User:Hkm/Sandbox - Revision history

Hkm at 00:32, 26 August 2025

2025-08-26T00:32:48Z

← Older revision		Revision as of 00:32, 26 August 2025
Line 335:		Line 335:
	== asdf ==		== asdf ==
	{{Harmonics in equal		{{Harmonics in equal
	\| steps = 29		\| steps = 57
	\| num = 3		\| num = 6
	\| denom = 1		\| denom = 1
	\| intervals = integer		\| intervals = integer
	}}		}}

Hkm at 00:32, 26 August 2025

2025-08-26T00:32:29Z

← Older revision		Revision as of 00:32, 26 August 2025
Line 333:		Line 333:
	\| 140 \|\| 139.97 \|\| 43.9 \|\| +0.12		\| 140 \|\| 139.97 \|\| 43.9 \|\| +0.12
	\|}		\|}
	== ~~128::256~~ ==		== asdf ==
			{{Harmonics in equal
			\| steps = 29
			\| num = 3
			\| denom = 1
			\| intervals = integer
			}}

Hkm at 01:30, 17 August 2025

2025-08-17T01:30:57Z

← Older revision		Revision as of 01:30, 17 August 2025
Line 3:		Line 3:
	== Sadbox ==		== Sadbox ==

	=== ~~Practicality~~ ===		=== Impractical ===
	3 Wedgies		3 Wedgies

Line 16:		Line 16:
	3 31ed2 (beginner-friendliness)		3 31ed2 (beginner-friendliness)

	=== ~~Writing~~ ===		=== Badly written ===
	5 Intro to Xenharmonics (can be supplemented with user:hkm/Intro_page)		5 Intro to Xenharmonics (can be supplemented with user:hkm/Intro_page)

Line 27:		Line 27:
	3 FAQ		3 FAQ

	=== ~~Criticality~~ ===		=== Unnecessary ===
	1 Oodako		1 Oodako

Line 36:		Line 36:
	2 A bunch of stub pages		2 A bunch of stub pages

	=== ~~Naming~~ ===		=== Badly named ===
	1 1025/1024		1 1025/1024

	=== ~~Design~~ ===		=== Badly designed ===
	2 Ploidacot (why the number names?)		2 Ploidacot (why the number names?)

	=== ~~Formatting~~ ===		=== Badly formatted ===
	2 Practically all edo pages <50 (algorithmically generated material, like GPVs and sagittal notations, should be moved to the GPV and sagittal pages, for example. The interval table gets to stay though)		2 Practically all edo pages <50 (algorithmically generated material, like GPVs and sagittal notations, should be moved to the GPV and sagittal pages, for example. The interval table gets to stay though)

Hkm at 19:03, 10 August 2025

2025-08-10T19:03:40Z

← Older revision		Revision as of 19:03, 10 August 2025
Line 333:		Line 333:
	\| 140 \|\| 139.97 \|\| 43.9 \|\| +0.12		\| 140 \|\| 139.97 \|\| 43.9 \|\| +0.12
	\|}		\|}
			== 128::256 ==

Hkm at 23:48, 7 August 2025

2025-08-07T23:48:17Z

Show changes

Hkm at 23:47, 7 August 2025

2025-08-07T23:47:08Z

Show changes

Hkm: /* Badness */

2025-08-03T21:22:35Z

Badness

← Older revision		Revision as of 21:22, 3 August 2025
Line 46:		Line 46:

	== Badness ==		== Badness ==
	$$\frac{a}{b}$$		$\frac{a}{b}$

Hkm at 21:22, 3 August 2025

2025-08-03T21:22:20Z

← Older revision		Revision as of 21:22, 3 August 2025
Line 46:		Line 46:

	== Badness ==		== Badness ==
	~~Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93 (if we say that step~~ a/b ~~has complexity a+b), and magic_number ~ 2. Let goodness_measurer be a variable.~~		$$\frac{a}{b}$$

	Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)*error_power) complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign to each note and just interval a tempered interval rooted on that note, and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.

Hkm: /* Badness */

2025-06-25T23:37:35Z

Badness

← Older revision		Revision as of 23:37, 25 June 2025
Line 48:		Line 48:
	Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93 (if we say that step a/b has complexity a+b), and magic_number ~ 2. Let goodness_measurer be a variable.		Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93 (if we say that step a/b has complexity a+b), and magic_number ~ 2. Let goodness_measurer be a variable.

	Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)*error_power) complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign ~~a JI interpretation~~ to each ~~pair of notes~~ and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.		Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)*error_power) complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign to each note and just interval a tempered interval rooted on that note, and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.

Hkm: /* Badness */

2025-06-25T23:32:09Z

Badness

← Older revision		Revision as of 23:32, 25 June 2025
Line 46:		Line 46:

	== Badness ==		== Badness ==
	Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93, and magic_number ~ 2. Let goodness_measurer be a variable.		Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93 (if we say that step a/b has complexity a+b), and magic_number ~ 2. Let goodness_measurer be a variable.

	Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)*error_power) complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.		Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)*error_power) complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.