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

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15,216 edits
m →Objects: Formatting and capitalisation. Last time I tried to do everything at once and screwed everything up.
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{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|-
|-
! rowspan="2" | equivalent expressions
! rowspan="2" | Equivalent<br />expressions
! rowspan="2" | variable
! rowspan="2" | Variable
! rowspan="2" | name
! rowspan="2" | Name
! colspan="3" | units
! colspan="3" | Units
! colspan="2" | shape
! colspan="2" | Shape
! colspan="2" | type
! colspan="2" | Type
! colspan="2" | EBK notation
! colspan="2" | EBK notation
! colspan="4" | subobjects
! colspan="4" | Subobjects
! rowspan="2" | notes
! rowspan="2" | Notes
|-
|-
! unreduced
! Unreduced
! reduced
! Reduced
! read as
! Read as
! unreduced
! Unreduced
! reduced
! Reduced
! numeric
! Numeric
! structural
! Structural
! row-first
! Row-first
! col-first
! Col-first
! row
! Row
! col
! Column
! diag
! Diagonal
! entry
! Entry
|-
|-
! colspan="17" | mapping
! colspan="17" | Mapping
|-
|-
|  
|  
| <math>\textbf{i}</math>
| <math>\textbf{i}</math>
| [[interval| (just) interval]]
| [[interval|(Just) interval]]
|  
|  
| <math>\small 𝗽</math>
| <math>\small 𝗽</math>
| primes
| Primes
|  
|  
| <math>\scriptsize (d, 1)</math>
| <math>\scriptsize (d, 1)</math>
| integer
| Integer
| vector
| Vector
|  
|  
| [...⟩
| [...⟩
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|  
|  
| <math>\mathrm{i}_i</math>
| <math>\mathrm{i}_i</math>
| specific type: vector ([[prime-count vector]] or PC-vector)
| Specific type: Vector ([[prime-count vector]] or PC-vector)
jargon name: monzo
Jargon name: Monzo
|-
|-
|  
|  
| <math>M</math>
| <math>M</math>
| [[Mapping| (temperament) mapping (matrix)]]
| [[Mapping|(Temperament) mapping (matrix)]]
|  
|  
| <math>\small 𝗴</math>/<math>\small 𝗽</math>
| <math>\small 𝗴</math>/<math>\small 𝗽</math>
| generators per prime
| Generators per prime
|  
|  
| <math>\scriptsize (r, d)</math>
| <math>\scriptsize (r, d)</math>
| integer
| Integer
| matrix
| Matrix
| [⟨...] ...}
| [⟨...] ...}
| ⟨[...} ...]
| ⟨[...} ...]
Line 109: Line 109:
|  
|  
| <math>m_{ij}</math>
| <math>m_{ij}</math>
| jargon name: val list
| Jargon name: Val list
|-
|-
| <math>M\textbf{i}</math>
| <math>M\textbf{i}</math>
| <math>\textbf{y}</math>
| <math>\textbf{y}</math>
| [[mapped interval]]
| [[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}  
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</math>
</math>
| <math>\small 𝗴</math>
| <math>\small 𝗴</math>
| generators
| Generators
| <math>\scriptsize  
| <math>\scriptsize  
\! \!  
\! \!  
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</math>
</math>
| <math>\scriptsize (r, 1)</math>
| <math>\scriptsize (r, 1)</math>
| integer
| Integer
| vector
| Vector
|  
|  
| [...}
| [...}
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|  
|  
|  
|  
| specific type: [[generator-count vector]] (GC-vector)
| Specific type: [[Generator-count vector]] (GC-vector)
jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
Jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
|-
|-
|  
|  
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|  
|  
| <math>\small 𝗴</math>/<math>\small 𝗽</math>
| <math>\small 𝗴</math>/<math>\small 𝗽</math>
| generators per prime
| Generators per prime
|  
|  
| <math>\scriptsize (1, d)</math>
| <math>\scriptsize (1, d)</math>
| integer
| Integer
| vector
| Vector
| ⟨...]
