User:Frostburn/SonicWeave: Difference between revisions
m →Real linear types: Include missing lower tier. |
Sketch up to real logarithmic types. |
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Theres a linear domain where 3/2 + 3/2 means 3 (as a ratio of two frequencies) and a logarithmic domain where 3\2 + 3\2 means 8 (as a ratio of two frequencies). | Theres a linear domain where 3/2 + 3/2 means 3 (as a ratio of two frequencies) and a logarithmic domain where 3\2 + 3\2 means 8 (as a ratio of two frequencies). | ||
== Tiers == | == Tiers == | ||
Types are organized into tiers consisting of integers, rationals, radicals (i.e. rationals raised to rational powers) and reals. | Types are organized into tiers consisting of booleans, integers, rationals, radicals (i.e. rationals raised to rational powers) and reals. | ||
<math> | <math> | ||
\mathbb{Z} \subset \mathbb{Q} \subset \mathrm{radical} \subset \mathbb{R} | \mathbb{B} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathrm{radical} \subset \mathbb{R} | ||
</math> | </math> | ||
== Type system == | == Type system == | ||
| Line 17: | Line 17: | ||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
\mathrm{boolean} &= \{0, 1\} \\ | \mathrm{boolean} &= \mathbb{B} = \{0, 1\} \\ | ||
\mathrm{integer} &= \mathbb{Z} \supset \{1, 2, 3, 4\} \\ | \mathrm{integer} &= \mathbb{Z} \supset \{1, 2, 3, 4\} \\ | ||
\mathrm{fraction} &\supset \{3/2, 5/3\} \\ | \mathrm{fraction} &\supset \{3/2, 5/3\} \\ | ||
\mathrm{decimal} &\supset \{(1.2), (1.4)\} \\ | \mathrm{decimal} &\supset \{(1.2), (1.4), (1,5)\} \\ | ||
\mathrm{rational} &= \mathbb{Q} = \mathrm{integer} \cup \mathrm{fraction} \cup \mathrm{decimal} | \mathrm{rational} &= \mathbb{Q} = \mathrm{integer} \cup \mathrm{fraction} \cup \mathrm{decimal} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Note: Decimals require surrounding parenthesis when using a decimal dot but may be entered plain when using a decimal comma. | |||
=== Radical linear types === | === Radical linear types === | ||
<math> | <math> | ||
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\begin{align} | \begin{align} | ||
\mathrm{integer!} &\supset \{69!, 420!\} \\ | \mathrm{integer!} &\supset \{69!, 420!\} \\ | ||
\mathrm{decimal!} &\supset \{3.14159!, 2.718!\} \\ | \mathrm{decimal!} &\supset \{(3.14159!), (2.718!)\} \\ | ||
\mathrm{real} &= \mathbb{R} = \mathrm{radical} \cup \mathrm{integer!} \cup \mathrm{decimal!} | \mathrm{real} &= \mathbb{R} = \mathrm{radical} \cup \mathrm{integer!} \cup \mathrm{decimal!} | ||
\end{align} | \end{align} | ||
| Line 41: | Line 44: | ||
Note: Real linear types are mostly an artifact of the catch-all property extended time monzos. Not recommended for everyday use. | Note: Real linear types are mostly an artifact of the catch-all property extended time monzos. Not recommended for everyday use. | ||
=== Rational logarithmic types === | |||
<math> | |||
\begin{align} | |||
\mathrm{fjs} &\supset \{ \mathrm{P5}, \mathrm{M3}^5 \} \\ | |||
\mathrm{ji} &= \mathrm{fjs} | |||
\end{align} | |||
</math> | |||
=== Radical logarithmic types === | |||
<math> | |||
\begin{align} | |||
\mathrm{nedo} &\supset \{ 5\backslash 7, 7\backslash 12 \} \\ | |||
\mathrm{nedji} &\supset \{ 7\backslash 13<3>, 1\backslash 3<5/3> \} \\ | |||
\mathrm{cents} &\supset \{.5, 1.955, 100., c \} \\ | |||
\mathrm{monzo} &\supset \{[-4, 4, -1>, [1/2, 1/3> \} \\ | |||
\mathrm{xfjs} &\supset \{\mathrm{n3}, \mathrm{m4.5}\} \\ | |||
\mathrm{pitch} &= \mathrm{ji} \cup \mathrm{nedo} \cup \mathrm{nedji} \cup \mathrm{cents} \cup \mathrm{monzo} \cup \mathrm{xfjs} | |||
\end{align} | |||
</math> | |||
=== Real logarithmic types === | |||
<math> | |||
\begin{align} | |||
\mathrm{cents!} &\supset \{.777!, 1901.955!, 69.!, c!\} \\ | |||
\mathrm{freePitch} &= \mathrm{pitch} \cup \mathrm{cents!} | |||
\end{align} | |||
</math> | |||
Similarly, the free pitch type is unlikely to be relevant in day-to-day use of SW3. | |||
Revision as of 11:49, 10 December 2023
This is my second attempt at creating a a Domain Specific Language (DSL) called SonicWeave for manipulating frequencies, ratios and pitches in Scale Workshop 3.
