User:FloraC/Critique on D&D's terminology - Revision history

FloraC: Deprecating this essay following a deeper research on terminology and the math of RTT

2023-11-29T19:03:06Z

Deprecating this essay following a deeper research on terminology and the math of RTT

← Older revision		Revision as of 19:03, 29 November 2023
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	~~<div style~~=~~"background: aliceblue; color: darkslategray; font-style: italic; border: 1px solid lightblue; margin: 15px; padding: 15px; text-align: center;">~~		{{Mbox\|text=
			This essay is deprecated. It no longer fully represents the author's POVs. Rework is planned.
	This ~~page~~ is ~~a work in progress~~.		}}

	~~</div>~~

	This is a critique on the term choices in ''Dave Keenan & Douglas Blumeyer's guide to RTT'' and related articles. The main purpose of this essay is to raise awareness of good communication tools and warn against an unnecessary community fragmentation. The entries will be ordered by difficulty – those which can be easily fixed come at the top and those which may require deeper investigations are given at the bottom.		This is a critique on the term choices in ''Dave Keenan & Douglas Blumeyer's guide to RTT'' and related articles. The main purpose of this essay is to raise awareness of good communication tools and warn against an unnecessary community fragmentation. The entries will be ordered by difficulty – those which can be easily fixed come at the top and those which may require deeper investigations are given at the bottom.

FloraC: /* "Domain basis" */ update to better reflect the current status

2023-11-20T09:27:34Z

"Domain basis": update to better reflect the current status

← Older revision		Revision as of 09:27, 20 November 2023
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	== "Domain basis" ==		== "Domain basis" ==
	''Domain'' and ''domain basis'' are D&D's replacements for ''subgroup'' and ''subgroup basis'', respectively. They ~~laid out a number of reasons. I will discuss them one by one.~~		''Domain'' and ''domain basis'' are D&D's replacements for ''subgroup'' and ''subgroup basis'', respectively. Currently the main reasoning is based on pedagogical needs. They argue for using linear algebra, the less advanced math theory, rather than group theory, the more advanced, since they believe the difference between the vector space and the free abelian group is negligible for practical purposes.

	~~=== Consistency ===~~
	~~<s>First~~, they ~~argue ''subgroup''~~ and ~~''basis'' are inconsistent terms since they are a mix from different mathematical fields~~.

	<blockquote>		<blockquote>

	~~The term "subgroup basis" mixes mathematical terminology from different mathematical fields: "subgroup" comes from~~ group theory, ~~while "basis" comes~~ from linear algebra. ~~The equivalent term for "subgroup" in~~ linear algebra ~~is "subspace"~~, ~~and~~ the ~~equivalent term for "basis" in group theory is "minimal generating set"~~.		This is because group theory is a relatively obscure and advanced field of mathematics, and this article prefers to leverage terminology from the more well-known and basic field of linear algebra whenever possible. […] some argue that RTT cannot be sufficiently described using only linear algebra. This article, however, prioritizes pedagogy of the basics over any potential considerations arising from such advanced RTT problems.

	</blockquote>		</blockquote>

	~~That~~ is ~~not~~ correct. ~~The basis is a concept~~ that ~~is used across linear algebra and a particular sector of group theory:~~ the ~~study of free abelian groups~~. ~~If you look up~~ the ~~definition of~~ the ~~free abelian group~~, it ~~is simple: a free abelian group is an abelian group~~ that ~~has a basis~~. ~~Indeed~~, in RTT, ~~JI is modeled as a free abelian group, rather than a group or module in general. That is why bases are used~~.		Here they admit that ''subgroup'' is technically more correct than ''subspace''. It should be pointed out that their reason seems to be one ''for'' taking the correct terms, not ''against''. Specifically, they draw the comparison between the two math disciplines, and it appears that RTT would be more difficult by taking the correct terms. The problem in their logic is, if "advanced RTT problems" only arise occasionally, the actual difficulty levels should be similar.

	~~Since a~~ free abelian ~~group is a group~~, ~~it naturally has subgroups. It is not a vector space~~, ~~so we do not speak of subspaces – but that has~~ to ~~do with their next point below~~. ~~</s>~~		The story behind it is that RTT does not make use of the full power of group theory. RTT only concerns free abelian groups, which as they appropriately noted, are similar to vector spaces.

