Temperament merging: Difference between revisions

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== Notation ==

The & ("ampersand") symbol is used (for example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool]) to notate map-merging, as in {{nowrap|12 & 19 {{=}} meantone}}; we can read this as "12-ET and 19-ET is meantone" or "12-ET map-merge 19-ET is meantone". Here, 12 and 19 are [[wart notation]] for 12-ET and 19-ET.

The & ("ampersand") symbol is used (for example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool]) to notate map-merging, as in {{nowrap|12 & 19 {{=}} meantone}}; we can read this as "12-ET and 19-ET is meantone" or "12-ET map-merge 19-ET is meantone". Here, 12 and 19 are [[wart notation]] for 12-ET and 19-ET. This is in fact a notation for the [[wedge product]].

The | ("pipe") symbol may be used to notate comma-merging, as in {{nowrap|meantone{{!}}porcupine {{=}} 7}}. We could read this as "meantone or porcupine" or "meantone comma-merge porcupine is 7-ET". As a mnemonic, because commas are represented by vectors, which are vertical columns, when they merge together into matrices, the pipe resembles the seam between them as they merge.

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[[File:Temperament merging 7-limit example.png|1000px|frameless|center]]

~~== Vs. the wedge product ==~~

~~Temperament merging is closely related to the wedge product. For more information, see: [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT#Temperament merging]].~~

== Cross-domain temperament merging ==

@@ Line 82: / Line 82: @@
 == Notation ==
-The &amp; ("ampersand") symbol is used (for example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool]) to notate map-merging, as in {{nowrap|12 &amp; 19 {{=}} meantone}}; we can read this as "12-ET and 19-ET is meantone" or "12-ET map-merge 19-ET is meantone". Here, 12 and 19 are [[wart notation]] for 12-ET and 19-ET.
+The &amp; ("ampersand") symbol is used (for example, on [http://x31eq.com/temper/ Graham Breed's temperament finding tool]) to notate map-merging, as in {{nowrap|12 &amp; 19 {{=}} meantone}}; we can read this as "12-ET and 19-ET is meantone" or "12-ET map-merge 19-ET is meantone". Here, 12 and 19 are [[wart notation]] for 12-ET and 19-ET. This is in fact a notation for the [[wedge product]].
 The | ("pipe") symbol may be used to notate comma-merging, as in {{nowrap|meantone{{!}}porcupine {{=}} 7}}. We could read this as "meantone or porcupine" or "meantone comma-merge porcupine is 7-ET". As a mnemonic, because commas are represented by vectors, which are vertical columns, when they merge together into matrices, the pipe resembles the seam between them as they merge.
@@ Line 227: / Line 227: @@
 [[File:Temperament merging 7-limit example.png|1000px|frameless|center]]
-== Vs. the wedge product ==
-Temperament merging is closely related to the wedge product. For more information, see: [[Dave Keenan &amp; Douglas Blumeyer's guide to EA for RTT#Temperament merging]].
 == Cross-domain temperament merging ==