Defactoring terminology proposal - Revision history

Cmloegcmluin: /* Enfactoring, to replace torsion and contorsion */

2024-06-16T16:32:49Z

Enfactoring, to replace torsion and contorsion

← Older revision		Revision as of 16:32, 16 June 2024
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	# Again, it does not have any obvious musical or mathematical meaning in this context.		# Again, it does not have any obvious musical or mathematical meaning in this context.
	# There is an argument that using torsion in this way is an abuse of the term, which was originally applied to periodicity blocks, not temperaments<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2937 which is also referred to here http://tonalsoft.com/enc/t/torsion.aspx</ref>. Both periodicity blocks and temperaments can be defined by lists of commas. And either way, these lists can be saturated or unsaturated. But in the case of periodicity blocks — where commas ''are not made to vanish'' — there is an audible difference in the choice between a saturated and unsaturated list, whereas with a temperament — where commas ''are made to vanish'' — there is no audible difference. In concrete terms, while it can make sense to construct a Fokker block with {{vector\|-4 4 -1}} in the middle and {{vector\|-8 8 -2}} = 2{{vector\|-4 4 -1}} at the edge — which leads to a pitch system with 24 pitches instead of 12 where half of the pitches are a copy of the other half but offset by a fixed amount — it does not make sense to imagine a temperament which makes 2{{vector\|-4 4 -1}} vanish but does not make {{vector\|-4 4 -1}} vanish. And so the conflation<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2405</ref> of the two situations by using the same term is misleading, so the authors of this article believe that the term torsion should not be used in RTT. While it is ''theoretically possible'' to interpret RTT using mathematical structures like quotient subgroups, lattices, and free abelian groups, or in other words, as if a temperament looked like a periodicity block, in which case one can imagine a reality where e.g. (81/80)² is made to vanish while 81/80 is not, this is not how temperaments actually sound from a musical point of view in our physical reality; in this case, the inherently projective approach to linear algebra, where a (81/80)² and a 81/80 that both have been made to vanish map to the same tempered lattice node, models this problem better. So "torsion" could be preserved as a term for the effect on periodicity blocks (though there's almost certainly something more helpful than that, but that's a battle for another day<ref>Furthermore, care should be taken to recognize the difference in behavior between, say<br><br>		# There is an argument that using torsion in this way is an abuse of the term, which was originally applied to periodicity blocks, not temperaments.<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2937 which is also referred to here http://tonalsoft.com/enc/t/torsion.aspx</ref> Both periodicity blocks and temperaments can be defined by lists of commas. And either way, these lists can be saturated or unsaturated. But in the case of periodicity blocks — where commas ''are not made to vanish'' — there is an audible difference in the choice between a saturated and unsaturated list, whereas with a temperament — where commas ''are made to vanish'' — there is no audible difference. In concrete terms, while it can make sense to construct a Fokker block with {{vector\|-4 4 -1}} in the middle and {{vector\|-8 8 -2}} = 2{{vector\|-4 4 -1}} at the edge — which leads to a pitch system with 24 pitches instead of 12 where half of the pitches are a copy of the other half but offset by a fixed amount — it does not make sense to imagine a temperament which makes 2{{vector\|-4 4 -1}} vanish but does not make {{vector\|-4 4 -1}} vanish. And so the conflation<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2405</ref> of the two situations by using the same term is misleading, so the authors of this article believe that the term torsion should not be used in RTT. While it is ''theoretically possible'' to interpret RTT using mathematical structures like quotient subgroups, lattices, and free abelian groups, or in other words, as if a temperament looked like a periodicity block, in which case one can imagine a reality where e.g. (81/80)² is made to vanish while 81/80 is not, this is not how temperaments actually sound from a musical point of view in our physical reality; in this case, the inherently projective approach to linear algebra, where a (81/80)² and a 81/80 that both have been made to vanish map to the same tempered lattice node, models this problem better. So "torsion" could be preserved as a term for the effect on periodicity blocks (though there's almost certainly something more helpful than that, but that's a battle for another day<ref>Furthermore, care should be taken to recognize the difference in behavior between, say<br><br>
	<math>		<math>
	\left[		\left[

