Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions

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Dave Keenan (talk | contribs)
autopatrolled, emailconfirmed
2,270 edits
Corrected bold "1"s to bold italic "1"s using our \slant command. Increased zigzag brackets to correct size.
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
reorganize mostly to reflect the extraction of generator embedding from main series
Line 1,658: Line 1,658:
|mnemonic: <math>k</math>ount
|mnemonic: <math>k</math>ount
|-
|-
! colspan="17" |held-intervals
! colspan="17" |held-intervals and unchanged-intervals
|-
|
|<math>\mathrm{H}</math>
|[[held-interval basis]]
|
|<math>\small 𝗽</math>
|primes
|
|<math>\scriptsize (d, h)</math>
|
|matrix
|
|[[...⟩ ...]
|
|<math>\textbf{h}_i</math>
|
|<math>\mathrm{h}_{ij}</math>
|
|-
|-
|
|
Line 1,695: Line 1,677:
|
|
|
|
|-
! colspan="17" |exploring temperaments
|-
|-
|
|
|<math>\mathrm{C}</math>
|<math>\mathrm{H}</math>
|[[comma basis]]
|[[held-interval basis]]
|
|
|<math>\small 𝗽</math>
|<math>\small 𝗽</math>
|primes
|primes
|
|
|<math>\scriptsize (d, n)</math>
|<math>\scriptsize (d, h)</math>
|integer
|
|matrix
|matrix
|
|
|[[...⟩ ...]
|[[...⟩ ...]
|
|
|<math>\textbf{c}_i</math>
|<math>\textbf{h}_i</math>
|
|<math>\mathrm{h}_{ij}</math>
|
|
|<math>\mathrm{c}_{ij}</math>
|jargon name: monzo list
|-
|-
|
|
|<math>\textbf{c}</math>
|<math>\mathrm{U}</math>
|[[comma]]
|[[unchanged-interval basis]]
|
|
|<math>\small 𝗽</math>
|<math>\small 𝗽</math>
|primes
|primes
|
|
|<math>\scriptsize (d, 1)</math>
|<math>\scriptsize (d, r)</math>
|integer
|vector
|
|
|[...⟩
|matrix
|
|
|[[...⟩ ...]
|
|
|<math>\textbf{u}_i</math>
|
|
|<math>\mathrm{c}_i</math>
|<math>\mathrm{u}_{ij}</math>
|specific type: [[prime-count vector]] (PC-vector)
|jargon name: eigenmonzo list
|-
|-
! colspan="17" |computation
! colspan="17" |exploring temperaments
|-
|-
|
|
|<math>G</math>
|<math>\mathrm{C}</math>
|[[generator embedding matrix|generator embedding (matrix)]]
|[[comma basis]]
|
|
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|<math>\small 𝗽</math>
|primes per generator
|primes
|
|
|<math>\scriptsize (d, r)</math>
|<math>\scriptsize (d, n)</math>
|real
|integer
|matrix
|matrix
|[{...] ...⟩
|{[...⟩ ...]
|<math>𝒈_i</math>
|
|
|[[...⟩ ...]
|
|
|<math>g_{ij}</math>
|<math>\textbf{c}_i</math>
|
|
|<math>\mathrm{c}_{ij}</math>
|jargon name: monzo list
|-
|-
|
|
|<math>\mathrm{U}</math>
|<math>\textbf{c}</math>
|[[unchanged-interval basis]]
|[[comma]]
|
|
|<math>\small 𝗽</math>
|<math>\small 𝗽</math>
|primes
|primes
|
|
|<math>\scriptsize (d, r)</math>
|<math>\scriptsize (d, 1)</math>
|integer
|vector
|
|
|matrix
|[...⟩
|
|
|[[...⟩ ...]
|
|
|<math>\textbf{u}_i</math>
|
|
|<math>\mathrm{u}_{ij}</math>
|<math>\mathrm{c}_i</math>
|jargon name: eigenmonzo list
|specific type: [[prime-count vector]] (PC-vector)
|-
|-
|
! colspan="17" |computation
|<math>K</math>
|[[constraint (matrix)]]
|
|
|
|
|<math>\scriptsize (r, k)</math>
|<math>\scriptsize \{0, +1, -1\}</math>
|matrix
|[[...] ...]
|
|<math>𝒌_i</math>
|
|
|<math>k_{ij}</math>
|mnemonic: <math>K</math>onstraint
|-
|-
|
|
Line 1,808: Line 1,772:
|
|
|-
|-
! colspan="17" |JI equivalents
! colspan="17" |all-interval tuning schemes
|-
|-
|<math>I</math>
|<math>I</math>
|<math>M_{\text{j}}</math>
|<math>\mathrm{T}_{\text{p}}</math>
|[[JI mapping (matrix)]]
|[[prime proxy target-interval (matrix)]]
|
|
|<math>\small 𝗴</math>/<math>\small 𝗽</math>
|<math>\small 𝗽</math>
|generators per prime
|primes
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|integer
|integer
|matrix
|matrix
|[⟨...] ...}
|
|⟨[...} ...]
|⟨[...⟩ ...]
|
|
|
|
Line 1,828: Line 1,792:
|
|
|-
|-
|<math>1200×\slant{\mathbf{1}}LG_{\text{j}}</math>
|<math>S_{\text{p}}^{-1}</math>
|<math>𝒈_{\text{j}}</math>
|<math>C_{\text{p}}</math>
|[[JI generator tuning map]]
|[[complexity prescaler]]
|<math>\scriptsize
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math>
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\small\mathsf{(C)}</math>
\begin{array} {c} \\[-2pt] · \end{array}
|complexity weight
\begin{array} {c} \slant{\mathbf{1}} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|
\begin{array} {c} \\[-2pt] · \end{array}
|<math>\scriptsize (d, d)</math>
\begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
|real
\begin{array} {c} \\[-2pt] · \end{array}
|matrix
\\ \scriptsize \quad
|[⟨...] ...⟩
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array}
|
</math>
|
|<math>\mathsf{¢}</math>/<math>\small 𝗴</math>
|cents per generator
|<math>\scriptsize
\!\!
