Temperament addition: Difference between revisions

Line 78:

\end{array} \right]

=

\left[ \begin{array} {rrr}

\left[ \begin{array} {rrr}min-g

(4+1) \\

Line 1,755:

And so we can see that meantone minus flattone is [[meanmag]].

=Glossary=

* <math>d</math>: [[dimensionality]], the dimension of a temperament's domain

* <math>r</math>: [[rank]], the dimension of a temperament's [[mapping]]

* <math>n</math>: [[nullity]], the dimension of a temperament's [[comma basis]]

* <math>g</math>: [[grade]], the generic term for rank or nullity

* <math>g_{\text{min}}</math>: min-grade, the minimum of a temperament's rank and nullity <math>\min(r,n)</math>

* <math>g_{\text{max}}</math>: max-grade, the maximum of a temperament's rank and nullity <math>\min(r,n)</math>

* <math>L_{\text{dep}}</math>: linear-dependence basis, a basis for all the linearly dependent vectors between two temperaments

* <math>L_{\text{ind}}</math>: linear-independence basis, a basis for all the vectors of a temperament that are linearly independent from a specific other temperament

* <math>l_{\text{dep}}</math>: linear-dependence, the dimension of the <math>L_{\text{dep}}</math>

* <math>l_{\text{ind}}</math>: linear-independence, the dimension of the <math>L_{\text{ind}}</math>

* '''[[dimensions]]''': the <math>d</math>, <math>r</math>, and <math>n</math> of a temperament

* '''addable''': two temperaments are addable when they have the same dimensions and have <math>l_{\text{ind}}</math> <math>= 1</math>

* '''negation''': a mapping is negated when the leading entry of its [[minors]] is negative; a comma basis is negated when the trailing entry of its minors is negative

=References=

@@ Line 78: / Line 78: @@
 \end{array} \right]
 =
-\left[ \begin{array} {rrr}
+\left[ \begin{array} {rrr}min-g
 (4+1) \\
@@ Line 1,755: / Line 1,755: @@
 And so we can see that meantone minus flattone is [[meanmag]].
+=Glossary=
+* <math>d</math>: [[dimensionality]], the dimension of a temperament's domain
+* <math>r</math>: [[rank]], the dimension of a temperament's [[mapping]]
+* <math>n</math>: [[nullity]], the dimension of a temperament's [[comma basis]]
+* <math>g</math>: [[grade]], the generic term for rank or nullity
+* <math>g_{\text{min}}</math>: min-grade, the minimum of a temperament's rank and nullity <math>\min(r,n)</math>
+* <math>g_{\text{max}}</math>: max-grade, the maximum of a temperament's rank and nullity <math>\min(r,n)</math>
+* <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span>: <span style="color: #3C8031;">linear-dependence basis</span>, a basis for all the <span style="color: #3C8031;">linearly dependent</span> vectors between two temperaments
+* <span style="color: #B6321C;"><math>L_{\text{ind}}</math></span>: <span style="color: #B6321C;">linear-independence basis</span>, a basis for all the vectors of a temperament that are <span style="color: #B6321C;">linearly independent</span> from a specific other temperament
+* <span style="color: #3C8031;"><math>l_{\text{dep}}</math></span>: <span style="color: #3C8031;">linear-dependence</span>, the dimension of the <span style="color: #3C8031;"><math>L_{\text{dep}}</math></span>
+* <span style="color: #B6321C;"><math>l_{\text{ind}}</math></span>: <span style="color: #B6321C;">linear-independence</span>, the dimension of the <span style="color: #B6321C;"><math>L_{\text{ind}}</math></span>
+* '''[[dimensions]]''': the <math>d</math>, <math>r</math>, and <math>n</math> of a temperament
+* '''addable''': two temperaments are addable when they have the same dimensions and have <span style="color: #B6321C;"><math>l_{\text{ind}}</math></span> <math>= 1</math>
+* '''negation''': a mapping is negated when the leading entry of its [[minors]] is negative; a comma basis is negated when the trailing entry of its minors is negative
 =References=