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

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Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
m β†’Objects: oops, missed a spot
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
remove 1200, 𝟏, and 𝐿 from computations sections of objects table; the first two never come up anymore, and the latter only comes up in all-interval tunings schemes, so move it to that section
Line 1,729: Line 1,729:
|-
|-
|
|
|<math>L</math>
|<math>G</math>
|[[log-prime matrix]]
|[[generator embedding matrix|generator embedding (matrix)]]
|
|
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|octaves per prime
|primes per generator
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, r)</math>
|real
|real
|matrix
|matrix
|[⟨...] ...⟩
|[{...] ...⟩
|⟨[...⟩ ...]
|{[...⟩ ...]
|<math>\textbf{𝓁}_i</math>
|<math>π’ˆ_i</math>
|
|
|
|<math>\textbf{𝓁}</math>
|<math>g_{ij}</math>
|<math>𝓁_{ij}</math>
|
|
|-
|-
|
|
|<math>\textbf{1}</math><ref>The summation map symbol ideally should be a bold italic (serif) numeral one. Unfortunately the wiki at present lacks the ability to do this inside of <nowiki><math> tags; this is possible in </nowiki><math>\small\LaTeX</math><nowiki> generally, but not in MathJax, which is what the wiki uses. Specifically, \textit{\textbf{1}} and \textbf{\textit{1}} work fine in </nowiki><math>\small\LaTeX</math>, as you can try here:
|<math>K</math>
https://quicklatex.com/
|[[constraint (matrix)]]
but not in in MathJax, as described here:
https://docs.mathjax.org/en/latest/input/tex/differences.html.
Symbols which are normally italic in math mode, such as letters, can be made bold italic using \boldsymbol{A}, except on Macs, e.g. <math>\small\boldsymbol{A}</math>. But unfortunately, \boldsymbol{\mathit{1}} does not work in MathJax, although it works in <math>\small\LaTeX</math>. The MathJax-specific command \style{font-weight:bold;font-style:italic}{1} doesn't work either. Unicode contains mathematical characters including numerals in several styles. Unfortunately it does not include bold italic numerals. Perhaps future wikizens will be able to follow through for us on a solution to this problem.</ref>
|[[summation map]]
|
|
|
|
|
|
|
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|<math>\scriptsize (1, d)</math>
|<math>\scriptsize (r, k)</math>
|integer
|<math>\scriptsize \{0, +1, -1\}</math>
|vector
|matrix
|⟨...]
|[[...] ...]
|
|
|<math>π’Œ_i</math>
|
|
|
|
|<math>k_{ij}</math>
|mnemonic: <math>K</math>onstraint
|-
|
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|<math>1</math>
|<math>{\large⧛}Β·{\large⧚}_p</math>
|[[power sum]] (<math>p</math>-sum)
|
|
|-
|
|
|<math>1200</math>
|[[octaves-to-cents conversion]]
|
|
|<math>\mathsf{Β’}</math>/<math>\small\mathsf{oct}</math>
|cents per octave
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|integer
|real
|scalar
|scalar
|
|
Line 1,786: Line 1,782:
|
|
|-
|-
|
! colspan="17" |projection
|<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>π’ˆ_i</math>
|
|
|<math>g_{ij}</math>
|
|-
|-
|<math>GM</math>
|<math>P</math>
|[[Projection matrix|projection (matrix)]]
|<math>\scriptsize
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
\begin{array} {c} \\[-2pt] Β· \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<ref>Note that "primes per prime" does not cancel out, because the first primes increment by rows while the second primes increment by columns. See [[Projection matrix#Units]] for details.</ref>
|<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>
|real
|matrix
|[⟨...] ...⟩
|⟨[...⟩ ...]
|<math>𝒑_i</math>
|
|
|<math>K</math>
|[[constraint (matrix)]]
|
|
|<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] Β· \end{array}
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] Β· \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>\scriptsize (r, k)</math>
|<math>\scriptsize \{0, +1, -1\}</math>
|matrix
|[[...] ...]
