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

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==Advanced==
==Intermediate==
===Objects===
===Objects===
{| class="wikitable mw-collapsible mw-collapsed"
| +
! rowspan="2" | equivalent expressions
! rowspan="2" | variable
! rowspan="2" | name
! colspan="3" | units
! colspan="2" | shape
! colspan="2" | type
! colspan="2" | EBK notation
! colspan="4" | subobjects
! rowspan="2" | notes
|-
! unreduced
! reduced
! read as
! unreduced
! reduced
! numeric
! structural
! row-first
! col-first
! row
! col
! diag
! entry
|-
! colspan="17" | mapping
|-
|
| <math>\textbf{i}</math>
| [[interval| (just) interval]]
|
| <math>\small 𝗽</math>
| primes
|
| <math>\scriptsize (d, 1)</math>
| integer
| vector
|
| [...⟩
|
|
|
| <math>\mathrm{i}_i</math>
| specific type: vector ([[prime-count vector]] or PC-vector)
jargon name: monzo
|-
|
| <math>M</math>
| [[Mapping| (temperament) mapping (matrix)]]
|
| <math>\small 𝗴</math>/<math>\small 𝗽</math>
| generators per prime
|
| <math>\scriptsize (r, d)</math>
| integer
| matrix
| [⟨...] ...}
| ⟨[...} ...]
| <math>𝒎_i</math>
|
|
| <math>m_{ij}</math>
| jargon name: val list
|-
| <math>M\textbf{i}</math>
| <math>\textbf{y}</math>
| [[mapped interval]]
| <math>\scriptsize
\begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\small 𝗴</math>
| generators
| <math>\scriptsize
\! \!
\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
\! \!
</math>
| <math>\scriptsize (r, 1)</math>
| integer
| vector
|
| [...}
|
|
|
|
| specific type: [[generator-count vector]] (GC-vector)
jargon name: tmonzo; mnemonic: <math>\textbf{y}</math>nterval
|-
|
| <math>𝒎</math>
| [[map| (temperament) map]]
|
| <math>\small 𝗴</math>/<math>\small 𝗽</math>
| generators per prime
|
| <math>\scriptsize (1, d)</math>
| integer
| vector
| ⟨...]
|
|
|
|
| <math>m_i</math>
| jargon name: val
|-
| <math>n + r</math>
| <math>d</math>
| [[dimensionality]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| integer
| scalar
|
|
|
|
|
|
|
|-
| <math>d - n</math>
| <math>r</math>
| [[rank]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| integer
| scalar
|
|
|
|
|
|
|
|-
| <math>d - r</math>
| <math>n</math>
| [[nullity]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| integer
| scalar
|
|
|
|
|
|
|
|-
! colspan="17" | tuning
|-
|
| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
| [[log-prime map]]
|
| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
| octaves per prime
|
| <math>\scriptsize (1, d)</math>
| real
| vector
| ⟨...]
|
|
|
|
| <math>{\large 𝓁}\hspace{2mu}_i</math>
|
|-
| <math>1200×{\large\textbf{𝓁}}\hspace{2mu}</math>
| <math>𝒋</math>
| [[just tuning map| just(-prime) tuning map]]
|
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
| cents per prime
|
| <math>\scriptsize (1, d)</math>
| real
| vector
| ⟨...]
|
|
|
|
| <math>j_i</math>
|
|-
|
| <math>𝒈</math>
| [[generator tuning map]]
|
| <math>\mathsf{¢}</math>/<math>\small 𝗴</math>
| cents per generator
|
| <math>\scriptsize (1, r)</math>
| real
| vector
| {...]
|
|
|
|
| <math>g_i</math>
|
|-
|
| <math>𝒕</math>
| [[tuning map| (tempered-prime) tuning map]]
|
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
| cents per prime
|
| <math>\scriptsize (1, d)</math>
| real
| vector
| ⟨...]
|
|
|
|
| <math>t_i</math>
|
|-
| <math>𝒕 - 𝒋 \\
1200×\slant{\mathbf{1}}L(P - I)</math>
| <math>𝒓</math>
| [[retuning map| retuning (or mistuning) map]]
|
| <math>\mathsf{¢}</math>/<math>\small 𝗽</math>
| cents per prime
|
| <math>\scriptsize (1, d)</math>
| real
| vector
| ⟨...]
|
|
|
|
| <math>r_i</math>
| previous name: prime error map
|-
| <math>𝒋\textbf{i}</math>
| <math>\mathrm{o}</math>
| [[interval span| (just) (interval) size]]
| <math>\scriptsize
\begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\mathsf{¢}</math>
| cents
| <math>\scriptsize
\! \!
