Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions
Dave Keenan (talk | contribs) Changed "D&D" to "D&D's guide". |
Dave Keenan (talk | contribs) Changed formatting of most units to match the units analysis article. More work needed. |
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|[[interval|(just) interval]] | |[[interval|(just) interval]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 99: | Line 99: | ||
|[[Mapping|(temperament) mapping (matrix)]] | |[[Mapping|(temperament) mapping (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 146: | Line 146: | ||
|[[map|(temperament) map]] | |[[map|(temperament) map]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 202: | Line 202: | ||
|[[just tuning map|just(-prime) tuning map]] | |[[just tuning map|just(-prime) tuning map]] | ||
| | | | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
| | | | ||
| Line 220: | Line 220: | ||
|[[generator tuning map]] | |[[generator tuning map]] | ||
| | | | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗴</math> | ||
|cents per generator | |cents per generator | ||
| | | | ||
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\begin{array} {c} 𝑀 \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | \begin{array} {c} 𝑀 \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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|[[retuning map|retuning (or mistuning) map]] | |[[retuning map|retuning (or mistuning) map]] | ||
| | | | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
| | | | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]] | |[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity|complexity]] | ||
|𝟙<ref>For educational purposes, we use the 𝟙 symbol here to represent the implicit [[Wikipedia:Dimensionless_quantity|dimensionless unit]] that the weighting annotation "(C)" is attached to. But this symbol should not be shown in the reduced result. Another way to understand how we arrive at a bare annotation for the units of this quantity is to consider that w = d / |e| whose units are ¢(W) / ¢ and the cents cancel.</ref>(C) | |𝟙<ref>For educational purposes, we use the 𝟙 symbol here to represent the implicit [[Wikipedia:Dimensionless_quantity|dimensionless unit]] that the weighting annotation "(C)" is attached to. But this symbol should not be shown in the reduced result. Another way to understand how we arrive at a bare annotation for the units of this quantity is to consider that w = d / |e| whose units are ¢(W) / ¢ and the cents cancel.</ref>(C) | ||
|(C) | |<math>\small\mathsf{(C)}</math> | ||
|complexity weight | |complexity weight | ||
| | | | ||
| Line 429: | Line 429: | ||
|[[simplicity]] | |[[simplicity]] | ||
|𝟙(S) | |𝟙(S) | ||
|(S) | |<math>\small\mathsf{(S)}</math> | ||
|simplicity weight | |simplicity weight | ||
| | | | ||
| Line 446: | Line 446: | ||
|<math>w</math> | |<math>w</math> | ||
|[[weight]] | |[[weight]] | ||
|𝟙(C) or 𝟙(S) | |𝟙(C) or 𝟙<math>\small\mathsf{(S)}</math> | ||
|(C) or (S) | |<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math> | ||
|complexity weight or simplicity weight | |complexity weight or simplicity weight | ||
| | | | ||
| Line 469: | Line 469: | ||
\begin{array} {c} w \\[-2pt] \text{(U, C, or S)} \end{array} | \begin{array} {c} w \\[-2pt] \text{(U, C, or S)} \end{array} | ||
</math> | </math> | ||
| ¢(U) or ¢(C) or ¢(S) | | <math>\mathsf{¢}\small\mathsf{(U)}</math> or <math>\mathsf{¢}\small\mathsf{(C)}</math> or <math>\mathsf{¢}\small\mathsf{(S)}</math> | ||
| (see damages tables) | | (see damages tables) | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 495: | Line 495: | ||
|[[target-interval list]] | |[[target-interval list]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 517: | Line 517: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 629: | Line 629: | ||
|[[target-interval weight matrix]] | |[[target-interval weight matrix]] | ||
|𝟙(C) or 𝟙(S) or 𝟙(U) | |𝟙(C) or 𝟙(S) or 𝟙(U) | ||
|(C) or (S) or (U) | |<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(U)}</math> | ||
|complexity weight or simplicity weight | |complexity weight or simplicity weight | ||
| | | | ||
| Line 647: | Line 647: | ||
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]] | |[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval complexity weight matrix]] | ||
|𝟙(C) | |𝟙(C) | ||
|(C) | |<math>\small\mathsf{(C)}</math> | ||
