Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions
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{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | Equivalent expressions | ||
! rowspan="2" | | ! rowspan="2" | Variable | ||
! rowspan="2" | | ! rowspan="2" | Name | ||
! colspan="3" | | ! colspan="3" | Units | ||
! colspan="2" | | ! colspan="2" | Shape | ||
! colspan="2" | | ! colspan="2" | Type | ||
! colspan="2" | EBK notation | ! colspan="2" | EBK notation | ||
! colspan="4" | | ! colspan="4" | Subobjects | ||
! rowspan="2" | | ! rowspan="2" | Notes | ||
|- | |- | ||
! | ! Unreduced | ||
! | ! Reduced | ||
! | ! Read as | ||
! | ! Unreduced | ||
! | ! Reduced | ||
! | ! Numeric | ||
! | ! Structural | ||
! | ! Row-first | ||
! | ! Col-first | ||
! | ! Row | ||
! | ! Col | ||
! | ! Diag | ||
! | ! Entry | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Mapping | ||
|- | |- | ||
| | | | ||
| <math>\textbf{i}</math> | | <math>\textbf{i}</math> | ||
| [[interval| ( | | [[interval|(Just) interval]] | ||
| | | | ||
| <math>\small 𝗽</math> | | <math>\small 𝗽</math> | ||
| | | Primes | ||
| | | | ||
| <math>\scriptsize (d, 1)</math> | | <math>\scriptsize (d, 1)</math> | ||
| | | Integer | ||
| | | Vector | ||
| | | | ||
| [...⟩ | | [...⟩ | ||
| Line 1,000: | Line 1,000: | ||
| | | | ||
| <math>\mathrm{i}_i</math> | | <math>\mathrm{i}_i</math> | ||
| | | Specific type: vector ([[prime-count vector]] or PC-vector) | ||
Jargon name: monzo | |||
|- | |- | ||
| | | | ||
| <math>M</math> | | <math>M</math> | ||
| [[Mapping| ( | | [[Mapping|(Temperament) mapping (matrix)]] | ||
| | | | ||
| <math>\small 𝗴</math>/<math>\small 𝗽</math> | | <math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
| | | Generators per prime | ||
| | | | ||
| <math>\scriptsize (r, d)</math> | | <math>\scriptsize (r, d)</math> | ||
| | | Integer | ||
| | | Matrix | ||
| [⟨...] ...} | | [⟨...] ...} | ||
| ⟨[...} ...] | | ⟨[...} ...] | ||
| Line 1,019: | Line 1,019: | ||
| | | | ||
| <math>m_{ij}</math> | | <math>m_{ij}</math> | ||
| | | Jargon name: val list | ||
|- | |- | ||
| <math>M\textbf{i}</math> | | <math>M\textbf{i}</math> | ||
| <math>\textbf{y}</math> | | <math>\textbf{y}</math> | ||
| [[ | | [[Mapped interval]] | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,030: | Line 1,030: | ||
</math> | </math> | ||
| <math>\small 𝗴</math> | | <math>\small 𝗴</math> | ||
| | | Generators | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array} | \begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array} | \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (r, 1)</math> | | <math>\scriptsize (r, 1)</math> | ||
| | | Integer | ||
| | | Vector | ||
| | | | ||
| [...} | | [...} | ||
| Line 1,047: | Line 1,047: | ||
| | | | ||
| | | | ||
| | | Specific type: [[generator-count vector]] (GC-vector) | ||
Jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval | |||
|- | |- | ||
| | | | ||
| <math>𝒎</math> | | <math>𝒎</math> | ||
| [[map| ( | | [[map|(Temperament) map]] | ||
| | | | ||
| <math>\small 𝗴</math>/<math>\small 𝗽</math> | | <math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
| | | Generators per prime | ||
| | | | ||
| <math>\scriptsize (1, d)</math> | | <math>\scriptsize (1, d)</math> | ||
| | | Integer | ||
| | | Vector | ||
| ⟨...] | | ⟨...] | ||
| | | | ||
| Line 1,066: | Line 1,066: | ||