\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \mathbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
\! \!
</math>
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
| mnemonic: <math>\mathrm{o}</math>riginal size
|-
| <math>𝒈M\textbf{i} \\
𝒕\textbf{i}</math>
| <math>\mathrm{a}</math>
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Example_3| tempered (interval) size]]
| <math>\scriptsize
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\mathsf{¢}</math>
| cents
| <math>\scriptsize
\! \!
\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
\! \!
</math>
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
| mnemonic: <math>\mathrm{a}</math>ltered size
|-
| <math>𝒕\textbf{i} - 𝒋\textbf{i} \\
a - o \\
𝒓\textbf{i}</math>
| <math>\mathrm{e}</math>
| [[error| (interval) error]]
| <math>\scriptsize
\begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \textbf{i} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\mathsf{¢}</math>
| cents
| <math>\scriptsize
\! \!
\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \textbf{i} \\[-3pt] (\cancel{d}, 1) \end{array}
\! \!
</math>
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
! colspan="17" | optimization
|-
|
| <math>p</math>
| [[optimization power]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
|
| <math>⟪\,·\,⟫_p</math>
| [[power mean]] (<math>p</math>-mean)
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
! colspan="17" | damage
|-
|
| <math>c</math>
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity| complexity]]
| colspan="3" | (see complexities section of complexities and simplicities table)
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
| <math>\dfrac1c</math>
| <math>s</math>
| [[simplicity]]
| colspan="3" | (see simplicities section of complexities and simplicities table)
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
| <math>c</math> or <math>s</math>
| <math>w</math>
| [[weight]]
| colspan="3" | (see complexities and simplicities table)
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
| <math>| \mathrm{e}| w</math>
| <math>\mathrm{d}</math>
| [[damage]]
| colspan="3" | (see damages table)
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
! colspan="17" | target-intervals
|-
|
| <math>\mathrm{T}</math>
| [[target-interval list]]
|
| <math>\small 𝗽</math>
| primes
|
| <math>\scriptsize (d, k)</math>
| integer
| matrix
|
| [[...⟩ ...]
|
| <math>\textbf{t}_i</math>
|
| <math>\mathrm{t}_{ij}</math>
|
|-
| <math>M\mathrm{T}</math>
| <math>\mathrm{Y}</math>
| [[mapped target-interval list]]
| <math>\scriptsize
\begin{array} {c} M \\[-2pt] 𝗴 \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\small 𝗴</math>
| generators
| <math>\scriptsize
\! \!
\begin{array} {c} M \\[-3pt] (r, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
\! \!
</math>
| <math>\scriptsize (r, k)</math>
| integer
| matrix
|
| [[...} ...]
|
| <math>\textbf{y}_i</math>
|
| <math>\mathrm{y}_{ij}</math>
| mnemonic: looks like bent-up 'T', or cross between 'M' and 'T'
|-
| <math>𝒋\mathrm{T}</math>
| <math>\textbf{o}</math>
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Primes| target-interval (just) size list]]
| <math>\scriptsize
\begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\mathsf{¢}</math>
| cents
| <math>\scriptsize
\! \!
\begin{array} {c} 𝒋 \\[-3pt] (1, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
\! \!
</math>
| <math>\scriptsize (1, k)</math>
| real
| list
| [...]
|
|
|
|
| <math>\mathrm{o}_i</math>
| mnemonic: <math>\textbf{o}</math>riginal size list
|-
| <math>𝒕\mathrm{T}</math>
| <math>\textbf{a}</math>
| [[tempered target-interval size list]]
| <math>\scriptsize
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\mathsf{¢}</math>
| cents
| <math>\scriptsize
\! \!
\begin{array} {c} 𝒕 \\[-3pt] (1, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
\! \!
