User:Frostburn/SonicWeave: Difference between revisions
Sketch up to real logarithmic types. |
Expand type hierarchy but leave TODOs for obscure types. |
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\mathrm{xfjs} &\supset \{\mathrm{n3}, \mathrm{m4.5}\} \\ | \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} | \mathrm{pitch} &= \mathrm{ji} \cup \mathrm{nedo} \cup \mathrm{nedji} \cup \mathrm{cents} \cup \mathrm{monzo} \cup \mathrm{xfjs} | ||
\end{align} | |||
</math> | |||
=== Radical co-logarithmic types === | |||
<math> | |||
\begin{align} | |||
\mathrm{jorp} &= \{€\} \\ | |||
\mathrm{warts} &\supset \{5@, 17c@, [email protected]/5, b13@\} \\ | |||
\mathrm{val} &\supset \{<12, 19, 28]\} \\ | |||
\mathrm{copitch} &= \mathrm{jorp} \cup \mathrm{warts} \cup \mathrm{val} | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
| Line 71: | Line 80: | ||
Similarly, the free pitch type is unlikely to be relevant in day-to-day use of SW3. | Similarly, the free pitch type is unlikely to be relevant in day-to-day use of SW3. | ||
=== Real co-logarithmic types === | |||
<math> | |||
\begin{align} | |||
\mathrm{jorp!} &= \{€!\} \\ | |||
\mathrm{freeCopitch} &= \{x * €!, x \in \mathbb{R}\} | |||
\end{align} | |||
</math> | |||
Note: Completionism is an illness. | |||
=== Linear unit quantities === | |||
<math> | |||
\begin{align} | |||
\mathrm{second} &= \{s\} \\ | |||
\mathrm{hertz} &= \{Hz\} | |||
\end{align} | |||
</math> | |||
=== Rational linear quantities === | |||
<math> | |||
\mathrm{rationalTime} = \{p * s^q, p \in \mathbb{Q}, q \in \mathbb{Q} \} | |||
</math> | |||
Note: Decimal numbers do not require parenthesis when implicitly multiplying unit quantities e.g. "261.6 Hz" is a valid expression. | |||
=== Radical linear quantities === | |||
<math> | |||
\mathrm{radicalTime} = \{p * s^q, p \in \mathrm{radical}, q \in \mathbb{Q} \} | |||
</math> | |||
=== Real linear quantities === | |||
<math> | |||
\mathrm{realTime} = \{p * s^q, p \in \mathbb{R}, q \in \mathbb{Q} \} | |||
</math> | |||
=== Rational logarithmic quantities === | |||
<math> | |||
\begin{align} | |||
\mathrm{afjs} &\supset \{\mathrm{C4}, \mathrm{E5}^5\} \\ | |||
\mathrm{aji} &= \mathrm{afjs} | |||
\end{align} | |||
</math> | |||
=== Rational co-logarithmic quantities === | |||
TODO | |||
=== Radical logarithmic quantities === | |||
<math> | |||
\begin{align} | |||
\mathrm{axfjs} &\supset \{\mathrm{C½♭4}, \mathrm{\alpha 3}\} \\ | |||
\mathrm{acents} &= \{ac\} \\ | |||
\mathrm{apitch} &= \mathrm{aji} \cup \mathrm{axfjs} \cup \mathrm{acents} | |||
\end{align} | |||
</math> | |||
=== Radical co-logarithmic quantities === | |||
TODO | |||
=== Real logarithmic quantities === | |||
TODO | |||
=== Real co-logarithmic quantities === | |||
TODO | |||
Note: Make it stop. | |||
=== Domain types === | |||
<math> | |||
\begin{align} | |||
\mathrm{linear} &= \ldots \\ | |||
\mathrm{logarithmic} &= \ldots \\ | |||
\end{align} | |||
</math> | |||