| | | | ||
| <math>m_i</math> | | <math>m_i</math> | ||
| | | Jargon name: val | ||
|- | |- | ||
| <math>n + r</math> | | <math>n + r</math> | ||
| <math>d</math> | | <math>d</math> | ||
| [[ | | [[Dimensionality]] | ||
| | | | ||
| | | | ||
| Line 1,076: | Line 1,076: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Integer | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,088: | Line 1,088: | ||
| <math>d - n</math> | | <math>d - n</math> | ||
| <math>r</math> | | <math>r</math> | ||
| [[ | | [[Rank]] | ||
| | | | ||
| | | | ||
| Line 1,094: | Line 1,094: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Integer | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,106: | Line 1,106: | ||
| <math>d - r</math> | | <math>d - r</math> | ||
| <math>n</math> | | <math>n</math> | ||
| [[ | | [[Nullity]] | ||
| | | | ||
| | | | ||
| Line 1,112: | Line 1,112: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Integer | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,122: | Line 1,122: | ||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Tuning | ||
|- | |- | ||
| | | | ||
| <math>{\large\textbf{𝓁}}\hspace{2mu}</math> | | <math>{\large\textbf{𝓁}}\hspace{2mu}</math> | ||
| [[ | | [[Log-prime map]] | ||
| | | | ||
| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math> | | <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math> | ||
| | | Octaves per prime | ||
| | | | ||
| <math>\scriptsize (1, d)</math> | | <math>\scriptsize (1, d)</math> | ||
| | | Real | ||
| | | Vector | ||
| ⟨...] | | ⟨...] | ||
| | | | ||
| Line 1,144: | Line 1,144: | ||
| <math>1200×{\large\textbf{𝓁}}\hspace{2mu}</math> | | <math>1200×{\large\textbf{𝓁}}\hspace{2mu}</math> | ||
| <math>𝒋</math> | | <math>𝒋</math> | ||
| [[just tuning map| | | [[just tuning map|Just(-prime) tuning map]] | ||
| | | | ||
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math> | | <math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
| | | Cents per prime | ||
| | | | ||
| <math>\scriptsize (1, d)</math> | | <math>\scriptsize (1, d)</math> | ||
| | | Real | ||
| | | Vector | ||
| ⟨...] | | ⟨...] | ||
| | | | ||
| Line 1,162: | Line 1,162: | ||
| | | | ||
| <math>𝒈</math> | | <math>𝒈</math> | ||
| [[ | | [[Generator tuning map]] | ||
| | | | ||
| <math>\mathsf{¢}</math>/<math>\small 𝗴</math> | | <math>\mathsf{¢}</math>/<math>\small 𝗴</math> | ||
| | | Cents per generator | ||
| | | | ||
| <math>\scriptsize (1, r)</math> | | <math>\scriptsize (1, r)</math> | ||
| | | Real | ||
| | | Vector | ||
| {...] | | {...] | ||
| | | | ||
| Line 1,180: | Line 1,180: | ||
| | | | ||
| <math>𝒕</math> | | <math>𝒕</math> | ||
| [[tuning map| ( | | [[tuning map|(Tempered-prime) tuning map]] | ||
| | | | ||
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math> | | <math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
| | | Cents per prime | ||
| | | | ||
| <math>\scriptsize (1, d)</math> | | <math>\scriptsize (1, d)</math> | ||
| | | Real | ||
| | | Vector | ||
| ⟨...] | | ⟨...] | ||
| | | | ||
| Line 1,199: | Line 1,199: | ||
1200×\slant{\mathbf{1}}L(P - I)</math> | 1200×\slant{\mathbf{1}}L(P - I)</math> | ||
| <math>𝒓</math> | | <math>𝒓</math> | ||
| [[retuning map| | | [[retuning map|Retuning (or mistuning) map]] | ||
| | | | ||
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math> | | <math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