|complexity weight | |complexity weight | ||
| | | | ||
| Line 665: | Line 665: | ||
|[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]] | |[[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage|target-interval simplicity weight matrix]] | ||
|𝟙(S) | |𝟙(S) | ||
|(S) | |<math>\small\mathsf{(S)}</math> | ||
|simplicity weight | |simplicity weight | ||
| | | | ||
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\begin{array} {c} W \\[-2pt] (\text{U, C, or S}) \end{array} | \begin{array} {c} W \\[-2pt] (\text{U, C, or S}) \end{array} | ||
</math> | </math> | ||
|¢(U), ¢(C), or ¢(S) | |<math>\mathsf{¢}\small\mathsf{(U)}</math>, <math>\mathsf{¢}\small\mathsf{(C)}</math>, or <math>\mathsf{¢}\small\mathsf{(S)}</math> | ||
|weighted cents | |weighted cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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|[[comma basis]] | |[[comma basis]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
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|[[comma]] | |[[comma]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 795: | Line 795: | ||
!vectorized | !vectorized | ||
|- | |- | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|yes | |yes | ||
|- | |- | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
|yes | |yes | ||
|- | |- | ||
|¢<ref>It seems there is no standard symbol for a musical cent, except the word spelled in full (see https://en.wikipedia.org/wiki/Cent_(music)). But it seems unlikely anyone will interpret the cent currency symbol "¢" following a number in a musical context as anything other than musical cents.</ref> | |<math>\mathsf{¢}</math><ref>It seems there is no standard symbol for a musical cent, except the word spelled in full (see https://en.wikipedia.org/wiki/Cent_(music)). But it seems unlikely anyone will interpret the cent currency symbol "¢" following a number in a musical context as anything other than musical cents.</ref> | ||
|cents | |cents | ||
| | | | ||
|- | |- | ||
|¢(U) | |<math>\mathsf{¢}\small\mathsf{(U)}</math> | ||
|unity-weighted cents | |unity-weighted cents | ||
| | | | ||
|- | |- | ||
|¢(C) | |<math>\mathsf{¢}\small\mathsf{(C)}</math> | ||
|complexity-weighted cents | |complexity-weighted cents | ||
| | | | ||
|- | |- | ||
|¢(S) | |<math>\mathsf{¢}\small\mathsf{(S)}</math> | ||
|simplicity-weighted cents | |simplicity-weighted cents | ||
| | | | ||
|- | |- | ||
|oct | |<math>\small\mathsf{oct}</math> | ||
|octaves | |octaves | ||
| | | | ||
|- | |- | ||
|(C) | |<math>\small\mathsf{(C)}</math> | ||
|complexity weight | |complexity weight | ||
| | | | ||
|- | |- | ||
|(S) | |<math>\small\mathsf{(S)}</math> | ||
|simplicity weight | |simplicity weight | ||
| | | | ||
| Line 888: | Line 888: | ||
|U-damage | |U-damage | ||
|unity-weight damage | |unity-weight damage | ||
|¢(U) | |<math>\mathsf{¢}\small\mathsf{(U)}</math> | ||
|unity-weighted cents | |unity-weighted cents | ||
|- | |- | ||
|C-damage | |C-damage | ||
|complexity-weight damage | |complexity-weight damage | ||
|¢(C) | |<math>\mathsf{¢}\small\mathsf{(C)}</math> | ||
|complexity-weighted cents | |complexity-weighted cents | ||
|- | |- | ||
|S-damage | |S-damage | ||
|simplicity-weight damage | |simplicity-weight damage | ||
|¢(S) | |<math>\mathsf{¢}\small\mathsf{(S)}</math> | ||
|simplicity-weighted cents | |simplicity-weighted cents | ||
|} | |} | ||
| Line 916: | Line 916: | ||
|C | |C | ||
|complexity | |complexity | ||
|(C) | |<math>\small\mathsf{(C)}</math> | ||
|complexity weight | |complexity weight | ||
|- | |- | ||
|S | |S | ||
|simplicity | |simplicity | ||
|(S) | |<math>\small\mathsf{(S)}</math> | ||
|simplicity weight | |simplicity weight | ||
|} | |} | ||
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|[[interval|(just) interval]] | |[[interval|(just) interval]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
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|[[Mapping|(temperament) mapping (matrix)]] | |[[Mapping|(temperament) mapping (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 1,002: | Line 1,002: | ||
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,027: | Line 1,027: | ||
|[[map|(temperament) map]] | |[[map|(temperament) map]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 1,114: | Line 1,114: | ||