\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
\!\!
\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] (\cancel{1}, \cancel{d}) \end{array}
\!\!
\begin{array} {c} L \\[-3pt] (\cancel{d}, \cancel{d}) \end{array}
\\ \scriptsize \quad
\!\!
\begin{array} {c} G_{\text{j}} \\[-3pt] (\cancel{d}, r) \end{array}
\!\!
</math>
|<math>\scriptsize (1, d)</math>
|real
|vector
|{...]
|
|
|
|<math>𝒄_{\text{p}}</math>
|
|<math>c_{\text{p}i}</math>
|
|<math>g_{\text{j}i}</math>
|
|
|-
|-
|<math>I</math>
|<math>C_{\text{p}}^{-1}</math>
|<math>G_{\text{j}}</math>
|<math>S_{\text{p}}</math>
|[[JI generator embedding matrix|JI generator embedding (matrix)]]
|[[simplicity prescaler]]
|
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|<math>\small\mathsf{(S)}</math>
|primes per generator
|simplicity weight
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|integer
|real
|matrix
|matrix
|[{...] ...⟩
|{[...⟩ ...]
|
|
|⟨[...⟩ ...]
|
|
|<math>\slant{\mathbf{1}}</math>
|
|
|<math>𝒔_{\text{p}}</math>
|<math>s_{\text{p}i}</math>
|
|
|-
|-
! colspan="17" |all-interval tuning schemes
|-
|<math>I</math>
|<math>\mathrm{T}_{\text{p}}</math>
|[[prime proxy target-interval (matrix)]]
|
|
|<math>\small 𝗽</math>
|<math>L</math>
|primes
|[[log-prime matrix]]
|
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|octaves per prime
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|integer
|real
|matrix
|matrix
|
|[⟨...] ...⟩
|⟨[...⟩ ...]
|⟨[...⟩ ...]
|<math>\textbf{𝓁}_i</math>
|
|
|<math>\textbf{𝓁}</math>
|<math>𝓁_{ij}</math>
|
|
|<math>\slant{\mathbf{1}}</math>
|-
|
|<math>q</math>
|[[interval complexity norm power]]
|
|
|
|
|-
|<math>S_{\text{p}}^{-1}</math>
|<math>C_{\text{p}}</math>
|[[complexity prescaler]]
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math>
|<math>\small\mathsf{(C)}</math>
|complexity weight
|
|
|<math>\scriptsize (d, d)</math>
|
|real
|<math>\scriptsize (1, 1)</math>
|matrix
|real
|[⟨...] ...⟩
| scalar
|
|
|
|
|
|
|<math>𝒄_{\text{p}}</math>
|<math>c_{\text{p}i}</math>
|
|
|-
|<math>C_{\text{p}}^{-1}</math>
|<math>S_{\text{p}}</math>
|[[simplicity prescaler]]
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
|<math>\small\mathsf{(S)}</math>
|simplicity weight
|
|
|<math>\scriptsize (d, d)</math>
|real
|matrix
|
|
|⟨[...⟩ ...]
|
|
|-
|
|
|<math>𝒔_{\text{p}}</math>
|<math>‖ · ‖_q</math>
|<math>s_{\text{p}i}</math>
|[[power norm]] (<math>q</math>-norm)
|
|
|-
|
|
|<math>L</math>
|[[log-prime matrix]]
|
|
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|octaves per prime
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (1, 1)</math>
|real
|real
|matrix
|scalar
|[⟨...] ...⟩
|
|⟨[...⟩ ...]
|<math>\textbf{𝓁}_i</math>
|
|<math>\textbf{𝓁}</math>
|<math>𝓁_{ij}</math>
|
|-
|
|<math>q</math>
|[[interval complexity norm power]]
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|
|
|
|
|
|-
|
|<math>‖ · ‖_q</math>
|[[power norm]] (<math>q</math>-norm)
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|
|
|
Line 1,995: Line 1,883:
|}
|}


===Units===
===Units ===


Same as the basic level.  
Same as the basic level.  
Line 2,019: Line 1,907:
! colspan="3" rowspan="1" |slope
! colspan="3" rowspan="1" |slope
! colspan="1" rowspan="2" |initial
! colspan="1" rowspan="2" |initial
! colspan="1" rowspan="2" |name
! colspan="1" rowspan="2" | name
! colspan="1" rowspan="2" |power
! colspan="1" rowspan="2" |power
|-
|-
!initial
!initial
!name
!name
!power
! power
!initial
!initial
!name
!name
!power
! power
!initial
!initial
!name
! name
!multiplier
!multiplier
! colspan="1" |abbreviated
! colspan="1" |abbreviated
Line 2,098: Line 1,986:
| rowspan="2" |C
| rowspan="2" |C
| rowspan="2" |complexity-weight
| rowspan="2" |complexity-weight
| rowspan="2" |complexity
| rowspan="2" | complexity
|<set> minimax-C
|<set> minimax-C
|<set> minimax complexity-weight damage
|<set> minimax complexity-weight damage
Line 2,177: Line 2,065:
| rowspan="2" |S
| rowspan="2" |S
| rowspan="2" |simplicity-weight
| rowspan="2" |simplicity-weight
| rowspan="2" |1/complexity
| rowspan="2" | 1/complexity
|<set> minimean-S
|<set> minimean-S
|<set> minimean simplicity-weight damage
|<set> minimean simplicity-weight damage
Line 2,211: Line 2,099:
|}
|}


===Damages===
===Damages ===


{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
Line 2,259: Line 2,147:
!abbreviation
!abbreviation
!name
!name
!symbol
! symbol
!name
!name
|-
|-
Line 2,268: Line 2,156:
|-
|-
|EC
|EC
|Euclideanized complexity
| Euclideanized complexity
|<math>\small\mathsf{(EC)}</math>
|<math>\small\mathsf{(EC)}</math>
|Euclideanized-complexity weight
|Euclideanized-complexity weight
Line 2,295: Line 2,183:
! colspan="2" |shape
! colspan="2" |shape
! colspan="2" |type
! colspan="2" |type
! colspan="2" |EBK notation
! colspan="2" | EBK notation
! colspan="4" |subobjects
! colspan="4" |subobjects
! rowspan="2" |notes
! rowspan="2" |notes
Line 2,301: Line 2,189:
!unreduced
!unreduced
!reduced
!reduced
!read as
! read as
!unreduced
!unreduced
!reduced
!reduced
Line 2,331: Line 2,219:
|
|
|<math>\mathrm{i}_i</math>
|<math>\mathrm{i}_i</math>
|specific type: [[prime-count vector]] (PC-vector)
| specific type: [[prime-count vector]] (PC-vector)
jargon name: monzo
jargon name: monzo
|-
|-
Line 2,591: Line 2,479:
|<math>\scriptsize (1, d)</math>
|<math>\scriptsize (1, d)</math>
|real
|real
|vector
| vector
|⟨...]