|
|<math>π’Œ_i</math>
|
|
|
|
|<math>k_{ij}</math>
|mnemonic: <math>K</math>onstraint
|-
|
|
|<math>{\large⧛}Β·{\large⧚}_p</math>
|[[power sum]] (<math>p</math>-sum)
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|specific type: [[prime-count vector]] (PC-vector)
|-
! colspan="17" |JI equivalents
|-
|<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
|[⟨...] ...}
|⟨[...} ...]
|
|
|
|
|<math>𝟏</math>
|
|
|
|
|-
|-
! colspan="17" |projection
|<math>1200Γ—\textbf{1}LG_{\text{j}}</math>
|-
|<math>π’ˆ_{\text{j}}</math>
|<math>GM</math>
|[[JI generator tuning map]]
|<math>P</math>
|[[Projection matrix|projection (matrix)]]
|<math>\scriptsize Β 
|<math>\scriptsize Β 
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{Β’}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
\begin{array} {c} \\[-2pt] Β· \end{array}
\begin{array} {c} \textbf{1} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
\begin{array} {c} \\[-2pt] Β· \end{array}
\begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] Β· \end{array}
\begin{array} {c} \\[-2pt] Β· \end{array}
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
\\ \scriptsize \quad
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array}
</math>
</math>
|<math>\small 𝗽</math>/<math>\small 𝗽</math>
|<math>\mathsf{Β’}</math>/<math>\small 𝗴</math>
|primes per prime<ref>Note that "primes per prime" does not cancel out, because the first primes increment by rows while the second primes increment by columns. See [[Projection matrix#Units]] for details.</ref>
|cents per generator
|<math>\scriptsize Β 
|<math>\scriptsize Β 
\!\!
\!\!
\begin{array} {c} G \\[-3pt] (d, \cancel{r}) \end{array}
\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
\!\!
\begin{array} {c} \textbf{1} \\[-3pt] (\cancel{1}, \cancel{d}) \end{array}
\!\!
\begin{array} {c} L \\[-3pt] (\cancel{d}, \cancel{d}) \end{array}
\\ \scriptsize \quad
\!\!
\!\!
\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}
\begin{array} {c} G_{\text{j}} \\[-3pt] (\cancel{d}, r) \end{array}
\!\!
\!\!
</math>
</math>
|<math>\scriptsize (1, d)</math>
|real
|vector
|{...]
|
|
|
|
|<math>g_{\text{j}i}</math>
|
|-
|<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 (d, d)</math>
|<math>\scriptsize (d, d)</math>
|real
|integer
|matrix
|matrix
|[⟨...] ...⟩
|[{...] ...⟩
|⟨[...⟩ ...]
|{[...⟩ ...]
|<math>𝒑_i</math>
|
|
|
|<math>𝟏</math>
|
|
|<math>p_i</math>
|
|
|-
|-
|<math>GM\textbf{i}</math>
! colspan="17" |all-interval tuning schemes
|<math>P\textbf{i}</math>
|-
|[[projected interval]]
|<math>I</math>
|<math>\scriptsize
|<math>\mathrm{T}_{\text{p}}</math>
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
|[[prime proxy target-interval (matrix)]]
\begin{array} {c} \\[-2pt] Β· \end{array}
|
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] Β· \end{array}
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
</math>
|<math>\small 𝗽</math>
|<math>\small 𝗽</math>
|primes
|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>\scriptsize (d, d)</math>
|integer
|matrix
|
|⟨[...⟩ ...]
|
|
|
|
|<math>𝟏</math>
|
|
|
|
|specific type: [[prime-count vector]] (PC-vector)
|-
|-
! colspan="17" |JI equivalents
|<math>S_{\text{p}}^{-1}</math>
|-
|<math>C_{\text{p}}</math>
|<math>I</math>
|[[complexity prescaler]]
|<math>M_{\text{j}}</math>
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math>
|[[JI mapping (matrix)]]
|<math>\small\mathsf{(C)}</math>
|
|complexity weight
|<math>\small 𝗴</math>/<math>\small 𝗽</math>
|generators per prime
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|integer
|real
|matrix
|matrix
|[⟨...] ...}
|[⟨...] ...⟩
|⟨[...} ...]