	~~Update~~: ~~Case closed~~.		My suggestion: use ''subgroup'' and ''subgroup basis''. These are technically correct, consistent, and as clear as they can get. Maybe even ''sub-'' is not needed, just ''group'', but that is another topic.

	=== ~~Simplicity~~ ===		=== Resolved issues ===
	~~They say~~ they ~~prefer linear algebra, the less advanced math theory, to group theory, the more advanced,~~ since they ~~believe the difference between the vector space and the free abelian group is negligible for practical purposes~~.		==== Consistency ====
			<s>First, they argue ''subgroup'' and ''basis'' are inconsistent terms since they are a mix from different mathematical fields.

	<blockquote>		<blockquote>

	~~This is because~~ group theory ~~is a relatively obscure and advanced field of mathematics~~, ~~and this article prefers to leverage terminology~~ from ~~the more well-known and basic field of~~ linear algebra ~~whenever possible~~. ~~[…] some argue that RTT cannot be sufficiently described using only~~ linear algebra~~. This article~~, ~~however, prioritizes pedagogy of~~ the ~~basics over any potential considerations arising from such advanced RTT problems~~.		The term "subgroup basis" mixes mathematical terminology from different mathematical fields: "subgroup" comes from group theory, while "basis" comes from linear algebra. The equivalent term for "subgroup" in linear algebra is "subspace", and the equivalent term for "basis" in group theory is "minimal generating set".

	</blockquote>		</blockquote>

	~~Here they admit that ''subgroup''~~ is ~~technically more~~ correct ~~than ''subspace''~~. ~~It should be pointed out~~ that ~~their reason seems to be one ''for'' taking~~ the ~~correct terms, not ''against''~~. ~~Specifically, they draw~~ the ~~comparison between~~ the ~~two math disciplines~~, ~~and~~ it ~~appears~~ that ~~RTT would be more difficult by taking the correct terms~~. ~~The problem~~ in ~~their logic~~ is, ~~if "advanced RTT problems" only arise occasionally, the actual difficulty levels should be similar~~.		That is not correct. The basis is a concept that is used across linear algebra and a particular sector of group theory: the study of free abelian groups. If you look up the definition of the free abelian group, it is simple: a free abelian group is an abelian group that has a basis. Indeed, in RTT, JI is modeled as a free abelian group, rather than a group or module in general. That is why bases are used.

	~~The story behind~~ it is ~~that RTT does~~ not ~~make use~~ of ~~the full power of group theory. RTT only concerns free abelian groups, which as they appropriately noted, are similar~~ to ~~vector spaces~~.		Since a free abelian group is a group, it naturally has subgroups. It is not a vector space, so we do not speak of subspaces – but that has to do with their next point below. </s>

	=== Specificity ===		==== Specificity ====
	<s>At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms.		<s>At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms.

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	To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete. </s>		To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete. </s>

	~~Update: Case closed.~~		==== Inclusivity ====

	=== Inclusivity ===
	<s>Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types.		<s>Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types.

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	The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''. </s>		The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''. </s>

	~~Update: Case closed.~~

	~~=== My suggestion ===~~
	~~My suggestion: use ''subgroup'' and ''subgroup basis''. These are technically correct, consistent, and as clear as they can get.~~

	~~Update: maybe even ''sub'' is not needed, just ''group'', but that is another topic.~~

	== "Prime-count vector" ==		== "Prime-count vector" ==

FloraC: Adopt semantic formatting

2023-11-20T09:16:27Z

Adopt semantic formatting

← Older revision		Revision as of 09:16, 20 November 2023
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	<s>First, they argue ''subgroup'' and ''basis'' are inconsistent terms since they are a mix from different mathematical fields.		<s>First, they argue ''subgroup'' and ''basis'' are inconsistent terms since they are a mix from different mathematical fields.

	<~~div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;"~~>		<blockquote>

	The term "subgroup basis" mixes mathematical terminology from different mathematical fields: "subgroup" comes from group theory, while "basis" comes from linear algebra. The equivalent term for "subgroup" in linear algebra is "subspace", and the equivalent term for "basis" in group theory is "minimal generating set".		The term "subgroup basis" mixes mathematical terminology from different mathematical fields: "subgroup" comes from group theory, while "basis" comes from linear algebra. The equivalent term for "subgroup" in linear algebra is "subspace", and the equivalent term for "basis" in group theory is "minimal generating set".