|⟨...]
|
|
Line 2,619: Line 2,507:
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
|real
|scalar
| scalar
|
|
|
|
Line 2,725: Line 2,613:
|
|
|-
|-
! colspan="17" |damage
! colspan="17" | damage
|-
|-
|<math>s^{-1}</math>
|<math>s^{-1}</math>
Line 2,782: Line 2,670:
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
|real
|scalar
| scalar
|
|
|
|
Line 2,916: Line 2,804:
|<math>\scriptsize (1, k)</math>
|<math>\scriptsize (1, k)</math>
|real
|real
|list
| list
|[...]
|[...]
|
|
Line 3,008: Line 2,896:
|mnemonic: <math>k</math>ount
|mnemonic: <math>k</math>ount
|-
|-
! colspan="17" |held-intervals
! colspan="17" |held-intervals and unchanged-intervals
|-
|
|<math>\mathrm{H}</math>
|[[held-interval basis]]
|
|<math>\small 𝗽</math>
|primes
|
|<math>\scriptsize (d, h)</math>
|
|matrix
|
|[[...⟩ ...]
|
|<math>\textbf{h}_i</math>
|
|<math>\mathrm{h}_{ij}</math>
|
|-
|-
|
|
Line 3,045: Line 2,915:
|
|
|
|
|-
! colspan="17" |exploring temperaments
|-
|-
|
|
|<math>\mathrm{C}</math>
|<math>\mathrm{H}</math>
|[[held-interval basis]]
|
|<math>\small 𝗽</math>
|primes
|
|<math>\scriptsize (d, h)</math>
|
|matrix
|
| [[...⟩ ...]
|
|<math>\textbf{h}_i</math>
|
|<math>\mathrm{h}_{ij}</math>
|
|-
|
|<math>\mathrm{U}</math>
|[[unchanged-interval basis]]
|
|<math>\small 𝗽</math>
|primes
|
|<math>\scriptsize (d, r)</math>
|
|matrix
|
|[[...⟩ ...]
|
|<math>\textbf{u}_i</math>
|
|<math>\mathrm{u}_{ij}</math>
|jargon name: eigenmonzo list
|-
! colspan="17" |exploring temperaments
|-
|
|<math>\mathrm{C}</math>
|[[comma basis]]
|[[comma basis]]
|
|
Line 3,085: Line 2,991:
|-
|-
! colspan="17" |computation
! colspan="17" |computation
|-
|
|<math>G</math>
|[[generator embedding matrix|generator embedding (matrix)]]
|
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|primes per generator
|
|<math>\scriptsize (d, r)</math>
|real
|matrix
|[{...] ...⟩
|{[...⟩ ...]
|<math>𝒈_i</math>
|
|
|<math>g_{ij}</math>
|
|-
|
|<math>\mathrm{U}</math>
|[[unchanged-interval basis]]
|
|<math>\small 𝗽</math>
|primes
|
|<math>\scriptsize (d, r)</math>
|
|matrix
|
|[[...⟩ ...]
|
|<math>\textbf{u}_i</math>
|
|<math>\mathrm{u}_{ij}</math>
|jargon name: eigenmonzo list
|-
|-
|
|
Line 3,148: Line 3,018:
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
| real
|scalar
|scalar
|
|
Line 3,158: Line 3,028:
|
|
|-
|-
! colspan="17" |projection
! colspan="17" |all-interval tuning schemes
|-
|-
|<math>G_cF^{-1}FM_c \\
|<math>I</math>
\mathrm{V}\textit{Λ}\mathrm{V}^{-1}</math>
|<math>\mathrm{T}_{\text{p}}</math>
|<math>P</math>
|[[prime proxy target-interval (matrix)]]
|[[Projection matrix|projection (matrix)]]
|
|<math>\scriptsize
|<math>\small 𝗽</math>
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
|primes
\begin{array} {c} \\[-2pt] · \end{array}
|
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
</math>
|<math>\small 𝗽</math>/<math>\small 𝗽</math>
|primes per prime
|<math>\scriptsize
\!\!
\begin{array} {c} G \\[-3pt] (d, \cancel{r}) \end{array}
\!\!
\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}
\!\!
</math>
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|real
|integer
|matrix
|matrix
|[⟨...] ...⟩
|
|⟨[...⟩ ...]
|⟨[...⟩ ...]
|<math>𝒑_i</math>
|
|
|
|
|<math>p_i</math>
|<math>\slant{\mathbf{1}}</math>
|
|
|
|-
|-
|<math>GM\textbf{i}</math>
|
|<math>P\textbf{i}</math>
|<math>C_{\text{p}}</math>
|[[projected interval]]
|[[complexity pretransformer]]
|<math>\scriptsize
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
|<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
\begin{array} {c} \\[-2pt] · \end{array}
|complexity weight or <alternative>-complexity weight
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
|
\begin{array} {c} \\[-2pt] · \end{array}
|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
</math>
|<math>\small 𝗽</math>
|primes
|<math>\scriptsize  
\!\!
\begin{array} {c} G \\[-3pt] (d, \cancel{r}) \end{array}
\!\!
\begin{array} {c} M \\[-3pt] (\cancel{r}, \cancel{d}) \end{array}
\!\!
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
\!\!