|
|
|
|
|<math>𝟏</math>
|
|
|<math>𝒄_{\text{p}}</math>
|<math>c_{\text{p}i}</math>
|
|
|-
|-
|<math>1200Γ—\textbf{1}LG_{\text{j}}</math>
|<math>C_{\text{p}}^{-1}</math>
|<math>π’ˆ_{\text{j}}</math>
|<math>S_{\text{p}}</math>
|[[JI generator tuning map]]
|[[simplicity prescaler]]
|<math>\scriptsize
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(S)}</math>
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{Β’}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\small\mathsf{(S)}</math>
\begin{array} {c} \\[-2pt] Β· \end{array}
|simplicity weight
\begin{array} {c} \textbf{1} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|
\begin{array} {c} \\[-2pt] Β· \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] Β· \end{array}
|matrix
\\ \scriptsize \quad
|
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array}
|⟨[...⟩ ...]
</math>
|
|<math>\mathsf{Β’}</math>/<math>\small 𝗴</math>
|
|cents per generator
|<math>𝒔_{\text{p}}</math>
|<math>\scriptsize Β 
|<math>s_{\text{p}i}</math>
\!\!
\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
\!\!
\begin{array} {c} \textbf{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>L</math>
|[[log-prime matrix]]
|
|
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|octaves per prime
|
|
|<math>g_{\text{j}i}</math>
|<math>\scriptsize (d, d)</math>
|real
|matrix
|[⟨...] ...⟩
|⟨[...⟩ ...]
|<math>\textbf{𝓁}_i</math>
|
|<math>\textbf{𝓁}</math>
|<math>𝓁_{ij}</math>
|
|
|-
|-
|<math>I</math>
|<math>G_{\text{j}}</math>
|[[JI generator embedding matrix|JI generator embedding (matrix)]]
|
|
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|<math>q</math>
|primes per generator
|[[interval complexity norm power]]
|
|
|<math>\scriptsize (d, d)</math>
|integer
|matrix
|[{...] ...⟩
|{[...⟩ ...]
|
|
|
|
|<math>𝟏</math>
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|-
! colspan="17" |all-interval tuning schemes
|-
|<math>I</math>
|<math>\mathrm{T}_{\text{p}}</math>
|[[prime proxy target-interval (matrix)]]
|
|
|<math>\small 𝗽</math>
|primes
|
|
|<math>\scriptsize (d, d)</math>
|integer
|matrix
|
|
|⟨[...⟩ ...]
|
|
|
|
|<math>𝟏</math>
|
|-
|
|<math>β€– Β· β€–_q</math>
|[[power norm]] (<math>q</math>-norm)
|
|
|
|
|
|-
|<math>S_{\text{p}}^{-1}</math>
|<math>C_{\text{p}}</math>
|[[complexity prescaler]]
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math>
|<math>\small\mathsf{(C)}</math>
|complexity weight
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (1, 1)</math>
|real
|real
|matrix
|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{πŸ™}\scriptsize\mathsf{(S)}</math>
|<math>\small\mathsf{(S)}</math>
|simplicity weight
|
|
|<math>\scriptsize (d, d)</math>
|real
|matrix
|
|
|⟨[...⟩ ...]
|
|
|<math>𝒔_{\text{p}}</math>
|<math>s_{\text{p}i}</math>
|
|
|}
===Units===
Same as the basic level.
===Tuning schemes===
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+
|-
|-
|
! colspan="3" rowspan="3" |retuning (or mistuning) magnitude
|<math>q</math>
! colspan="9" |damage
|[[interval complexity norm power]]
! rowspan="4" |target
|
Β 
|
intervals
|
! colspan="2" rowspan="3" |systematic name
|
! rowspan="4" |previously named tuning schemes that are specific types of this tuning scheme
|<math>\scriptsize (1, 1)</math>
! rowspan="4" |of interest?
|real
|-
|scalar
! colspan="6" |weight
|
! colspan="3" rowspan="1" |optimization
|
|
|
|
|
|
|-
|-
|
! colspan="3" |interval complexity
|<math>β€– Β· β€–_q</math>
! colspan="3" rowspan="1" |slope
|[[power norm]] (<math>q</math>-norm)
! colspan="1" rowspan="2" |initial
|
! colspan="1" rowspan="2" |name
|
! colspan="1" rowspan="2" |power
|
|
|<math>\scriptsize (1, 1)</math>
|real
|scalar
|
|
|
|
|
|
|
|}
Β 
===Units===
Β 
Same as the basic level.