| ⟨...]
|  
|  
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|  
|  
| <math>m_i</math>
| <math>m_i</math>
| jargon name: val
| Jargon name: val
|-
|-
|  
|  
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|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| integer
| Integer
| scalar
| Scalar
|  
|  
|  
|  
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|  
|  
| <math>r</math>
| <math>r</math>
| [[rank]]
| [[Rank]]
|  
|  
|  
|  
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|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| integer
| Integer
| scalar
| Scalar
|  
|  
|  
|  
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|  
|  
|-
|-
! colspan="17" | tuning
! colspan="17" | Tuning
|-
|-
|  
|  
| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
| [[log-prime map]]
| [[Log-prime map]]
|  
|  
| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
| octaves per prime
| Octaves per prime
|  
|  
| <math>\scriptsize (1, d)</math>
| <math>\scriptsize (1, d)</math>
| real
| Real
| vector
| Vector
| ⟨...]
| ⟨...]
|  
|  
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| <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(-prime) 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
| Cents per prime
|  
|  
| <math>\scriptsize (1, d)</math>
| <math>\scriptsize (1, d)</math>
| real
| Real
| vector
| Vector
| ⟨...]
| ⟨...]
|  
|  
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|  
|  
| <math>𝒈</math>
| <math>𝒈</math>
| [[generator tuning map]]
| [[Generator tuning map]]
|  
|  
| <math>\mathsf{¢}</math>/<math>\small 𝗴</math>
| <math>\mathsf{¢}</math>/<math>\small 𝗴</math>
| cents per generator
| Cents per generator
|  
|  
| <math>\scriptsize (1, r)</math>
| <math>\scriptsize (1, r)</math>
| real
| Real
| vector
| Vector
| {...]
| {...]
|  
|  
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| <math>𝒈M</math>
| <math>𝒈M</math>
| <math>𝒕</math>
| <math>𝒕</math>
| [[tuning map| (tempered-prime) tuning map]]
| [[tuning map|(Tempered-prime) tuning map]]
| <math>\scriptsize  
| <math>\scriptsize  
\begin{array} {c} 𝒈 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}  
\begin{array} {c} 𝒈 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗴} \end{array}  
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</math>
</math>
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
| cents per prime
| Cents per prime
| <math>\scriptsize  
| <math>\scriptsize  
\! \!  
\! \!  
\begin{array} {c} 𝒈 \\[-3pt] (1, \cancel{r}) \end{array}  
\begin{array} {c} 𝒈 \\[-3pt] \left(1, \cancel{r}\right) \end{array}  
\! \!  
\! \!  
\begin{array} {c} M \\[-3pt] (\cancel{r}, d) \end{array}  
\begin{array} {c} M \\[-3pt] \left(\cancel{r}, d\right) \end{array}  
\! \!  
\! \!  
</math>
</math>
| <math>\scriptsize (1, d)</math>
| <math>\scriptsize (1, d)</math>
| real
| Real
| vector
| Vector
| ⟨...]
| ⟨...]
|  
|  
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| <math>𝒕 - 𝒋</math>
| <math>𝒕 - 𝒋</math>
| <math>𝒓</math>
| <math>𝒓</math>
| [[retuning map| retuning (or mistuning) map]]
| [[retuning map|Retuning (or mistuning) map]]
|  
|  
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
| cents per prime
| Cents per prime
|  
|  
| <math>\scriptsize (1, d)</math>
| <math>\scriptsize (1, d)</math>
| real
| Real
| vector
| Vector
| ⟨...]
| ⟨...]