Cmloegcmluin: /* Defactoring, to replace saturation */

2024-06-16T16:32:26Z

Defactoring, to replace saturation

← Older revision		Revision as of 16:32, 16 June 2024
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	# To "saturate" in everyday use means to ''add'' to something, whereas in this mathematical sense it means to ''remove'' something, which can be very confusing. We suggest an effective way to look at it is that saturating is accomplished not by adding more information into the container but rather by shrinking the container itself so that it has no wasted capacity, and thereby attains a saturated state, but still feel that this is a bit of a stretch.		# To "saturate" in everyday use means to ''add'' to something, whereas in this mathematical sense it means to ''remove'' something, which can be very confusing. We suggest an effective way to look at it is that saturating is accomplished not by adding more information into the container but rather by shrinking the container itself so that it has no wasted capacity, and thereby attains a saturated state, but still feel that this is a bit of a stretch.
	# The most common everyday usage of that word is for "saturated fats", which are the bad kind of fats, so it has negative associations, despite "saturation" being the ''good'' state for a matrix to be in.		# The most common everyday usage of that word is for "saturated fats", which are the bad kind of fats, so it has negative associations, despite "saturation" being the ''good'' state for a matrix to be in.
	# Furthermore, there is another common but conflicting sense of saturation for matrices which clamps entry values to between -1 and 1<ref>See https://math.stackexchange.com/questions/1964814/linear-transformation-of-a-saturated-vector and https://faculty.uml.edu//thu/tcs01-june.pdf</ref>.		# Furthermore, there is another common but conflicting sense of saturation for matrices which clamps entry values to between -1 and 1.<ref>See https://math.stackexchange.com/questions/1964814/linear-transformation-of-a-saturated-vector and https://faculty.uml.edu//thu/tcs01-june.pdf</ref>

	== Enfactoring, to replace torsion and contorsion ==		== Enfactoring, to replace torsion and contorsion ==

Dave Keenan: /* Enfactoring, to replace torsion and contorsion */ Deleted "annoying".

2023-12-22T22:50:30Z

Enfactoring, to replace torsion and contorsion: Deleted "annoying".