	</~~div~~>		</blockquote>

	That is not correct. The basis is a concept that is used across linear algebra and a particular sector of group theory: the study of free abelian groups. If you look up the definition of the free abelian group, it is simple: a free abelian group is an abelian group that has a basis. Indeed, in RTT, JI is modeled as a free abelian group, rather than a group or module in general. That is why bases are used.		That is not correct. The basis is a concept that is used across linear algebra and a particular sector of group theory: the study of free abelian groups. If you look up the definition of the free abelian group, it is simple: a free abelian group is an abelian group that has a basis. Indeed, in RTT, JI is modeled as a free abelian group, rather than a group or module in general. That is why bases are used.
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	Since a free abelian group is a group, it naturally has subgroups. It is not a vector space, so we do not speak of subspaces – but that has to do with their next point below. </s>		Since a free abelian group is a group, it naturally has subgroups. It is not a vector space, so we do not speak of subspaces – but that has to do with their next point below. </s>

	Case closed.		Update: Case closed.

	=== Simplicity ===		=== Simplicity ===
	They say they prefer linear algebra, the less advanced math theory, to group theory, the more advanced, since they believe the difference between the vector space and the free abelian group is negligible for practical purposes.		They say they prefer linear algebra, the less advanced math theory, to group theory, the more advanced, since they believe the difference between the vector space and the free abelian group is negligible for practical purposes.

	<~~div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;"~~>		<blockquote>

	This is because group theory is a relatively obscure and advanced field of mathematics, and this article prefers to leverage terminology from the more well-known and basic field of linear algebra whenever possible. […] some argue that RTT cannot be sufficiently described using only linear algebra. This article, however, prioritizes pedagogy of the basics over any potential considerations arising from such advanced RTT problems.		This is because group theory is a relatively obscure and advanced field of mathematics, and this article prefers to leverage terminology from the more well-known and basic field of linear algebra whenever possible. […] some argue that RTT cannot be sufficiently described using only linear algebra. This article, however, prioritizes pedagogy of the basics over any potential considerations arising from such advanced RTT problems.

	</~~div~~>		</blockquote>

	Here they admit that ''subgroup'' is technically more correct than ''subspace''. It should be pointed out that their reason seems to be one ''for'' taking the correct terms, not ''against''. Specifically, they draw the comparison between the two math disciplines, and it appears that RTT would be more difficult by taking the correct terms. The problem in their logic is, if "advanced RTT problems" only arise occasionally, the actual difficulty levels should be similar.		Here they admit that ''subgroup'' is technically more correct than ''subspace''. It should be pointed out that their reason seems to be one ''for'' taking the correct terms, not ''against''. Specifically, they draw the comparison between the two math disciplines, and it appears that RTT would be more difficult by taking the correct terms. The problem in their logic is, if "advanced RTT problems" only arise occasionally, the actual difficulty levels should be similar.
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	<s>At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms.		<s>At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms.

	<~~div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;"~~>		<blockquote>

	This article prefers to use specialized terminology for objects in our RTT application, so that we can clearly discuss them independently from the mathematical structures that represent them.		This article prefers to use specialized terminology for objects in our RTT application, so that we can clearly discuss them independently from the mathematical structures that represent them.

	</~~div~~>		</blockquote>

	To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete. </s>		To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete. </s>

	Case closed.		Update: Case closed.

	=== Inclusivity ===		=== Inclusivity ===
	<s>Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types.		<s>Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types.

	<~~div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;"~~>		<blockquote>

	"Subgroup" in many typical RTT usages is apparently intended to exclude the standard prime-limit subgroups. This makes it more difficult than necessary to communicate about the standard prime-limit basis, which are still very much subgroups — of the entire space of primes, for one example. So we think this is unnecessary complexity with no clear benefit.		"Subgroup" in many typical RTT usages is apparently intended to exclude the standard prime-limit subgroups. This makes it more difficult than necessary to communicate about the standard prime-limit basis, which are still very much subgroups — of the entire space of primes, for one example. So we think this is unnecessary complexity with no clear benefit.

