Xenharmonic Wiki

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

← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
→Objects: add temperament addition links
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
→Objects: removed newly advanced material from intermediate table, and clarify material in advanced table
Line 1,123: Line 1,123:
! colspan="17" |tuning
! colspan="17" |tuning
|-
|-
|<math>1200×\slant{\mathbf{1}}LG_{\text{j}}M_{\text{j}} \\
|
1200×\slant{\mathbf{1}}L \\
𝒈_{\text{j}}M_{\text{j}}</math>
|<math>𝒋</math>
|<math>𝒋</math>
|[[just tuning map|just(-prime) tuning map]]
|[[just tuning map|just(-prime) tuning map]]
|<math>\scriptsize
|
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\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}
\begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\\ \scriptsize \quad
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} M_{\text{j}} \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
</math>
|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
|cents per prime
|cents per prime
|<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}, \cancel{r}) \end{array}
\!\!
\begin{array} {c} M_{\text{j}} \\[-3pt] (\cancel{r}, d) \end{array}
\!\!
</math>
|<math>\scriptsize (1, d)</math>
|<math>\scriptsize (1, d)</math>
|real
|real
Line 1,167: Line 1,141:
|
|
|-
|-
|<math>1200×\slant{\mathbf{1}}LG</math>
|
|<math>𝒈</math>
|<math>𝒈</math>
|[[generator tuning map]]
|[[generator tuning map]]
|<math>\scriptsize
|
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\mathsf{¢}</math>/<math>\small 𝗴</math>
\begin{array} {c} \\[-2pt] · \end{array}
|cents per generator
\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}
\begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\\ \scriptsize \quad
\begin{array} {c} G \\[-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 \\[-3pt] (\cancel{d}, r) \end{array}
\!\!
</math>
|<math>\scriptsize (1, r)</math>
|<math>\scriptsize (1, r)</math>
|real
|real
Line 1,205: Line 1,159:
|
|
|-
|-
|<math>1200×\slant{\mathbf{1}}LGM \\
|
1200×\slant{\mathbf{1}}LP \\
𝒈M</math>
|<math>𝒕</math>
|<math>𝒕</math>
|[[tuning map|(tempered-prime) tuning map]]
|[[tuning map|(tempered-prime) tuning map]]
|<math>\scriptsize
|
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
\begin{array} {c} \\[-2pt] · \end{array}
|cents per prime
\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 (1, 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}
\\ \scriptsize \quad
\begin{array} {c} G \\[-2pt] \cancel{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} 𝗽 \end{array}
</math>
|<math>\mathsf{¢}</math>/<math>\small 𝗽</math>
|cents per prime
|<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 \\[-3pt] (\cancel{d}, \cancel{r}) \end{array}
\!\!
\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}
\!\!
</math>
|<math>\scriptsize (1, d)</math>
|real
|vector
|vector
|⟨...]
|⟨...]
Line 1,260: Line 1,188:
|real
|real
|vector
|vector
|⟨...]
| ⟨...]
|
|
|
|
Line 1,346: Line 1,274:
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
|real
|scalar
| scalar
|
|
|
|
Line 1,472: Line 1,400:
|matrix
|matrix
|
|
|[[...⟩ ...]
| [[...⟩ ...]
|
|
|<math>\textbf{t}_i</math>
|<math>\textbf{t}_i</math>
Line 1,641: Line 1,569:
|
|
|-
|-
|<math>|\textbf{e}|W \\
|<math>|\textbf{e}|W</math>
1200×\slant{\mathbf{1}}L|P - I|\mathrm{T}W</math>
|<math>\textbf{d}</math>
|<math>\textbf{d}</math>
|[[target-interval damage list]]
|[[target-interval damage list]]
Line 1,836: Line 1,763:
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|real
| real
|matrix
|matrix
|[⟨...] ...⟩
|[⟨...] ...⟩
Line 1,854: Line 1,781:
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
| real
| scalar
|scalar
|
|
|
|
Line 1,883: Line 1,810:
|}
|}


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


Same as the basic level.  
Same as the basic level.  