← Older revision		Revision as of 22:50, 22 December 2023
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	# Again, it does not have any obvious musical or mathematical meaning in this context. It's a word that was invented specially for RTT in 2002. The prefix co- or con- is sometimes used to form terms for things that are the duals of others (e.g. vectors and ''co''vectors), so the term "con-torsion" was coined to refer to the dual concept of torsion. But "torsion" already has a couple problems as described above, so "contorsion" just compounds those. So the authors here believe it would be best to banish the term "contorsion" from the RTT community altogether.		# Again, it does not have any obvious musical or mathematical meaning in this context. It's a word that was invented specially for RTT in 2002. The prefix co- or con- is sometimes used to form terms for things that are the duals of others (e.g. vectors and ''co''vectors), so the term "con-torsion" was coined to refer to the dual concept of torsion. But "torsion" already has a couple problems as described above, so "contorsion" just compounds those. So the authors here believe it would be best to banish the term "contorsion" from the RTT community altogether.
	# A word with the same spelling was also coined with a different mathematical meaning outside of RTT, in the field of differential geometry: https://en.wikipedia.org/wiki/Contorsion_tensor<ref>In this field, it does definitely represent twisting, like in a Möbius strip. Also, DG contorsion is related to DG torsion by subtraction, not duality.</ref>		# A word with the same spelling was also coined with a different mathematical meaning outside of RTT, in the field of differential geometry: https://en.wikipedia.org/wiki/Contorsion_tensor<ref>In this field, it does definitely represent twisting, like in a Möbius strip. Also, DG contorsion is related to DG torsion by subtraction, not duality.</ref>
	# It is prone to spelling confusion. People commonly refer to temperaments with contorsion as "contorted". But contorted is the adjective form of a different word, contortion, with a t, not an s. The proper adjective form of contorsion would be contorsioned. It also exerts confusion back on usages of "torsion"; would you use "torted" instead of torsioned? Or would people prefer "torsional" and "contorsional", even though that suggests only of or pertaining to in general rather than having the effect applied.<ref>If it was meant to most strongly evoke duality with torsion, it should have been spelled "cotorsion". Naming it "contorsion" is ~~an annoying~~ step toward "contortion" but stopping halfway there. But this isn't a strong point, because duality with torsion was the false assumption mentioned above.</ref>		# It is prone to spelling confusion. People commonly refer to temperaments with contorsion as "contorted". But contorted is the adjective form of a different word, contortion, with a t, not an s. The proper adjective form of contorsion would be contorsioned. It also exerts confusion back on usages of "torsion"; would you use "torted" instead of torsioned? Or would people prefer "torsional" and "contorsional", even though that suggests only of or pertaining to in general rather than having the effect applied.<ref>If it was meant to most strongly evoke duality with torsion, it should have been spelled "cotorsion". Naming it "contorsion" is a step toward "contortion" but stopping halfway there. But this isn't a strong point, because duality with torsion was the false assumption mentioned above.</ref>
	# Due to its similarity with the word "contortion", the word contorsion evokes bending, twisting, and knotting. But there is nothing bendy, twisty, or knotted about the effect it has on JI lattices or tuning space, except when you attempt to understand them as if they were periodicity blocks, as criticized above.		# Due to its similarity with the word "contortion", the word contorsion evokes bending, twisting, and knotting. But there is nothing bendy, twisty, or knotted about the effect it has on JI lattices or tuning space, except when you attempt to understand them as if they were periodicity blocks, as criticized above.

