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

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{{breadcrumb}}
This is an appendix to [[Dave Keenan]] & [[Douglas Blumeyer]]'s guide to RTT, or "[[D&D's guide]]" for short. The tables in this article present our recommendations for communicating about [[regular temperament theory]] (RTT), in particular the names and notations for temperament matrices, tuning schemes, interval complexities, and measurement units.  
This is an appendix to [[Dave Keenan]] & [[Douglas Blumeyer]]'s guide to RTT, or "[[D&D's guide]]" for short. The tables in this article present our recommendations for communicating about [[regular temperament theory]] (RTT), in particular the names and notations for temperament matrices, tuning schemes, interval complexities, and measurement units.  


Our recommendations are designed to make this topic easy to learn for musicians who do not have technical backgrounds, though we have generally deferred to established mathematical, scientific, and engineering conventions for the benefit of those who do.
Our recommendations are designed to make this topic easy to learn for musicians who do not have technical backgrounds, though we have generally deferred to established mathematical, scientific, and engineering conventions for the benefit of those who do.


For more information on our variation on extended bra-ket notation, please see [[Extended_bra-ket_notation#Variant_including_curly_and_square_brackets|Extended bra-ket notation: Variant including curly and square brackets]].
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 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:


{| class="wikitable center-all"  
{| class="wikitable center-all"
|-
!  
!  
| Units →
| units →
! rowspan="2" |  
! rowspan="2" |  
| Simple units
| simple units
| Compound or no units
| compound or no units
|-
|-
| ↓ Order
| ↓ order
| ↓ Style →
| ↓ style →
| Upright
| upright
| ''Italic''
| ''italic''
 
|-
|-
! scope="col" height="8px" ! colspan="2" |  
! scope="col" height="8px" ! colspan="2" |  
Line 25: Line 26:
|-
|-
| 0
| 0
| Plain
| plain
! rowspan="3" |  
! rowspan="3" |  
| Scalar with simple unit
| scalar with simple unit
| ''Scalar'' with no unit
| ''scalar'' with no unit
|-
|-
| 1
| 1
| '''Bold'''
| '''bold'''
| '''Vector'''
| '''vector'''
| '''''Map''''' (row vector)
| '''''map''''' (row vector)
|-
|-
| 2
| 2
| UPPERCASE
| UPPERCASE
| LIST or BASIS
| LIST or BASIS
| True ''MATRIX''
| true ''MATRIX''
|}
|}


We present our conventions here in three separate sections, one for each level of this article series: '''basic''', '''intermediate''', and '''advanced'''. The basic section contains only information covered in the basic part of the series, the intermediate section contains both basic and intermediate, and the advanced section contains it all (that is to say, the sections are cumulative)<ref group="note">The advanced section also contains conventions collected from other RTT-related articles Dave and Douglas have contributed to but are outside the main guide to RTT series.</ref>. We expect that for most readers, the basic tier will be the best reference (this is the reference designed primarily for musicians interested in RTT, as opposed to scientists, engineers, mathematicians, or theoreticians), and so we've left the other two sections initially collapsed.
We present our conventions here in three separate sections, one for each level of this article series: '''basic''', '''intermediate''', and '''advanced'''. The basic section contains only information covered in the basic part of the series, the intermediate section contains both basic and intermediate, and the advanced section contains it all (that is to say, the sections are cumulative)<ref>The advanced section also contains conventions collected from other RTT-related articles Dave and Douglas have contributed to but are outside the main guide to RTT series.</ref>. We expect that for most readers, the basic tier will be the best reference (this is the reference designed primarily for musicians interested in RTT, as opposed to scientists, engineers, mathematicians, or theoreticians), and so we've left the other two sections initially collapsed.