Line 1,912: Line 1,839:
!initial
!initial
!name
!name
! power
!power
!initial
!initial
!name
!name
! power
!power
!initial
!initial
! name
!name
!multiplier
! multiplier
! colspan="1" |abbreviated
! colspan="1" |abbreviated
! colspan="1" |read ("____ tuning scheme")
! colspan="1" |read ("____ tuning scheme")
Line 1,935: Line 1,862:
| rowspan="7" |∞
| rowspan="7" |∞
| rowspan="2" |all
| rowspan="2" |all
|minimax-S
| minimax-S
|minimax simplicity-weight damage
|minimax simplicity-weight damage
|"[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*, "[[BOP tuning|BOP]]", "[[Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space|Weil]]", "[[Kees]]"
|"[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*, "[[BOP tuning|BOP]]", "[[Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space|Weil]]", "[[Kees]]"
Line 1,956: Line 1,883:
|unity-weight
|unity-weight
|<none>
|<none>
| rowspan="15" |<set>
| rowspan="15" | <set>
|<set> minimax-U
|<set> minimax-U
|<set> minimax unity-weight-damage
|<set> minimax unity-weight-damage
Line 1,986: Line 1,913:
| 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 2,065: Line 1,992:
| 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 2,090: Line 2,017:
|yes
|yes
|-
|-
|E
| E
|Euclidean
|Euclidean
|2
|2
Line 2,099: Line 2,026:
|}
|}


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


{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
Line 2,109: Line 2,036:
!abbreviation
!abbreviation
!name
!name
!symbol
! symbol
!name
!name
|-
|-
|U-damage
| U-damage
|unity-weight damage
|unity-weight damage
|<math>\mathsf{¢}\small\mathsf{(U)}</math>
|<math>\mathsf{¢}\small\mathsf{(U)}</math>
Line 2,130: Line 2,057:
|simplicity-weight damage
|simplicity-weight damage
|<math>\mathsf{¢}\small\mathsf{(S)}</math>
|<math>\mathsf{¢}\small\mathsf{(S)}</math>
|simplicity-weighted cents
| simplicity-weighted cents
|-
|-
|ES-damage
|ES-damage
Line 2,145: Line 2,072:
! colspan="2" |unit
! colspan="2" |unit
|-
|-
!abbreviation
! abbreviation
!name
!name
! symbol
!symbol
!name
!name
|-
|-
Line 2,156: Line 2,083:
|-
|-
|EC
|EC
| Euclideanized complexity
|Euclideanized complexity
|<math>\small\mathsf{(EC)}</math>
|<math>\small\mathsf{(EC)}</math>
|Euclideanized-complexity weight
|Euclideanized-complexity weight
Line 2,168: Line 2,095:
|Euclideanized simplicity
|Euclideanized simplicity
|<math>\small\mathsf{(ES)}</math>
|<math>\small\mathsf{(ES)}</math>
|Euclideanized-simplicity weight
| Euclideanized-simplicity weight
|}
|}


Line 2,183: Line 2,110:
! 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 2,189: Line 2,116:
!unreduced
!unreduced
!reduced
!reduced
! read as
!read as
!unreduced
!unreduced
!reduced
! reduced
!numeric
!numeric
!structural
!structural
Line 2,212: Line 2,139:
|<math>\scriptsize (d, 1)</math>
|<math>\scriptsize (d, 1)</math>
|integer
|integer
|vector
| vector
|
|
|[...⟩
|[...⟩
Line 2,219: Line 2,146:
|
|
|<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 2,230: Line 2,157:
|
|
|<math>\scriptsize (r, d)</math>
|<math>\scriptsize (r, d)</math>
|integer
| integer
|matrix
|matrix
|[⟨...] ...}
|[⟨...] ...}
Line 2,249: Line 2,176:
</math>
</math>
|<math>\small 𝗴</math>
|<math>\small 𝗴</math>
|generators
| generators
|<math>\scriptsize  
|<math>\scriptsize  
\!\!
\!\!
Line 2,314: Line 2,241:
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|integer
|integer
|scalar
| scalar
|
|
|
|
Line 2,479: Line 2,406:
|<math>\scriptsize (1, d)</math>
|<math>\scriptsize (1, d)</math>
|real
|real
| vector
|vector
|⟨...]
|⟨...]
