Nexus comma - Revision history

BudjarnLambeth at 23:47, 3 November 2024

2024-11-03T23:47:23Z

← Older revision		Revision as of 23:47, 3 November 2024
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	[[Category:Alpharabian]]		[[Category:Alpharabian]]
	[[Category:Nexus]]		[[Category:Nexus]]
			[[Category:Commas named for their regular temperament properties]]

BudjarnLambeth: /* Temperaments and Name */ user:Aura —> Aura

2024-10-14T03:23:51Z

Temperaments and Name: user:Aura —> Aura

← Older revision		Revision as of 03:23, 14 October 2024
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	== Temperaments and Name ==		== Temperaments and Name ==

	Tempering out this comma in the full 11-limit leads to the rank-4 [[nexus family #Nexus\|nexus]] temperament, or, in the 2.3.11 subgroup, the rank-2 [[tribilo family #Tribilo\|tribilo]] temperament. Either way, it leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both ''p''-limits, led to [[~~User:Aura\|~~Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most of this comma's names. Furthermore, the names have since turned out to be justified in light of the comma's additional functions, such as splitting the [[Pythagorean comma]] into three instances of the rastma, splitting the [[perfect fourth]] into two [[semifourth]]s, and in turn splitting the [[Pythagorean limma]] into two as well – all functions that contribute to both diatonic and paradiatonic significance, hence the longer descriptive name "diatonic-paradiatonic nexus comma".		Tempering out this comma in the full 11-limit leads to the rank-4 [[nexus family #Nexus\|nexus]] temperament, or, in the 2.3.11 subgroup, the rank-2 [[tribilo family #Tribilo\|tribilo]] temperament. Either way, it leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both ''p''-limits, led to [[Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most of this comma's names. Furthermore, the names have since turned out to be justified in light of the comma's additional functions, such as splitting the [[Pythagorean comma]] into three instances of the rastma, splitting the [[perfect fourth]] into two [[semifourth]]s, and in turn splitting the [[Pythagorean limma]] into two as well – all functions that contribute to both diatonic and paradiatonic significance, hence the longer descriptive name "diatonic-paradiatonic nexus comma".

	While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]).		While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]).

Aura at 16:27, 10 January 2024

2024-01-10T16:27:28Z

← Older revision		Revision as of 16:27, 10 January 2024
Line 6:		Line 6:
	}}		}}

	The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Axirabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the ~~difference between the~~ [[243/242\|rastma]] and the [[Alpharabian comma]], and the ~~sum~~ of the [[32805/32768\|schisma]] and the [[parimo]].		The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Axirabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the interval that separates [[243/242\|rastma]] and the [[Alpharabian comma]], and the result of stacking the [[32805/32768\|schisma]] and the [[parimo]].

	== Temperaments and Name ==		== Temperaments and Name ==

Aura at 20:59, 29 December 2023

2023-12-29T20:59:51Z

← Older revision		Revision as of 20:59, 29 December 2023
Line 6:		Line 6:
	}}		}}

	The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] ~~Alpharabian~~ diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].		The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Axirabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].

	== Temperaments and Name ==		== Temperaments and Name ==

Aura at 16:19, 17 October 2023

2023-10-17T16:19:53Z

← Older revision		Revision as of 16:19, 17 October 2023
Line 6:		Line 6:
	}}		}}

	The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].		The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].

	== Temperaments and Name ==		== Temperaments and Name ==

Aura at 16:19, 17 October 2023

2023-10-17T16:19:36Z

← Older revision		Revision as of 16:19, 17 October 2023
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 1771561/1769472		\| Ratio = 1771561/1769472
	\| Name = nexus comma, nexisma, nexuma		\| Name = diatonic-paradiatonic nexus comma, nexus comma, nexisma, nexuma
	\| Color name = Tribilo comma		\| Color name = Tribilo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

	The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].		The '''diatonic-paradiatonic nexus comma''', otherwise known as the '''nexus comma''', '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].