| | | Cents per prime | ||
| | | | ||
| <math>\scriptsize (1, d)</math> | | <math>\scriptsize (1, d)</math> | ||
| | | Real | ||
| | | Vector | ||
| ⟨...] | | ⟨...] | ||
| | | | ||
| Line 1,213: | Line 1,213: | ||
| | | | ||
| <math>r_i</math> | | <math>r_i</math> | ||
| | | Previous name: prime error map | ||
|- | |- | ||
| <math>𝒋\textbf{i}</math> | | <math>𝒋\textbf{i}</math> | ||
| <math>\mathrm{o}</math> | | <math>\mathrm{o}</math> | ||
| [[interval span| ( | | [[interval span|(Just) (interval) size]] | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,224: | Line 1,224: | ||
</math> | </math> | ||
| <math>\mathsf{¢}</math> | | <math>\mathsf{¢}</math> | ||
| | | Cents | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array} | \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \mathbf{i} \\[-3pt] (\cancel{d}, 1) \end{array} | \begin{array} {c} \mathbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,241: | Line 1,241: | ||
| | | | ||
| | | | ||
| | | Mnemonic: <math>\mathrm{o}</math>riginal size | ||
|- | |- | ||
| <math>𝒈M\textbf{i} \\ | | <math>𝒈M\textbf{i} \\ | ||
𝒕\textbf{i}</math> | 𝒕\textbf{i}</math> | ||
| <math>\mathrm{a}</math> | | <math>\mathrm{a}</math> | ||
| {{subpage|tuning fundamentals|uprev|s=Example 3|text= | | {{subpage|tuning fundamentals|uprev|s=Example 3|text=Tempered (interval) size}} | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,253: | Line 1,253: | ||
</math> | </math> | ||
| <math>\mathsf{¢}</math> | | <math>\mathsf{¢}</math> | ||
| | | Cents | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array} | \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array} | \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,270: | Line 1,270: | ||
| | | | ||
| | | | ||
| | | Mnemonic: <math>\mathrm{a}</math>ltered size | ||
|- | |- | ||
| <math>𝒕\textbf{i} - 𝒋\textbf{i} \\ | | <math>𝒕\textbf{i} - 𝒋\textbf{i} \\ | ||
| Line 1,276: | Line 1,276: | ||
𝒓\textbf{i}</math> | 𝒓\textbf{i}</math> | ||
| <math>\mathrm{e}</math> | | <math>\mathrm{e}</math> | ||
| [[error| ( | | [[error|(Interval) error]] | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,283: | Line 1,283: | ||
</math> | </math> | ||
| <math>\mathsf{¢}</math> | | <math>\mathsf{¢}</math> | ||
| | | Cents | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array} | \begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array} | \begin{array} {c} \textbf{i} \\[-3pt] \left(\cancel{d}, 1\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,302: | Line 1,302: | ||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Optimization | ||
|- | |- | ||
| | | | ||
| <math>p</math> | | <math>p</math> | ||
| [[ | | [[Optimization power]] | ||
| | | | ||
| | | | ||
| Line 1,312: | Line 1,312: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,323: | Line 1,323: | ||
|- | |- | ||
| | | | ||
| <math> | | <math>\llangle\,·\,\rrangle_p</math> | ||
| [[ | | [[Power mean]] (<math>p</math>-mean) | ||
| | | | ||
| | | | ||
| Line 1,330: | Line 1,330: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,340: | Line 1,340: | ||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Damage | ||
|- | |- | ||
| | | | ||
| <math>c</math> | | <math>c</math> | ||
| {{subpage|tuning_fundamentals|uprev|s= | | {{subpage|tuning_fundamentals|uprev|s=Complexity}} | ||