\begin{array} {c} M_{\text{j}} \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | \begin{array} {c} M_{\text{j}} \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,154: | Line 1,154: | ||
\begin{array} {c} G \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | \begin{array} {c} G \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗴</math> | ||
|cents per generator | |cents per generator | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,228: | Line 1,228: | ||
|[[retuning map|retuning (or mistuning) map]] | |[[retuning map|retuning (or mistuning) map]] | ||
| | | | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
| | | | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,439: | Line 1,439: | ||
|[[target-interval list]] | |[[target-interval list]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 1,461: | Line 1,461: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|<math>\scriptsize | |<math>\scriptsize | ||
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\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,517: | Line 1,517: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,547: | Line 1,547: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,656: | Line 1,656: | ||
|[[unchanged-interval basis]] | |[[unchanged-interval basis]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 1,694: | Line 1,694: | ||
|[[comma basis]] | |[[comma basis]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 1,712: | Line 1,712: | ||
|[[comma]] | |[[comma]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 1,732: | Line 1,732: | ||
|[[log-prime matrix]] | |[[log-prime matrix]] | ||
| | | | ||
|oct/ | |<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math> | ||
|octaves per prime | |octaves per prime | ||
| | | | ||
| Line 1,772: | Line 1,772: | ||
|[[octaves-to-cents conversion]] | |[[octaves-to-cents conversion]] | ||
| | | | ||
|¢/oct | |<math>\mathsf{¢}</math>/<math>\small\mathsf{oct}</math> | ||
|cents per octave | |cents per octave | ||
| | | | ||
| Line 1,790: | Line 1,790: | ||
|[[generator embedding matrix|generator embedding (matrix)]] | |[[generator embedding matrix|generator embedding (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗽</math>/<math>\small 𝗴</math> | ||
|primes per generator | |primes per generator | ||
| | | | ||
| Line 1,850: | Line 1,850: | ||
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | ||
</math> | </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> | |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 | |<math>\scriptsize | ||
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\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,908: | Line 1,908: | ||
|[[JI mapping (matrix)]] | |[[JI mapping (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 1,935: | Line 1,935: | ||
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | \begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗴</math> | ||
|cents per generator | |cents per generator | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 1,964: | Line 1,964: | ||
|[[JI generator embedding matrix|JI generator embedding (matrix)]] | |[[JI generator embedding matrix|JI generator embedding (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗽</math>/<math>\small 𝗴</math> | ||
|primes per generator | |primes per generator | ||
| | | | ||
| Line 1,984: | Line 1,984: | ||
|[[prime proxy target-interval (matrix)]] | |[[prime proxy target-interval (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 2,002: | Line 2,002: | ||
|[[complexity prescaler]] | |[[complexity prescaler]] | ||
|𝟙(C) | |𝟙(C) | ||
|(C) | |<math>\small\mathsf{(C)}</math> | ||
|complexity weight | |complexity weight | ||
| | | | ||
| Line 2,020: | Line 2,020: | ||
|[[simplicity prescaler]] | |[[simplicity prescaler]] | ||
|𝟙(S) | |𝟙(S) | ||
|(S) | |<math>\small\mathsf{(S)}</math> | ||
|simplicity weight | |simplicity weight | ||
| | | | ||
| Line 2,302: | Line 2,302: | ||
|U-damage | |U-damage | ||
|unity-weight damage | |unity-weight damage | ||
|¢(U) | |<math>\mathsf{¢}\small\mathsf{(U)}</math> | ||
|unity-weighted cents | |unity-weighted cents | ||
|- | |- | ||
|C-damage | |C-damage | ||
|complexity-weight damage | |complexity-weight damage | ||
|¢(C) | |<math>\mathsf{¢}\small\mathsf{(C)}</math> | ||
|complexity-weighted cents | |complexity-weighted cents | ||
|- | |- | ||
|EC-damage | |EC-damage | ||