|  
|  
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|  
|  
| <math>r_i</math>
| <math>r_i</math>
| previous name: prime error map
| Previous name: prime error map
|-
|-
| <math>𝒋\textbf{i}</math>
| <math>𝒋\textbf{i}</math>
| <math>\mathrm{o}</math>
| <math>\mathrm{o}</math>
| [[interval span| (just) (interval) size]]
| [[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}  
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</math>
</math>
| <math>\mathsf{¢}</math>
| <math>\mathsf{¢}</math>
| cents
| 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} \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
| Real
| scalar
| Scalar
|  
|  
|  
|  
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|  
|  
|  
|  
| mnemonic: <math>\mathrm{o}</math>riginal size
| 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=tempered (interval) size}}
| {{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}  
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</math>
</math>
| <math>\mathsf{¢}</math>
| <math>\mathsf{¢}</math>
| cents
| 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
| Real
| scalar
| Scalar
|  
|  
|  
|  
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|  
|  
|  
|  
| mnemonic: <math>\mathrm{a}</math>ltered size
| Mnemonic: <math>\mathrm{a}</math>ltered size
|-
|-
| <math>𝒕\textbf{i} - 𝒋\textbf{i} \\
| <math>𝒕\textbf{i} - 𝒋\textbf{i} \\
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𝒓\textbf{i}</math>
𝒓\textbf{i}</math>
| <math>\mathrm{e}</math>
| <math>\mathrm{e}</math>
| [[error| (interval) 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}  
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</math>
</math>
| <math>\mathsf{¢}</math>
| <math>\mathsf{¢}</math>
| cents
| 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
| Real
| scalar
| Scalar
|  
|  
|  
|  
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|  
|  
|-
|-
! colspan="17" | optimization
! colspan="17" | Optimization
|-
|-
|  
|  
| <math>p</math>
| <math>p</math>
| [[optimization power]]
| [[Optimization power]]
|  
|  
|  
|  
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|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| real
| Real
| scalar
| Scalar
|  
|  
|  
|  
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|-
|-
|  
|  
| <math>⟪\,·\,⟫_p</math>
| <math>\llangle\,·\,\rrangle_p</math>
| [[power mean]] (<math>p</math>-mean)
| [[Power mean]] (<math>p</math>-mean)
|  
|  
|  
|  
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|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| real
| Real
| scalar
| Scalar
|  
|  
|  
|  
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|  
|  
|-
|-
! colspan="17" | damage
! colspan="17" | Damage
|-
|-
|  
|  
| <math>c</math>
| <math>c</math>
| {{subpage|tuning_fundamentals|uprev|s=complexity}}
| {{subpage|tuning_fundamentals|uprev|s=complexity}}
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math><ref group="note">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>
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math><ref group="note">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 {{nowrap|''w'' {{=}} ''d''/{{!}}''e''{{!}}}} whose units are {{nowrap|¢(W) / ¢}} and the cents cancel.</ref>
| <math>\small\mathsf{(C)}</math>
| <math>\small\mathsf{(C)}</math>
| complexity weight
| Complexity weight
|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| real
| Real
| scalar
| Scalar
|  
|  
|  
|  
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| <math>\dfrac1c</math>
| <math>\dfrac1c</math>
| <math>s</math>
| <math>s</math>
| [[simplicity]]
| [[Simplicity]]
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
| <math>\small\mathsf{(S)}</math>
| <math>\small\mathsf{(S)}</math>
| simplicity weight
| Simplicity weight
|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| real
| Real
| scalar
| Scalar
|  
|  
|  
|  
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| <math>c</math> or <math>s</math>
| <math>c</math> or <math>s</math>
| <math>w</math>
| <math>w</math>
| [[weight]]
| [[Weight]]
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or 𝟙<math>\small\mathsf{(S)}</math>
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or 𝟙<math>\small\mathsf{(S)}</math>
| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math>
| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math>
| complexity weight or simplicity weight
| Complexity weight or simplicity weight
|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| real
| Real
| scalar
| Scalar
|  
|  
|  
|  
Line 477: Line 477:
|  
|  
|-
|-
| <math>| \mathrm{e}| w</math>
| <math>|\mathrm{e}| w</math>
| <math>\mathrm{d}</math>
| <math>\mathrm{d}</math>
| [[damage]]
| [[Damage]]
| <math>\scriptsize  
| <math>\scriptsize  
\begin{array} {c} | \mathrm{e}| \\[-2pt] {\small\mathsf{¢}} \end{array}  
\begin{array} {c} |\mathrm{e}| \\[-2pt] {\small\mathsf{¢}} \end{array}  
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} w \\[-2pt] \mathsf{(U, C, or\,S)} \end{array}  
\begin{array} {c} w \\[-2pt] \mathsf{(U, C, \text{or}\,S)} \end{array}  
</math>
</math>
| <math>\mathsf{¢}\small\mathsf{(U)}</math> or <math>\mathsf{¢}\small\mathsf{(C)}</math> or <math>\mathsf{¢}\small\mathsf{(S)}</math>
| <math>\mathsf{¢}\small\mathsf{(U)}</math> or <math>\mathsf{¢}\small\mathsf{(C)}</math> or <math>\mathsf{¢}\small\mathsf{(S)}</math>
| (see damages table)
| (See damages table)
| <math>\scriptsize  
| <math>\scriptsize  
\! \!  
