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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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See [[Extended bra-ket notation#Variant including curly and square brackets|here]] for more information on our variation on extended bra-ket notation.
See [[Extended bra-ket notation#Variant including curly and square brackets|here]] for more information on our variation on extended bra-ket notation.


We've followed a symbol formatting pattern, explained by the table below, which we hope serves as an aid to quickly identifying objects and remembering their properties and purposes, but at the least we hope our choices are unobtrusive. In short, the objects with simple units of primes, generators or cents, i.e. the things which are actually audible in our application, are distinguished by upright formatting, while other variables are italic as is conventional. This is crossed with the mathematical convention that objects of order-1 like vectors are bolded and order-2 like matrices are uppercased:
We've followed a variable styling convention, explained in the table below, which we hope serves as an aid to quickly identifying objects and remembering their properties and purposes, but at the least we hope our choices are unobtrusive. In short, the objects with simple units of primes, generators or cents, i.e. the things which are actually audible in our application, are distinguished by upright formatting, while other variables are italic as is conventional. This is crossed with the linear-algebra convention that objects of order-1 like vectors are bolded and order-2 like matrices are uppercased:


{| class="wikitable center-all"
{| class="wikitable center-all"
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| &darr; Order
| &darr; Order
| &darr; Style &rarr;
| &darr; Style &rarr;
| Upright
| Roman (upright)
| ''Italic''
| ''Italic''
|-
|-
! scope="col" height="8px" ! colspan="2" | &nbsp;
! scope="col" height="8px" ! colspan="2" |
!  
!
! colspan="2" | &nbsp;
! colspan="2" |
|-
|-
| 0
| 0
| Plain
| lowercase
! rowspan="3" | &nbsp;
! rowspan="3" | &nbsp;
| Scalar with simple unit
| scalar (with simple unit)
| ''Scalar'' with no unit
| ''scalar'' (with no unit)
|-
|-
| 1
| 1
| '''Bold'''
| '''bold lowercase'''
| '''Vector'''
| '''vector'''
| '''''Map''''' (row vector)
| '''''map''''' (row vector)
|-
|-
| 2
| 2
| UPPERCASE
| UPPERCASE
| LIST or BASIS
| BASIS or LIST (of vectors)
| True ''MATRIX''
| ''MATRIX''
|}
|}


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=== Objects ===
=== Objects ===
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|+ style="font-size: 105%;" | Objects
|+ style="font-size: 105%;" |  
|-
|-
! rowspan="2" | Equivalent<br />expressions
! rowspan="2" | Equivalent<br />expressions
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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}</math><br />
𝒕\textbf{i}</math>
<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}}
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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}</math><br />
a - o \\
<math>a - o</math><br />
𝒓\textbf{i}</math>
<math>𝒓\textbf{i}</math>
| <math>\mathrm{e}</math>
| <math>\mathrm{e}</math>
| [[error|(Interval) error]]
| [[error|(Interval) error]]
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| Mnemonic: <math>\textbf{o}</math>riginal size list
| Mnemonic: <math>\textbf{o}</math>riginal size list
|-
|-
| <math>𝒕\mathrm{T} \\
| <math>𝒕\mathrm{T}</math><br />
𝒈M\mathrm{T}</math>
<math>𝒈M\mathrm{T}</math>
| <math>\textbf{a}</math>
| <math>\textbf{a}</math>
| [[Tempered target-interval size list]]
| [[Tempered target-interval size list]]
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| 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}</math><br />
\textbf{a} - \textbf{o} \\
<math>\textbf{a} - \textbf{o}</math><br />
𝒓\mathrm{T}
<math>𝒓\mathrm{T}</math>
</math>
| <math>\textbf{e}</math>
| <math>\textbf{e}</math>
| [[Target-interval error list]]
| [[Target-interval error list]]
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{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
|+ style="font-size: 105%;" | Units
|+ style="font-size: 105%;" |  
|-
|-
! Symbol
! Symbol
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{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