| colspan="3" | ( | | colspan="3" | (See complexities section of complexities and simplicities table) | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,360: | Line 1,360: | ||
| <math>\dfrac1c</math> | | <math>\dfrac1c</math> | ||
| <math>s</math> | | <math>s</math> | ||
| [[ | | [[Simplicity]] | ||
| colspan="3" | ( | | colspan="3" | (See simplicities section of complexities and simplicities table) | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,377: | Line 1,377: | ||
| <math>w</math> | | <math>w</math> | ||
| [[weight]] | | [[weight]] | ||
| colspan="3" | ( | | colspan="3" | (See complexities and simplicities table) | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,390: | Line 1,390: | ||
| | | | ||
|- | |- | ||
| <math> | | <math>\abs{\mathrm{e}} w</math> | ||
| <math>\mathrm{d}</math> | | <math>\mathrm{d}</math> | ||
| [[ | | [[Damage]] | ||
| colspan="3" | ( | | colspan="3" | (See damages table) | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,406: | Line 1,406: | ||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Target-intervals | ||
|- | |- | ||
| | | | ||
| <math>\mathrm{T}</math> | | <math>\mathrm{T}</math> | ||
| [[ | | [[Target-interval list]] | ||
| | | | ||
| <math>\small 𝗽</math> | | <math>\small 𝗽</math> | ||
| | | Primes | ||
| | | | ||
| <math>\scriptsize (d, k)</math> | | <math>\scriptsize (d, k)</math> | ||
| | | Integer | ||
| | | Matrix | ||
| | | | ||
| [[...⟩ ...] | | [[...⟩ ...] | ||
| Line 1,428: | Line 1,428: | ||
| <math>M\mathrm{T}</math> | | <math>M\mathrm{T}</math> | ||
| <math>\mathrm{Y}</math> | | <math>\mathrm{Y}</math> | ||
| [[ | | [[Mapped target-interval list]] | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,435: | Line 1,435: | ||
</math> | </math> | ||
| <math>\small 𝗴</math> | | <math>\small 𝗴</math> | ||
| | | Generators | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array} | \begin{array} {c} M \\[-3pt] \left(r, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array} | \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (r, k)</math> | | <math>\scriptsize (r, k)</math> | ||
| | | Integer | ||
| | | Matrix | ||
| | | | ||
| [[...} ...] | | [[...} ...] | ||
| Line 1,452: | Line 1,452: | ||
| | | | ||
| <math>\mathrm{y}_{ij}</math> | | <math>\mathrm{y}_{ij}</math> | ||
| | | Mnemonic: looks like bent-up 'T', or cross between 'M' and 'T' | ||
|- | |- | ||
| <math>𝒋\mathrm{T}</math> | | <math>𝒋\mathrm{T}</math> | ||
| <math>\textbf{o}</math> | | <math>\textbf{o}</math> | ||
| {{subpage|tuning fundamentals|uprev|s=primes|text= | | {{subpage|tuning fundamentals|uprev|s=primes|text=Target-interval (just) size list}} | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,463: | Line 1,463: | ||
</math> | </math> | ||
| <math>\mathsf{¢}</math> | | <math>\mathsf{¢}</math> | ||
| | | Cents | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array} | \begin{array} {c} 𝒋 \\[-3pt] \left(1, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array} | \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (1, k)</math> | | <math>\scriptsize (1, k)</math> | ||
| | | Real | ||
| | | List | ||
| [...] | | [...] | ||
| | | | ||
| Line 1,480: | Line 1,480: | ||
| | | | ||
| <math>\mathrm{o}_i</math> | | <math>\mathrm{o}_i</math> | ||
| | | Mnemonic: <math>\textbf{o}</math>riginal size list | ||
|- | |- | ||