\! \!  
\begin{array} {c} | \mathrm{e}| \\[-3pt] (1, \cancel{1}) \end{array}  
\begin{array} {c} |\mathrm{e}| \\[-3pt] \left(1, \cancel{1}\right) \end{array}  
\! \!  
\! \!  
\begin{array} {c} w \\[-3pt] (\cancel{1}, 1) \end{array}
\begin{array} {c} w \\[-3pt] \left(\cancel{1}, 1\right) \end{array}
\! \!  
\! \!  
</math>
</math>
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| real
| Real
| scalar
| Scalar
|  
|  
|  
|  
Line 505: Line 505:
|  
|  
|-
|-
! colspan="17" | target-intervals
! colspan="17" | Target-intervals
|-
|-
|  
|  
| <math>\mathrm{T}</math>
| <math>\mathrm{T}</math>
| [[target-interval list]]
| [[Target-interval list]]
|  
|  
| <math>\small 𝗽</math>
| <math>\small 𝗽</math>
| primes
| Primes
|  
|  
| <math>\scriptsize (d, k)</math>
| <math>\scriptsize (d, k)</math>
| integer
| Integer
| matrix
| Matrix
|  
|  
| [[...⟩ ...]
| [[...⟩ ...]
Line 527: Line 527:
| <math>M\mathrm{T}</math>
| <math>M\mathrm{T}</math>
| <math>\mathrm{Y}</math>
| <math>\mathrm{Y}</math>
| [[mapped target-interval list]]
| [[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 534: Line 534:
</math>
</math>
| <math>\small 𝗴</math>
| <math>\small 𝗴</math>
| generators
| 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
| Integer
| matrix
| Matrix
|  
|  
| [[...} ...]
| [[...} ...]
Line 551: Line 551:
|  
|  
| <math>\mathrm{y}_{ij}</math>
| <math>\mathrm{y}_{ij}</math>
| mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
| 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=target-interval (just) size list}}
| {{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 562: Line 562:
</math>
</math>
| <math>\mathsf{¢}</math>
| <math>\mathsf{¢}</math>
| cents
| 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
| Real
| list
| List
| [...]
| [...]
|  
|  
Line 579: Line 579:
|  
|  
| <math>\mathrm{o}_i</math>
| <math>\mathrm{o}_i</math>
| mnemonic: <math>\textbf{o}</math>riginal size list
| Mnemonic: <math>\textbf{o}</math>riginal size list
|-
|-
| <math>𝒕\mathrm{T} \\
| <math>𝒕\mathrm{T} \\
𝒈M\mathrm{T}</math>
𝒈M\mathrm{T}</math>
| <math>\textbf{a}</math>
| <math>\textbf{a}</math>
| [[tempered target-interval size list]]
| [[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 591: Line 591:
</math>
</math>
| <math>\mathsf{¢}</math>
| <math>\mathsf{¢}</math>
| cents
| 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
| Real
| list
| List
| [...]
| [...]