Dave Keenan: /* Enfactoring, to replace torsion and contorsion */ Deleted "while being a made-up word". It can't be so, since it was already used in differential geometry.

2023-12-22T22:48:58Z

Enfactoring, to replace torsion and contorsion: Deleted "while being a made-up word". It can't be so, since it was already used in differential geometry.

← Older revision		Revision as of 22:48, 22 December 2023
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	And as for the word "contorsion", here are its problems:		And as for the word "contorsion", here are its problems:

	# Again, it does not have any obvious musical or mathematical meaning in this context. It's a word that was invented specially for RTT in 2002. The prefix co- or con- is sometimes used to form terms for things that are the duals of others (e.g. vectors and ''co''vectors), so the term "con-torsion" was coined to refer to the dual concept of torsion. But "torsion" already has a couple problems as described above, so "contorsion" just compounds those~~, while being a made-up word~~. So the authors here believe it would be best to banish the term "contorsion" from the RTT community altogether.		# Again, it does not have any obvious musical or mathematical meaning in this context. It's a word that was invented specially for RTT in 2002. The prefix co- or con- is sometimes used to form terms for things that are the duals of others (e.g. vectors and ''co''vectors), so the term "con-torsion" was coined to refer to the dual concept of torsion. But "torsion" already has a couple problems as described above, so "contorsion" just compounds those. So the authors here believe it would be best to banish the term "contorsion" from the RTT community altogether.
	# A word with the same spelling was also coined with a different mathematical meaning outside of RTT, in the field of differential geometry: https://en.wikipedia.org/wiki/Contorsion_tensor<ref>In this field, it does definitely represent twisting, like in a Möbius strip. Also, DG contorsion is related to DG torsion by subtraction, not duality.</ref>		# A word with the same spelling was also coined with a different mathematical meaning outside of RTT, in the field of differential geometry: https://en.wikipedia.org/wiki/Contorsion_tensor<ref>In this field, it does definitely represent twisting, like in a Möbius strip. Also, DG contorsion is related to DG torsion by subtraction, not duality.</ref>
	# It is prone to spelling confusion. People commonly refer to temperaments with contorsion as "contorted". But contorted is the adjective form of a different word, contortion, with a t, not an s. The proper adjective form of contorsion would be contorsioned. It also exerts confusion back on usages of "torsion"; would you use "torted" instead of torsioned? Or would people prefer "torsional" and "contorsional", even though that suggests only of or pertaining to in general rather than having the effect applied.<ref>If it was meant to most strongly evoke duality with torsion, it should have been spelled "cotorsion". Naming it "contorsion" is an annoying step toward "contortion" but stopping halfway there. But this isn't a strong point, because duality with torsion was the false assumption mentioned above.</ref>		# It is prone to spelling confusion. People commonly refer to temperaments with contorsion as "contorted". But contorted is the adjective form of a different word, contortion, with a t, not an s. The proper adjective form of contorsion would be contorsioned. It also exerts confusion back on usages of "torsion"; would you use "torted" instead of torsioned? Or would people prefer "torsional" and "contorsional", even though that suggests only of or pertaining to in general rather than having the effect applied.<ref>If it was meant to most strongly evoke duality with torsion, it should have been spelled "cotorsion". Naming it "contorsion" is an annoying step toward "contortion" but stopping halfway there. But this isn't a strong point, because duality with torsion was the false assumption mentioned above.</ref>