== Basic ==
== Basic ==
=== Objects ===
=== Objects ===
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
|-
! rowspan="2" | equivalent expressions
! rowspan="2" | equivalent expressions
! rowspan="2" | variable
! rowspan="2" | variable
Line 325: Line 327:
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}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Example_3| tempered (interval) size]]
| <math>\scriptsize  
| <math>\scriptsize  
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
Line 423: Line 425:
|  
|  
| <math>c</math>
| <math>c</math>
| {{subpage|tuning_fundamentals|uprev|s=complexity}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity| 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>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{(C)}</math>
| <math>\small\mathsf{(C)}</math>
| complexity weight
| complexity weight
Line 553: Line 555:
| <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}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Primes| 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 659: Line 661:
|  
|  
| <math>C</math>
| <math>C</math>
| {{subpage|tuning_fundamentals|uprev|s=complexity-weight_damage|text=target-interval complexity weight matrix}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage| 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>
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| <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}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity-weight_damage| 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>
Line 691: Line 693:
| <math>𝒔</math>
| <math>𝒔</math>
| <math>s_i</math>
| <math>s_i</math>
| entry-wise reciprocal of <math>C</math>
| entrywise 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>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}  
Line 817: Line 819:


=== Units ===
=== Units ===
We recommend using a narrow no-break space (U+202F) between quantities and their units.<ref group="note">Per https://physics.nist.gov/cuu/Units/checklist.html and https://academia.stackexchange.com/questions/54885/should-there-be-a-space-between-a-value-and-the-units-used
We recommend using a narrow no-break space (U+202F) between quantities and their units.<ref>Per https://physics.nist.gov/cuu/Units/checklist.html and https://academia.stackexchange.com/questions/54885/should-there-be-a-space-between-a-value-and-the-units-used
.</ref> For how to type this, see the [[#WinCompose| WinCompose]] section below.
.</ref> For how to type this, see the [[#WinCompose| WinCompose]] section below.


{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
|-
! symbol
! symbol
! name
! name
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| yes
| yes
|-
|-
| <math>\mathsf{¢}</math><ref group="note">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
|  
|  
Line 863: Line 866:


=== Tuning schemes ===
=== Tuning schemes ===
Copied from {{subpage|tuning fundamentals|uprev|s=Systematic tuning scheme names}}.
Copied from [[Dave Keenan & Douglas Blumeyer's guide to RTT: tuning fundamentals#Systematic tuning scheme names]].