Still very much a work in progress. Expect things to shift around as I design a parseable grammar.
Values
Values consist of strings, functions and extended time monzos which combine a rational time exponent, rational prime exponents, a multiplicative rational residual and a catch-all real cents offset.
Domains
Theres a linear domain where 3/2 + 3/2 means 3 (as a ratio of two frequencies) and a logarithmic domain where 3\2 + 3\2 means 8 (as a ratio of two frequencies).
Tiers
Types are organized into tiers consisting of booleans, integers, rationals, radicals (i.e. rationals raised to rational powers) and reals.
[math]\displaystyle{ \mathbb{B} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathrm{radical} \subset \mathbb{R} }[/math]
Type system
Values are dressed into types to implement domain-specific operator overloading and type-aware function overloading.
Rational linear types
[math]\displaystyle{ \begin{align} \mathrm{boolean} &= \mathbb{B} = \{0, 1\} \\ \mathrm{integer} &= \mathbb{Z} \supset \{1, 2, 3, 4\} \\ \mathrm{fraction} &\supset \{3/2, 5/3\} \\ \mathrm{decimal} &\supset \{(1.2), (1.4), (1,5)\} \\ \mathrm{rational} &= \mathbb{Q} = \mathrm{integer} \cup \mathrm{fraction} \cup \mathrm{decimal} \end{align} }[/math]
Note: Decimals require surrounding parenthesis when using a decimal dot but may be entered plain when using a decimal comma.
Radical linear types
[math]\displaystyle{ \begin{align} \mathrm{radicalExpression} &\supset \{\sqrt{3}, 2^\frac{5}{3}\} \\ \mathrm{radical} &= \mathrm{rational} \cup \mathrm{radicalExpression} \end{align} }[/math]
Real linear types
[math]\displaystyle{ \begin{align} \mathrm{integer!} &\supset \{69!, 420!\} \\ \mathrm{decimal!} &\supset \{(3.14159!), (2.718!)\} \\ \mathrm{real} &= \mathbb{R} = \mathrm{radical} \cup \mathrm{integer!} \cup \mathrm{decimal!} \end{align} }[/math]
Note: Real linear types are mostly an artifact of the catch-all property extended time monzos. Not recommended for everyday use.
Rational logarithmic types
[math]\displaystyle{ \begin{align} \mathrm{fjs} &\supset \{ \mathrm{P5}, \mathrm{M3}^5 \} \\ \mathrm{ji} &= \mathrm{fjs} \end{align} }[/math]
Radical logarithmic types
[math]\displaystyle{ \begin{align} \mathrm{nedo} &\supset \{ 5\backslash 7, 7\backslash 12 \} \\ \mathrm{nedji} &\supset \{ 7\backslash 13<3>, 1\backslash 3<5/3> \} \\ \mathrm{cents} &\supset \{.5, 1.955, 100., c \} \\ \mathrm{monzo} &\supset \{[-4, 4, -1>, [1/2, 1/3> \} \\ \mathrm{xfjs} &\supset \{\mathrm{n3}, \mathrm{m4.5}\} \\ \mathrm{pitch} &= \mathrm{ji} \cup \mathrm{nedo} \cup \mathrm{nedji} \cup \mathrm{cents} \cup \mathrm{monzo} \cup \mathrm{xfjs} \end{align} }[/math]
Real logarithmic types
[math]\displaystyle{ \begin{align} \mathrm{cents!} &\supset \{.777!, 1901.955!, 69.!, c!\} \\ \mathrm{freePitch} &= \mathrm{pitch} \cup \mathrm{cents!} \end{align} }[/math]
Similarly, the free pitch type is unlikely to be relevant in day-to-day use of SW3.