	</~~div~~>		</blockquote>

	There is no explicit, clear-cut exclusion of standard subgroups in the definition. Technically, a full prime-limit JI is a subgroup of a larger prime-limit JI. It happens that we have distinct vocabulary for standard subgroups, so the word only tends to appear at the nonstandard type. They also say the term "has taken on a specialized meaning in RTT", which I am again not sure about. For one thing, it has never gained a distinct definition. Still, according to my observation, whether it is meant to include the standard type is up to the context.		There is no explicit, clear-cut exclusion of standard subgroups in the definition. Technically, a full prime-limit JI is a subgroup of a larger prime-limit JI. It happens that we have distinct vocabulary for standard subgroups, so the word only tends to appear at the nonstandard type. They also say the term "has taken on a specialized meaning in RTT", which I am again not sure about. For one thing, it has never gained a distinct definition. Still, according to my observation, whether it is meant to include the standard type is up to the context.
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	The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''. </s>		The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''. </s>

	Case closed.		Update: Case closed.

	=== My suggestion ===		=== My suggestion ===
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	Until I do a further research on the original thread. However this part, which I reckon is used to suggest that ''val'' be wrong, does not hold:		Until I do a further research on the original thread. However this part, which I reckon is used to suggest that ''val'' be wrong, does not hold:

	<~~div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;"~~>		<blockquote>

	"p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").		"p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").

	</~~div~~>		</blockquote>

	There is only ''valuation'', not ''p-adic valuation'', and each element is indeed a valuation i.e. how many generators that make the prime.		There is only ''valuation'', not ''p-adic valuation'', and each element is indeed a valuation i.e. how many generators that make the prime.
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	The other philosophy embedded in ''uniform map'' and ''integer uniform map'' is a turn of conceptual framing:		The other philosophy embedded in ''uniform map'' and ''integer uniform map'' is a turn of conceptual framing:

	<~~div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;"~~>		<blockquote>

	For patent vals and GPVs, patent vals are considered the base case, and GPVs a generalization thereof, whereas for uniform maps and integer uniform maps, uniform maps are considered the base case and integer uniform maps a specialization thereof. There is an argument that uniform maps are the more fundamental and important concept to regular temperament theory and therefore that this framing is the superior of the two.		For patent vals and GPVs, patent vals are considered the base case, and GPVs a generalization thereof, whereas for uniform maps and integer uniform maps, uniform maps are considered the base case and integer uniform maps a specialization thereof. There is an argument that uniform maps are the more fundamental and important concept to regular temperament theory and therefore that this framing is the superior of the two.

	</~~div~~>		</blockquote>

	Yet think of how we learned division. It is the same cognitive process: we first divide things by integers, and then we learn to extend the divisors to non-integers. That leads to the reason why the base name of ''patent val'' is arguably more friendly to our minds.		Yet think of how we learned division. It is the same cognitive process: we first divide things by integers, and then we learn to extend the divisors to non-integers. That leads to the reason why the base name of ''patent val'' is arguably more friendly to our minds.

FloraC: I just discovered that these had been responded already

2023-05-27T09:48:41Z

I just discovered that these had been responded already

← Older revision		Revision as of 09:48, 27 May 2023
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	=== Consistency ===		=== Consistency ===
	First, they argue ''subgroup'' and ''basis'' are inconsistent terms since they are a mix from different mathematical fields.		<s>First, they argue ''subgroup'' and ''basis'' are inconsistent terms since they are a mix from different mathematical fields.

	<div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;">		<div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;">
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	That is not correct. The basis is a concept that is used across linear algebra and a particular sector of group theory: the study of free abelian groups. If you look up the definition of the free abelian group, it is simple: a free abelian group is an abelian group that has a basis. Indeed, in RTT, JI is modeled as a free abelian group, rather than a group or module in general. That is why bases are used.		That is not correct. The basis is a concept that is used across linear algebra and a particular sector of group theory: the study of free abelian groups. If you look up the definition of the free abelian group, it is simple: a free abelian group is an abelian group that has a basis. Indeed, in RTT, JI is modeled as a free abelian group, rather than a group or module in general. That is why bases are used.

	Since a free abelian group is a group, it naturally has subgroups. It is not a vector space, so we do not speak of subspaces – but that has to do with their next point below.		Since a free abelian group is a group, it naturally has subgroups. It is not a vector space, so we do not speak of subspaces – but that has to do with their next point below. </s>

			Case closed.

	=== Simplicity ===		=== Simplicity ===
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	=== Specificity ===		=== Specificity ===
	At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms.		<s>At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms.

	<div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;">		<div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;">
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	</div>		</div>

	To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete.		To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete. </s>

			Case closed.

	=== Inclusivity ===		=== Inclusivity ===
	Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types.		<s>Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types.

