1/0 - Revision history

VectorGraphics at 07:45, 25 September 2025

2025-09-25T07:45:57Z

← Older revision		Revision as of 07:45, 25 September 2025
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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.		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 ==		== In scale building ==

VectorGraphics at 06:16, 13 February 2025

2025-02-13T06:16:29Z

← Older revision		Revision as of 06:16, 13 February 2025
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	{{Wikipedia\| Division by zero }}		{{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).		'''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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	== In scale building ==		== In scale building ==
	Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[antidiatonic\|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5 × 2 + (-2) × 5 = 0), and as such, the sizes of the steps go to infinity – the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]].		Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[antidiatonic\|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5 × 2 + (-2) × 5 = 0), and as such, the sizes of the steps go to infinity – the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]].

	~~== Temperaments ==~~
	~~If 1/0 is taken as a comma to be tempered out, it leads to the [[singularity]] temperament.~~

	== Practical application ==		== Practical application ==

VectorGraphics at 21:36, 11 February 2025

2025-02-11T21:36:15Z

← Older revision		Revision as of 21:36, 11 February 2025
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	== In scale building ==		== In scale building ==
	Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[antidiatonic\|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5 × 2 + (-2) × 5 = 0), and as such, the sizes of the steps go to infinity – the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]].		Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[antidiatonic\|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5 × 2 + (-2) × 5 = 0), and as such, the sizes of the steps go to infinity – the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]].

			== Temperaments ==
			If 1/0 is taken as a comma to be tempered out, it leads to the [[singularity]] temperament.

	== Practical application ==		== Practical application ==

FloraC: Category was fixed

2024-01-16T14:10:37Z

Category was fixed

← Older revision		Revision as of 14:10, 16 January 2024
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	{{Todo\| review \| explain its xenharmonic value }}		{{Todo\| review \| explain its xenharmonic value }}
	~~<!-- fix module: Rational or module: Infobox Interval for category -->~~

FloraC: +wikipedia article on the related topic; style

2024-01-07T09:07:37Z

+wikipedia article on the related topic; style

← Older revision		Revision as of 09:07, 7 January 2024
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	\| Name = singularitone		\| Name = singularitone
	}}		}}
			{{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 [[0edo]], another undefined interval.''

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	== Mathematics ==		== Mathematics ==
	As a fraction, the value of 1/0 is undefined due to the fact that 0*n=0, causing all other intervals to vanish (as the resulting ratio can be simplified down to 1/0), which, if defined, causes absurdities.		As a fraction, the value of 1/0 is undefined due to the fact that 0∙''n'' = 0, causing all other intervals to vanish (as the resulting ratio can be simplified down to 1/0), which, if defined, causes absurdities.

	For example, you could take a descending 1/0 from ~~440Hz~~ to ~~0Hz~~, and then an ascending 1/0 from ~~0Hz~~ to ~~660Hz~~, 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.		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.

	== In scale building ==		== In scale building ==
	Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[~~Antidiatonic~~\|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 52+(-2)5 = 0), and as such, the sizes of the steps go to infinity - the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]].		Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[antidiatonic\|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5 × 2 + (-2) × 5 = 0), and as such, the sizes of the steps go to infinity – the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]].

	== Practical application ==		== Practical application ==
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	So, if an interval of 1/1 is played, and it slides gradually wider, to 2/1, 4/1, 8/1 and so on, until it exits the human hearing range, this might be seen as implying 1/0.		So, if an interval of 1/1 is played, and it slides gradually wider, to 2/1, 4/1, 8/1 and so on, until it exits the human hearing range, this might be seen as implying 1/0.

	{{Todo\| review \| explain its xenharmonic value }}		{{Todo\| review \| explain its xenharmonic value }}
	<!-- fix module: Rational or module: Infobox Interval for category -->		<!-- fix module: Rational or module: Infobox Interval for category -->

Frostburn: Also call 0 Hz a DC-offset based on thumbs up on the suggestion in Discord.

2024-01-07T07:35:46Z

Also call 0 Hz a DC-offset based on thumbs up on the suggestion in Discord.

← Older revision		Revision as of 07:35, 7 January 2024
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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 [[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 with an infinite frequency (which does not exist).		'''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).

	== Mathematics ==		== Mathematics ==

Eliora: adopt the name

2024-01-06T23:42:27Z

adopt the name

← Older revision		Revision as of 23:42, 6 January 2024
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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 [[0edo]], another undefined interval.''

	1/0 is an "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 with an infinite frequency (which does not exist).		'''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 with an infinite frequency (which does not exist).

	== Mathematics ==		== Mathematics ==

FloraC: 1\0 isn't the unison

2024-01-06T14:50:12Z

1\0 isn't the unison

← Older revision		Revision as of 14:50, 6 January 2024
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	\| Name = singularitone		\| Name = singularitone
	}}		}}
	(''Not to be confused with 1\0, the first ~~and only interval~~ of [[0edo]], ~~a [[1/1\|perfect unison]]~~.'')		:''Not to be confused with 1\0, the first step of [[0edo]], another undefined interval.''

	1/0 is an "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 with an infinite frequency (which does not exist).		1/0 is an "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 with an infinite frequency (which does not exist).

BudjarnLambeth at 20:20, 3 January 2024

2024-01-03T20:20:44Z

← Older revision		Revision as of 20:20, 3 January 2024
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	\| Name = singularitone		\| Name = singularitone
	}}		}}
	''Not to be confused with 1\0, the first and only interval of [[0edo]], a [[1/1\|perfect unison]].''		(''Not to be confused with 1\0, the first and only interval of [[0edo]], a [[1/1\|perfect unison]].'')

	1/0 is an "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 with an infinite frequency (which does not exist).		1/0 is an "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 with an infinite frequency (which does not exist).

BudjarnLambeth: Added not to be confused line

2024-01-03T20:20:33Z

Added not to be confused line

← Older revision		Revision as of 20:20, 3 January 2024
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	\| Name = singularitone		\| Name = singularitone
	}}		}}
			''Not to be confused with 1\0, the first and only interval of [[0edo]], a [[1/1\|perfect unison]].''

	1/0 is an "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 with an infinite frequency (which does not exist).		1/0 is an "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 with an infinite frequency (which does not exist).