| <math>𝒕\mathrm{T}</math> | | <math>𝒕\mathrm{T}</math> | ||
| <math>\textbf{a}</math> | | <math>\textbf{a}</math> | ||
| [[ | | [[Tempered target-interval size list]] | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,491: | Line 1,491: | ||
</math> | </math> | ||
| <math>\mathsf{¢}</math> | | <math>\mathsf{¢}</math> | ||
| | | Cents | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array} | \begin{array} {c} 𝒕 \\[-3pt] \left(1, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array} | \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (1, k)</math> | | <math>\scriptsize (1, k)</math> | ||
| | | Real | ||
| | | List | ||
| [...] | | [...] | ||
| | | | ||
| Line 1,508: | Line 1,508: | ||
| | | | ||
| <math>\mathrm{a}_i</math> | | <math>\mathrm{a}_i</math> | ||
| | | Mnemonic: <math>\textbf{a}</math>ltered size list | ||
|- | |- | ||
| <math>𝒕\mathrm{T} - 𝒋\mathrm{T} \\ | | <math>𝒕\mathrm{T} - 𝒋\mathrm{T} \\ | ||
| Line 1,514: | Line 1,514: | ||
\textbf{a} - \textbf{o}</math> | \textbf{a} - \textbf{o}</math> | ||
| <math>\textbf{e}</math> | | <math>\textbf{e}</math> | ||
| [[ | | [[Target-interval error list]] | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | \begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array} | ||
| Line 1,521: | Line 1,521: | ||
</math> | </math> | ||
| <math>\mathsf{¢}</math> | | <math>\mathsf{¢}</math> | ||
| | | Cents | ||
| <math>\scriptsize | | <math>\scriptsize | ||
\! \! | \! \! | ||
\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array} | \begin{array} {c} 𝒓 \\[-3pt] \left(1, \cancel{d}\right) \end{array} | ||
\! \! | \! \! | ||
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array} | \begin{array} {c} \mathrm{T} \\[-3pt] \left(\cancel{d}, k\right) \end{array} | ||
\! \! | \! \! | ||
</math> | </math> | ||
| <math>\scriptsize (1, k)</math> | | <math>\scriptsize (1, k)</math> | ||
| | | Real | ||
| | | List | ||
| [...] | | [...] | ||
| | | | ||
| Line 1,542: | Line 1,542: | ||
| <math>C</math> or <math>S</math> | | <math>C</math> or <math>S</math> | ||
| <math>W</math> | | <math>W</math> | ||
| [[ | | [[Target-interval weight matrix]] | ||
| colspan="3" | ( | | colspan="3" | (See complexities and simplicities table) | ||
| | | | ||
| <math>\scriptsize (k, k)</math> | | <math>\scriptsize (k, k)</math> | ||
| | | Real | ||
| | | Matrix | ||
| | | | ||
| [[...] ...] | | [[...] ...] | ||
| Line 1,558: | Line 1,558: | ||
| | | | ||
| <math>C</math> | | <math>C</math> | ||
| {{subpage|tuning_fundamentals|uprev|s=complexity-weight damage|text= | | {{subpage|tuning_fundamentals|uprev|s=complexity-weight damage|text=Target-interval complexity weight matrix}} | ||
| colspan="3" | ( | | colspan="3" | (See complexities section of complexities and simplicities table) | ||
| | | | ||
| <math>\scriptsize (k, k)</math> | | <math>\scriptsize (k, k)</math> | ||
| | | Real | ||
| | | Matrix | ||
| | | | ||
| [[...] ...] | | [[...] ...] | ||
| Line 1,574: | Line 1,574: | ||
| <math>\dfrac1C</math> | | <math>\dfrac1C</math> | ||
| <math>S</math> | | <math>S</math> | ||
| {{subpage|tuning_fundamentals|uprev|s=complexity-weight_damage|text= | | {{subpage|tuning_fundamentals|uprev|s=complexity-weight_damage|text=Target-interval simplicity weight matrix}} | ||
| colspan="3" | ( | | colspan="3" | (See simplicities section of complexities and simplicities table) | ||
| | | | ||