|
|
Line 2,486: Line 2,413:
|
|
|<math>r_i</math>
|<math>r_i</math>
|previous name: prime error map
| previous name: prime error map
|-
|-
|<math>𝒋\textbf{i}</math>
|<math>𝒋\textbf{i}</math>
Line 2,507: Line 2,434:
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
|real
| scalar
|scalar
|
|
|
|
Line 2,535: Line 2,462:
</math>
</math>
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
| real
|scalar
|scalar
|
|
Line 2,613: Line 2,540:
|
|
|-
|-
! colspan="17" | damage
! colspan="17" |damage
|-
|-
|<math>s^{-1}</math>
|<math>s^{-1}</math>
Line 2,670: Line 2,597:
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|real
|real
| scalar
|scalar
|
|
|
|
Line 2,692: Line 2,619:
|matrix
|matrix
|
|
|[[...⟩ ...]
| [[...⟩ ...]
|
|
|<math>\textbf{t}_i</math>
|<math>\textbf{t}_i</math>
Line 2,764: Line 2,691:
</math>
</math>
|<math>\mathsf{¢}</math>
|<math>\mathsf{¢}</math>
|cents
| cents
|<math>\scriptsize  
|<math>\scriptsize  
\!\!  
\!\!  
Line 2,804: Line 2,731:
|<math>\scriptsize (1, k)</math>
|<math>\scriptsize (1, k)</math>
|real
|real
| list
|list
|[...]
|[...]
|
|
Line 2,909: Line 2,836:
|matrix
|matrix
|
|
| [[...⟩ ...]
|[[...⟩ ...]
|
|
|<math>\textbf{h}_i</math>
|<math>\textbf{h}_i</math>
Line 2,945: Line 2,872:
|<math>\scriptsize (d, n)</math>
|<math>\scriptsize (d, n)</math>
|integer
|integer
|matrix
| matrix
|
|
|[[...⟩ ...]
|[[...⟩ ...]
Line 2,982: Line 2,909:
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
| real
|real
|scalar
|scalar
|
|
Line 2,992: Line 2,919:
|
|
|-
|-
! colspan="17" |all-interval tuning schemes
! colspan="17" | all-interval tuning schemes
|-
|-
|<math>I</math>
|<math>I</math>
Line 3,005: Line 2,932:
|matrix
|matrix
|
|
|⟨[...⟩ ...]
| ⟨[...⟩ ...]
|
|
|
|
Line 3,022: Line 2,949:
|real
|real
|matrix
|matrix
|[⟨...] ...⟩
| [⟨...] ...⟩
|
|
|<math>𝒄_{\text{p}_i}</math>
|<math>𝒄_{\text{p}_i}</math>
Line 3,123: Line 3,050:
|-
|-
|
|
|<math>Z</math>
|<math>\slant{\mathbf{1}}</math>
|[[size-sensitizing matrix]]
|[[summation map]]
|
|
|
|
|
|
|
|<math>\scriptsize (1, d)</math>
|integer
|vector
|⟨...]
|
|
|<math>\scriptsize (d+1, d)</math>
|real
|matrix
|[⟨…]...]
|
|
|<math>𝒛_i</math>
|
|
|
|
|<math>z_{ij}</math>
|<math>1</math>
|
|
|-
|-
! colspan="17" |non-standard domain bases
|
|-
|<math>1200</math>
| rowspan="2" |
|[[octaves-to-cents conversion]]
|<math>B_s</math>
|
| rowspan="2" |[[(domain) basis (change) matrix]]
|¢/oct
|cents per octave
|
|<math>\scriptsize (1, 1)</math>
|integer
|scalar
|
|
|
|
|
|
|
|-
|
|<math>Z</math>
|[[size-sensitizing matrix]]
|
|
|
|
|<math>\scriptsize (d+1, d)</math>
|real
|matrix
|[⟨…]...]
|
|<math>𝒛_i</math>
|
|
|<math>z_{ij}</math>
|
|-
! colspan="17" |non-standard domain bases
|-
| rowspan="2" |
|<math>B_s</math>
| rowspan="2" |[[(domain) basis (change) matrix]]
| rowspan="2" |
| rowspan="2" |
|<math>\small 𝗽</math>/<math>\small 𝗯</math>
|<math>\small 𝗽</math>/<math>\small 𝗯</math>
Line 3,152: Line 3,115:
| rowspan="2" |integer
| rowspan="2" |integer
| rowspan="2" |matrix
| rowspan="2" |matrix
| rowspan="2" | [[...] ...]
| rowspan="2" |[[...] ...]
| rowspan="2" |[[...] ...]
| rowspan="2" |[[...] ...]
| rowspan="2" |
| rowspan="2" |
Line 3,176: Line 3,139:
|<math>\scriptsize (d, r)</math>
|<math>\scriptsize (d, r)</math>
|real
|real
| matrix
|matrix
|[{...] ...⟩
|[{...] ...⟩
|{[...⟩ ...]
|{[...⟩ ...]