	== Temperaments and Name ==		== Temperaments and Name ==

	Tempering out this comma in the full 11-limit leads to the rank-4 [[nexus family #Nexus\|nexus]] temperament, or, in the 2.3.11 subgroup, the rank-2 [[tribilo family #Tribilo\|tribilo]] temperament. Either way, it leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both ''p''-limits, led to [[User:Aura\|Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most of this comma's names. Furthermore, the names have since turned out to be justified in light of the comma's additional functions, such as splitting the [[Pythagorean comma]] into three instances of the rastma, splitting the [[perfect fourth]] into two [[semifourth]]s, and in turn splitting the [[Pythagorean limma]] into two as well – all functions that contribute to both diatonic and paradiatonic significance.		Tempering out this comma in the full 11-limit leads to the rank-4 [[nexus family #Nexus\|nexus]] temperament, or, in the 2.3.11 subgroup, the rank-2 [[tribilo family #Tribilo\|tribilo]] temperament. Either way, it leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both ''p''-limits, led to [[User:Aura\|Aura]] considering the temperament that tempers out this comma to be some sort of "nexus temperament", which it turn gave rise to most of this comma's names. Furthermore, the names have since turned out to be justified in light of the comma's additional functions, such as splitting the [[Pythagorean comma]] into three instances of the rastma, splitting the [[perfect fourth]] into two [[semifourth]]s, and in turn splitting the [[Pythagorean limma]] into two as well – all functions that contribute to both diatonic and paradiatonic significance, hence the longer descriptive name "diatonic-paradiatonic nexus comma".

	While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]).		While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of 128/121 diatonic semitones (see [[Alpharabian tuning]]).

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:51:52Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:51, 25 October 2022
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 1771561/1769472		\| Ratio = 1771561/1769472
	~~\| Monzo = -16 -3 0 0 6~~		\| Name = nexus comma, nexisma, nexuma
	~~\| Cents = 2.04265~~
	\| Name = nexus comma, ~~<br>~~ nexisma ~~<br>~~ nexuma
	\| Color name = Tribilo comma		\| Color name = Tribilo comma
	\| ~~FJS name =~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}

Line 23:		Line 19:
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]

	~~[[Category:11-limit]]~~
	~~[[Category:Unnoticeable commas]]~~
	[[Category:Alpharabian]]		[[Category:Alpharabian]]
	[[Category:Nexus]]		[[Category:Nexus]]

Aura at 15:39, 16 October 2022

2022-10-16T15:39:04Z

← Older revision		Revision as of 15:39, 16 October 2022
Line 10:		Line 10:
	}}		}}

	The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].		The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of six [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].

	== Temperaments and Name ==		== Temperaments and Name ==

Aura at 10:55, 12 October 2022

2022-10-12T10:55:08Z

← Older revision		Revision as of 10:55, 12 October 2022
Line 10:		Line 10:
	}}		}}

	The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96's exceeds the octave. It is also the amount by which a stack of [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].		The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96 intervals exceeds the octave. It is also the amount by which a stack of [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].

	== Temperaments and Name ==		== Temperaments and Name ==

Aura at 10:54, 12 October 2022

2022-10-12T10:54:45Z

← Older revision		Revision as of 10:54, 12 October 2022
Line 10:		Line 10:
	}}		}}

	The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96's exceeds the octave. It is also the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], or the sum of the [[32805/32768\|schisma]] and the [[parimo]].		The '''nexus comma''', otherwise known as the '''nexisma''', or – in the earliest materials where this comma is named outside of [[color notation]] – the '''nexuma''', is an [[11-limit]] (also 2.3.11 subgroup) [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. In color notation, this same comma is referred to as the '''tribilo comma'''. It is the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third, or equivalently stated, the amount by which a stack of three 121/96's exceeds the octave. It is also the amount by which a stack of [[12/11]] neutral seconds fall short of a [[27/16]] major sixth, the difference between the [[243/242\|rastma]] and the [[Alpharabian comma]], and the sum of the [[32805/32768\|schisma]] and the [[parimo]].

	== Temperaments and Name ==		== Temperaments and Name ==