| <math>\scriptsize (k, k)</math> | | <math>\scriptsize (k, k)</math> | ||
| | | Real | ||
| | | Matrix | ||
| | | | ||
| [[...] ...] | | [[...] ...] | ||
| Line 1,586: | Line 1,586: | ||
| <math>𝒔</math> | | <math>𝒔</math> | ||
| <math>s_i</math> | | <math>s_i</math> | ||
| | | Entry-wise reciprocal of <math>C</math> | ||
|- | |- | ||
| <math> | | <math>\abs{\textbf{e}} W</math> | ||
| <math>\textbf{d}</math> | | <math>\textbf{d}</math> | ||
| [[ | | [[Target-interval damage list]] | ||
| colspan="3" | ( | | colspan="3" | (See damages table) | ||
| | | | ||
| <math>\scriptsize (1, k)</math> | | <math>\scriptsize (1, k)</math> | ||
| | | Real | ||
| | | List | ||
| [...] | | [...] | ||
| | | | ||
| Line 1,606: | Line 1,606: | ||
| | | | ||
| <math>k</math> | | <math>k</math> | ||
| [[ | | [[Target-interval count]] | ||
| | | | ||
| | | | ||
| Line 1,612: | Line 1,612: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Integer | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,620: | Line 1,620: | ||
| | | | ||
| | | | ||
| | | Mnemonic: <math>k</math>ount | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Held-intervals | ||
|- | |- | ||
| | | | ||
| <math>\mathrm{H}</math> | | <math>\mathrm{H}</math> | ||
| [[ | | [[Held-interval basis]] | ||
| | | | ||
| <math>\small 𝗽</math> | | <math>\small 𝗽</math> | ||
| | | Primes | ||
| | | | ||
| <math>\scriptsize (d, h)</math> | | <math>\scriptsize (d, h)</math> | ||
| | | | ||
| | | Matrix | ||
| | | | ||
| [[...⟩ ...] | | [[...⟩ ...] | ||
| Line 1,644: | Line 1,644: | ||
| | | | ||
| <math>h</math> | | <math>h</math> | ||
| [[ | | [[Held-interval count]] | ||
| | | | ||
| | | | ||
| Line 1,650: | Line 1,650: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Integer | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,660: | Line 1,660: | ||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Exploring temperaments | ||
|- | |- | ||
| | | | ||
| <math>\mathrm{C}</math> | | <math>\mathrm{C}</math> | ||
| [[ | | [[Comma basis]] | ||
| | | | ||
| <math>\small 𝗽</math> | | <math>\small 𝗽</math> | ||
| | | Primes | ||
| | | | ||
| <math>\scriptsize (d, n)</math> | | <math>\scriptsize (d, n)</math> | ||
| | | Integer | ||
| | | Matrix | ||
| | | | ||
| [[...⟩ ...] | | [[...⟩ ...] | ||
| Line 1,678: | Line 1,678: | ||
| | | | ||
| <math>\mathrm{c}_{ij}</math> | | <math>\mathrm{c}_{ij}</math> | ||
| | | Jargon name: monzo list | ||
|- | |- | ||
| | | | ||
| <math>\textbf{c}</math> | | <math>\textbf{c}</math> | ||
| [[ | | [[Comma]] | ||
| | | | ||
| <math>\small 𝗽</math> | | <math>\small 𝗽</math> | ||
| Line 1,688: | Line 1,688: | ||
| | | | ||
| <math>\scriptsize (d, 1)</math> | | <math>\scriptsize (d, 1)</math> | ||
| | | Integer | ||
| | | Vector | ||
| | | | ||
| [...⟩ | | [...⟩ | ||
| Line 1,696: | Line 1,696: | ||
| | | | ||
| <math>\mathrm{c}_i</math> | | <math>\mathrm{c}_i</math> | ||
| | | Specific type: vector ([[prime-count vector]] or PC-vector) | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | Computation | ||
|- | |- | ||
| | | | ||
| <math>\llzigzag·\,\rrzigzag\! _p</math> | | <math>\llzigzag·\,\rrzigzag\! _p</math> | ||
| [[ | | [[Power sum]] (<math>p</math>-sum) | ||
| | | | ||
| | | | ||
| Line 1,708: | Line 1,708: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,718: | Line 1,718: | ||
| | | | ||
|- | |- | ||