	<div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;">		<div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;">
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	There is no explicit, clear-cut exclusion of standard subgroups in the definition. Technically, a full prime-limit JI is a subgroup of a larger prime-limit JI. It happens that we have distinct vocabulary for standard subgroups, so the word only tends to appear at the nonstandard type. They also say the term "has taken on a specialized meaning in RTT", which I am again not sure about. For one thing, it has never gained a distinct definition. Still, according to my observation, whether it is meant to include the standard type is up to the context.		There is no explicit, clear-cut exclusion of standard subgroups in the definition. Technically, a full prime-limit JI is a subgroup of a larger prime-limit JI. It happens that we have distinct vocabulary for standard subgroups, so the word only tends to appear at the nonstandard type. They also say the term "has taken on a specialized meaning in RTT", which I am again not sure about. For one thing, it has never gained a distinct definition. Still, according to my observation, whether it is meant to include the standard type is up to the context.

	The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''.		The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''. </s>

			Case closed.

	=== My suggestion ===		=== My suggestion ===
	My suggestion: use ''subgroup'' and ''subgroup basis''. These are technically correct, consistent, and as clear as they can get.		My suggestion: use ''subgroup'' and ''subgroup basis''. These are technically correct, consistent, and as clear as they can get.

			Update: maybe even ''sub'' is not needed, just ''group'', but that is another topic.

	== "Prime-count vector" ==		== "Prime-count vector" ==
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	My suggestion: use ''monzo'', and if you need to explain it, try saying they are ''harmonic space coordinates''.		My suggestion: use ''monzo'', and if you need to explain it, try saying they are ''harmonic space coordinates''.

	~~== "Held~~ interval~~" ==~~		Update: There are probably some fundamental discrepancies in our understandings of what a vector, and what an interval in RTT is, and I do not believe it has to do with the field. My main point remains that monzo is the presentational form and vector is not, and that all intervals are vectors in RTT however they are presented.
	I ~~really don't get~~ the ~~obsession of expressing a single coherent concept in multiple words~~. ~~A held interval~~ is ~~simply a constraint. A constraint~~ is ~~something~~ that ~~constrains the system~~.

	~~My suggestion~~: ~~use~~ ''~~constraint~~''.		== "Held-interval" ==
			<s>I really don't get the obsession of expressing a single coherent concept in multiple words. A held interval is simply a constraint. A constraint is something that constrains the system. </s>

			Update: I admit there is nothing inherently wrong about ''held-interval''. ''Constraint'' is used in the context where we talk about optimization of an abstract math problem so it is a term that one would always encounter. A purely tuned, purely constrained, or held interval is the real-world counterpart of it. So it is up to the user which aspect of the concept they are thinking of.

	== "Map" ==		== "Map" ==
	See [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7525.html ''Vals?''] where Gene Ward Smith presented in-depth explanation and defense of the term. There is nothing to repeat and I find it uncool to revive the topic after Gene's death.		<s>See [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7525.html ''Vals?''] where Gene Ward Smith presented in-depth explanation and defense of the term. There is nothing to repeat and I find it uncool to revive the topic after Gene's death.</s>

			Until I do a further research on the original thread. However this part, which I reckon is used to suggest that ''val'' be wrong, does not hold:

			<div style="font-style: italic; border: 1px solid silver; margin: 15px; padding: 15px;">

			"p-adic valuation" is an obscure term for "prime count", which would be an element of a prime-count vector ("monzo"), not a map ("val").

			</div>

			There is only ''valuation'', not ''p-adic valuation'', and each element is indeed a valuation i.e. how many generators that make the prime.

	== "Simple map" ==		== "Simple map" ==

FloraC: Recommend "just tuning map"

2023-05-27T08:46:10Z

Recommend "just tuning map"

← Older revision		Revision as of 08:46, 27 May 2023
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	My suggestion: use ''enfactoring'' when there is no need to distinguish its two types. But we should probably never forget ''torsion'' and ''contorsion''.		My suggestion: use ''enfactoring'' when there is no need to distinguish its two types. But we should probably never forget ''torsion'' and ''contorsion''.

			== "Just tuning map" ==
			''Just tuning map'' is D&D's replacement for ''just intonation point'' (''JIP''). I feel very positive about this replacement, as the neologism concisely conveys both the structure (a tuning map) and its contents (JI). In the original term ''intonation'' is one word's space wasted and ''point'' sounds no more than a filler word without the right context (a point in the tuning space).

			I recommend ''just tuning map''.