</math>
| <math>\scriptsize (1, k)</math>
| real
| list
| [...]
|
|
|
|
| <math>\mathrm{a}_i</math>
| mnemonic: <math>\textbf{a}</math>ltered size list
|-
| <math>𝒕\mathrm{T} - 𝒋\mathrm{T} \\
𝒓\mathrm{T} \\
\textbf{a} - \textbf{o}</math>
| <math>\textbf{e}</math>
| [[target-interval error list]]
| <math>\scriptsize
\begin{array} {c} 𝒓 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}
\begin{array} {c} \\[-2pt] · \end{array}
\begin{array} {c} \mathrm{T} \\[-2pt] \cancel{𝗽} \end{array}
</math>
| <math>\mathsf{¢}</math>
| cents
| <math>\scriptsize
\! \!
\begin{array} {c} 𝒓 \\[-3pt] (1, \cancel{d}) \end{array}
\! \!
\begin{array} {c} \mathrm{T} \\[-3pt] (\cancel{d}, k) \end{array}
\! \!
</math>
| <math>\scriptsize (1, k)</math>
| real
| list
| [...]
|
|
|
|
| <math>\mathrm{e}_i</math>
|
|-
| <math>C</math> or <math>S</math>
| <math>W</math>
| [[target-interval weight matrix]]
| colspan="3" | (see complexities and simplicities table)
|
| <math>\scriptsize (k, k)</math>
| real
| matrix
|
| [[...] ...]
|
|
| <math>𝒘</math>
| <math>w_i</math>
|
|-
|
| <math>C</math>
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage| target-interval complexity weight matrix]]
| colspan="3" | (see complexities section of complexities and simplicities table)
|
| <math>\scriptsize (k, k)</math>
| real
| matrix
|
| [[...] ...]
|
|
| <math>𝒄</math>
| <math>c_i</math>
|
|-
| <math>\dfrac1C</math>
| <math>S</math>
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage| target-interval simplicity weight matrix]]
| colspan="3" | (see simplicities section of complexities and simplicities table)
|
| <math>\scriptsize (k, k)</math>
| real
| matrix
|
| [[...] ...]
|
|
| <math>𝒔</math>
| <math>s_i</math>
| entrywise reciprocal of <math>C</math>
|-
| <math>| \textbf{e}| W</math>
| <math>\textbf{d}</math>
| [[target-interval damage list]]
| colspan="3" | (see damages table)
|
| <math>\scriptsize (1, k)</math>
| real
| list
| [...]
|
|
|
|
| <math>\mathrm{d}_i</math>
|
|-
|
| <math>k</math>
| [[target-interval count]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| integer
| scalar
|
|
|
|
|
|
| mnemonic: <math>k</math>ount
|-
! colspan="17" | held-intervals
|-
|
| <math>\mathrm{H}</math>
| [[held-interval basis]]
|
| <math>\small 𝗽</math>
| primes
|
| <math>\scriptsize (d, h)</math>
|
| matrix
|
| [[...⟩ ...]
|
| <math>\textbf{h}_i</math>
|
| <math>\mathrm{h}_{ij}</math>
|
|-
|
| <math>h</math>
| [[held-interval count]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| integer
| scalar
|
|
|
|
|
|
|
|-
! colspan="17" | exploring temperaments
|-
|
| <math>\mathrm{C}</math>
| [[comma basis]]
|
| <math>\small 𝗽</math>
| primes
|
| <math>\scriptsize (d, n)</math>
| integer
| matrix
|
| [[...⟩ ...]
|
| <math>\textbf{c}_i</math>
|
| <math>\mathrm{c}_{ij}</math>
| jargon name: monzo list
|-
|
| <math>\textbf{c}</math>
| [[comma]]
|
| <math>\small 𝗽</math>
| primes
|
| <math>\scriptsize (d, 1)</math>
| integer
| vector
|
| [...⟩
|
|
|
| <math>\mathrm{c}_i</math>
| specific type: vector ([[prime-count vector]] or PC-vector)
|-
! colspan="17" | computation
|-
|
| <math>\llzigzag·\,\rrzigzag\! _p</math>
| [[power sum]] (<math>p</math>-sum)
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
! colspan="17" | all-interval tuning schemes
|-
| <math>\mathrm{I}</math>
| <math>\mathrm{T}_{\text{p}}</math>
| [[prime proxy target-interval list]]
|
| <math>\small 𝗽</math>
| primes
|
| <math>\scriptsize (d, d)</math>
| integer
| matrix
|
| ⟨[...⟩ ...]