Β 
===Tuning schemes===
Β 
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+
|-
|-
! colspan="3" rowspan="3" |retuning (or mistuning) magnitude
!initial
! colspan="9" |damage
!name
! rowspan="4" |target
!power
Β 
!initial
intervals
!name
! colspan="2" rowspan="3" |systematic name
! rowspan="4" |previously named tuning schemes that are specific types of this tuning scheme
! rowspan="4" |of interest?
|-
! colspan="6" |weight
! colspan="3" rowspan="1" |optimization
|-
! colspan="3" |interval complexity
! colspan="3" rowspan="1" |slope
! colspan="1" rowspan="2" |initial
! colspan="1" rowspan="2" |name
! colspan="1" rowspan="2" |power
|-
!initial
!name
!power
!initial
!name
!power
!power
!initial
!initial
Line 3,162: Line 3,122:
! colspan="17" |computation
! colspan="17" |computation
|-
|-
|<math>\text{diag}(\log_2(\textbf{p}))</math>
|<math>L</math>
|[[log-prime matrix]]
|
|
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|<math>G</math>
|octaves per prime
|[[generator embedding matrix|generator embedding (matrix)]]
|
|
|<math>\scriptsize (d, d)</math>
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|primes per generator
|
|<math>\scriptsize (d, r)</math>
|real
|real
|matrix
|matrix
|[⟨...] ...⟩
|[{...] ...⟩
|⟨[...⟩ ...]
|{[...⟩ ...]
|<math>\textbf{𝓁}_i</math>
|<math>π’ˆ_i</math>
|
|
|
|<math>\textbf{𝓁}</math>
|<math>g_{ij}</math>
|<math>𝓁_{ij}</math>
|
|
|-
|-
|
|
|<math>\textbf{1}</math>
|<math>K</math>
|[[summation map]]
|[[constraint (matrix)]]
|
|
|
|
|
|
|
|
|<math>\scriptsize (1, d)</math>
|<math>\scriptsize (r, k)</math>
|integer
|<math>\scriptsize \{0, +1, -1\}</math>
|vector
|matrix
|⟨...]
|[[...] ...]
|
|
|<math>π’Œ_i</math>
|
|
|
|
|<math>k_{ij}</math>
|mnemonic: <math>K</math>onstraint
|-
|
|
|<math>1</math>
|<math>{\large⧛}Β·{\large⧚}_p</math>
|[[power sum]] (<math>p</math>-sum)
|
|
|-
|
|
|<math>1200</math>
|[[octaves-to-cents conversion]]
|
|
|<math>\mathsf{Β’}</math>/<math>\small\mathsf{oct}</math>
|cents per octave
|
|
|<math>\scriptsize (1, 1)</math>
|<math>\scriptsize (1, 1)</math>
|integer
|real
|scalar
|scalar
|
|
Line 3,216: Line 3,176:
|
|
|-
|-
|
! colspan="17" |projection
|<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>π’ˆ_i</math>
|
|
|<math>g_{ij}</math>
|
|-
|-
|
|<math>G_cF^{-1}FM_c \\
|<math>K</math>
\mathrm{V}\textit{Ξ›}\mathrm{V}^{-1}</math>
|[[constraint (matrix)]]
|<math>P</math>
|
|[[Projection matrix|projection (matrix)]]
|
|<math>\scriptsize
|
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
|
\begin{array} {c} \\[-2pt] Β· \end{array}
|<math>\scriptsize (r, k)</math>
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array}
|<math>\scriptsize \{0, +1, -1\}</math>
</math>
|<math>\small 𝗽</math>/<math>\small 𝗽</math>
|primes per prime
|<math>\scriptsize Β 
\!\!
