Xenness - Revision history

Inthar: /* Xenness of Tuning Systems */

2026-02-24T03:53:51Z

Xenness of Tuning Systems

← Older revision		Revision as of 03:53, 24 February 2026
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	A related metric is to calculate the distance from nearby low-complexity just intonation ratios, such as 4/3 or 9/7. This is not true xenness as there are many LCJI intervals that are simple but very far from 12edo, such as 11/8. This method is also more mathematically complicated, as it may require an infinite sum of distances from various intervals divided by some complexity measure, such as N*D.		A related metric is to calculate the distance from nearby low-complexity just intonation ratios, such as 4/3 or 9/7. This is not true xenness as there are many LCJI intervals that are simple but very far from 12edo, such as 11/8. This method is also more mathematically complicated, as it may require an infinite sum of distances from various intervals divided by some complexity measure, such as N*D.

	== Xenness of ~~Tuning Systems~~ ==		== Xenness of tuning systems ==
	Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.		Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.

	{{Cat\|Core knowledge}}		{{Cat\|Core knowledge}}

Inthar at 10:23, 14 February 2026

2026-02-14T10:23:50Z

← Older revision		Revision as of 10:23, 14 February 2026
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	'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music, for which xenness is often a compositional goal.		'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music, for which xenness is often a compositional goal.

	===Distance from 12edo===		== Distance from 12edo ==
	{\| class="wikitable" style="float:right; margin-left: 10px;"		{\| class="wikitable" style="float:right; margin-left: 10px;"
	\|+ Staggered Xenness		\|+ Staggered Xenness
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	<nowiki>*</nowiki> Note that 25¢ is [[User:Ground\|Ground]]'s recommendation for the lower bound of an [[Aberrisma]].		<nowiki>*</nowiki> Note that 25¢ is [[User:Ground\|Ground]]'s recommendation for the lower bound of an [[Aberrisma]].

	===Distance from LCJI===		== Distance from LCJI ==

	A related metric is to calculate the distance from nearby low-complexity just intonation ratios, such as 4/3 or 9/7. This is not true xenness as there are many LCJI intervals that are simple but very far from 12edo, such as 11/8. This method is also more mathematically complicated, as it may require an infinite sum of distances from various intervals divided by some complexity measure, such as N*D.		A related metric is to calculate the distance from nearby low-complexity just intonation ratios, such as 4/3 or 9/7. This is not true xenness as there are many LCJI intervals that are simple but very far from 12edo, such as 11/8. This method is also more mathematically complicated, as it may require an infinite sum of distances from various intervals divided by some complexity measure, such as N*D.

	===Xenness of Tuning Systems===		== Xenness of Tuning Systems ==

	Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.		Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.

	{{Cat\|Core knowledge}}		{{Cat\|Core knowledge}}

Ground at 23:02, 31 January 2026

2026-01-31T23:02:37Z

← Older revision		Revision as of 23:02, 31 January 2026
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	'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music.		'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music, for which xenness is often a compositional goal.

	===Distance from 12edo===		===Distance from 12edo===

Inthar: /* Xenness of Tuning Systems */

2026-01-30T11:05:52Z

Xenness of Tuning Systems

← Older revision		Revision as of 11:05, 30 January 2026
Line 76:		Line 76:
	Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.		Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.

	~~[[index.php?title=Category:~~Core knowledge]]		{{Cat\|Core knowledge}}

Vector: I don't see any ambiguity with "neutral second"

2025-12-13T09:35:09Z

I don't see any ambiguity with "neutral second"

← Older revision		Revision as of 09:35, 13 December 2025
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	Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic.		Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic.

	Intervals can be categorized by whether they are closer to a 12edo interval or an alternating 24edo interval. For example, 75¢ to 125¢ is closer to a minor second and 125¢ to 175¢ is closer to a neutral second~~. This category could be called "middle second" to avoid ambiguity~~.		Intervals can be categorized by whether they are closer to a 12edo interval or an alternating 24edo interval. For example, 75¢ to 125¢ is closer to a minor second and 125¢ to 175¢ is closer to a neutral second.

	Generally, the most obviously xenharmonic intervals are far from 12edo and the size of typical melodic steps. This includes intervals closer to a quartertone, [[Neutral second]], and semifourth.		Generally, the most obviously xenharmonic intervals are far from 12edo and the size of typical melodic steps. This includes intervals closer to a quartertone, [[Neutral second]], and semifourth.
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	Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.		Tuning systems as a whole can also be evaluated for xenness. This could either be based on a lack of "unxen" intervals, the presence of "xen" intervals, or certain structural properties like the stacking of approximations of 3/2.

	[[Category:Core knowledge]]		[[index.php?title=Category:Core knowledge]]

Ground: /* Distance from 12edo */

2025-10-26T01:54:49Z

Distance from 12edo

← Older revision		Revision as of 01:54, 26 October 2025
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	===Distance from 12edo===		===Distance from 12edo===

	{\| class="wikitable" style="float:right; margin-left: 10px;"		{\| class="wikitable" style="float:right; margin-left: 10px;"
	\|+ Staggered Xenness		\|+ Staggered Xenness
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	Generally, the most obviously xenharmonic intervals are far from 12edo and the size of typical melodic steps. This includes intervals closer to a quartertone, [[Neutral second]], and semifourth.		Generally, the most obviously xenharmonic intervals are far from 12edo and the size of typical melodic steps. This includes intervals closer to a quartertone, [[Neutral second]], and semifourth.

