Domain basis: Difference between revisions

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So, for instance, a temperament in the 2.3.5 domain cannot map the intervals 7/6 or 11/8, because there is no way to represent either of those intervals using only the primes 2, 3, and 5. It could, however, temper 6/5, 5/4, 10/9, or 9/8, etc., because those intervals ''can'' be represented using only those three primes.

A basis may be used to label the columns of a mapping, with one basis element per column. Here's [[~~Chromatic pairs~~#Slendric|slendric]], a temperament of the 2.3.7 domain:

A basis may be used to label the columns of a mapping, with one basis element per column. Here's [[Gamelismic clan#Slendric|slendric]], a temperament of the 2.3.7 domain:

<math>

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== Column Hermite normal form ==

To be exact, we want to use the ''column-style'' Hermite normal form, sometimes called column Hermite normal form for short. All this means is that we put the HNF call in an antitranspose sandwich, [[Normal_lists#~~Defactored_Hermite_form_2~~|as described here]]).

To be exact, we want to use the ''column-style'' Hermite normal form, sometimes called column Hermite normal form for short. All this means is that we put the HNF call in an antitranspose sandwich, [[Normal_lists#Antitransposed defactored Hermite form|as described here]]).

== Vs. canonical form for temperaments themselves: do not defactor ==

@@ Line 52: / Line 52: @@
 So, for instance, a temperament in the 2.3.5 domain cannot map the intervals 7/6 or 11/8, because there is no way to represent either of those intervals using only the primes 2, 3, and 5. It could, however, temper 6/5, 5/4, 10/9, or 9/8, etc., because those intervals ''can'' be represented using only those three primes.
-A basis may be used to label the columns of a mapping, with one basis element per column. Here's [[Chromatic pairs#Slendric|slendric]], a temperament of the 2.3.7 domain:
+A basis may be used to label the columns of a mapping, with one basis element per column. Here's [[Gamelismic clan#Slendric|slendric]], a temperament of the 2.3.7 domain:
 <math>
@@ Line 185: / Line 185: @@
 == Column Hermite normal form ==
-To be exact, we want to use the ''column-style'' Hermite normal form, sometimes called column Hermite normal form for short. All this means is that we put the HNF call in an antitranspose sandwich, [[Normal_lists#Defactored_Hermite_form_2|as described here]]).
+To be exact, we want to use the ''column-style'' Hermite normal form, sometimes called column Hermite normal form for short. All this means is that we put the HNF call in an antitranspose sandwich, [[Normal_lists#Antitransposed defactored Hermite form|as described here]]).
 == Vs. canonical form for temperaments themselves: do not defactor ==