\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>
|real
|matrix
|matrix
|[[...] ...]
|[⟨...] ...⟩
|⟨[...⟩ ...]
|<math>𝒑_i</math>
|
|
|<math>π’Œ_i</math>
|
|
|<math>p_i</math>
|
|
|<math>k_{ij}</math>
|mnemonic: <math>K</math>onstraint
|-
|-
|<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] Β· \end{array}
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] Β· \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>{\large⧛}Β·{\large⧚}_p</math>
|[...⟩
|[[power sum]] (<math>p</math>-sum)
|
|
|
|
|
|
|
|
|<math>\scriptsize (1, 1)</math>
|specific type: [[prime-count vector]] (PC-vector)
|real
|-
|scalar
|
|
|<math>\textit{Ξ›}</math>
|[[scaling factor (eigenvalue) matrix|scaling factor matrix]]
|
|
|
|
|
|
|
|
|<math>\scriptsize (d, d)</math>
|
|
|matrix
|[βŸ¨β€¦] β€¦βŸ©
|⟨[β€¦βŸ© …]
|
|
|
|<math>𝝀</math>
|<math>Ξ»_i</math>
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Ξ›}</math> which it combines with to create the projection matrix; previous name: eigenvalue matrix
|-
|-
! colspan="17" |projection
|
|-
|<math>\mathrm{V}</math>
|<math>G_cF^{-1}FM_c \\
|[[unrotated vector (eigenvector) list|unrotated vector list]]
\mathrm{V}\textit{Ξ›}\mathrm{V}^{-1}</math>
|
|<math>P</math>
|<math>\small 𝗽</math>
|[[Projection matrix|projection (matrix)]]
|primes
|<math>\scriptsize
|
\begin{array} {c} G \\[-2pt] 𝗽 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}
|<math>\scriptsize (d, d)</math>
\begin{array} {c} \\[-2pt] Β· \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>
|real
|matrix
|matrix
|[⟨...] ...⟩
|
|⟨[...⟩ ...]
|⟨[...⟩ ...]
|<math>𝒑_i</math>
|
|
|<math>\textbf{v}_i</math>
|
|<math>\mathrm{v}_{ij}</math>
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Ξ›}</math> which it combines with to create the projection matrix; jargon name: eigenmonzo and comma list
|-
|
|
|<math>p_i</math>
|<math>F</math>
|[[generator form matrix]]
|
|
|-
|<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] Β· \end{array}
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] Β· \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>\scriptsize (r, r)</math>
|
|
|matrix
|[{...] …}
|
|
|specific type: [[prime-count vector]] (PC-vector)
|-
|
|
|<math>\textit{Ξ›}</math>
|<math>𝒇_i</math>
|[[scaling factor (eigenvalue) matrix|scaling factor matrix]]
|
|
|<math>f_{ij}</math>
|
|
|-
! colspan="17" |JI equivalents
|-
|<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>
|<math>\scriptsize (d, d)</math>
|
|integer
|matrix
|matrix
|[βŸ¨β€¦] β€¦βŸ©
|[⟨...] ...}
|⟨[β€¦βŸ© …]
|⟨[...} ...]
|
|
|
|
|<math>𝝀</math>
|<math>𝟏</math>
|<math>Ξ»_i</math>
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Ξ›}</math> which it combines with to create the projection matrix; previous name: eigenvalue matrix
|-
|
|<math>\mathrm{V}</math>
|[[unrotated vector (eigenvector) list|unrotated vector list]]
|
|
|<math>\small 𝗽</math>
|primes
|
|
|<math>\scriptsize (d, d)</math>
|-
|
|<math>1200Γ—\textbf{1}LG_{\text{j}}</math>
|matrix
|<math>π’ˆ_{\text{j}}</math>
|
|[[JI generator tuning map]]
|⟨[...⟩ ...]
|<math>\scriptsize
|
\begin{array} {c} 1200 \\[-2pt] {\small\mathsf{Β’}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\textbf{v}_i</math>
\begin{array} {c} \\[-2pt] Β· \end{array}
|
\begin{array} {c} \textbf{1} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\mathrm{v}_{ij}</math>
\begin{array} {c} \\[-2pt] Β· \end{array}
|mnemonic: <math>\mathrm{V}</math> is mirrored of <math>\textit{Ξ›}</math> which it combines with to create the projection matrix; jargon name: eigenmonzo and comma list
\begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
|-
\begin{array} {c} \\[-2pt] Β· \end{array}
|
\\ \scriptsize \quad
|<math>F</math>
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array}
|[[generator form matrix]]
</math>
|<math>\mathsf{Β’}</math>/<math>\small 𝗴</math>
|cents per generator
|<math>\scriptsize
\!\!