FloraC: /* "Prime-count vector" */

2023-03-30T04:18:41Z

"Prime-count vector"

← Older revision		Revision as of 04:18, 30 March 2023
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	On the other hand, the monzo is not the ket, nor should it really include kets by definition. A monzo can be rendered with kets, like {{ket\| -4 4 -1 }}, or brackets with the transpose symbol, like [-4 4 -1]<sup>T</sup>, or parentheses and comma separators, like (-4, 4, -1). Just as emphasis can be rendered using italic, bold or underscore. The common spirit among these rendering is the bracketed and appropriately spaced part.		On the other hand, the monzo is not the ket, nor should it really include kets by definition. A monzo can be rendered with kets, like {{ket\| -4 4 -1 }}, or brackets with the transpose symbol, like [-4 4 -1]<sup>T</sup>, or parentheses and comma separators, like (-4, 4, -1). Just as emphasis can be rendered using italic, bold or underscore. The common spirit among these rendering is the bracketed and appropriately spaced part.

	I will not have a problem with Plainsound Music Edition's ''harmonic space coordinates'' as a synonym of ''monzo'', because a list of coordinates is indeed a form of presentation. ''Monzo'' has the advantage that it is concise – more on the name side than on the description side.		I will not have a problem with Plainsound Music Edition's ''harmonic space coordinates'' as a synonym of ''monzo'', because a list of coordinates is indeed a form of presentation. ''Monzo'' has the advantage that it is concise – more on the name side than on the description side. A name points to a definition with minimal connotations at face value, whereas a description stays intermediate between the conciseness of a name and the rigor of a definition – and so it does not work as a replacement of either.

	My suggestion: use ''monzo'', and if you need to explain it, try saying they are ''harmonic space coordinates''.		My suggestion: use ''monzo'', and if you need to explain it, try saying they are ''harmonic space coordinates''.

FloraC: /* "Map" */

2023-03-30T04:11:18Z

"Map"

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	== "Map" ==		== "Map" ==
	See: [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7525.html ''Vals?'']		See [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_7525.html ''Vals?''] where Gene Ward Smith presented in-depth explanation and defense of the term. There is nothing to repeat and I find it uncool to revive the topic after Gene's death.

	== "Simple map" ==		== "Simple map" ==

FloraC: /* "Prime-count vector" */

2023-02-22T10:26:04Z

"Prime-count vector"

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	== "Prime-count vector" ==		== "Prime-count vector" ==
	''Prime-count vector'' is D&D's replacement for ''monzo''. This is one of the worse proposed terms as it includes an inaccurate use of the term ''vector''. A vector is a mathematical structure rather than a form of presentation, so a JI interval is a vector no matter how it is written. For example, the syntonic comma, 81/80, and {{monzo\| -4 4 -1 }} are all vectors, and since the vectors represent the number of each prime harmonics, they are prime-count vectors. It would be ridiculous in RTT to say the syntonic comma was not a vector, or to say 81/80 was not a vector.		''Prime-count vector'' is D&D's replacement for ''monzo''. This is one of the worse proposed terms as it includes an inaccurate use of the term ''vector''. A vector is a mathematical structure rather than a form of presentation, so a JI interval is essentially a vector no matter how it is written and what face value it takes on. For example, the syntonic comma, 81/80, and {{monzo\| -4 4 -1 }} are all vectors, and since the vectors represent the number of each prime harmonics, they are prime-count vectors. It would be ridiculous in RTT to say the syntonic comma was not a vector, or to say 81/80 was not a vector. It follows that wherever we use ''vector'' we may as well use ''interval''.

	A monzo is a particular notation of a vector. The ''monzo'' article clearly tells us a monzo is "a way of notating a JI interval". The more technical ''monzos and interval space'' article reads: "this is often written in ket vector notation as […] in which case it is called a monzo." It often happens that the different forms of an interval such as the name, ratio, and monzo are shown side by side. In the above example, neither the syntonic comma nor 81/80 is a monzo, but {{monzo\| -4 4 -1 }}.		A monzo is a particular notation of a vector. The ''monzo'' article clearly tells us a monzo is "a way of notating a JI interval". The more technical ''monzos and interval space'' article reads: "this is often written in ket vector notation as […] in which case it is called a monzo." It often happens that the different forms of an interval such as the name, ratio, and monzo are shown side by side. In the above example, neither the syntonic comma nor 81/80 is a monzo, but {{monzo\| -4 4 -1 }}.