</math>
|<math>\scriptsize (d, 1)</math>
|real
|real
|vector
|matrix
|[⟨...] ...⟩
|
|
|[...⟩
|<math>𝒄_{\text{p}_i}</math>
|
|
|<math>𝒄_{\text{p}}</math>
|<math>c_{\text{p}i}</math> or [math]c_{\text{p}ij}[/math]
|
|
|-
|
|
|<math>S_{\text{p}}</math>
|[[simplicity pretransformer]]
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{S)}</math>
|<math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
|simplicity weight or <alternative>-simplicity weight
|
|
|specific type: [[prime-count vector]] (PC-vector)
|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
|-
|real
|matrix
|
|
|<math>\textit{Λ}</math>
|⟨[...⟩ ...]
|[[scaling factor (eigenvalue) matrix|scaling factor matrix]]
|<math>𝒔_{\text{p}i}</math>
|
|
|<math>𝒔_{\text{p}}</math>
|<math>s_{\text{p}i}</math> or [math]s_{\text{p}ij}[/math]
|
|
|-
|<math>\text{diag}(\log_2(\textbf{p}))</math>
|<math>L</math>
|[[log-prime matrix]]
|
|
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|octaves per prime
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|
|real
|matrix
|matrix
|[⟨…] …⟩
|[⟨...] ...⟩
|⟨[…⟩ …]
|⟨[...⟩ ...]
|<math>\textbf{𝓁}_i</math>
|
|
|<math>\textbf{𝓁}</math>
|<math>𝓁_{ij}</math>
|
|
|<math>𝝀</math>
|<math>λ_i</math>
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; previous name: eigenvalue matrix
|-
|-
|
|
|<math>\mathrm{V}</math>
|<math>q</math>
|[[unrotated vector (eigenvector) list|unrotated vector list]]
|[[interval complexity norm power]]
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|
|<math>\small 𝗽</math>
|primes
|
|
|<math>\scriptsize (d, d)</math>
|
|
|matrix
|
|
|⟨[...⟩ ...]
|
|
|<math>\textbf{v}_i</math>
|
|
|<math>\mathrm{v}_{ij}</math>
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; jargon name: eigenmonzo and comma list
|-
|-
|
|
|<math>F</math>
|<math>‖ · ‖_q</math>
|[[generator form matrix]]
|[[power norm]] (<math>q</math>-norm)
|
|
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|
|
|<math>\scriptsize (r, r)</math>
|
|
|matrix
|[{...] …}
|
|
|
|
|<math>𝒇_i</math>
|
|
|<math>f_{ij}</math>
|
|
|-
|-
! colspan="17" |JI equivalents
! colspan="17" |alternative complexities
|-
|-
|<math>I</math>
|<math>M_{\text{j}}</math>
|[[JI mapping (matrix)]]
|
|
|<math>\small 𝗴</math>/<math>\small 𝗽</math>
|<math>𝒑</math>
|generators per prime
|[[prime list]]<ref>May be used for a prime-limit or for any prime-only list.</ref>
|
|
|
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (1, d)</math>
|integer
|integer
|list
|[...]
|
|
|
|
|<math>p_i</math>
|
|-
|
|<math>Z</math>
|[[size-sensitizing matrix]]
|
|
|
|
|<math>\scriptsize (d+1, d)</math>
|real
|matrix
|matrix
|[⟨...] ...}
|[⟨…]...]
|⟨[...} ...]
|
|
|<math>𝒛_i</math>
|
|
|<math>\slant{\mathbf{1}}</math>
|
|
|<math>z_{ij}</math>
|
|
|-
|-
|<math>1200×\slant{\mathbf{1}}LG_{\text{j}}</math>
! colspan="17" |non-standard domain bases
|<math>𝒈_{\text{j}}</math>
|-
|[[JI generator tuning map]]
| rowspan="2" |
|<math>\scriptsize
|<math>B_s</math>
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
| rowspan="2" |[[(domain) basis (change) matrix]]
\begin{array} {c} \\[-2pt] · \end{array}
| rowspan="2" |
\begin{array} {c} \slant{\mathbf{1}} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\small 𝗽</math>/<math>\small 𝗯</math>
\begin{array} {c} \\[-2pt] · \end{array}
|primes per nonprime basis elements
\begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
| rowspan="2" |
\begin{array} {c} \\[-2pt] · \end{array}
|<math>\scriptsize (d_p, d_b)</math>
\\ \scriptsize \quad
| rowspan="2" |integer
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array}
| rowspan="2" |matrix
</math>
| rowspan="2" | [[...] ...]
|<math>\mathsf{¢}</math>/<math>\small 𝗴</math>
| rowspan="2" |[[...] ...]
|cents per generator
| rowspan="2" |
|<math>\scriptsize  
| rowspan="2" |<math>b_i</math>
\!\!
| rowspan="2" |
\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
| rowspan="2" |<math>b_{ij}</math>
\!\!
| rowspan="2" |
\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] (\cancel{1}, \cancel{d}) \end{array}
|-
\!\!
|<math>B_{Ls}</math>
\begin{array} {c} L \\[-3pt] (\cancel{d}, \cancel{d}) \end{array}
|<math>\small 𝗕</math>/<math>\small 𝗯</math>
\\ \scriptsize \quad
|superspace basis elements per (subspace) basis elements
\!\!
|<math>\scriptsize (d_L, d_s)</math>
\begin{array} {c} G_{\text{j}} \\[-3pt] (\cancel{d}, r) \end{array}
|-
\!\!