\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
\!\!
\begin{array} {c} \textbf{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>\scriptsize (r, r)</math>
|<math>g_{\text{j}i}</math>
|
|-
|<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 (d, d)</math>
|integer
|matrix
|matrix
|[{...] …}
|[{...] ...⟩
|{[...⟩ ...]
|
|
|
|
|<math>𝒇_i</math>
|<math>𝟏</math>
|
|
|<math>f_{ij}</math>
|
|
|-
|-
! 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 3,407: Line 3,389:
|
|
|-
|-
|<math>1200Γ—\textbf{1}LG_{\text{j}}</math>
|
|<math>π’ˆ_{\text{j}}</math>
|<math>C_{\text{p}}</math>
|[[JI generator tuning map]]
|[[complexity pretransformer]]
|<math>\scriptsize
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{πŸ™}\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} 1200 \\[-2pt] {\small\mathsf{Β’}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
\begin{array} {c} \\[-2pt] Β· \end{array}
|complexity weight or <alternative>-complexity weight
\begin{array} {c} \textbf{1} \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{\mathsf{oct}} \end{array}
|
\begin{array} {c} \\[-2pt] Β· \end{array}
|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
\begin{array} {c} L \\[-2pt] \cancel{\mathsf{oct}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] Β· \end{array}
\\ \scriptsize \quad
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array}
</math>
|<math>\mathsf{Β’}</math>/<math>\small 𝗴</math>
|cents per generator
|<math>\scriptsize
\!\!
\begin{array} {c} 1200 \\[-3pt] (1, \cancel{1}) \end{array}
\!\!
\begin{array} {c} \textbf{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
|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>g_{\text{j}i}</math>
|
|
|-
|-
|<math>I</math>
|<math>G_{\text{j}}</math>
|[[JI generator embedding matrix|JI generator embedding (matrix)]]
|
|
|<math>\small 𝗽</math>/<math>\small 𝗴</math>
|<math>S_{\text{p}}</math>
|primes per generator
|[[simplicity pretransformer]]
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{πŸ™}\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>
|<math>\scriptsize (d, d)</math> or <math>\scriptsize (d+1, d+1)</math>
|integer
|real
|matrix
|matrix
|[{...] ...⟩
|{[...⟩ ...]
|
|
|⟨[...⟩ ...]
|<math>𝒔_{\text{p}i}</math>
|
|
|<math>𝟏</math>
|<math>𝒔_{\text{p}}</math>
|
|<math>s_{\text{p}i}</math> or [math]s_{\text{p}ij}[/math]
|
|
|-
|-
! colspan="17" |all-interval tuning schemes
|<math>\text{diag}(\log_2(\textbf{p}))</math>
|-
|<math>L</math>
|<math>I</math>
|[[log-prime matrix]]
|<math>\mathrm{T}_{\text{p}}</math>
|[[prime proxy target-interval (matrix)]]
|
|
|<math>\small 𝗽</math>
|<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
|primes
|octaves per prime
|
|
|<math>\scriptsize (d, d)</math>
|<math>\scriptsize (d, d)</math>
|integer
|matrix
|
|⟨[...⟩ ...]
|
|
|<math>𝟏</math>
|
|
|-
|
|<math>C_{\text{p}}</math>
|[[complexity pretransformer]]
|<math>\small\mathsf{πŸ™}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{πŸ™}\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
|real
|matrix
|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{πŸ™}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{πŸ™}\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>\textbf{𝓁}_i</math>
|
|
|<math>𝒔_{\text{p}}</math>
|<math>\textbf{𝓁}</math>
|<math>s_{\text{p}i}</math> or [math]s_{\text{p}ij}[/math]
|<math>𝓁_{ij}</math>
|
|
|-
|-
Line 3,590: Line 3,514:
|
|
|
|
|<math>z_ij</math>
|<math>z_{ij}</math>
|
|
|-
|-
Retrieved from "https://en.xen.wiki/w/Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT/Conventions_for_names,_variables,_units,_and_notations"