Cmloegcmluin: temper out → vanish

2022-12-27T17:51:21Z

temper out → vanish

← Older revision		Revision as of 17:51, 27 December 2022
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	# Again, it does not have any obvious musical or mathematical meaning in this context.		# Again, it does not have any obvious musical or mathematical meaning in this context.
	# There is an argument that using torsion in this way is an abuse of the term, which was originally applied to periodicity blocks, not temperaments<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2937 which is also referred to here http://tonalsoft.com/enc/t/torsion.aspx</ref>. Both periodicity blocks and temperaments can be defined by lists of commas. And either way, these lists can be saturated or unsaturated. But in the case of periodicity blocks — where commas ''are not ~~tempered out~~'' — there is an audible difference in the choice between a saturated and unsaturated list, whereas with a temperament — where commas ''are ~~tempered out~~'' — there is no audible difference. In concrete terms, while it can make sense to construct a Fokker block with {{vector\|-4 4 -1}} in the middle and {{vector\|-8 8 -2}} = 2{{vector\|-4 4 -1}} at the edge — which leads to a pitch system with 24 pitches instead of 12 where half of the pitches are a copy of the other half but offset by a fixed amount — it does not make sense to imagine a temperament which ~~tempers out~~ 2{{vector\|-4 4 -1}} but does not ~~temper out~~ {{vector\|-4 4 -1}}. And so the conflation<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2405</ref> of the two situations by using the same term is misleading, so the authors of this ~~particle~~ believe that the term torsion should not be used in RTT. While it is ''theoretically possible'' to interpret RTT using mathematical structures like quotient subgroups, lattices, and free abelian groups, or in other words, as if a temperament looked like a periodicity block, in which case one can imagine a reality where e.g. (81/80)² is ~~tempered out~~ while 81/80 is not, this is not how temperaments actually sound from a musical point of view in our physical reality; in this case, the inherently projective approach to linear algebra, where ~~tempered out~~ (81/80)² and 81/80 map to the same tempered lattice node, models this problem better. So "torsion" could be preserved as a term for the effect on periodicity blocks (though there's almost certainly something more helpful than that, but that's a battle for another day<ref>Furthermore, care should be taken to recognize the difference in behavior between, say<br><br>		# There is an argument that using torsion in this way is an abuse of the term, which was originally applied to periodicity blocks, not temperaments<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2937 which is also referred to here http://tonalsoft.com/enc/t/torsion.aspx</ref>. Both periodicity blocks and temperaments can be defined by lists of commas. And either way, these lists can be saturated or unsaturated. But in the case of periodicity blocks — where commas ''are not made to vanish'' — there is an audible difference in the choice between a saturated and unsaturated list, whereas with a temperament — where commas ''are made to vanish'' — there is no audible difference. In concrete terms, while it can make sense to construct a Fokker block with {{vector\|-4 4 -1}} in the middle and {{vector\|-8 8 -2}} = 2{{vector\|-4 4 -1}} at the edge — which leads to a pitch system with 24 pitches instead of 12 where half of the pitches are a copy of the other half but offset by a fixed amount — it does not make sense to imagine a temperament which makes 2{{vector\|-4 4 -1}} vanish but does not make {{vector\|-4 4 -1}} vanish. And so the conflation<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2405</ref> of the two situations by using the same term is misleading, so the authors of this article believe that the term torsion should not be used in RTT. While it is ''theoretically possible'' to interpret RTT using mathematical structures like quotient subgroups, lattices, and free abelian groups, or in other words, as if a temperament looked like a periodicity block, in which case one can imagine a reality where e.g. (81/80)² is made to vanish while 81/80 is not, this is not how temperaments actually sound from a musical point of view in our physical reality; in this case, the inherently projective approach to linear algebra, where a (81/80)² and a 81/80 that both have been made to vanish map to the same tempered lattice node, models this problem better. So "torsion" could be preserved as a term for the effect on periodicity blocks (though there's almost certainly something more helpful than that, but that's a battle for another day<ref>Furthermore, care should be taken to recognize the difference in behavior between, say<br><br>
	<math>		<math>
	\left[		\left[