! colspan="17" |embedding and projection
</math>
|<math>\scriptsize (1, d)</math>
|real
|vector
|{...]
|
|
|
|
|<math>g_{\text{j}i}</math>
|
|-
|-
|<math>I</math>
|
|<math>G_{\text{j}}</math>
|<math>G</math>
|[[JI generator embedding matrix|JI generator embedding (matrix)]]
|[[generator embedding matrix|generator embedding (matrix)]]
|
|
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|primes per generator
|primes per generator
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, r)</math>
|integer
|real
|matrix
| matrix
|[{...] ...⟩
|[{...] ...⟩
|{[...⟩ ...]
|{[...⟩ ...]
|<math>𝒈_i</math>
|
|
|
|
|<math>\slant{\mathbf{1}}</math>
|<math>g_{ij}</math>
|
|
|
|-
|-
! colspan="17" |all-interval tuning schemes
|<math>G_cF^{-1}FM_c \\
|-
\mathrm{V}\textit{Λ}\mathrm{V}^{-1}</math>
|<math>I</math>
|<math>P</math>
|<math>\mathrm{T}_{\text{p}}</math>
|[[Projection matrix|projection (matrix)]]
|[[prime proxy target-interval (matrix)]]
|<math>\scriptsize
|
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
|<math>\small 𝗽</math>
\begin{array} {c} \\[-2pt] · \end{array}
|primes
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
|
</math>
|<math>\small 𝗽</math>/<math>\small 𝗽</math>
|primes per prime
|<math>\scriptsize
\!\!
\begin{array} {c} G \\[-3pt] (d, \cancel{r}) \end{array}
\!\!
\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}
\!\!
</math>
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|integer
|real
|matrix
|matrix
|
|[⟨...] ...⟩
|⟨[...⟩ ...]
|⟨[...⟩ ...]
|<math>𝒑_i</math>
|
|
|
|
|<math>\slant{\mathbf{1}}</math>
|<math>p_i</math>
|
|
|
|-
|-
|<math>GM\textbf{i}</math>
|<math>P\textbf{i}</math>
|[[projected interval]]
|<math>\scriptsize
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
</math>
|<math>\small 𝗽</math>
|primes
|<math>\scriptsize
\!\!
\begin{array} {c} G \\[-3pt] (d, \cancel{r}) \end{array}
\!\!
\begin{array} {c} M \\[-3pt] (\cancel{r}, \cancel{d}) \end{array}
\!\!
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
\!\!
</math>
|<math>\scriptsize (d, 1)</math>
|real
|vector
|
|[...⟩
|
|
|<math>C_{\text{p}}</math>
|[[complexity pretransformer]]
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
|<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
|complexity weight or <alternative>-complexity weight
|
|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
|real
|matrix
|[⟨...] ...⟩
|
|
|<math>𝒄_{\text{p}_i}</math>
|
|
|<math>𝒄_{\text{p}}</math>
|<math>c_{\text{p}i}</math> or [math]c_{\text{p}ij}[/math]
|
|
|specific type: [[prime-count vector]] (PC-vector)
|-
|-
|
|
|<math>S_{\text{p}}</math>
|<math>\textit{Λ}</math>
|[[simplicity pretransformer]]
|[[scaling factor (eigenvalue) matrix|scaling factor matrix]]
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{S)}</math>
|<math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
|simplicity weight or <alternative>-simplicity weight
|
|
|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
|real
|matrix
|
|
|⟨[...⟩ ...]
|<math>𝒔_{\text{p}i}</math>
|
|
|<math>𝒔_{\text{p}}</math>
|<math>s_{\text{p}i}</math> or [math]s_{\text{p}ij}[/math]
|
|
|-
|<math>\scriptsize (d, d)</math>
|<math>\text{diag}(\log_2(\textbf{p}))</math>
|<math>L</math>
|[[log-prime matrix]]
|
|
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|octaves per prime
|
|<math>\scriptsize (d, d)</math>
|real
|matrix
|matrix
|[⟨...] ...⟩
|[⟨…] …⟩
|⟨[...⟩ ...]
|⟨[…⟩ …]
|<math>\textbf{𝓁}_i</math>
|
|
|<math>\textbf{𝓁}</math>
|<math>𝓁_{ij}</math>
|
|
|<math>𝝀</math>
|<math>λ_i</math>
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; previous name: eigenvalue matrix
|-
|-
|
|
|<math>q</math>
|<math>\mathrm{V}</math>
|[[interval complexity norm power]]
|[[unrotated vector (eigenvector) list|unrotated vector list]]
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|
|<math>\small 𝗽</math>
|primes
|
|
|<math>\scriptsize (d, d)</math>
|
|
|matrix
|
|
|⟨[...⟩ ...]
|
|
|<math>\textbf{v}_i</math>
|
|
|<math>\mathrm{v}_{ij}</math>
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Λ}</math> which it combines with to create the projection matrix; jargon name: eigenmonzo and comma list
|-
|-
|
|
|<math>‖ · ‖_q</math>
|<math>F</math>
|[[power norm]] (<math>q</math>-norm)
|[[generator form matrix]]
|
|
|
|
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (r, r)</math>
|real
|scalar
|
|
|matrix
|[{...] …}
|
|
|
|
|<math>𝒇_i</math>
|
|
|<math>f_{ij}</math>
|
|
|-
|<math>I</math>
|<math>M_{\text{j}}</math>
|[[JI mapping (matrix)]]
|
|
|<math>\small 𝗴</math>/<math>\small 𝗽</math>
|generators per prime
|
|<math>\scriptsize (d, d)</math>
|integer
|matrix
|[⟨...] ...}
|⟨[...} ...]
|
|
|-
! colspan="17" |alternative complexities
|-
|
|
|<math>𝒑</math>
|<math>\slant{\mathbf{1}}</math>
|[[prime list]]<ref>May be used for a prime-limit or for any prime-only list.</ref>
|
|
|
|
|-
|<math>I</math>
|<math>G_{\text{j}}</math>
|[[JI generator embedding matrix|JI generator embedding (matrix)]]
|
|
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|primes per generator
|
|
|<math>\scriptsize (1, d)</math>
|<math>\scriptsize (d, d)</math>
|integer
|integer
|list
|matrix
|[...]
|[{...] ...⟩
|{[...⟩ ...]
|
|
|
|
|<math>\slant{\mathbf{1}}</math>
|
|
|
|
|<math>p_i</math>
|-
|
! colspan="17" | exterior algebra
|-
|-
|
|
|<math>Z</math>
|<math>𝕞</math>
|[[size-sensitizing matrix]]
|[[multimap]]
|
|
|
|<math>\small 𝗴</math>/<math>\small 𝗽</math>
|generators per prime
|
|
|<math>\scriptsize (1, d)</math>
|integer
|multivector
|⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
|
|
|<math>\scriptsize (d+1, d)</math>
|real
|matrix
|[⟨…]...]
