Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions
Dave Keenan (talk | contribs) →Objects: Corrected \slant{\mathbf{1}} to \mathbf{i} in shape column of (just) (interval) size row. |
Cmloegcmluin (talk | contribs) reorganize with respect to held-intervals and unchanged-intervals |
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|- | |- | ||
! colspan="17" |held-intervals | ! colspan="17" |held-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 1,658: | Line 1,676: | ||
|mnemonic: <math>k</math>ount | |mnemonic: <math>k</math>ount | ||
|- | |- | ||
! colspan="17" |held | ! colspan="17" |held-intervals | ||
|- | |- | ||
| | | | ||
|<math> | |<math>\mathrm{H}</math> | ||
|[[held-interval | |[[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>h</math> | |||
|[[held-interval count]] | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|<math>\scriptsize (1, 1)</math> | |||
|integer | |||
|scalar | |||
|<math>\scriptsize ( | |||
| | |||
| | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|- | |- | ||
! colspan="17" |exploring temperaments | ! colspan="17" |exploring temperaments | ||
| Line 2,896: | Line 2,896: | ||
|mnemonic: <math>k</math>ount | |mnemonic: <math>k</math>ount | ||
|- | |- | ||
! colspan="17" |held | ! colspan="17" |held-intervals | ||
|- | |- | ||
| | | | ||
|<math>h</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>h</math> | |||
|[[held-interval count]] | |[[held-interval count]] | ||
| | | | ||
| Line 2,915: | Line 2,933: | ||
| | | | ||
| | | | ||
|- | |||
! colspan="17" |exploring temperaments | |||
|- | |- | ||
| | | | ||
|<math>\mathrm{ | |<math>\mathrm{C}</math> | ||
|[[ | |[[comma basis]] | ||
| | | | ||
|<math>\small 𝗽</math> | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
|<math>\scriptsize (d, | |<math>\scriptsize (d, n)</math> | ||
| | |integer | ||
|matrix | |matrix | ||
| | | | ||
| [[...⟩ ...] | |[[...⟩ ...] | ||
| | | | ||
|<math>\textbf{ | |<math>\textbf{c}_i</math> | ||
| | | | ||
|<math>\mathrm{c}_{ij}</math> | |||
|jargon name: monzo list | |||
|- | |- | ||
| | | | ||
|<math>\ | |<math>\textbf{c}</math> | ||
|[[ | |[[comma]] | ||
| | | | ||
|<math>\small 𝗽</math> | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
|<math>\scriptsize (d, | |<math>\scriptsize (d, 1)</math> | ||
|integer | |||
|vector | |||
| | | | ||
| | |[...⟩ | ||
| | | | ||
| | | | ||
| | | | ||
|<math>\mathrm{ | |<math>\mathrm{c}_i</math> | ||
| | |specific type: [[prime-count vector]] (PC-vector) | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" |computation | ||
|- | |- | ||
| | | | ||
|<math>\ | |<math>\llzigzag·\,\rrzigzag\!_p</math> | ||
|[[ | |[[power sum]] (<math>p</math>-sum) | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|<math>\ | |<math>\scriptsize (1, 1)</math> | ||
| real | |||
|scalar | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" |all-interval tuning schemes | ||
|- | |- | ||
|<math>I</math> | |||
|<math>\mathrm{T}_{\text{p}}</math> | |||
|[[prime proxy target-interval (matrix)]] | |||
| | | | ||
|<math> | |<math>\small 𝗽</math> | ||
| | |primes | ||
| | | | ||
|<math>\scriptsize (d, d)</math> | |||
|integer | |||
|matrix | |||
| | | | ||
|⟨[...⟩ ...] | |||
| | | | ||
| | | | ||
|<math>\ | |<math>\slant{\mathbf{1}}</math> | ||
| | | | ||
| | | | ||
|- | |||
| | | | ||
|<math> | |<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>\ | |<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] | |||
| | | | ||
|- | |||
| | | | ||
|<math>\scriptsize ( | |<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 | |||
| | | | ||
|<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>\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 | |||
|[⟨...] ...⟩ | |||
|⟨[...⟩ ...] | |||
|<math>\textbf{𝓁}_i</math> | |||
| | |||
|<math>\textbf{𝓁}</math> | |||
|<math>𝓁_{ij}</math> | |||
| | | | ||
|- | |- | ||
| | | | ||
|<math> | |<math>q</math> | ||
| | |[[interval complexity norm power]] | ||
| | |||
| | | | ||
| | | | ||
| | | | ||
|<math>\scriptsize (1, 1)</math> | |||
|real | |||
|scalar | |||
| | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
| | |- | ||
| | | | ||
|<math> | |<math>‖ · ‖_q</math> | ||
|[[power norm]] (<math>q</math>-norm) | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|<math>\scriptsize ( | |<math>\scriptsize (1, 1)</math> | ||