|
|
| <math>\mathbf{1}</math>
|
|
|-
|
| <math>X</math>
| [[complexity prescaler]]
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math>
| <math>\small\mathsf{(C)}</math>
| complexity weight
|
| <math>\scriptsize (d, d)</math>
| real
| matrix
| [⟨...] ...⟩
|
|
|
| <math>𝒙</math>
| <math>x_i</math>
|
|-
| <math>\text{diag}({\large\textbf{𝓁}}\hspace{2mu})</math>
| <math>L</math>
| [[log-prime matrix]]
|
| <math>\small\mathsf{oct}</math>/<math>\small 𝗽</math>
| octaves per prime
|
| <math>\scriptsize (d, d)</math>
| real
| matrix
| [⟨...] ...⟩
| ⟨[...⟩ ...]
| <math>{\large\textbf{𝓁}}\hspace{2mu}_i</math>
|
| <math>{\large\textbf{𝓁}}\hspace{2mu}</math>
| <math>{\large 𝓁}\hspace{2mu}_{ij}</math>
|
|-
|
| <math>q</math>
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms| interval complexity norm power]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
|
| <math>‖ · ‖_q</math>
| [[power norm]] (<math>p</math>-norm)
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
| <math>\dfrac1{1-\frac1q}</math>
| <math>\text{dual}(q)</math>
| [[Dave_Keenan_%26_Douglas_Blumeyer's_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms| dual norm power]]
|
|
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
|
| <math>‖X\mathbf{i}‖_q</math>
| [[interval complexity]]
|
| <math>\small\mathsf{(C)}</math>
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|-
|
| <math>‖𝒓X^{-1}‖_{\text{dual}(q)}</math>
| [[retuning magnitude]]
|
| <math>\mathsf{¢}\small\mathsf{(C^{-1})}</math>
|
|
| <math>\scriptsize (1, 1)</math>
| real
| scalar
|
|
|
|
|
|
|
|}
===Units===
Same as the basic level.
===Tuning schemes===
{| class="wikitable center-all mw-collapsible mw-collapsed"
| +
|-
! colspan="3" rowspan="3" | retuning (or mistuning) magnitude
! colspan="9" | damage
! rowspan="4" | target
intervals
! colspan="2" rowspan="3" | systematic name
! rowspan="4" | previously named tuning schemes that are specific types of this tuning scheme
! rowspan="4" | of interest?
|-
! colspan="6" | weight
! colspan="3" rowspan="1" | optimization
|-
! colspan="3" | interval complexity
! colspan="3" rowspan="1" | slope
! colspan="1" rowspan="2" | initial
! colspan="1" rowspan="2" | name
! colspan="1" rowspan="2" | power
|-
! initial
! name
! power
! initial
! name
! power
! initial
! name
! multiplier
! colspan="1" | abbreviated
! colspan="1" | read ("____ tuning scheme")
|-
| <n/a>
| maximum
| ∞
| (t)
| taxicab
| 1
| rowspan="2" | S
| rowspan="2" | simplicity-weight
| rowspan="2" | 1/complexity
| rowspan="17" | <n/a>
| rowspan="7" | minimax
| rowspan="7" | ∞
| rowspan="2" | all
| minimax-S
| minimax simplicity-weight damage
| "[[TOP]]"/"[[T1]]"/"[[TIPTOP]]"*, "[[CTOP]]", "[[POTOP]]"/"[[POTT]]"*, "[[BOP tuning| BOP]]", "[[Weil Norms, Tenney-Weil Norms, and TWp Interval and Tuning Space| Weil]]", "[[Kees]]"
| yes
|-
| <n/a>
| Euclidean
| 2
| E
| Euclidean
| 2
| minimax-ES
| minimax Euclideanized-simplicity-weight damage
| "[[Tenney-Euclidean tuning| TE]]"/"[[T2]]"/"[[TOP-RMS]]", "[[CTE tuning| CTE]]", "[[POTE tuning| POTE]]", "[[Frobenius]]", "[[BE]]", "[[WE]]", "[[KE]]"
|
|-
| colspan="3" rowspan="15" | <n/a>
| colspan="3" | <n/a>
| U
| unity-weight
| <none>
| rowspan="15" | <set>
| <set> minimax-U
| <set> minimax unity-weight-damage
| "[[Minimax tuning| minimax]]"
| yes
|-
| (t)
| taxicab
| 1
| rowspan="2" | S
| rowspan="2" | simplicity-weight
| rowspan="2" | 1/complexity
| <set> minimax-S