|
|
|<math>𝒛_i</math>
|
|
|
|
|<math>z_{ij}</math>
|<math>𝕞_i</math>
|
|
|-
|-
! colspan="17" |non-standard domain bases
|
|-
|<math>𝕔</math>
| rowspan="2" |
|[[multicomma]]
|<math>B_s</math>
|
| rowspan="2" |[[(domain) basis (change) matrix]]
|<math>\small 𝗽</math>
| rowspan="2" |
| primes
|<math>\small 𝗽</math>/<math>\small 𝗯</math>
|
|primes per nonprime basis elements
|<math>\scriptsize (1, n)</math>
| rowspan="2" |
|integer
|<math>\scriptsize (d_p, d_b)</math>
|multivector
| rowspan="2" |integer
|
| rowspan="2" |matrix
|[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
| rowspan="2" |[[...] ...]
|
| rowspan="2" |[[...] ...]
|
| rowspan="2" |
|
| rowspan="2" |<math>b_i</math>
|<math>𝕔_i</math>
| rowspan="2" |
|
| rowspan="2" |<math>b_{ij}</math>
| rowspan="2" |
|-
|<math>B_{Ls}</math>
|<math>\small 𝗕</math>/<math>\small 𝗯</math>
|superspace basis elements per (subspace) basis elements
|<math>\scriptsize (d_L, d_s)</math>
|-
! colspan="17" |exterior algebra
|-
|-
|
|
|<math>𝕞</math>
|<math>𝕧</math>
|[[multimap]]
|[[(generic temperament multivector)]]
|
|
|
|
|<math>\small 𝗴</math>/<math>\small 𝗽</math>
|generators per prime
|
|
|<math>\scriptsize (1, d)</math>
|<math>\scriptsize (1, {{d}\choose{r}})</math> or <math>\scriptsize (1, {{d}\choose{n}})</math>
|integer
|integer
|multivector
|multivector
|⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
|⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
|[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
|
|
|
|
|
|
|<math>𝕧_i</math>
|
|
|<math>𝕞_i</math>
|-
|
|
|-
|<math>A</math>
|
|[[(generic temperament matrix)]]
|<math>𝕔</math>
|[[multicomma]]
|
|<math>\small 𝗽</math>
|primes
|
|<math>\scriptsize (1, n)</math>
|integer
|multivector
|
|[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
|
|
|
|<math>𝕔_i</math>
|
|-
|
|<math>𝕧</math>
|[[(generic temperament multivector)]]
|
|
|
|
|<math>\scriptsize (1, {{d}\choose{r}})</math> or <math>\scriptsize (1, {{d}\choose{n}})</math>
|integer
|multivector
|⟨...] or ⟨⟨...]] or ⟨⟨⟨...]]] ...
|[...⟩ or [[...⟩⟩ or [[[...⟩⟩⟩ ...
|
|
|
|<math>𝕧_i</math>
|
|-
|
|<math>A</math>
|[[(generic temperament matrix)]]
|
|
|
|
Line 3,624: Line 3,472:
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|integer
| integer
|scalar
|scalar
|
|
Line 3,682: Line 3,530:
|integer
|integer
|matrix
|matrix
|[⟨...]] or [[...] ...⟩
| [⟨...]] or [[...] ...⟩
|⟨[...]] or [[...⟩ ...]
|⟨[...]] or [[...⟩ ...]
|<math>\textbf{𝓁}_{\text{dep}i}</math>
|<math>\textbf{𝓁}_{\text{dep}i}</math>
Line 3,786: Line 3,634:
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+
|+
! colspan="6" rowspan="3" |retuning (or mistuning) magnitude
! colspan="6" rowspan="3" | retuning (or mistuning) magnitude
! colspan="12" rowspan="1" |damage
! colspan="12" rowspan="1" |damage
! rowspan="5" |target
! rowspan="5" | target


intervals
intervals
Line 3,795: Line 3,643:
! rowspan="5" |of interest?
! rowspan="5" |of interest?
|-
|-
! colspan="9" rowspan="1" |weight
! colspan="9" rowspan="1" | weight
! colspan="3" rowspan="1" |optimization
! colspan="3" rowspan="1" |optimization
|-
|-
Line 3,804: Line 3,652:
! colspan="1" rowspan="3" |power
! colspan="1" rowspan="3" |power
|-
|-
! colspan="3" rowspan="1" |norm pretransformer
! colspan="3" rowspan="1" | norm pretransformer
! colspan="3" rowspan="1" |norm power
! colspan="3" rowspan="1" |norm power
! colspan="3" rowspan="1" |norm pretransformer
! colspan="3" rowspan="1" |norm pretransformer
Line 3,817: Line 3,665:
!initial
!initial
!name
!name
!power
! power
!initial
!initial
!name
!name
Line 3,824: Line 3,672:
!name
!name
!power
!power
! colspan="1" |abbreviated        
! colspan="1" |abbreviated
! colspan="1" |read ("____ tuning scheme")                                            
! colspan="1" |read ("____ tuning scheme")
|-
|-
| colspan="3" |<none>
| colspan="3" |<none>
Line 3,848: Line 3,696:
|-
|-
| colspan="3" |<various>
| colspan="3" |<various>
| colspan="3" |<various>
| colspan="3" | <various>
|minimax-<alt>-S
|minimax-<alt>-S
|minimax <alternative>-simplicity-weight damage
|minimax <alternative>-simplicity-weight damage
Line 3,882: Line 3,730:
|<set> minimax unity-weight damage
|<set> minimax unity-weight damage
|"[[Minimax tuning|minimax]]"
|"[[Minimax tuning|minimax]]"
|yes
| yes
|-
|-
| colspan="3" |<none>
| colspan="3" |<none>
Line 3,945: Line 3,793:
|-
|-
| colspan="3" |<various>
| colspan="3" |<various>
|<set> minimax-E-<alt>-C
| <set> minimax-E-<alt>-C
|<set> minimax Euclideanized-<alternative>-complexity-weight damage
|<set> minimax Euclideanized-<alternative>-complexity-weight damage
|
|
Line 3,971: Line 3,819:
|<set> miniRMS simplicity-weight damage
|<set> miniRMS simplicity-weight damage
|
|
|yes
| yes
|-
|-
| colspan="3" |<various>
| colspan="3" |<various>
Line 3,988: Line 3,836:
|
|
|-
|-
| colspan="3" |<various>
| colspan="3" | <various>
|<set> miniRMS-E-<alt>-S
|<set> miniRMS-E-<alt>-S
|<set> miniRMS Euclideanized-<alternative>-simplicity-weight damage
|<set> miniRMS Euclideanized-<alternative>-simplicity-weight damage