Cmloegcmluin: references and footnotes

2022-01-09T00:06:45Z

references and footnotes

← Older revision		Revision as of 00:06, 9 January 2022
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	# Due to its similarity with the word "contortion", the word contorsion evokes bending, twisting, and knotting. But there is nothing bendy, twisty, or knotted about the effect it has on JI lattices or tuning space, except when you attempt to understand them as if they were periodicity blocks, as criticized above.		# Due to its similarity with the word "contortion", the word contorsion evokes bending, twisting, and knotting. But there is nothing bendy, twisty, or knotted about the effect it has on JI lattices or tuning space, except when you attempt to understand them as if they were periodicity blocks, as criticized above.

	== References ==		== References and footnotes ==
			<references/>

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Math]]		[[Category:Math]]

Cmloegcmluin at 19:25, 3 January 2022

2022-01-03T19:25:16Z

← Older revision		Revision as of 19:25, 3 January 2022
Line 24:		Line 24:

	# Again, it does not have any obvious musical or mathematical meaning in this context.		# Again, it does not have any obvious musical or mathematical meaning in this context.
	# There is an argument that using torsion in this way is an abuse of the term, which was originally applied to periodicity blocks, not temperaments<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2937 which is also referred to here http://tonalsoft.com/enc/t/torsion.aspx</ref>. Both periodicity blocks and temperaments can be defined by lists of commas. And either way, these lists can be saturated or unsaturated. But in the case of periodicity blocks — where commas ''are not tempered out'' — there is an audible difference in the choice between a saturated and unsaturated list, whereas with a temperament — where commas ''are tempered out'' — there is no audible difference. In concrete terms, while it can make sense to construct a Fokker block with {{vector\|-4 4 -1}} in the middle and {{vector\|-8 8 -2}} = 2{{vector\|-4 4 -1}} at the edge — which leads to a pitch system with 24 pitches instead of 12 where half of the pitches are a copy of the other half but offset by a fixed amount — it does not make sense to imagine a temperament which tempers out 2{{vector\|-4 4 -1}} but does not temper out {{vector\|-4 4 -1}}. And so the conflation<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2405</ref> of the two situations by using the same term is misleading, so the authors of this particle believe that the term torsion should not be used in RTT. While ~~it can be argued that~~ it is ''theoretically possible'' to interpret RTT using mathematical structures like quotient subgroups, lattices, and free abelian groups, or in other words, as if a temperament looked like a periodicity block, in which case one can imagine a reality where e.g. (81/80)² is tempered out while 81/80 is not, this is not how temperaments actually sound from a musical point of view in our physical reality; in this case, the inherently projective approach to linear algebra, where tempered out (81/80)² and 81/80 map to the same tempered lattice node, models this problem better. So "torsion" could be preserved as a term for the effect on periodicity blocks (though there's almost certainly something more helpful than that, but that's a battle for another day<ref>Furthermore, care should be taken to recognize the difference in behavior between, say<br><br>		# There is an argument that using torsion in this way is an abuse of the term, which was originally applied to periodicity blocks, not temperaments<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2937 which is also referred to here http://tonalsoft.com/enc/t/torsion.aspx</ref>. Both periodicity blocks and temperaments can be defined by lists of commas. And either way, these lists can be saturated or unsaturated. But in the case of periodicity blocks — where commas ''are not tempered out'' — there is an audible difference in the choice between a saturated and unsaturated list, whereas with a temperament — where commas ''are tempered out'' — there is no audible difference. In concrete terms, while it can make sense to construct a Fokker block with {{vector\|-4 4 -1}} in the middle and {{vector\|-8 8 -2}} = 2{{vector\|-4 4 -1}} at the edge — which leads to a pitch system with 24 pitches instead of 12 where half of the pitches are a copy of the other half but offset by a fixed amount — it does not make sense to imagine a temperament which tempers out 2{{vector\|-4 4 -1}} but does not temper out {{vector\|-4 4 -1}}. And so the conflation<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2405</ref> of the two situations by using the same term is misleading, so the authors of this particle believe that the term torsion should not be used in RTT. While it is ''theoretically possible'' to interpret RTT using mathematical structures like quotient subgroups, lattices, and free abelian groups, or in other words, as if a temperament looked like a periodicity block, in which case one can imagine a reality where e.g. (81/80)² is tempered out while 81/80 is not, this is not how temperaments actually sound from a musical point of view in our physical reality; in this case, the inherently projective approach to linear algebra, where tempered out (81/80)² and 81/80 map to the same tempered lattice node, models this problem better. So "torsion" could be preserved as a term for the effect on periodicity blocks (though there's almost certainly something more helpful than that, but that's a battle for another day<ref>Furthermore, care should be taken to recognize the difference in behavior between, say<br><br>
	<math>		<math>
	\left[		\left[

Cmloegcmluin: consolidate categories

2021-12-25T13:24:37Z

consolidate categories

← Older revision		Revision as of 13:24, 25 December 2021
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	== References ==		== References ==

	~~[[Category:Temperament]]~~
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	~~[[Category:Theory]]~~
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Math]]		[[Category:Math]]

Cmloegcmluin: another argument I realized was not made explicit

2021-12-20T16:21:00Z

another argument I realized was not made explicit

← Older revision		Revision as of 16:21, 20 December 2021
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	# "Enfactored" sounds a bit like "infected", better suggesting the [[The pathology of enfactoring\|pathological case]] of unsaturation.		# "Enfactored" sounds a bit like "infected", better suggesting the [[The pathology of enfactoring\|pathological case]] of unsaturation.
	# They don't have any of the problems listed for the other terms.		# They don't have any of the problems listed for the other terms.
			# When you use both of them together, the relationship between torsion/contorsion and saturation becomes obvious through the terminology, where before it was unapparent.

	== Defactoring, to replace saturation ==		== Defactoring, to replace saturation ==

Cmloegcmluin: add categories

2021-12-10T17:07:13Z

add categories

← Older revision		Revision as of 17:07, 10 December 2021
Line 43:		Line 43:

	== References ==		== References ==

			[[Category:Temperament]]
			[[Category:Regular temperament theory]]
			[[Category:Theory]]
			[[Category:Terms]]
			[[Category:Math]]