| <set> minimax simplicity-weight damage
|
| yes
|-
| E
| Euclidean
| 2
| <set> minimax-ES
| <set> minimax Euclideanized-simplicity-weight damage
|
|
|-
| (t)
| taxicab
| 1
| rowspan="2" | C
| rowspan="2" | complexity-weight
| rowspan="2" | complexity
| <set> minimax-C
| <set> minimax complexity-weight damage
|
| yes
|-
| E
| Euclidean
| 2
| <set> minimax-EC
| <set> minimax Euclideanized-complexity-weight damage
|
|
|-
| colspan="3" | <n/a>
| U
| unity-weight
| <none>
| rowspan="5" | miniRMS
| rowspan="5" | 2
| <set> miniRMS-U
| <set> miniRMS unity-weight damage
| "[[least squares]]"
| yes
|-
| (t)
| taxicab
| 1
| rowspan="2" | S
| rowspan="2" | simplicity-weight
| rowspan="2" | 1/complexity
| <set> miniRMS-S
| <set> miniRMS simplicity-weight damage
|
| yes
|-
| E
| Euclidean
| 2
| <set> miniRMS-ES
| <set> miniRMS Euclideanized-simplicity-weight damage
|
|
|-
| (t)
| taxicab
| 1
| rowspan="2" | C
| rowspan="2" | complexity-weight
| rowspan="2" | complexity
| <set> miniRMS-C
| <set> miniRMS complexity-weight damage
|
| yes
|-
| E
| Euclidean
| 2
| <set> miniRMS-EC
| <set> miniRMS Euclideanized-complexity-weight damage
|
|
|-
| colspan="3" | <n/a>
| U
| unity-weight
| <none>
| rowspan="5" | miniaverage
| rowspan="5" | 1
| <set> miniaverage-U
| <set> miniaverage unity-weight damage
|
| yes
|-
| (t)
| taxicab
| 1
| rowspan="2" | S
| rowspan="2" | simplicity-weight
| rowspan="2" | 1/complexity
| <set> miniaverage-S
| <set> miniaverage simplicity-weight damage
|
| yes
|-
| E
| Euclidean
| 2
| <set> miniaverage-ES
| <set> miniaverage Euclideanized-simplicity-weight damage
|
|
|-
| (t)
| taxicab
| 1
| rowspan="2" | C
| rowspan="2" | complexity-weight
| rowspan="2" | complexity
| <set> miniaverage-C
| <set> miniaverage complexity-weight damage
|
| yes
|-
| E
| Euclidean
| 2
| <set> miniaverage-EC
| <set> miniaverage Euclideanized-complexity-weight damage
|
|
|}
===Damages===
{| class="wikitable center-all mw-collapsible mw-collapsed"
|-
! colspan="2" | Quantity
! colspan="2" | Unit
|-
! Abbreviation
! Name
! Symbol
! Name
|-
| U-damage
| Unity-weight damage
| <math>\mathsf{¢}\small\mathsf{(U)}</math>
| Unity-weighted cents
|-
| C-damage
| Complexity-weight damage
| <math>\mathsf{¢}\small\mathsf{(C)}</math>
| Complexity-weighted cents
|-
| EC-damage
| Euclideanized-complexity-weight damage
| <math>\mathsf{¢}</math><math>\small\mathsf{(EC)}</math>
| Euclideanized-complexity-weighted cents
|-
| S-damage
| Simplicity-weight damage
| <math>\mathsf{¢}\small\mathsf{(S)}</math>
| Simplicity-weighted cents
|-
| ES-damage
| Euclideanized-simplicity-weight damage
| <math>\mathsf{¢}</math><math>\small\mathsf{(ES)}</math>
| Euclideanized-simplicity-weighted cents
|}
=== Complexity and simplicity ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
! colspan="2" | Quantity
! colspan="2" | Unit
|-
! Abbreviation
! Name
! Symbol
! Name
|-
| C
| complexity
| <math>\small\mathsf{(C)}</math>
| complexity weight
|-
| EC
| Euclideanized complexity
| <math>\small\mathsf{(EC)}</math>
| Euclideanized-complexity weight
|-
| S
| simplicity
| <math>\small\mathsf{(S)}</math>
| simplicity weight
|-
| ES
| Euclideanized simplicity
| <math>\small\mathsf{(ES)}</math>
| Euclideanized-simplicity weight
|}
== Advanced ==
=== Objects ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
! rowspan="2" | Equivalent expressions
! rowspan="2" | Equivalent expressions
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