Line 4,000: Line 3,848:
| rowspan="4" |C
| rowspan="4" |C
| rowspan="4" |complexity-weight
| rowspan="4" |complexity-weight
| rowspan="4" |complexity
| rowspan="4" | complexity
|<set> miniRMS-C
| <set> miniRMS-C
|<set> miniRMS complexity-weight damage
|<set> miniRMS complexity-weight damage
|
|
Line 4,016: Line 3,864:
| rowspan="2" |Euclidean
| rowspan="2" |Euclidean
| rowspan="2" |2
| rowspan="2" |2
|<set> miniRMS-EC
| <set> miniRMS-EC
|<set> miniRMS Euclideanized-complexity-weight damage
|<set> miniRMS Euclideanized-complexity-weight damage
|
|
|
|
|-
|-
| colspan="3" |<various>
| colspan="3" | <various>
|<set> miniRMS-E-<alt>-C
|<set> miniRMS-E-<alt>-C
|<set> miniRMS Euclideanized-<alternative>-complexity-weight damage
|<set> miniRMS Euclideanized-<alternative>-complexity-weight damage
Line 4,029: Line 3,877:
| colspan="6" |<n/a>
| colspan="6" |<n/a>
|U
|U
|unity-weight
| unity-weight
|<none>
|<none>
| rowspan="9" |minimean
| rowspan="9" |minimean
Line 4,043: Line 3,891:
| rowspan="2" |1
| rowspan="2" |1
| rowspan="4" |S
| rowspan="4" |S
| rowspan="4" |simplicity-weight
| rowspan="4" | simplicity-weight
| rowspan="4" |1/complexity
| rowspan="4" |1/complexity
|<set> minimean-S
|<set> minimean-S
Line 4,092: Line 3,940:
| rowspan="2" |E
| rowspan="2" |E
| rowspan="2" |Euclidean
| rowspan="2" |Euclidean
| rowspan="2" |2
| rowspan="2" | 2
|<set> minimean-EC
|<set> minimean-EC
|<set> minimean Euclideanized-complexity-weight damage
|<set> minimean Euclideanized-complexity-weight damage
Line 4,123: Line 3,971:
|-
|-
|C-damage
|C-damage
|complexity-weight damage
| complexity-weight damage
|<math>\mathsf{¢}\small\mathsf{(C)}</math>
|<math>\mathsf{¢}\small\mathsf{(C)}</math>
|complexity-weighted cents
|complexity-weighted cents
Line 4,133: Line 3,981:
|-
|-
|EC-damage
|EC-damage
|Euclideanized-complexity-weight damage
| Euclideanized-complexity-weight damage
|<math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math>
|<math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math>
|Euclideanized-complexity-weighted cents
| Euclideanized-complexity-weighted cents
|-
|-
|E-<alt>-C-damage
|E-<alt>-C-damage
Line 4,147: Line 3,995:
|simplicity-weighted cents
|simplicity-weighted cents
|-
|-
|<alt>-S-damage
| <alt>-S-damage
|<alternative>-simplicity-weight damage
|<alternative>-simplicity-weight damage
|<math>\mathsf{¢}</math><math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
|<math>\mathsf{¢}</math><math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math>
|<alternative>-simplicity-weighted cents
|<alternative>-simplicity-weighted cents
|-
|-
|ES-damage
| ES-damage
|Euclideanized-simplicity-weight damage
|Euclideanized-simplicity-weight damage
|<math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math>
|<math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math>
Line 4,181: Line 4,029:
|-
|-
|<alt>-C
|<alt>-C
|<alternative> complexity
| <alternative> complexity
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
|<alternative>-complexity weight
| <alternative>-complexity weight
|-
|-
|EC
|EC
Line 4,190: Line 4,038:
|Euclideanized-complexity weight
|Euclideanized-complexity weight
|-
|-
|E-<alt>-C
| E-<alt>-C
|Euclideanized-<alternative> complexity
|Euclideanized-<alternative> complexity
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(E}</math>-<alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{C)}</math>
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(E}</math>-<alt>-<math>\scriptsize\mathsf{C)}</math> = <math>\small\mathsf{(E}</math>-<alt>-<math>\small\mathsf{C)}</math>
|Euclideanized-<alternative>-complexity weight
|Euclideanized-<alternative>-complexity weight
|-
|-
|S
| S
|simplicity
|simplicity
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> = <math>\small\mathsf{(S)}</math>
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> = <math>\small\mathsf{(S)}</math>
Line 4,205: Line 4,053:
|<alternative>-simplicity weight
|<alternative>-simplicity weight
|-
|-
|ES
| ES
|Euclideanized simplicity
|Euclideanized simplicity
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(ES)}</math> = <math>\small\mathsf{(ES)}</math>
|<math>\small\mathsf{𝟙}\scriptsize\mathsf{(ES)}</math> = <math>\small\mathsf{(ES)}</math>
Line 4,216: Line 4,064:
|}
|}


==WinCompose==
==WinCompose ==


Are you tired of every time web-searching for and copy-pasting special characters that you use over and over in RTT discussions, or would like to use if only it were easy, such as ♯, ♭, ¢, √, °, ₂, ×, ⁻¹, ⟩, ∞, and ϕ? Well, try [http://wincompose.info/ WinCompose]! This tool lets you communicate about these ideas without disrupting your train of thought, by typing these characters with simple and memorable key sequences. These sequences always begin with your chosen Compose-key, which defaults to being your right Alt key. When describing these sequences we represent this key with the symbol ⎄. So for example, you type ♯ as ⎄##, ♭ as ⎄bb, ¢ as ⎄c/, √ as ⎄v/, ° as ⎄00, ₂ as ⎄-2, × as ⎄xx, ⁻¹ as ⎄11, ⟩ as ⎄>>, ∞ as ⎄88, and ϕ as ⎄8f.  