{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
Line 904: Line 907:
=== Damages ===
=== Damages ===
{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
|-
! colspan="2" | quantity
! colspan="2" | quantity
! colspan="2" | unit
! colspan="2" | unit
Line 930: Line 934:
=== Complexity and simplicity ===
=== Complexity and simplicity ===
{| class="wikitable center-all mw-collapsible"
{| class="wikitable center-all mw-collapsible"
|-
! colspan="2" | quantity
! colspan="2" | quantity
! colspan="2" | unit
! colspan="2" | unit
Line 959: Line 964:
=== Objects ===
=== Objects ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|-
! rowspan="2" | equivalent expressions
! rowspan="2" | equivalent expressions
! rowspan="2" | variable
! rowspan="2" | variable
Line 1,247: Line 1,253:
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}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Example_3| tempered (interval) size]]
| <math>\scriptsize  
| <math>\scriptsize  
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
Line 1,345: Line 1,351:
|  
|  
| <math>c</math>
| <math>c</math>
| {{subpage|tuning_fundamentals|uprev|s=complexity}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity| complexity]]
| colspan="3" | (see complexities section of complexities and simplicities table)
| colspan="3" | (see complexities section of complexities and simplicities table)
|  
|  
Line 1,457: Line 1,463:
| <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}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Primes| target-interval (just) size list]]
| <math>\scriptsize  
| <math>\scriptsize  
\begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
\begin{array} {c} 𝒋 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
Line 1,559: Line 1,565:
|  
|  
| <math>C</math>
| <math>C</math>
| {{subpage|tuning_fundamentals|uprev|s=complexity-weight damage|text=target-interval complexity weight matrix}}
| [[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)
| colspan="3" | (see complexities section of complexities and simplicities table)
|  
|  
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| <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}}
| [[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)
| colspan="3" | (see simplicities section of complexities and simplicities table)
|  
|  
Line 1,587: Line 1,593:
| <math>𝒔</math>
| <math>𝒔</math>
| <math>s_i</math>
| <math>s_i</math>
| entry-wise reciprocal of <math>C</math>
| entrywise reciprocal of <math>C</math>
|-
|-
| <math>| \textbf{e}| W</math>
| <math>| \textbf{e}| W</math>
Line 1,777: Line 1,783:
|  
|  
| <math>q</math>
| <math>q</math>
| {{subpage|all-interval_tuning_schemes|uprev|s=Dual norms|text=interval complexity norm power}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms| interval complexity norm power]]
|  
|  
|  
|  
Line 1,813: Line 1,819:
| <math>\dfrac1{1-\frac1q}</math>
| <math>\dfrac1{1-\frac1q}</math>
| <math>\text{dual}(q)</math>
| <math>\text{dual}(q)</math>
| {{subpage|all-interval tuning schemes|uprev|s=Dual norms|text=dual norm power}}
| [[Dave_Keenan_%26_Douglas_Blumeyer's_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms| dual norm power]]
|  
|  
|  
|  
Line 2,118: Line 2,124:
=== Complexity and simplicity ===
=== Complexity and simplicity ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|-
! colspan="2" | quantity
! colspan="2" | quantity
! colspan="2" | unit
! colspan="2" | unit
Line 2,150: Line 2,157:
=== Objects ===
=== Objects ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|-
! rowspan="2" | equivalent expressions
! rowspan="2" | equivalent expressions
! rowspan="2" | variable
! rowspan="2" | variable
Line 2,510: Line 2,518:
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}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Example_3| tempered (interval) size]]
| <math>\scriptsize  
| <math>\scriptsize  
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
\begin{array} {c} 𝒕 \\[-2pt] {\small\mathsf{¢}} \hspace{-2mu} / \hspace{-2mu} \cancel{𝗽} \end{array}  
Line 2,608: Line 2,616:
|  
|  
| <math>c</math>
| <math>c</math>
| {{subpage|tuning_fundamentals|uprev|s=complexity}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Complexity| complexity]]
| colspan="3" | (see complexities section of complexities and simplicities table)
| colspan="3" | (see complexities section of complexities and simplicities table)
|  
|  
Line 2,720: Line 2,728:
| <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}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#Primes| 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 2,822: Line 2,830:
|  
|  
| <math>C</math>
| <math>C</math>
| {{subpage|tuning fundamentals|uprev|s=complexity-weight damage|text=target-interval complexity weight matrix}}
| [[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)
| colspan="3" | (see complexities section of complexities and simplicities table)
|  
|  
Line 2,838: Line 2,846:
| <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}}
| [[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)
| colspan="3" | (see simplicities section of complexities and simplicities table)
|  
|  
Line 2,850: Line 2,858:
| <math>𝒔</math>
| <math>𝒔</math>
| <math>s_i</math>