|Euclideanized-complexity-weight damage | |Euclideanized-complexity-weight damage | ||
|¢(EC) | |<math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math> | ||
|Euclideanized-complexity-weighted cents | |Euclideanized-complexity-weighted cents | ||
|- | |- | ||
|S-damage | |S-damage | ||
|simplicity-weight damage | |simplicity-weight damage | ||
|¢(S) | |<math>\mathsf{¢}\small\mathsf{(S)}</math> | ||
|simplicity-weighted cents | |simplicity-weighted cents | ||
|- | |- | ||
|ES-damage | |ES-damage | ||
|Euclideanized-simplicity-weight damage | |Euclideanized-simplicity-weight damage | ||
|¢(ES) | |<math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math> | ||
|Euclideanized-simplicity-weighted cents | |Euclideanized-simplicity-weighted cents | ||
|} | |} | ||
| Line 2,340: | Line 2,340: | ||
|C | |C | ||
|complexity | |complexity | ||
|(C) | |<math>\small\mathsf{(C)}</math> | ||
|complexity weight | |complexity weight | ||
|- | |- | ||
|EC | |EC | ||
|Euclideanized complexity | |Euclideanized complexity | ||
|(EC) | |<math>\small\mathsf{(EC)}</math> | ||
|Euclideanized-complexity weight | |Euclideanized-complexity weight | ||
|} | |} | ||
| Line 2,361: | Line 2,361: | ||
|S | |S | ||
|simplicity | |simplicity | ||
|S | |<math>\small\mathsf{(S)}</math> | ||
|simplicity weight | |simplicity weight | ||
|- | |- | ||
|ES | |ES | ||
|Euclideanized simplicity | |Euclideanized simplicity | ||
|(ES) | |<math>\small\mathsf{(ES)}</math> | ||
|Euclideanized-simplicity weight | |Euclideanized-simplicity weight | ||
|} | |} | ||
| Line 2,406: | Line 2,406: | ||
|[[interval|(just) interval]] | |[[interval|(just) interval]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 2,425: | Line 2,425: | ||
|[[Mapping|(temperament) mapping (matrix)]] | |[[Mapping|(temperament) mapping (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 2,447: | Line 2,447: | ||
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,472: | Line 2,472: | ||
|[[map|(temperament) map]] | |[[map|(temperament) map]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 2,559: | Line 2,559: | ||
\begin{array} {c} M_{\text{j}} \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | \begin{array} {c} M_{\text{j}} \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,599: | Line 2,599: | ||
\begin{array} {c} G \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | \begin{array} {c} G \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗴</math> | ||
|cents per generator | |cents per generator | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,641: | Line 2,641: | ||
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,673: | Line 2,673: | ||
|[[retuning map|retuning (or mistuning) map]] | |[[retuning map|retuning (or mistuning) map]] | ||
| | | | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗽</math> | ||
|cents per prime | |cents per prime | ||
| | | | ||
| Line 2,695: | Line 2,695: | ||
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,724: | Line 2,724: | ||
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,754: | Line 2,754: | ||
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,884: | Line 2,884: | ||
|[[target-interval list]] | |[[target-interval list]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 2,906: | Line 2,906: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,934: | Line 2,934: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,962: | Line 2,962: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 2,992: | Line 2,992: | ||
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 3,101: | Line 3,101: | ||
|[[unchanged-interval basis]] | |[[unchanged-interval basis]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 3,139: | Line 3,139: | ||
|[[comma basis]] | |[[comma basis]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 3,157: | Line 3,157: | ||
|[[comma]] | |[[comma]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 3,177: | Line 3,177: | ||
|[[log-prime matrix]] | |[[log-prime matrix]] | ||
| | | | ||
|oct/ | |<math>\small\mathsf{oct}</math>/<math>\small 𝗽</math> | ||
|octaves per prime | |octaves per prime | ||
| | | | ||
| Line 3,213: | Line 3,213: | ||
|[[octaves-to-cents conversion]] | |[[octaves-to-cents conversion]] | ||
| | | | ||
|¢/oct | |<math>\mathsf{¢}</math>/<math>\small\mathsf{oct}</math> | ||
|cents per octave | |cents per octave | ||
| | | | ||
| Line 3,231: | Line 3,231: | ||