Line 3,363: Line 3,326:
|<math>\scriptsize (k, r)</math>
|<math>\scriptsize (k, r)</math>
|<math>\scriptsize \{0, +1, -1\}</math>
|<math>\scriptsize \{0, +1, -1\}</math>
|matrix
| matrix
|[[...] ...]
|[[...] ...]
|
|
Line 3,372: Line 3,335:
|mnemonic: <math>K</math>onstraint
|mnemonic: <math>K</math>onstraint
|-
|-
! colspan="17" | exterior algebra
! colspan="17" |exterior algebra
|-
|-
|
|
Line 3,397: Line 3,360:
|
|
|<math>\small 𝗽</math>
|<math>\small 𝗽</math>
| primes
|primes
|
|
|<math>\scriptsize (1, n)</math>
|<math>\scriptsize (1, n)</math>
Line 3,472: Line 3,435:
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
| integer
|integer
|scalar
|scalar
|
|
Line 3,530: Line 3,493:
|integer
|integer
|matrix
|matrix
| [⟨...]] or [[...] ...⟩
|[⟨...]] or [[...] ...⟩
|⟨[...]] or [[...⟩ ...]
|⟨[...]] or [[...⟩ ...]
|<math>\textbf{𝓁}_{\text{dep}i}</math>
|<math>\textbf{𝓁}_{\text{dep}i}</math>
Line 3,603: Line 3,566:
|<math>\small 𝗴</math>
|<math>\small 𝗴</math>
|generators
|generators
|yes
| yes
|-
|-
|<math>\small 𝗽</math>
|<math>\small 𝗽</math>
Line 3,634: Line 3,597:
{| 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
! colspan="2" rowspan="4" |systematic name
! colspan="2" rowspan="4" |systematic name
! rowspan="5" |previously named tuning schemes that are specific types of this tuning scheme
! rowspan="5" | previously named tuning schemes that are specific types of this tuning scheme
! 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 3,652: Line 3,615:
! 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 3,691: Line 3,654:
| rowspan="4" |all
| rowspan="4" |all
|minimax-S
|minimax-S
|minimax simplicity-weight damage
| minimax simplicity-weight damage
|"[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*
|"[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*
|yes
|yes
|-
|-
| 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 3,726: Line 3,689:
|unity-weight
|unity-weight
|<none>
|<none>
| rowspan="27" |<set>
| rowspan="27" | <set>
|<set> minimax-U
|<set> minimax-U
|<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 3,793: Line 3,756:
|-
|-
| 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 3,801: Line 3,764:
|U
|U
|unity-weight
|unity-weight
|<none>
| <none>
| rowspan="9" |miniRMS
| rowspan="9" |miniRMS
| rowspan="9" |2
| rowspan="9" |2
|<set> miniRMS-U
| <set> miniRMS-U
|<set> miniRMS unity-weight damage
|<set> miniRMS unity-weight damage
|"[[least squares]]"
|"[[least squares]]"
Line 3,810: Line 3,773:
|-
|-
| colspan="3" |<none>
| colspan="3" |<none>
| rowspan="2" |(t)
| rowspan="2" | (t)
| rowspan="2" |taxicab
| rowspan="2" |taxicab
| rowspan="2" |1
| rowspan="2" | 1
| rowspan="4" |S
| rowspan="4" |S
| rowspan="4" |simplicity-weight
| rowspan="4" |simplicity-weight
Line 3,819: Line 3,782:
|<set> miniRMS simplicity-weight damage
|<set> miniRMS simplicity-weight damage
|
|
| yes
|yes
|-
|-
| colspan="3" |<various>
| colspan="3" |<various>
Line 3,831: Line 3,794:
| rowspan="2" |Euclidean
| rowspan="2" |Euclidean
| rowspan="2" |2
| rowspan="2" |2
|<set> miniRMS-ES
| <set> miniRMS-ES
|<set> miniRMS Euclideanized-simplicity-weight damage
|<set> miniRMS Euclideanized-simplicity-weight damage
|
|
|
|
|-
|-
| 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 3,848: Line 3,811:
| 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 3,864: Line 3,827:
| 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
|
|
Line 3,877: Line 3,840:
| colspan="6" |<n/a>
| colspan="6" |<n/a>
|U
|U
| unity-weight
|unity-weight
|<none>
|<none>
| rowspan="9" |minimean
| rowspan="9" |minimean
| rowspan="9" |1
| rowspan="9" |1
|<set> minimean-U
| <set> minimean-U