| <math>s_i</math>
| entry-wise reciprocal of <math>C</math>
| entrywise reciprocal of <math>C</math>
|-
|-
| <math>| \textbf{e}| W \\
| <math>| \textbf{e}| W \\
Line 3,005: Line 3,013:
|  
|  
| <math>X</math>
| <math>X</math>
| {{subpage|alternative complexities|uprev|s=Prescaling_vs._pretransforming|text=complexity pretransformer}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Prescaling_vs_pretransforming| complexity pretransformer]]
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref group="note">In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
| <math>\small\mathsf{𝟙}\scriptsize\mathsf{(C)}</math> or <math>\small\mathsf{𝟙}\scriptsize\mathsf{(}</math><alt>-<math>\scriptsize\mathsf{C)}</math><ref>In these tables, "alternative" means any complexity other than the default of log-product complexity, and "alt" stands for its abbreviation.</ref>
| <math>\small\mathsf{(C)}</math> or <math>\small\mathsf{(}</math><alt>-<math>\small\mathsf{C)}</math>
| <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 3,041: Line 3,049:
|  
|  
| <math>q</math>
| <math>q</math>
| {{subpage|all-interval_tuning_schemes|uprev|s=dual_norms|text=interval complexity norm power}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms| interval complexity norm power]]
|  
|  
|  
|  
Line 3,077: Line 3,085:
| <math>\dfrac1{1-\frac1q}</math>
| <math>\dfrac1{1-\frac1q}</math>
| <math>\text{dual}(q)</math>
| <math>\text{dual}(q)</math>
| {{subpage|all-interval tuning schemes|uprev|s=dual_norms|text=dual norm power}}
| [[Dave_Keenan_%26_Douglas_Blumeyer's_guide_to_RTT:_all-interval_tuning_schemes#Dual_norms| dual norm power]]
|  
|  
|  
|  
Line 3,133: Line 3,141:
|  
|  
| <math>𝒑</math>
| <math>𝒑</math>
| {{subpage|alternative complexities|uprev|s=formulas|text=prime list}}<ref group="note">May be used for a prime-limit or for any prime-only list.</ref>
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Formulas| prime list]]<ref>May be used for a prime-limit or for any prime-only list.</ref>
|  
|  
|  
|  
Line 3,151: Line 3,159:
|  
|  
| <math>\slant{\mathbf{1}}</math>
| <math>\slant{\mathbf{1}}</math>
| {{subpage|alternative complexities|uprev|s=proportionality to size|text=summation map}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Proportionality_to_size| summation map]]
|  
|  
|  
|  
Line 3,169: Line 3,177:
|  
|  
| <math>1200</math>
| <math>1200</math>
| {{subpage|alternative complexities|uprev|s=Proportionality to size|text=octaves-to-cents conversion}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Proportionality_to_size| octaves-to-cents conversion]]
|  
|  
| ¢/oct
| ¢/oct
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|  
|  
| <math>Z</math>
| <math>Z</math>
| {{subpage|alternative complexities|uprev|s=Normifying: size-sensitizing matrix|text=size-sensitizing matrix}}
| [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_alternative_complexities#Normifying:_size-sensitizing_matrix| size-sensitizing matrix]]
|  
|  
|  
|  
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=== Units ===
=== Units ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|-
! symbol
! symbol
! name
! name
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=== Tuning schemes ===
=== Tuning schemes ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|-
! colspan="6" rowspan="3" | retuning (or mistuning) magnitude
! colspan="6" rowspan="3" | retuning (or mistuning) magnitude
! colspan="12" rowspan="1" | damage
! colspan="12" rowspan="1" | damage
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=== Damages ===
=== Damages ===
{| class="wikitable center-all mw-collapsible mw-collapsed"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|-
! colspan="2" | quantity
! colspan="2" | quantity
! colspan="2" | unit
! colspan="2" | unit
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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"
|-
! colspan="2" | quantity
! colspan="2" | quantity
! colspan="2" | unit
! colspan="2" | unit
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=== Table of noteworthy sequences ===
=== Table of noteworthy sequences ===
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|-
! scope="col" width="130px" | Compose-key sequence
! scope="col" width="130px" | Compose-key sequence
! scope="col" width="75px" | resulting text
! scope="col" width="75px" | resulting text
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| ⎄(.)
| ⎄(.)
| ⨀
| ⨀
| entry-wise vector multiplication operator
| entrywise vector multiplication operator
|-
|-
| ⎄(..)
| ⎄(..)
| ⊙
| ⊙
| alternative entry-wise vector multiplication operator
| alternative entrywise vector multiplication operator
|-
|-
| ⎄(/)
| ⎄(/)
| ⊘
| ⊘
| entry-wise vector division operator
| entrywise vector division operator
|-
|-
! colspan="3" | Mathematical letter and digit prefixes
! colspan="3" | Mathematical letter and digit prefixes
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== Footnotes ==
== Footnotes ==
<references group="note" />
<references />


[[Category:Dave Keenan & Douglas Blumeyer's guide to RTT]]
[[Category:Dave Keenan & Douglas Blumeyer's guide to RTT]]
[[Category:Tuning]]
[[Category:Tuning]]
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