VectorGraphics at 21:31, 15 June 2025

2025-06-15T21:31:14Z

← Older revision		Revision as of 21:31, 15 June 2025
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	<math>		<math>
	\sim2.\sim3/2 \left[ \begin{array}{rr}		\sim2.\sim3/2 \left[ \begin{array}{rr}
	12 & 7		12 & 7 \\
	\end{array} \right]		\end{array} \right]

VectorGraphics at 21:30, 15 June 2025

2025-06-15T21:30:32Z

← Older revision		Revision as of 21:30, 15 June 2025
Line 45:		Line 45:

	<math>		<math>
	~2.~3/2 \left[ \begin{array}{rr}		\sim2.\sim3/2 \left[ \begin{array}{rr}
	12 & 7		12 & 7
	\end{array} \right]		\end{array} \right]

	2.3.5 \left[ \begin{array}{rr}		2.3.5 \left[ \begin{array}{rr}
	1 & 1 & 0 \\		1 & 1 & 0 \\

VectorGraphics at 21:29, 15 June 2025

2025-06-15T21:29:49Z

@@ Line 1: / Line 1: @@
-The operation of "tempering" can be thought of as establishing a relationship or equality between two intervals. This can be seen as a "flattening" from a higher-dimensional interval space (such as just intonation) down to a lower-dimensional space, called a ''regular temperament''; while an interval in 5-limit just intonation requires 3 numbers to represent (see [[User:VectorGraphics/Monzo notation|Monzo notation]]), an interval in meantone temperament requires only 2 numbers to represent. A '''mapping''' essentially tells you how to do that flattening, and can be seen as a list of monzos in the temperament telling you where to find each basis interval of the original interval space.
+The operation of "tempering" can be thought of as establishing a relationship or equality between two intervals. This can be seen as a "flattening" from a higher-dimensional interval space (such as just intonation) down to a lower-dimensional space, called a ''regular temperament''; while an interval in 5-limit just intonation requires 3 numbers to represent (see [[User:VectorGraphics/Monzo notation|Monzo notation]]), an interval in meantone temperament requires only 2 numbers to represent.
 For example, for meantone temperament, the mapping is:
 <math>
@@ Line 9: / Line 78: @@
 \end{array} \right]
 </math>

VectorGraphics at 20:52, 15 June 2025

2025-06-15T20:52:41Z

← Older revision		Revision as of 20:52, 15 June 2025
Line 4:		Line 4:

	<math>		<math>
	\left[ \begin{array}{rr}		2.3.5 \left[ \begin{array}{rr}
	1 & 0 & -4 \\		1 & 0 & -4 \\
	0 & 1 & 4 \\		0 & 1 & 4 \\
	\end{array} \right]		\end{array} \right]
	</math>		</math>

VectorGraphics: Created page with "The operation of "tempering" can be thought of as establishing a relationship or equality between two intervals. This can be seen as a "flattening" from a higher-dimensional interval space (such as just intonation) down to a lower-dimensional space, called a ''regular temperament''; while an interval in 5-limit just intonation requires 3 numbers to represent (see Monzo notation), an interval in meantone temperament requires only 2 n..."

2025-06-15T20:52:30Z

Created page with "The operation of "tempering" can be thought of as establishing a relationship or equality between two intervals. This can be seen as a "flattening" from a higher-dimensional interval space (such as just intonation) down to a lower-dimensional space, called a ''regular temperament''; while an interval in 5-limit just intonation requires 3 numbers to represent (see Monzo notation), an interval in meantone temperament requires only 2 n..."

New page

The operation of "tempering" can be thought of as establishing a relationship or equality between two intervals. This can be seen as a "flattening" from a higher-dimensional interval space (such as just intonation) down to a lower-dimensional space, called a ''regular temperament''; while an interval in 5-limit just intonation requires 3 numbers to represent (see [[User:VectorGraphics/Monzo notation|Monzo notation]]), an interval in meantone temperament requires only 2 numbers to represent. A '''mapping''' essentially tells you how to do that flattening, and can be seen as a list of monzos in the temperament telling you where to find each basis interval of the original interval space.

For example, for meantone temperament, the mapping is:

<math>
\left[ \begin{array}{rr}
1 & 0 & -4 \\
0 & 1 & 4 \\
\end{array} \right]
</math>

User:VectorGraphics/Mapping - Revision history

VectorGraphics at 21:31, 15 June 2025

VectorGraphics at 21:30, 15 June 2025

VectorGraphics at 21:29, 15 June 2025

VectorGraphics at 20:52, 15 June 2025