Are you tired of every time web-searching for and copy-pasting special characters that you use over and over in RTT discussions, or would like to use if only it were easy, such as ♯, ♭, ¢, √, °, ₂, ×, ⁻¹, ⟩, ∞, and ϕ? Well, try [http://wincompose.info/ WinCompose]! This tool lets you communicate about these ideas without disrupting your train of thought, by typing these characters with simple and memorable key sequences. These sequences always begin with your chosen Compose-key, which defaults to being your right Alt key. When describing these sequences we represent this key with the symbol ⎄. So for example, you type ♯ as ⎄##, ♭ as ⎄bb, ¢ as ⎄c/, √ as ⎄v/, ° as ⎄00, ₂ as ⎄-2, × as ⎄xx, ⁻¹ as ⎄11, ⟩ as ⎄>>, ∞ as ⎄88, and ϕ as ⎄8f.  
Line 4,228: Line 4,076:
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+
|+
! scope="col" width="130px" | Compose-key sequence
! scope="col" width="130px" |Compose-key sequence
! scope="col" width="75px" | resulting text
! scope="col" width="75px" |resulting text
!description
!description
|-
|-
Line 4,301: Line 4,149:
|-
|-
|⎄;;
|⎄;;
|◌̲̅
| ◌̲̅
|combining overline and low line (undirected value)
|combining overline and low line (undirected value)
|-
|-
Line 4,438: Line 4,286:
|large multiplication sign (a better symbol for cross product)
|large multiplication sign (a better symbol for cross product)
|-
|-
|⎄x*
| ⎄x*
|⋆
| ⋆
|star operator (prefix: tensor complement, Hodge)
| star operator (prefix: tensor complement, Hodge)
|-
|-
|⎄X*
|⎄X*
Line 4,451: Line 4,299:
|-
|-
|⎄X.
|⎄X.
|•
| •
|bullet (infix: fat dot product, Dorst)
|bullet (infix: fat dot product, Dorst)
|-
|-
Line 4,470: Line 4,318:
|⎄-+
|⎄-+
|₊
|₊
|subscript plus sign
| subscript plus sign
|-
|-
|⎄--
|⎄--
|₋
|₋
|subscript minus sign
| subscript minus sign
|-
|-
|⎄-=
|⎄-=
Line 4,482: Line 4,330:
|⎄++
|⎄++
|⁺
|⁺
|superscript plus sign (matrix pseudoinverse)
| superscript plus sign (matrix pseudoinverse)
|-
|-
|⎄+- or ⎄+=
|⎄+- or ⎄+=
Line 4,490: Line 4,338:
|⎄=+
|⎄=+
|∓
|∓
|minus or plus sign
| minus or plus sign
|-
|-
|⎄=-
| ⎄=-
|−
| −
|minus sign
|minus sign
|-
|-
Line 4,513: Line 4,361:
|-
|-
|⎄⎄\/
|⎄⎄\/
|⋁
| ⋁
|larger logical OR, vee product, regressive product
|larger logical OR, vee product, regressive product
|-
|-
Line 4,529: Line 4,377:
|-
|-
|<nowiki>⎄^|</nowiki>
|<nowiki>⎄^|</nowiki>
|⌉
| ⌉
|right ceiling
|right ceiling
|-
|-
Line 4,544: Line 4,392:
|not sign (prefix: multivector complement)
|not sign (prefix: multivector complement)
|-
|-
|⎄⎄<>
| ⎄⎄<>
|⋄
|⋄
|diamond operator (prefix: multivector dual)
|diamond operator (prefix: multivector dual)
Line 4,553: Line 4,401:
|-
|-
|⎄(..)
|⎄(..)
|⊙
| ⊙
|alternative entrywise vector multiplication operator
|alternative entrywise vector multiplication operator
|-
|-
Line 4,571: Line 4,419:
|-
|-
|⎄5◌
|⎄5◌
|𝔞
| 𝔞
|fraktur, ⎄5a
|fraktur, ⎄5a
|-
|-
Line 4,582: Line 4,430:
|superscript greek, ⎄68b is superscript beta (only a few)
|superscript greek, ⎄68b is superscript beta (only a few)
|-
|-
|⎄7◌
| ⎄7◌
|𝒶
|𝒶
|script, ⎄7a
|script, ⎄7a
|-
|-
|⎄8◌
| ⎄8◌
|α
|α
|greek, ⎄8a is alpha (by sound where possible otherwise letter-shape)
|greek, ⎄8a is alpha (by sound where possible otherwise letter-shape)
|-
|-
|⎄8.◌
| ⎄8.◌
|ς
|ς
|greek variants, ⎄8.s is final sigma
| greek variants, ⎄8.s is final sigma
|-
|-
|⎄9◌
|⎄9◌
Line 4,602: Line 4,450:
|bold fraktur, ⎄95a
|bold fraktur, ⎄95a
|-
|-
|⎄97◌
| ⎄97◌
|𝓪
|𝓪
|bold script, ⎄97a
|bold script, ⎄97a
Line 4,611: Line 4,459:
|-
|-
|⎄90◌
|⎄90◌
|𝒂
| 𝒂
|bold italic, ⎄90a
|bold italic, ⎄90a
|-
|-
|⎄908◌
|⎄908◌
|𝜶
| 𝜶
|bold italic greek, ⎄908a is bold italic alpha
| bold italic greek, ⎄908a is bold italic alpha
|-
|-
|⎄0◌
|⎄0◌
Line 4,714: Line 4,562:


{| class="wikitable mw-collapsible mw-collapsed"  
{| class="wikitable mw-collapsible mw-collapsed"  
|+  
|+
| [[File:WinCompose keyboard map.png|1000px]]  
|[[File:WinCompose keyboard map.png|1000px]]
|}
|}


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