|<set> minimean unity-weight damage
|<set> minimean unity-weight damage
|
|
Line 3,887: Line 3,850:
|-
|-
| colspan="3" |<none>
| colspan="3" |<none>
| rowspan="2" |(t)
| rowspan="2" | (t)
| rowspan="2" |taxicab
| rowspan="2" |taxicab
| 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
|<set> minimean simplicity-weight damage
|<set> minimean simplicity-weight damage
Line 3,940: Line 3,903:
| 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 3,971: Line 3,934:
|-
|-
|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 3,980: Line 3,943:
|<alternative>-complexity-weighted cents
|<alternative>-complexity-weighted cents
|-
|-
|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 3,995: Line 3,958:
|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 4,029: Line 3,992:
|-
|-
|<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 4,038: Line 4,001:
|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 4,053: Line 4,016:
|<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 4,064: Line 4,027:
|}
|}


==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 4,149: Line 4,112:
|-
|-
|⎄;;
|⎄;;
| ◌̲̅
|◌̲̅
|combining overline and low line (undirected value)
|combining overline and low line (undirected value)
|-
|-
Line 4,237: Line 4,200:
|-
|-
|⎄ll
|⎄ll
|ℓ
| ℓ
|script small L
|script small L
|-
|-
Line 4,261: Line 4,224:
|-
|-
|⎄TT
|⎄TT
|ᵀ
| ᵀ
|superscript capital T (matrix transpose)
|superscript capital T (matrix transpose)
|-
|-
Line 4,274: Line 4,237:
! colspan="3" rowspan="1" |Multiplication operators
! colspan="3" rowspan="1" |Multiplication operators
|-
|-
|⎄xx
| ⎄xx
|×
|×
|multiplication sign
|multiplication sign
Line 4,282: Line 4,245:
|vector or cross product (barely distinguishable from multiplication sign)
|vector or cross product (barely distinguishable from multiplication sign)
|-
|-
|⎄XX
| ⎄XX
|✕
|✕
|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)
Line 4,294: Line 4,257:
|asterisk operator (infix: scalar product, Dorst)
|asterisk operator (infix: scalar product, Dorst)
|-
|-
|⎄x.
| ⎄x.
|⋅
|⋅
|dot (product) operator
|dot (product) operator
|-
|-
|⎄X.
|⎄X.
| •
|•
|bullet (infix: fat dot product, Dorst)
|bullet (infix: fat dot product, Dorst)
|-
|-
Line 4,306: Line 4,269:
|⎄v/
|⎄v/
|√
|√
|square root sign
| square root sign
|-
|-
|⎄3v/
|⎄3v/
|∛
| ∛
|cube root sign
|cube root sign
|-
|-
Line 4,316: Line 4,279:
|fourth root sign
|fourth root sign
|-
|-
|⎄-+
| ⎄-+
|₊
|₊
| subscript plus sign
|subscript plus sign
|-
|-
|⎄--
|⎄--
|₋
|₋
| subscript minus sign
|subscript minus sign
|-
|-
|⎄-=
|⎄-=
Line 4,329: Line 4,292:
|-
|-
|⎄++
|⎄++
|⁺
| ⁺
| superscript plus sign (matrix pseudoinverse)
| superscript plus sign (matrix pseudoinverse)
|-
|-
Line 4,338: Line 4,301:
|⎄=+
|⎄=+
|∓
|∓
| minus or plus sign
|minus or plus sign
|-
|-
| ⎄=-
|⎄=-
| −
|−
|minus sign
| minus sign
|-
|-
|⎄==
|⎄==
Line 4,354: Line 4,317:
|⎄\/
|⎄\/
|∨
|∨
|logical OR, vee product, regressive product
| logical OR, vee product, regressive product
|-
|-
|⎄⎄/\
|⎄⎄/\
|⋀
|⋀
|larger logical AND, wedge product, progressive product
| larger logical AND, wedge product, progressive product
|-
|-
|⎄⎄\/
|⎄⎄\/
| ⋁
|⋁
|larger logical OR, vee product, regressive product
|larger logical OR, vee product, regressive product
|-
|-
Line 4,377: Line 4,340:
|-
|-
|<nowiki>⎄^|</nowiki>
|<nowiki>⎄^|</nowiki>
| ⌉
|⌉
|right ceiling
|right ceiling
|-
|-
Line 4,392: Line 4,355:
|not sign (prefix: multivector complement)
|not sign (prefix: multivector complement)
|-
|-
| ⎄⎄<>
|⎄⎄<>
|⋄
|⋄
|diamond operator (prefix: multivector dual)
|diamond operator (prefix: multivector dual)
Line 4,398: Line 4,361:
|⎄(.)
