Kite's thoughts on twin squares - Revision history

Overthink: Overthink moved page Kite'sthoughts on twin squares to Kite's thoughts on twin squares: Misspelled title

2026-01-11T20:34:34Z

Overthink moved page Kite'sthoughts on twin squares to Kite's thoughts on twin squares: Misspelled title

← Older revision	Revision as of 20:34, 11 January 2026
(No difference)

TallKite: TallKite moved page Twin squares to Kite'sthoughts on twin squares: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

2025-08-20T02:00:44Z

TallKite moved page Twin squares to Kite'sthoughts on twin squares: Editor VectorGraphics has repeatedly edited pages I've written about my own research and inserted misinformation. On discord he is openly hostile to me. This move is necessary to avoid a toxic work environment for me.

← Older revision	Revision as of 02:00, 20 August 2025
(No difference)

TallKite at 09:39, 19 December 2023

2023-12-19T09:39:54Z

← Older revision		Revision as of 09:39, 19 December 2023
Line 30:		Line 30:
	* discard the rows in the mapping matrix that corresponds to those commas		* discard the rows in the mapping matrix that corresponds to those commas

	The two matrices follow a simple rule: the dot product of any row in one with any row in another is 1 if the 2 rows are opposite each other (e.g. 2nd row of each matrix), and 0 if not (e.g. 1st row of one and 3rd row of the other). Thus one can easily verify that one is the inverse of the other. In fact, it's not too difficult to derive both matrices from either the comma list or the mapping. One proceeds step by step, checking as ~~you go~~, similar to solving a sudoku puzzle.		The two matrices follow a simple rule: the dot product of any row in one with any row in another is 1 if the two rows are opposite each other (e.g. 2nd row of each matrix), and 0 if not (e.g. 1st row of one and 3rd row of the other). Thus one can easily verify that one is the inverse of the other. In fact, it's not too difficult to derive both matrices from either the comma list or the mapping. One proceeds step by step, checking as one goes, similar to solving a sudoku puzzle.

	[[Category:Mapping]]		[[Category:Mapping]]

	{{todo\|review}}		{{todo\|review}}

TallKite at 09:35, 19 December 2023

2023-12-19T09:35:37Z

← Older revision		Revision as of 09:35, 19 December 2023
Line 3:		Line 3:
	<math>		<math>
	\begin{array} {rrr}		\begin{array} {rrr}
	~~per~~ \\		period \\
	~~gen~~ \\		generator \\
	~~com~~ \\		comma \\
	\end{array}		\end{array}
	\left[ \begin{array} {rrr}		\left[ \begin{array} {rrr}

TallKite at 08:44, 19 December 2023

2023-12-19T08:44:36Z

← Older revision		Revision as of 08:44, 19 December 2023
Line 7:		Line 7:
	com \\		com \\
	\end{array}		\end{array}
	\left[ \begin{array} {~~rrrr~~}		\left[ \begin{array} {rrr}
	~~2 & 3 & 5 \\~~		1 & 0 & 0 \\
	~~\left[~~ 1 & 0 & 0 \\
	-1 & 1 & 0 \\		-1 & 1 & 0 \\
	\hline		\hline

TallKite at 08:44, 19 December 2023

2023-12-19T08:44:10Z

← Older revision		Revision as of 08:44, 19 December 2023
Line 9:		Line 9:
	\left[ \begin{array} {rrrr}		\left[ \begin{array} {rrrr}
	2 & 3 & 5 \\		2 & 3 & 5 \\
	\left[		\left[ 1 & 0 & 0 \\
	1 & 0 & 0 \\
	-1 & 1 & 0 \\		-1 & 1 & 0 \\
	\hline		\hline

TallKite at 08:43, 19 December 2023

2023-12-19T08:43:39Z

← Older revision		Revision as of 08:43, 19 December 2023
Line 7:		Line 7:
	com \\		com \\
	\end{array}		\end{array}
	\begin{array} {r}		\left[ \begin{array} {rrrr}
	2 & 3 & 5 \\		2 & 3 & 5 \\
	~~\end{array}~~		\left[
	\left[ ~~\begin{array} {rrr}~~
	1 & 0 & 0 \\		1 & 0 & 0 \\
	-1 & 1 & 0 \\		-1 & 1 & 0 \\

TallKite at 08:42, 19 December 2023

2023-12-19T08:42:18Z

← Older revision		Revision as of 08:42, 19 December 2023
Line 1:		Line 1:
	'''Twin squares'''{{idiosyncratic}} (term proposed by [[Kite Giedraitis]]) is a format for presenting a [[regular temperament]]. The [[gencom]] matrix is shown side by side with its inverse, the [[mapping matrix]], which has rows for not only each generator but also each comma. Here's 5-limit meantone temperament, with period 2/1, generator 3/2 and comma 81/80:		'''Twin squares'''{{idiosyncratic}} (term proposed by [[Kite Giedraitis]]) is a format for presenting a [[regular temperament]]. The [[gencom]] matrix is shown side by side with its inverse, the [[mapping matrix]], which has rows for not only each generator but also each comma. Here's 5-limit meantone temperament, with period 2/1, generator 3/2 and comma 81/80:
	~~<math>~~
	~~2 3 5~~
	~~</math>~~
	<math>		<math>
	\begin{array} {rrr}		\begin{array} {rrr}
Line 8:		Line 6:
	gen \\		gen \\
	com \\		com \\
			\end{array}
			\begin{array} {r}
			2 & 3 & 5 \\
	\end{array}		\end{array}
	\left[ \begin{array} {rrr}		\left[ \begin{array} {rrr}

TallKite at 08:40, 19 December 2023

2023-12-19T08:40:33Z

← Older revision		Revision as of 08:40, 19 December 2023
Line 1:		Line 1:
	'''Twin squares'''{{idiosyncratic}} (term proposed by [[Kite Giedraitis]]) is a format for presenting a [[regular temperament]]. The [[gencom]] matrix is shown side by side with its inverse, the [[mapping matrix]], which has rows for not only each generator but also each comma. Here's 5-limit meantone temperament, with period 2/1, generator 3/2 and comma 81/80:		'''Twin squares'''{{idiosyncratic}} (term proposed by [[Kite Giedraitis]]) is a format for presenting a [[regular temperament]]. The [[gencom]] matrix is shown side by side with its inverse, the [[mapping matrix]], which has rows for not only each generator but also each comma. Here's 5-limit meantone temperament, with period 2/1, generator 3/2 and comma 81/80:
			<math>
			2 3 5
			</math>
	<math>		<math>
	\begin{array} {rrr}		\begin{array} {rrr}

TallKite at 08:38, 19 December 2023

2023-12-19T08:38:11Z

← Older revision		Revision as of 08:38, 19 December 2023
Line 1:		Line 1:
	'''Twin squares'''{{idiosyncratic}} (term proposed by [[Kite Giedraitis]]) is a format for presenting a [[regular temperament]]. The [[gencom]] matrix is shown side by side with its inverse, the [[mapping matrix]], which ~~is transposed so that rows multiply with~~ rows. Here's 5-limit meantone temperament, with period 2/1, generator 3/2 and comma 81/80:		'''Twin squares'''{{idiosyncratic}} (term proposed by [[Kite Giedraitis]]) is a format for presenting a [[regular temperament]]. The [[gencom]] matrix is shown side by side with its inverse, the [[mapping matrix]], which has rows for not only each generator but also each comma. Here's 5-limit meantone temperament, with period 2/1, generator 3/2 and comma 81/80:

	<math>		<math>