|  
|  
Line 608: Line 608:
|  
|  
| <math>\mathrm{a}_i</math>
| <math>\mathrm{a}_i</math>
| mnemonic: <math>\textbf{a}</math>ltered size list
| Mnemonic: <math>\textbf{a}</math>ltered size list
|-
|-
| <math>𝒕\mathrm{T} - 𝒋\mathrm{T}\\
| <math>𝒕\mathrm{T} - 𝒋\mathrm{T}\\
Line 615: Line 615:
</math>
</math>
| <math>\textbf{e}</math>
| <math>\textbf{e}</math>
| [[target-interval error list]]
| [[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 622: Line 622:
</math>
</math>
| <math>\mathsf{¢}</math>
| <math>\mathsf{¢}</math>
| cents
| 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
| Real
| list
| List
| [...]
| [...]
|  
|  
Line 643: Line 643:
| <math>C</math> or <math>S</math>
| <math>C</math> or <math>S</math>
| <math>W</math>
| <math>W</math>
| [[target-interval weight matrix]]
| [[Target-interval weight matrix]]
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(U)}</math>
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(U)}</math>
| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(S)}</math> or <math>\small\mathsf{(U)}</math>
| <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
|  
|  
| <math>\scriptsize (k, k)</math>
| <math>\scriptsize (k, k)</math>
| real
| Real
| matrix
| Matrix
|  
|  
| [[...] ...]
| [[...] ...]
Line 661: Line 661:
|  
|  
| <math>C</math>
| <math>C</math>
| {{subpage|tuning_fundamentals|uprev|s=complexity-weight_damage|text=target-interval complexity weight matrix}}
| {{subpage|tuning_fundamentals|uprev|s=complexity-weight_damage|text=Target-interval complexity weight matrix}}
| <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
| Complexity weight
|  
|  
| <math>\scriptsize (k, k)</math>
| <math>\scriptsize (k, k)</math>
| real
| Real
| matrix
| Matrix
|  
|  
| [[...] ...]
| [[...] ...]
Line 679: Line 679:
| <math>\dfrac1C</math>
| <math>\dfrac1C</math>
| <math>S</math>
| <math>S</math>
| {{subpage|tuning fundamentals|uprev|s=complexity-weight_damage|text=target-interval simplicity weight matrix}}
| {{subpage|tuning fundamentals|uprev|s=complexity-weight_damage|text=Target-interval simplicity weight matrix}}
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(S)}</math>
| <math>\small\mathsf{(S)}</math>
| <math>\small\mathsf{(S)}</math>
| simplicity weight
| Simplicity weight
|  
|  
| <math>\scriptsize (k, k)</math>
| <math>\scriptsize (k, k)</math>
| real
| Real
| matrix
| Matrix
|  
|  
| [[...] ...]
| [[...] ...]
Line 693: Line 693:
| <math>𝒔</math>
| <math>𝒔</math>
| <math>s_i</math>
| <math>s_i</math>
| entry-wise reciprocal of <math>C</math>
| Entry-wise reciprocal of <math>C</math>
|-
|-
| <math>| \textbf{e}| W</math>
| <math>|\textbf{e}| W</math>
| <math>\textbf{d}</math>
| <math>\textbf{d}</math>
| [[target-interval damage list]]<ref group="note">You may sometimes see annotated units without parentheses, such as "dBA", but this is not compliant with SI standards, so we always keep the parentheses.</ref>
| [[Target-interval damage list]]<ref group="note">You may sometimes see annotated units without parentheses, such as "dBA", but this is not compliant with SI standards, so we always keep the parentheses.</ref>
| <math>\scriptsize  
| <math>\scriptsize  
\begin{array} {c} | \textbf{e}| \\[-2pt] {\small\mathsf{¢}} \end{array}  
\begin{array} {c} |\textbf{e}| \\[-2pt] {\small\mathsf{¢}} \end{array}  
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} W \\[-2pt] (\mathsf{U, C, or\,S}) \end{array}  
\begin{array} {c} W \\[-2pt] (\mathsf{U, C, \text{or}\,S}) \end{array}  
</math>
</math>
| <math>\mathsf{¢}\small\mathsf{(U)}</math>, <math>\mathsf{¢}\small\mathsf{(C)}</math>, or <math>\mathsf{¢}\small\mathsf{(S)}</math>
| <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  
\! \!  
