User:Inthar/Sandbox - Revision history

Inthar at 03:24, 3 January 2026

2026-01-03T03:24:47Z

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-== Mode names ==
+== Theorem 9 (Ternary product words) ==
-=== 5L4s ===
+If a [[product word]] of two MOS words of the same length is ternary, then it is pairwise-MOS.
-Inthar and cellularAutomaton have proposed mode names for 5L4s based on scientific names of various corvids. The names as of 5/2/23{{Clarify}} are as follows.
+=== Proof ===
+Assume that the product of two MOS words ''v''('''a''', '''b''') and ''w''('''c''', '''d''') contains exactly three letters, say ('''a''', '''c'''), ('''a''', '''d'''), ('''b''', '''c'''). Equating ('''a''', '''c''') and ('''a''', '''d''') recovers ''v'', and equating ('''a''', '''c''') and ('''b''', '''c''') recovers ''w''. What does equating ('''a''', '''d''') and ('''b''', '''c''') do?

Inthar: /* Mode names */

2025-03-06T15:13:41Z

Mode names

← Older revision		Revision as of 15:13, 6 March 2025
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	== Mode names ==		== Mode names ==
			=== 5L4s ===
	Inthar and cellularAutomaton have proposed mode names for 5L4s based on scientific names of various corvids. The names as of 5/2/23{{Clarify}} are as follows.		Inthar and cellularAutomaton have proposed mode names for 5L4s based on scientific names of various corvids. The names as of 5/2/23{{Clarify}} are as follows.

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	\| debug={{lc:}}		\| debug={{lc:}}
	}}		}}

	== Theory versus Math ==		== Theory versus Math ==
	An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's concepts and terms. This is because music theory by nature includes the value judgments of the theorist.		An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's concepts and terms. This is because music theory by nature includes the value judgments of the theorist.

Inthar at 15:13, 6 March 2025

2025-03-06T15:13:26Z

← Older revision		Revision as of 15:13, 6 March 2025
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	Inthar and cellularAutomaton have proposed mode names for 5L4s based on scientific names of various corvids. The names as of 5/2/23{{Clarify}} are as follows.		Inthar and cellularAutomaton have proposed mode names for 5L4s based on scientific names of various corvids. The names as of 5/2/23{{Clarify}} are as follows.
	{{~~MOS modes~~
	\| Mode Names=		{{#invoke: MOS_modes \| modes_table
	Cristatan$		\| Scale Signature=5L4s
			\| Mode Names=Cristatan$
	Pican$		Pican$
	Stellerian$		Stellerian$
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	Pyrrhian		Pyrrhian
	\| Table Headers=Name Origin		\| Table Headers=Name Origin
	\| Table Entries=		\| Table Entries=Bluejay ''(Cyanocitta cristata)''$
	Bluejay ''(Cyanocitta cristata)''$
	Magpie ''(Pica pica)''$		Magpie ''(Pica pica)''$
	Steller's jay ''(Cyanocitta stelleri)''$		Steller's jay ''(Cyanocitta stelleri)''$
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	Ratchet-tailed treepie ''(genus Temnurus)''$		Ratchet-tailed treepie ''(genus Temnurus)''$
	Chough ''(genus Pyrrhocorax)''$		Chough ''(genus Pyrrhocorax)''$
			\| Collapsed=
			\| debug={{lc:}}
	}}		}}
	== Theory versus Math ==		== Theory versus Math ==

Inthar at 15:00, 6 March 2025

2025-03-06T15:00:41Z

← Older revision		Revision as of 15:00, 6 March 2025
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			== Mode names ==

			Inthar and cellularAutomaton have proposed mode names for 5L4s based on scientific names of various corvids. The names as of 5/2/23{{Clarify}} are as follows.
			{{MOS modes
			\| Mode Names=
			Cristatan$
			Pican$
			Stellerian$
			Podocian$
			Nucifragan$
			Coracian$
			Frugilegian$
			Temnurial$
			Pyrrhian
			\| Table Headers=Name Origin
			\| Table Entries=
			Bluejay ''(Cyanocitta cristata)''$
			Magpie ''(Pica pica)''$
			Steller's jay ''(Cyanocitta stelleri)''$
			Ground jay ''(genus Podoces)''$
			Nutcracker ''(genus Nucifraga)''$
			Common raven ''(Corvus corax)''$
			Rook ''(Corvus frugilegus)''$
			Ratchet-tailed treepie ''(genus Temnurus)''$
			Chough ''(genus Pyrrhocorax)''$
			}}
	== Theory versus Math ==		== Theory versus Math ==
	An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's concepts and terms. This is because music theory by nature includes the value judgments of the theorist.		An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's concepts and terms. This is because music theory by nature includes the value judgments of the theorist.

Inthar: /* Theory versus Math */

2024-02-26T10:21:55Z

Theory versus Math

← Older revision		Revision as of 10:21, 26 February 2024
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	An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's concepts and terms. This is because music theory by nature includes the value judgments of the theorist.		An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's concepts and terms. This is because music theory by nature includes the value judgments of the theorist.