|+ style="font-size: 105%;" | Tuning schemes
|+ style="font-size: 105%;" |  
|-
|-
! Damage weight
! Damage weight
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=== Damages ===
=== Damages ===
{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
|+ style="font-size: 105%;" | Damages
|+ style="font-size: 105%;" |  
|-
|-
! colspan="2" | Quantity
! colspan="2" | Quantity
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=== Complexity and simplicity ===
=== Complexity and simplicity ===
{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
|+ style="font-size: 105%;" | Complexity and simplicity
|+ style="font-size: 105%;" |  
|-
|-
! colspan="2" | Quantity
! colspan="2" | Quantity
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=== Objects ===
=== Objects ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Objects
|+ style="font-size: 105%;" |  
|-
|-
! rowspan="2" | Equivalent expressions
! rowspan="2" | Equivalent expressions
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|  
|  
|-
|-
| <math>𝒕 - 𝒋 \\
| <math>𝒕 - 𝒋</math><br />
1200×\slant{\mathbf{1}}L(P - I)</math>
<math>1200×\slant{\mathbf{1}}L(P - I)</math>
| <math>𝒓</math>
| <math>𝒓</math>
| [[retuning map|Retuning (or mistuning) map]]
| [[retuning map|Retuning (or mistuning) map]]
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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}</math><br />
𝒕\textbf{i}</math>
<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}}
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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}</math><br />
a - o \\
<math>a - o</math><br />
𝒓\textbf{i}</math>
<math>𝒓\textbf{i}</math>
| <math>\mathrm{e}</math>
| <math>\mathrm{e}</math>
| [[error|(Interval) error]]
| [[error|(Interval) error]]
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| 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}</math><br />
𝒓\mathrm{T} \\
<math>𝒓\mathrm{T}</math><br />
\textbf{a} - \textbf{o}</math>
<math>\textbf{a} - \textbf{o}</math>
| <math>\textbf{e}</math>
| <math>\textbf{e}</math>
| [[Target-interval error list]]
| [[Target-interval error list]]
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|-
|-
|  
|  
| <math>\llzigzag·\,\rrzigzag\! _p</math>
| {{llzigzag}}<math>\,·\,</math>{{rrzigzag}}<math>_p</math>
| [[Power sum]] (<math>p</math>-sum)
| [[Power sum]] (<math>p</math>-sum)
|  
|  
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=== Tuning schemes ===
=== Tuning schemes ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Tuning schemes
|+ style="font-size: 105%;" |  
|-
|-
! colspan="3" rowspan="3" | Retuning (or mistuning) magnitude
! colspan="3" rowspan="3" | Retuning (or mistuning) magnitude
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=== Damages ===
=== Damages ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Damages
|+ style="font-size: 105%;" |  
|-
|-
! colspan="2" | Quantity
! colspan="2" | Quantity
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=== Complexity and simplicity ===
=== Complexity and simplicity ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Complexity and simplicity
|+ style="font-size: 105%;" |  
|-
|-
! colspan="2" | Quantity
! colspan="2" | Quantity
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=== Objects ===
=== Objects ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Objects
|+ style="font-size: 105%;" |  
|-
|-
! rowspan="2" | Equivalent expressions
! rowspan="2" | Equivalent expressions
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|  
|  
|-
|-
| <math>1200×\slant{\mathbf{1}}LG_{\text{j}}M_{\text{j}} \\
| <math>1200×\slant{\mathbf{1}}LG_{\text{j}}M_{\text{j}}</math><br />
1200×\slant{\mathbf{1}}L \\
<math>1200×\slant{\mathbf{1}}L</math><br />
𝒈_{\text{j}}M_{\text{j}}</math>
<math>𝒈_{\text{j}}M_{\text{j}}</math>
| <math>𝒋</math>
| <math>𝒋</math>
| [[just tuning map|Just(-prime) tuning map]]
| [[just tuning map|Just(-prime) tuning map]]
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\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] \left(\cancel{1}, \cancel{d}\right) \end{array}
\begin{array} {c} \slant{\mathbf{1}} \\[-3pt] \left(\cancel{1}, \cancel{d}\right) \end{array}
\! \!  
\! \!  
\begin{array} {c} L \\[-3pt] \left(\cancel{d}, \cancel{d}) \end{array}
\begin{array} {c} L \\[-3pt] \left(\cancel{d}, \cancel{d}\right) \end{array}
\\ \scriptsize \quad  
\\ \scriptsize \quad  
\! \!  
\! \!  