\! \!  
\begin{array} {c} | \textbf{e}| \\[-3pt] (1, \cancel{k}) \end{array}  
\begin{array} {c} | \textbf{e}| \\[-3pt] \left(1, \cancel{k}\right) \end{array}  
\! \!  
\! \!  
\begin{array} {c} W \\[-3pt] (\cancel{k}, k) \end{array}
\begin{array} {c} W \\[-3pt] \left(\cancel{k}, k\right) \end{array}
\! \!  
\! \!  
</math>
</math>
| <math>\scriptsize (1, k)</math>
| <math>\scriptsize (1, k)</math>
| real
| Real
| list
| List
| [...]
| [...]
|  
|  
Line 725: Line 725:
|  
|  
| <math>k</math>
| <math>k</math>
| [[target-interval count]]
| [[Target-interval count]]
|  
|  
|  
|  
Line 731: Line 731:
|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| integer
| Integer
| scalar
| Scalar
|  
|  
|  
|  
Line 739: Line 739:
|  
|  
|  
|  
| mnemonic: <math>k</math>ount
| Mnemonic: <math>k</math>ount
|-
|-
! colspan="17" | held-intervals
! colspan="17" | Held-intervals
|-
|-
|  
|  
| <math>\mathrm{H}</math>
| <math>\mathrm{H}</math>
| [[held-interval basis]]
| [[Held-interval basis]]
|  
|  
| <math>\small 𝗽</math>
| <math>\small 𝗽</math>
| primes
| Primes
|  
|  
| <math>\scriptsize (d, h)</math>
| <math>\scriptsize (d, h)</math>
|  
|  
| matrix
| Matrix
|  
|  
| [[...⟩ ...]
| [[...⟩ ...]
Line 763: Line 763:
|  
|  
| <math>h</math>
| <math>h</math>
| [[held-interval count]]
| [[Held-interval count]]
|  
|  
|  
|  
Line 769: Line 769:
|  
|  
| <math>\scriptsize (1, 1)</math>
| <math>\scriptsize (1, 1)</math>
| integer
| Integer
| scalar
| Scalar
|  
|  
|  
|  
Line 779: Line 779:
|  
|  
|-
|-
! colspan="17" | exploring temperaments
! colspan="17" | Exploring temperaments
|-
|-
|  
|  
| <math>\mathrm{C}</math>
| <math>\mathrm{C}</math>
| [[comma basis]]
| [[Comma basis]]
|  
|  
| <math>\small 𝗽</math>
| <math>\small 𝗽</math>
| primes
| Primes
|  
|  
| <math>\scriptsize (d, n)</math>
| <math>\scriptsize (d, n)</math>
| integer
| Integer
| matrix
| Matrix
|  
|  
| [[...⟩ ...]
| [[...⟩ ...]
Line 797: Line 797:
|  
|  
| <math>\mathrm{c}_{ij}</math>
| <math>\mathrm{c}_{ij}</math>
| jargon name: monzo list
| Jargon name: monzo list
|-
|-
|  
|  
| <math>\textbf{c}</math>
| <math>\textbf{c}</math>
| [[comma]]
| [[Comma]]
|  
|  
| <math>\small 𝗽</math>
| <math>\small 𝗽</math>
| primes
| Primes
|  
|  
| <math>\scriptsize (d, 1)</math>
| <math>\scriptsize (d, 1)</math>
| integer
| Integer
| vector
| Vector
|  
|  
| [...⟩
| [...⟩
Line 815: Line 815:
|  
|  
| <math>\mathrm{c}_i</math>
| <math>\mathrm{c}_i</math>
| specific type: vector ([[prime-count vector]] or PC-vector)
| Specific type: vector ([[prime-count vector]] or PC-vector)
|}
|}


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