|real | |real | ||
| | |scalar | ||
| | |||
| | |||
| | |||
| | |||
| | | | ||
| | | | ||
| | | | ||
|- | |- | ||
| | ! colspan="17" |alternative complexities | ||
| | |- | ||
| | | | ||
|<math> | |<math>𝒑</math> | ||
|[[prime list]]<ref>May be used for a prime-limit or for any prime-only list.</ref> | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|<math>\scriptsize (1, d)</math> | |||
|integer | |||
|list | |||
|[...] | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|<math>p_i</math> | |||
| | | | ||
|- | |||
| | | | ||
|<math>Z</math> | |||
|[[size-sensitizing matrix]] | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|<math>\scriptsize (d+1, d)</math> | |||
|real | |||
|matrix | |||
|[⟨…]...] | |||
|<math>\scriptsize (1, | |||
|real | |||
| | |||
| | |||
| | | | ||
|<math>𝒛_i</math> | |||
| | | | ||
| | | | ||
|<math>z_{ij}</math> | |||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" |non-standard domain bases | ||
|- | |||
| rowspan="2" | | |||
|<math>B_s</math> | |||
| rowspan="2" |[[(domain) basis (change) matrix]] | |||
| rowspan="2" | | |||
|<math>\small 𝗽</math>/<math>\small 𝗯</math> | |||
|primes per nonprime basis elements | |||
| rowspan="2" | | |||
|<math>\scriptsize (d_p, d_b)</math> | |||
| rowspan="2" |integer | |||
| rowspan="2" |matrix | |||
| rowspan="2" | [[...] ...] | |||
| rowspan="2" |[[...] ...] | |||
| rowspan="2" | | |||
| rowspan="2" |<math>b_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" |embedding and projection | |||
|- | |- | ||
| | | | ||
|<math> | |<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> | | | ||
|<math>g_{ij}</math> | |||
| | | | ||
|- | |- | ||
| | |<math>G_cF^{-1}FM_c \\ | ||
|<math> | \mathrm{V}\textit{Λ}\mathrm{V}^{-1}</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] · \end{array} | ||
|<math>\scriptsize (d | \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 | |real | ||
|matrix | |matrix | ||
|[ | |[⟨...] ...⟩ | ||
|⟨[...⟩ ...] | |||
|<math>𝒑_i</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 | |||
| | |||
|[...⟩ | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|specific type: [[prime-count vector]] (PC-vector) | |||
|- | |- | ||
| | | | ||
|<math> | |<math>\mathrm{U}</math> | ||
|[[ | |[[unchanged-interval basis]] | ||
| | |||
|<math>\small 𝗽</math> | |||
|primes | |||
| | | | ||
|<math>\ | |<math>\scriptsize (d, r)</math> | ||
| | | | ||
|matrix | |||
| matrix | |||
| | | | ||
|[[...⟩ ...] | |||
| | | | ||
|<math> | |<math>\textbf{u}_i</math> | ||
| | | | ||
|<math>\mathrm{u}_{ij}</math> | |||
|jargon name: eigenmonzo list | |||
|- | |- | ||
|<math> | | | ||
|<math>\textit{Λ}</math> | |||
|[[scaling factor (eigenvalue) matrix|scaling factor matrix]] | |||
|[[ | | | ||
|<math>\scriptsize | | | ||
| | |||
| | |||
|<math>\scriptsize (d, d)</math> | |||
</math> | | | ||
|<math>\ | |matrix | ||
| | |[⟨…] …⟩ | ||
|<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> | |- | ||
| | |||
|<math>\mathrm{V}</math> | |||
|[[unrotated vector (eigenvector) list|unrotated vector list]] | |||
| | |||
|<math>\small 𝗽</math> | |||
|primes | |||
| | |||
|<math>\scriptsize (d, d)</math> | |<math>\scriptsize (d, d)</math> | ||
| | | | ||
|matrix | |matrix | ||
| | | | ||
|⟨[...⟩ ...] | |⟨[...⟩ ...] | ||
| | | | ||
|<math>\textbf{v}_i</math> | |||
| | | | ||
|<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> | |||
|[[generator form matrix]] | |||
|<math> | |||
|[[ | |||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|<math>\scriptsize (r, r)</math> | |||
| | | | ||
| | |matrix | ||
|[{...] …} | |||
| | | | ||
| | | | ||
|<math>𝒇_i</math> | |||
|<math>𝒇_i</math> | |||
| | | | ||
|<math>f_{ij}</math> | |<math>f_{ij}</math> | ||
| Line 3,371: | Line 3,353: | ||
| | | | ||
| | | | ||
|- | |||
| | |||
|<math>K</math> | |||
|[[constraint (matrix)]] | |||
| | |||
| | |||
| | |||
| | |||
|<math>\scriptsize (k, r)</math> | |||
|<math>\scriptsize \{0, +1, -1\}</math> | |||
|matrix | |||
|[[...] ...] | |||
| | |||
|<math>𝒌_i</math> | |||
| | |||
| | |||
|<math>k_{ij}</math> | |||
|mnemonic: <math>K</math>onstraint | |||
|- | |- | ||
! colspan="17" | exterior algebra | ! colspan="17" | exterior algebra | ||