|[[generator embedding matrix|generator embedding (matrix)]] | |[[generator embedding matrix|generator embedding (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗽</math>/<math>\small 𝗴</math> | ||
|primes per generator | |primes per generator | ||
| | | | ||
| Line 3,292: | Line 3,292: | ||
\begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | \begin{array} {c} M \\[-2pt] \cancel{𝗴} \hspace{-2mu} / \hspace{-2mu} 𝗽 \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗽</math>/<math>\small 𝗽</math> | ||
|primes per prime | |primes per prime | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 3,322: | Line 3,322: | ||
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | \begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array} | ||
</math> | </math> | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 3,366: | Line 3,366: | ||
|[[unrotated vector (eigenvector) list|unrotated vector list]] | |[[unrotated vector (eigenvector) list|unrotated vector list]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 3,404: | Line 3,404: | ||
|[[JI mapping (matrix)]] | |[[JI mapping (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 3,431: | Line 3,431: | ||
\begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | \begin{array} {c} G_{\text{j}} \\[-2pt] \cancel{𝗽} \hspace{-2mu} / \hspace{-2mu} 𝗴 \end{array} | ||
</math> | </math> | ||
|¢/ | |<math>\mathsf{¢}</math>/<math>\small 𝗴</math> | ||
|cents per generator | |cents per generator | ||
|<math>\scriptsize | |<math>\scriptsize | ||
| Line 3,460: | Line 3,460: | ||
|[[JI generator embedding matrix|JI generator embedding (matrix)]] | |[[JI generator embedding matrix|JI generator embedding (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗽</math>/<math>\small 𝗴</math> | ||
|primes per generator | |primes per generator | ||
| | | | ||
| Line 3,480: | Line 3,480: | ||
|[[prime proxy target-interval (matrix)]] | |[[prime proxy target-interval (matrix)]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 3,498: | Line 3,498: | ||
|[[complexity pretransformer]] | |[[complexity pretransformer]] | ||
|𝟙(C) or 𝟙(<alt<ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>>-C) | |𝟙(C) or 𝟙(<alt<ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>>-C) | ||
|(C) or (<alt>-C) | |<math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math> | ||
|complexity weight or <alternative>-complexity weight | |complexity weight or <alternative>-complexity weight | ||
| | | | ||
| Line 3,515: | Line 3,515: | ||
|<math>S_{\text{p}}</math> | |<math>S_{\text{p}}</math> | ||
|[[simplicity pretransformer]] | |[[simplicity pretransformer]] | ||
|𝟙(S) or 𝟙(<alt>-S) | |𝟙(S) or 𝟙<math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math> | ||
|(S) or (<alt>-S) | |<math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math> | ||
|simplicity weight or <alternative>-simplicity weight | |simplicity weight or <alternative>-simplicity weight | ||
| | | | ||
| Line 3,625: | Line 3,625: | ||
|- | |- | ||
|<math>B_{Ls}</math> | |<math>B_{Ls}</math> | ||
| | |<math>\small 𝗕</math>/<math>\small 𝗯</math> | ||
|superspace basis elements per (subspace) basis elements | |superspace basis elements per (subspace) basis elements | ||
|<math>\scriptsize (d_L, d_s)</math> | |<math>\scriptsize (d_L, d_s)</math> | ||
| Line 3,633: | Line 3,633: | ||
|[[generator preimage transversal]] | |[[generator preimage transversal]] | ||
| | | | ||
| | |<math>\small 𝗽</math>/<math>\small 𝗴</math> | ||
|primes per generator | |primes per generator | ||
| | | | ||
| Line 3,653: | Line 3,653: | ||
|[[multimap]] | |[[multimap]] | ||
| | | | ||
| | |<math>\small 𝗴</math>/<math>\small 𝗽</math> | ||
|generators per prime | |generators per prime | ||
| | | | ||
| Line 3,671: | Line 3,671: | ||
|[[multicomma]] | |[[multicomma]] | ||
| | | | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
| | | | ||
| Line 3,876: | Line 3,876: | ||
!vectorized | !vectorized | ||
|- | |- | ||
| | |<math>\small 𝗴</math> | ||
|generators | |generators | ||
|yes | |yes | ||
|- | |- | ||
| | |<math>\small 𝗽</math> | ||
|primes | |primes | ||
|yes | |yes | ||
|- | |- | ||
| | |<math>\small 𝗯</math> | ||
|(subspace) basis elements | |(subspace) basis elements | ||
|yes | |yes | ||
|- | |- | ||
| | |<math>\small 𝗕</math> | ||
|superspace basis elements | |superspace basis elements | ||
|yes | |yes | ||
|- | |- | ||
