User:FloraC/Critique on D&D's terminology: Difference between revisions

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=== 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.

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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.

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 ===

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=== 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.

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</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 So the reason is obsolete.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 So the reason is obsolete.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 ===

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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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: 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" ==

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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" ==

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:

"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" ==

@@ Line 11: / Line 11: @@
 === 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;">
@@ Line 21: / Line 21: @@
 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 ===
@@ Line 37: / Line 39: @@
 === 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;">
@@ Line 45: / Line 47: @@
 </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 ===
-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;">
@@ Line 58: / Line 62: @@
 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: 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" ==
@@ Line 74: / Line 82: @@
 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" ==
-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" ==