', the '''singularitone''', is a degenerate "interval" with an undefined numeric value. As a ratio, it can be taken to refer to the distance between any [[note]] and the note with a frequency of 0 Hz (equivalent to silence or a DC offset in Fourier Transform parlance), or with an infinite frequency (which does not exist).
@@ Line 13: / Line 13: @@
 For example, you could take a descending 1/0 from 440 Hz to 0 Hz, and then an ascending 1/0 from 0 Hz to 660 Hz, seemingly implying that a [[3/2|perfect fifth]] is the same as a [[unison]]. This problem is solved by declaring that 1/0 cannot be used to make any mathematical statements, leaving it mathematically undefined. However, it can be represented as a [[ratio]] between any number and 0.
+=== Absurdities ===
+* 1/0 is [[S-expression|S1]], and as a result defines a self-referential temperament which tempers 1/0 out, yet at the same time equates it to the octave while simultaneously splitting it in two.
 == In scale building ==