FloraC: /* "Prime-count vector" */ monzo vs ket

2023-02-13T12:31:01Z

"Prime-count vector": monzo vs ket

← Older revision		Revision as of 12:31, 13 February 2023
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	''Prime-count vector'' is D&D's replacement for ''monzo''. This is one of the worse proposed terms as it includes an inaccurate use of the term ''vector''. A vector is a mathematical structure rather than a form of presentation, so a JI interval is a vector no matter how it is written. For example, the syntonic comma, 81/80, and {{monzo\| -4 4 -1 }} are all vectors, and since the vectors represent the number of each prime harmonics, they are prime-count vectors. It would be ridiculous in RTT to say the syntonic comma was not a vector, or to say 81/80 was not a vector.		''Prime-count vector'' is D&D's replacement for ''monzo''. This is one of the worse proposed terms as it includes an inaccurate use of the term ''vector''. A vector is a mathematical structure rather than a form of presentation, so a JI interval is a vector no matter how it is written. For example, the syntonic comma, 81/80, and {{monzo\| -4 4 -1 }} are all vectors, and since the vectors represent the number of each prime harmonics, they are prime-count vectors. It would be ridiculous in RTT to say the syntonic comma was not a vector, or to say 81/80 was not a vector.

	A monzo is a particular ~~form~~ of ~~presentation~~. The ''monzo'' article clearly tells us a monzo is "a way of notating a JI interval". ~~In the~~ more technical ''monzos and interval space'' article it reads: "this is often written in ket vector notation as […] in which case it is called a monzo." It often happens that the different forms of an interval such as the name, ratio, and monzo are shown side by side. In the above example, neither the syntonic comma nor 81/80 is a monzo, but {{monzo\| -4 4 -1 }}.		A monzo is a particular notation of a vector. The ''monzo'' article clearly tells us a monzo is "a way of notating a JI interval". The more technical ''monzos and interval space'' article reads: "this is often written in ket vector notation as […] in which case it is called a monzo." It often happens that the different forms of an interval such as the name, ratio, and monzo are shown side by side. In the above example, neither the syntonic comma nor 81/80 is a monzo, but {{monzo\| -4 4 -1 }}.

			On the other hand, the monzo is not the ket, nor should it really include kets by definition. A monzo can be rendered with kets, like {{ket\| -4 4 -1 }}, or brackets with the transpose symbol, like [-4 4 -1]<sup>T</sup>, or parentheses and comma separators, like (-4, 4, -1). Just as emphasis can be rendered using italic, bold or underscore. The common spirit among these rendering is the bracketed and appropriately spaced part.

	I will not have a problem with Plainsound Music Edition's ''harmonic space coordinates'' as a synonym of ''monzo'', because a list of coordinates is indeed a form of presentation. ''Monzo'' has the advantage that it is concise – more on the name side than on the description side.		I will not have a problem with Plainsound Music Edition's ''harmonic space coordinates'' as a synonym of ''monzo'', because a list of coordinates is indeed a form of presentation. ''Monzo'' has the advantage that it is concise – more on the name side than on the description side.

	My suggestion: use ''monzo'', and if you need to explain it, try saying they are ''harmonic space coordinates''.		My suggestion: use ''monzo'', and if you need to explain it, try saying they are ''harmonic space coordinates''.

	== "Held interval" ==		== "Held interval" ==

FloraC at 06:12, 31 January 2023

2023-01-31T06:12:21Z

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	== "Simple map" ==		== "Simple map" ==
	''Simple map'' is D&D's ~~replacements~~ for ''generalized patent val'' (''GPV'').		''Simple map'' is D&D's replacement for ''generalized patent val'' (''GPV'').

	I have forgotten if it was me who suggested ''simple map'' when they were discussing it, because it does look like a term that I could come up with, in the same way I suggested ''simple JI''. Unlike ''simple JI'', the main problem of ''simple map'' is again lack of specificity while taking on a very specific and rigorous meaning. ''Simple'' and ''complex'' are definitely reasonable qualities of a ''map'', which means ''val''.		I have forgotten if it was me who suggested ''simple map'' when they were discussing it, because it does look like a term that I could come up with, in the same way I suggested ''simple JI''. Unlike ''simple JI'', the main problem of ''simple map'' is again lack of specificity while taking on a very specific and rigorous meaning. ''Simple'' and ''complex'' are definitely reasonable qualities of a ''map'', which means ''val''.