|⎄(.)
|⨀
|⨀
|entrywise vector multiplication operator
| entrywise vector multiplication operator
|-
|-
|⎄(..)
|⎄(..)
| ⊙
|⊙
|alternative entrywise vector multiplication operator
|alternative entrywise vector multiplication operator
|-
|-
Line 4,412: Line 4,375:
|⎄3◌
|⎄3◌
|я
|я
|cyrillic, ⎄3q is ya (example)
| cyrillic, ⎄3q is ya (example)
|-
|-
|⎄4◌
|⎄4◌
Line 4,419: Line 4,382:
|-
|-
|⎄5◌
|⎄5◌
| 𝔞
|𝔞
|fraktur, ⎄5a
|fraktur, ⎄5a
|-
|-
Line 4,430: Line 4,393:
|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◌
|𝐚 𝟏 𝟓 𝟕 𝟖 𝟎
| 𝐚 𝟏 𝟓 𝟕 𝟖 𝟎
|bold, ⎄9a ⎄91 ⎄95␣ ⎄97␣ ⎄98␣ ⎄90␣
|bold, ⎄9a ⎄91 ⎄95␣ ⎄97␣ ⎄98␣ ⎄90␣
|-
|-
Line 4,450: Line 4,413:
|bold fraktur, ⎄95a
|bold fraktur, ⎄95a
|-
|-
| ⎄97◌
|⎄97◌
|𝓪
|𝓪
|bold script, ⎄97a
|bold script, ⎄97a
Line 4,459: Line 4,422:
|-
|-
|⎄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 4,470: Line 4,433:
|italic, ⎄0a
|italic, ⎄0a
|-
|-
|⎄08◌
| ⎄08◌
|𝛼
|𝛼
|italic greek, ⎄08a is italic alpha
|italic greek, ⎄08a is italic alpha
Line 4,495: Line 4,458:
|-
|-
|<nowiki>⎄|◌</nowiki>
|<nowiki>⎄|◌</nowiki>
|𝕒 𝟙 𝟠 𝟘
| 𝕒 𝟙 𝟠 𝟘
|<nowiki>double-struck, ⎄|a ⎄|1 ⎄|8␣ ⎄|0␣</nowiki>
|<nowiki>double-struck, ⎄|a ⎄|1 ⎄|8␣ ⎄|0␣</nowiki>
|-
|-
Line 4,503: Line 4,466:
|-
|-
|<nowiki>⎄|0◌</nowiki>
|<nowiki>⎄|0◌</nowiki>
|ⅇ ⅈ
| ⅇ ⅈ
|<nowiki>double-struck italic, ⎄|0e ⎄|i (only a few)</nowiki>
|<nowiki>double-struck italic, ⎄|0e ⎄|i (only a few)</nowiki>
|-
|-
Line 4,526: Line 4,489:
|⎄⎄<<
|⎄⎄<<
|⟪
|⟪
|left power-mean bracket
| left power-mean bracket
|-
|-
|⎄⎄>>
|⎄⎄>>
Line 4,537: Line 4,500:
|-
|-
|<nowiki>⎄⎄}}</nowiki>
|<nowiki>⎄⎄}}</nowiki>
|⧚
| ⧚
|right power-sum bracket (substitute for {{rrzigzag}} when HTML is not available)
|right power-sum bracket (substitute for {{rrzigzag}} when HTML is not available)
|-
|-
Line 4,543: Line 4,506:
|-
|-
|⎄\-
|⎄\-
|◌̶
| ◌̶
|combining strike-thru
|combining strike-thru
|-
|-
Line 4,566: Line 4,529:
|}
|}


==Footnotes==
== Footnotes==


<references />
<references />
Retrieved from "https://en.xen.wiki/w/Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT/Conventions_for_names,_variables,_units,_and_notations"