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|  
|  
|-
|-
| <math>1200×\slant{\mathbf{1}}LGM \\
| <math>1200×\slant{\mathbf{1}}LGM</math><br />
1200×\slant{\mathbf{1}}LP \\
<math>1200×\slant{\mathbf{1}}LP</math><br />
𝒈M</math>
<math>𝒈M</math>
| <math>𝒕</math>
| <math>𝒕</math>
| [[tuning map|(Tempered-prime) tuning map]]
| [[tuning map|(Tempered-prime) tuning map]]
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|  
|  
|-
|-
| <math>𝒕 - 𝒋 \\
| <math>𝒕 - 𝒋</math><br />
1200×\slant{\mathbf{1}}L(P - I)</math>
<math>1200×\slant{\mathbf{1}}L(P - I)</math>
| <math>𝒓</math>
| <math>𝒓</math>
| [[retuning map|Retuning (or mistuning) map]]
| [[retuning map|Retuning (or mistuning) map]]
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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}</math><br />
𝒕\textbf{i}</math>
<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}}
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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}</math><br />
a - o \\
<math>a - o</math><br />
𝒓\textbf{i}</math>
<math>𝒓\textbf{i}</math>
| <math>\mathrm{e}</math>
| <math>\mathrm{e}</math>
| [[error|(Interval) error]]
| [[error|(Interval) error]]
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| 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}</math><br />
𝒓\mathrm{T} \\
<math>𝒓\mathrm{T}</math><br />
\textbf{a} - \textbf{o}</math>
<math>\textbf{a} - \textbf{o}</math>
| <math>\textbf{e}</math>
| <math>\textbf{e}</math>
| [[target-interval error list]]
| [[target-interval error list]]
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| Entry-wise reciprocal of <math>C</math>
| Entry-wise reciprocal of <math>C</math>
|-
|-
| <math>\abs{\textbf{e}} W \\
| <math>\abs{\textbf{e}} W</math><br />
1200×\slant{\mathbf{1}}L\abs{P - I} \mathrm{T}W</math>
<math>1200×\slant{\mathbf{1}}L\abs{P - I} \mathrm{T}W</math>
| <math>\textbf{d}</math>
| <math>\textbf{d}</math>
| [[Target-interval damage list]]
| [[Target-interval damage list]]
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|-
|-
|  
|  
| <math>\llzigzag·\,\rrzigzag\! _p</math>
| {{llzigzag}}<math>\,·\,</math>{{rrzigzag}}<math>_p</math>
| [[Power sum]] (<math>p</math>-sum)
| [[Power sum]] (<math>p</math>-sum)
|  
|  
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|  
|  
|-
|-
| <math>G_cF^{-1}FM_c \\
| <math>G_cF^{-1}FM_c</math><br />
\mathrm{V}\textit{Λ}\mathrm{V}^{-1}</math>
<math>\mathrm{V}\textit{Λ}\mathrm{V}^{-1}</math>
| <math>P</math>
| <math>P</math>
| [[Projection matrix|Projection (matrix)]]
| [[Projection matrix|Projection (matrix)]]
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=== Units ===
=== Units ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Units
|+ style="font-size: 105%;" |  
|-
|-
! Symbol
! Symbol
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=== Tuning schemes ===
=== Tuning schemes ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Tuning schemes
|+ style="font-size: 105%;" |  
|-
|-
! colspan="6" rowspan="3" | Retuning (or mistuning) magnitude
! colspan="6" rowspan="3" | Retuning (or mistuning) magnitude
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| colspan="3" | <none>
| colspan="3" | <none>
| rowspan="2" | (t)
| rowspan="2" | (t)
| rowspan="2" | Raxicab
| rowspan="2" | Taxicab
| rowspan="2" | 1
| rowspan="2" | 1
| rowspan="4" | S
| rowspan="4" | S
Line 4,097: Line 4,096:
=== Damages ===
=== Damages ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Damages
|+ style="font-size: 105%;" |  
|-
|-
! colspan="2" | Quantity
! colspan="2" | Quantity
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=== Complexity and simplicity ===
=== Complexity and simplicity ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | Complexity and simplicity
|+ style="font-size: 105%;" |  
|-
|-
! colspan="2" | Quantity
! colspan="2" | Quantity
Line 4,313: Line 4,312:
| Black star
| Black star
|-
|-
| ⎄{{''}}
| ⎄&#39;&#39;
| ′
| ′
| prime mark
| prime mark
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