	~~In contrast~~, ~~mathematical~~ constructions, even if originally developed in close association with that theory, may be described in a more idiosyncratic style (if ~~necessarily~~, a more conventionally mathematical one), with the proviso that it must be (accessibly!) transparent as to what the construction is guaranteed to satisfy and what it is not.		With the theorist's permission, an associated concept may have a non-guarded page, but any sections explaining the significance to that theory itself should be guarded.

			Mathematical constructions, even if originally developed in close association with that theory, may be described in a more idiosyncratic style (if necessary, a more conventionally mathematical one), with the proviso that it must be (accessibly!) transparent as to what the construction is guaranteed to satisfy and what it is not.

	~~With the theorist's permission, an associated concept may have a non-guarded page, but any sections explaining the significance to that theory itself should be guarded.~~

	Example: [[aberrismic theory]] is a guarded page since it's a Theory page, while [[MOS substitution]] is not, since it's a Math page. What about [[blackdye]]?		Example: [[aberrismic theory]] is a guarded page since it's a Theory page, while [[MOS substitution]] is not, since it's a Math page. What about [[blackdye]]?

Inthar: /* Theory versus Math */

2024-02-26T10:13:21Z

Theory versus Math

← Older revision		Revision as of 10:13, 26 February 2024
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	== Theory versus Math ==		== Theory versus Math ==
	An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's ~~ontology~~ and terms. This is because music theory by nature includes the value judgments of the theorist.		An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's concepts and terms. This is because music theory by nature includes the value judgments of the theorist.

	In contrast, mathematical constructions, even if originally developed in close association with that theory, may be described in a more idiosyncratic style (if necessarily, a more conventionally mathematical one), with the proviso that it must be (accessibly!) transparent as to what the construction is guaranteed to satisfy and what it is not.		In contrast, mathematical constructions, even if originally developed in close association with that theory, may be described in a more idiosyncratic style (if necessarily, a more conventionally mathematical one), with the proviso that it must be (accessibly!) transparent as to what the construction is guaranteed to satisfy and what it is not.

Inthar: /* Theory versus Math */

2024-02-26T10:13:09Z

Theory versus Math

← Older revision		Revision as of 10:13, 26 February 2024
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	== Theory versus Math ==		== Theory versus Math ==
	An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's ontology and ~~terminology~~. This is because music theory by nature includes the value judgments of the theorist.		An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's ontology and terms. This is because music theory by nature includes the value judgments of the theorist.

	In contrast, mathematical constructions, even if originally developed in close association with that theory, may be described in a more idiosyncratic style (if necessarily, a more conventionally mathematical one), with the proviso that it must be (accessibly!) transparent as to what the construction is guaranteed to satisfy and what it is not.		In contrast, mathematical constructions, even if originally developed in close association with that theory, may be described in a more idiosyncratic style (if necessarily, a more conventionally mathematical one), with the proviso that it must be (accessibly!) transparent as to what the construction is guaranteed to satisfy and what it is not.

Inthar: /* Other guidelines */

2024-02-26T10:10:55Z

Other guidelines

← Older revision		Revision as of 10:10, 26 February 2024
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	~~== Other guidelines ==~~		== Theory versus Math ==
	=== Theory versus Math ===
	An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's ontology and terminology. This is because music theory by nature includes the value judgments of the theorist.		An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's ontology and terminology. This is because music theory by nature includes the value judgments of the theorist.

Inthar at 10:10, 26 February 2024

2024-02-26T10:10:35Z

← Older revision		Revision as of 10:10, 26 February 2024
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	== ~~Conjectures~~ ==		== Other guidelines ==
			=== Theory versus Math ===
			An article about a music theory framework merits a ''guarded page''. Guarded pages should stay maximally true to the theory's ontology and terminology. This is because music theory by nature includes the value judgments of the theorist.

	~~== Procedures vs~~. ~~properties ==~~		In contrast, mathematical constructions, even if originally developed in close association with that theory, may be described in a more idiosyncratic style (if necessarily, a more conventionally mathematical one), with the proviso that it must be (accessibly!) transparent as to what the construction is guaranteed to satisfy and what it is not.

			With the theorist's permission, an associated concept may have a non-guarded page, but any sections explaining the significance to that theory itself should be guarded.

			Example: [[aberrismic theory]] is a guarded page since it's a Theory page, while [[MOS substitution]] is not, since it's a Math page. What about [[blackdye]]?

Inthar: /* Conjectures */ this probably fails badly, there are many good approximations that are not convergents or stacks.

2024-02-18T11:21:02Z

Conjectures: this probably fails badly, there are many good approximations that are not convergents or stacks.

← Older revision		Revision as of 11:21, 18 February 2024
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	== Conjectures ==		== Conjectures ==
	* Give precise estimates and bounds for the following: "If ''N''-edo approximates ''p''/''q'' with relative error δ = δ(''p'', ''q''), then any neji in mode ''m'' for any ''m'' ≤ ''M''(''p'', ''q'', ''N'') must have more than ε relative error."
	== Procedures vs. properties ==		== Procedures vs. properties ==