			See also: [[2.3.35 and 2.3.49]]

	<nowiki>*</nowiki> Note that 25¢ is [[User:Ground\|Ground]]'s recommendation for the lower bound of an [[Aberrisma]].		<nowiki>*</nowiki> Note that 25¢ is [[User:Ground\|Ground]]'s recommendation for the lower bound of an [[Aberrisma]].

Ground at 00:27, 26 October 2025

2025-10-26T00:27:31Z

← Older revision		Revision as of 00:27, 26 October 2025
Line 1:		Line 1:
	'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music.		'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music.

			===Distance from 12edo===

	{\| class="wikitable" style="float:right; margin-left: 10px;"		{\| class="wikitable" style="float:right; margin-left: 10px;"
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	\| 75 ~ 125 \|\| Semitone		\| 75 ~ 125 \|\| Semitone
	\|-		\|-
	\| 125 ~ 175 \|\| '''[[Neutral second~~\|Neutral second]]~~'''		\| 125 ~ 175 \|\| '''Neutral second'''
	\|-		\|-
	\| 175 ~ 225 \|\| Whole Tone		\| 175 ~ 225 \|\| Whole Tone
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	\| 1175 ~ 1225 \|\| Octave		\| 1175 ~ 1225 \|\| Octave
	\|}		\|}

	~~===Distance from 12edo===~~

	Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic.		Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic.
Line 63:		Line 63:
	Intervals can be categorized by whether they are closer to a 12edo interval or an alternating 24edo interval. For example, 75¢ to 125¢ is closer to a minor second and 125¢ to 175¢ is closer to a neutral second. This category could be called "middle second" to avoid ambiguity.		Intervals can be categorized by whether they are closer to a 12edo interval or an alternating 24edo interval. For example, 75¢ to 125¢ is closer to a minor second and 125¢ to 175¢ is closer to a neutral second. This category could be called "middle second" to avoid ambiguity.

	<nowiki>*</nowiki> Note that 25¢ is [[User:Ground\|Ground]]'s recommendation for the lower bound of an [[~~Aberrisma\|~~Aberrisma]].		Generally, the most obviously xenharmonic intervals are far from 12edo and the size of typical melodic steps. This includes intervals closer to a quartertone, [[Neutral second]], and semifourth.

			<nowiki>*</nowiki> Note that 25¢ is [[User:Ground\|Ground]]'s recommendation for the lower bound of an [[Aberrisma]].

	===Distance from LCJI===		===Distance from LCJI===

Ground at 16:56, 25 October 2025

2025-10-25T16:56:46Z

@@ Line 1: / Line 1: @@
 '''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music.
 ===Distance from 12edo===
@@ Line 5: / Line 61: @@
 Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic.
-Intervals can be categorized by whether they are closer to a 12edo interval or an alternating 24edo interval. For example, 75¢ to 125¢ is closer to a minor second and 125¢ to 175¢ is closer to a neutral second. This category could be called "middle second" to avoid ambiguity. Main article: [[Neutral second]]
+Intervals can be categorized by whether they are closer to a 12edo interval or an alternating 24edo interval. For example, 75¢ to 125¢ is closer to a minor second and 125¢ to 175¢ is closer to a neutral second. This category could be called "middle second" to avoid ambiguity.
 ===Distance from LCJI===
-===Xenness of Edos===
+A related metric is to calculate the distance from nearby low-complexity just intonation ratios, such as 4/3 or 9/7. This is not true xenness as there are many LCJI intervals that are simple but very far from 12edo, such as 11/8. This method is also more mathematically complicated, as it may require an infinite sum of distances from various intervals divided by some complexity measure, such as N*D.

Ground: Created page with "'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music. ===Distance from 12edo=== Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic. Intervals can be catego..."

2025-10-25T04:03:58Z

Created page with "'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music. ===Distance from 12edo=== Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic. Intervals can be catego..."

New page

'''Xenness''' is a subjective measure of how xenharmonic an interval or chord is. There are many ways to quantify it, but an understanding can be helpful when making xenharmonic music.

===Distance from 12edo===

Being the dominant tuning system worldwide, 12edo is the standard against which xenharmonic music is judged. By this metric, all intervals 50¢ from the nearest 12edo step (alternating steps of 24edo) are considered the most xenharmonic.

Intervals can be categorized by whether they are closer to a 12edo interval or an alternating 24edo interval. For example, 75¢ to 125¢ is closer to a minor second and 125¢ to 175¢ is closer to a neutral second. This category could be called "middle second" to avoid ambiguity. Main article: [[Neutral second]]

===Distance from LCJI===

===Xenness of Edos===