Dave Keenan & Douglas Blumeyer's guide to RTT/Conventions for names, variables, units, and notations: Difference between revisions
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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. | 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. | ||
== Basic == | == Basic == | ||
| Line 325: | Line 325: | ||
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}} | ||
| <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 423: | ||
| | | | ||
| <math>c</math> | | <math>c</math> | ||
| | | {{subpage|tuning_fundamentals|uprev|s=complexity}} | ||
| <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{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{(C)}</math> | | <math>\small\mathsf{(C)}</math> | ||
| complexity weight | | complexity weight | ||
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| <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}} | ||
| <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 659: | ||
| | | | ||
| <math>C</math> | | <math>C</math> | ||
| | | {{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> | ||
| Line 677: | Line 677: | ||
| <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}} | ||
| <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 695: | Line 695: | ||
| <math>| \textbf{e}| W</math> | | <math>| \textbf{e}| W</math> | ||
| <math>\textbf{d}</math> | | <math>\textbf{d}</math> | ||
| [[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> | | [[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} | ||
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=== Units === | === Units === | ||
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 | 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 | ||
.</ref> For how to type this, see the [[#WinCompose| WinCompose]] section below. | .</ref> For how to type this, see the [[#WinCompose| WinCompose]] section below. | ||
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| yes | | yes | ||
|- | |- | ||
| <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> | | <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> | ||
| cents | | cents | ||
| | | | ||
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=== Tuning schemes === | === Tuning schemes === | ||
Copied from | Copied from {{subpage|tuning fundamentals|uprev|s=Systematic tuning scheme names}}. | ||
{| class="wikitable center-all mw-collapsible" | {| class="wikitable center-all mw-collapsible" | ||
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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}} | ||
| <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>c</math> | | <math>c</math> | ||
| | | {{subpage|tuning_fundamentals|uprev|s=complexity}} | ||
| 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>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}} | ||
| <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 1,559: | ||
| | | | ||
| <math>C</math> | | <math>C</math> | ||
| | | {{subpage|tuning_fundamentals|uprev|s=complexity-weight damage|text=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}} | ||
| colspan="3" | (see simplicities section of complexities and simplicities table) | | colspan="3" | (see simplicities section of complexities and simplicities table) | ||
| | | | ||
| Line 1,777: | Line 1,777: | ||
| | | | ||
| <math>q</math> | | <math>q</math> | ||
| | | {{subpage|all-interval_tuning_schemes|uprev|s=Dual norms|text=interval complexity norm power}} | ||
| | | | ||
| | | | ||
| Line 1,813: | Line 1,813: | ||
| <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}} | ||
| | | | ||
| | | | ||
| Line 2,510: | Line 2,510: | ||
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}} | ||
| <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 2,608: | ||
| | | | ||
| <math>c</math> | | <math>c</math> | ||
| | | {{subpage|tuning_fundamentals|uprev|s=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 2,720: | ||
| <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}} | ||
| <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 2,822: | ||
| | | | ||
| <math>C</math> | | <math>C</math> | ||
| | | {{subpage|tuning fundamentals|uprev|s=complexity-weight damage|text=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 2,838: | ||
| <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}} | ||
| colspan="3" | (see simplicities section of complexities and simplicities table) | | colspan="3" | (see simplicities section of complexities and simplicities table) | ||
| | | | ||
| Line 3,005: | Line 3,005: | ||
| | | | ||
| <math>X</math> | | <math>X</math> | ||
| | | {{subpage|alternative complexities|uprev|s=Prescaling_vs._pretransforming|text=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>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 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{(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 3,041: | ||
| | | | ||
| <math>q</math> | | <math>q</math> | ||
| | | {{subpage|all-interval_tuning_schemes|uprev|s=dual_norms|text=interval complexity norm power}} | ||
| | | | ||
| | | | ||
| Line 3,077: | Line 3,077: | ||
| <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}} | ||
| | | | ||
| | | | ||
| Line 3,133: | Line 3,133: | ||
| | | | ||
| <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> | ||
| | | | ||
| | | | ||
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| | | | ||
| <math>\slant{\mathbf{1}}</math> | | <math>\slant{\mathbf{1}}</math> | ||
| | | {{subpage|alternative complexities|uprev|s=proportionality to size|text=summation map}} | ||
| | | | ||
| | | | ||
| Line 3,169: | Line 3,169: | ||
| | | | ||
| <math>1200</math> | | <math>1200</math> | ||
| | | {{subpage|alternative complexities|uprev|s=Proportionality to size|text=octaves-to-cents conversion}} | ||
| | | | ||
| ¢/oct | | ¢/oct | ||
| Line 3,187: | Line 3,187: | ||
| | | | ||
| <math>Z</math> | | <math>Z</math> | ||
| | | {{subpage|alternative complexities|uprev|s=Normifying: size-sensitizing matrix|text=size-sensitizing matrix}} | ||
| | | | ||
| | | | ||
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== Footnotes == | == Footnotes == | ||
<references /> | <references group="note" /> | ||
[[Category:Dave Keenan & Douglas Blumeyer's guide to RTT]] | [[Category:Dave Keenan & Douglas Blumeyer's guide to RTT]] | ||
[[Category:Tuning]] | [[Category:Tuning]] | ||