|¢ | |<math>\mathsf{¢}</math> | ||
|cents | |cents | ||
| | | | ||
|- | |- | ||
|¢(<weight>) | |<math>\mathsf{¢}</math>(<weight>) | ||
|weighted cents | |weighted cents | ||
| | | | ||
|- | |- | ||
|oct | |<math>\small\mathsf{oct}</math> | ||
|octaves | |octaves | ||
| | | | ||
| Line 4,242: | Line 4,242: | ||
|U-damage | |U-damage | ||
|unity-weight damage | |unity-weight damage | ||
|¢(U) | |<math>\mathsf{¢}\small\mathsf{(U)}</math> | ||
|unity-weighted cents | |unity-weighted cents | ||
|- | |- | ||
|C-damage | |C-damage | ||
|complexity-weight damage | |complexity-weight damage | ||
|¢(C) | |<math>\mathsf{¢}\small\mathsf{(C)}</math> | ||
|complexity-weighted cents | |complexity-weighted cents | ||
|- | |- | ||
|<alt>-C-damage | |<alt>-C-damage | ||
|<alternative>-complexity-weight damage | |<alternative>-complexity-weight damage | ||
|¢(<alt>-C) | |<math>\mathsf{¢}</math><math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math> | ||
|<alternative>-complexity-weighted cents | |<alternative>-complexity-weighted cents | ||
|- | |- | ||
|EC-damage | |EC-damage | ||
|Euclideanized-complexity-weight damage | |Euclideanized-complexity-weight damage | ||
|¢(EC) | |<math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math> | ||
|Euclideanized-complexity-weighted cents | |Euclideanized-complexity-weighted cents | ||
|- | |- | ||
|E-<alt>-C-damage | |E-<alt>-C-damage | ||
|Euclideanized-<alternative>-complexity-weight damage | |Euclideanized-<alternative>-complexity-weight damage | ||
|¢(E-<alt>-C) | |<math>\mathsf{¢}</math>(E-<alt>-C) | ||
|Euclideanized-<alternative>-complexity-weighted cents | |Euclideanized-<alternative>-complexity-weighted cents | ||
|- | |- | ||
|S-damage | |S-damage | ||
|simplicity-weight damage | |simplicity-weight damage | ||
|¢(S) | |<math>\mathsf{¢}\small\mathsf{(S)}</math> | ||
|simplicity-weighted cents | |simplicity-weighted cents | ||
|- | |- | ||
|<alt>-S-damage | |<alt>-S-damage | ||
|<alternative>-simplicity-weight damage | |<alternative>-simplicity-weight damage | ||
|¢(<alt>-S) | |<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 | ||
|¢(ES) | |<math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math> | ||
|Euclideanized-simplicity-weighted cents | |Euclideanized-simplicity-weighted cents | ||
|- | |- | ||
|E-<alt>-S-damage | |E-<alt>-S-damage | ||
|Euclideanized-<alternative>-simplicity-weight damage | |Euclideanized-<alternative>-simplicity-weight damage | ||
|¢(E-<alt>-S) | |<math>\mathsf{¢}</math>(E-<alt>-S) | ||
|Euclideanized-<alternative>-simplicity-weighted cents | |Euclideanized-<alternative>-simplicity-weighted cents | ||
|} | |} | ||
| Line 4,305: | Line 4,305: | ||
|<alt>-C | |<alt>-C | ||
|<alternative> complexity | |<alternative> complexity | ||
|𝟙(<alt>-C) = (<alternative>-C) | |𝟙<math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math> = (<alternative>-C) | ||
|<alternative>-complexity weight | |<alternative>-complexity weight | ||
|- | |- | ||
|EC | |EC | ||
|Euclideanized complexity | |Euclideanized complexity | ||
|𝟙(EC) = (EC) | |𝟙<math>\small\mathsf{(EC)}</math> = <math>\small\mathsf{(EC)}</math> | ||
|Euclideanized-complexity weight | |Euclideanized-complexity weight | ||
|- | |- | ||
| Line 4,325: | Line 4,325: | ||
|<alt>-S | |<alt>-S | ||
|<alternative> simplicity | |<alternative> simplicity | ||
|𝟙(<alt>-S) = (<alternative>-S) | |𝟙<math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math> = (<alternative>-S) | ||
|<alternative>-simplicity weight | |<alternative>-simplicity weight | ||
|- | |- | ||
|ES | |ES | ||
|Euclideanized simplicity | |Euclideanized simplicity | ||
|𝟙(ES) = (ES) | |𝟙<math>\small\mathsf{(ES)}</math> = <math>\small\mathsf{(ES)}</math> | ||
|Euclideanized-simplicity weight | |Euclideanized-simplicity weight | ||
|- | |- | ||
| Line 4,356: | Line 4,356: | ||
|<alt>-S | |<alt>-S | ||
|<alternative> simplicitity | |<alternative> simplicitity | ||
|𝟙(<alt>-S) = (<alternative>-S) | |𝟙<math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{S)}</math> = (<alternative>-S) | ||
|<alternative>-simplicity | |<alternative>-simplicity | ||
|- | |- | ||
|ES | |ES | ||
|Euclideanized simplicity | |Euclideanized simplicity | ||
|𝟙(ES) = (ES) | |𝟙<math>\small\mathsf{(ES)}</math> = <math>\small\mathsf{(ES)}</math> | ||
|Euclideanized-simplicicty weight | |Euclideanized-simplicicty weight | ||
|- | |- | ||