! colspan="17" | | ! colspan="17" | All-interval tuning schemes | ||
|- | |- | ||
| <math>\mathrm{I}</math> | | <math>\mathrm{I}</math> | ||
| <math>\mathrm{T}_{\text{p}}</math> | | <math>\mathrm{T}_{\text{p}}</math> | ||
| [[ | | [[Prime proxy target-interval list]] | ||
| | | | ||
| <math>\small 𝗽</math> | | <math>\small 𝗽</math> | ||
| | | Primes | ||
| | | | ||
| <math>\scriptsize (d, d)</math> | | <math>\scriptsize (d, d)</math> | ||
| | | Integer | ||
| | | Matrix | ||
| | | | ||
| ⟨[...⟩ ...] | | ⟨[...⟩ ...] | ||
| Line 1,740: | Line 1,740: | ||
| | | | ||
| <math>X</math> | | <math>X</math> | ||
| [[ | | [[Complexity prescaler]] | ||
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> | | <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> | ||
| <math>\small\mathsf{(C)}</math> | | <math>\small\mathsf{(C)}</math> | ||
| | | Complexity weight | ||
| | | | ||
| <math>\scriptsize (d, d)</math> | | <math>\scriptsize (d, d)</math> | ||
| | | Real | ||
| | | Matrix | ||
| [⟨...] ...⟩ | | [⟨...] ...⟩ | ||
| | | | ||
| Line 1,758: | Line 1,758: | ||
| <math>\text{diag}({\large\textbf{𝓁}}\hspace{2mu})</math> | | <math>\text{diag}({\large\textbf{𝓁}}\hspace{2mu})</math> | ||
| <math>L</math> | | <math>L</math> | ||
| [[ | | [[Log-prime matrix]] | ||
| | | | ||
| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math> | | <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math> | ||
| | | Octaves per prime | ||
| | | | ||
| <math>\scriptsize (d, d)</math> | | <math>\scriptsize (d, d)</math> | ||
| | | Real | ||
| | | Matrix | ||
| [⟨...] ...⟩ | | [⟨...] ...⟩ | ||
| ⟨[...⟩ ...] | | ⟨[...⟩ ...] | ||
| Line 1,776: | Line 1,776: | ||
| | | | ||
| <math>q</math> | | <math>q</math> | ||
| {{subpage|all-interval_tuning_schemes|uprev|s=Dual norms|text= | | {{subpage|all-interval_tuning_schemes|uprev|s=Dual norms|text=Interval complexity norm power}} | ||
| | | | ||
| | | | ||
| Line 1,782: | Line 1,782: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,793: | Line 1,793: | ||
|- | |- | ||
| | | | ||
| <math> | | <math>\norm{\cdot}_q</math> | ||
| [[ | | [[Power norm]] (<math>p</math>-norm) | ||
| | | | ||
| | | | ||
| Line 1,800: | Line 1,800: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,812: | Line 1,812: | ||
| <math>\dfrac1{1-\frac1q}</math> | | <math>\dfrac1{1-\frac1q}</math> | ||
| <math>\text{dual}(q)</math> | | <math>\text{dual}(q)</math> | ||
| {{subpage|all-interval tuning schemes|uprev|s=Dual norms|text= | | {{subpage|all-interval tuning schemes|uprev|s=Dual norms|text=Dual norm power}} | ||
| | | | ||
| | | | ||
| Line 1,818: | Line 1,818: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,829: | Line 1,829: | ||
|- | |- | ||
| | | | ||
| <math> | | <math>\norm{X\mathbf{i}}_q</math> | ||
| [[interval complexity]] | | [[interval complexity]] | ||
| | | | ||
| Line 1,836: | Line 1,836: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||
| Line 1,847: | Line 1,847: | ||
|- | |- | ||
| | | | ||
| <math> | | <math>\norm{𝒓X^{-1}}_{\text{dual}(q)}</math> | ||
| [[ | | [[Retuning magnitude]] | ||
| | | | ||
| <math>\mathsf{¢}\small\mathsf{(C^{-1})}</math> | | <math>\mathsf{¢}\small\mathsf{(C^{-1})}</math> | ||
| Line 1,854: | Line 1,854: | ||
| | | | ||
| <math>\scriptsize (1, 1)</math> | | <math>\scriptsize (1, 1)</math> | ||
| | | Real | ||
| | | Scalar | ||
| | | | ||
| | | | ||