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Given a [[rank]]-''r'' [[regular temperament|temperament]] ''W'' and a [[comma]] ''m'' not [[tempering out|tempered out]] by ''W'', the '''interior product''' of ''W'' and ''m'' is the rank-{{nowrap|(''r'' − 1)}} temperament {{nowrap|''W'' ∨ ''m''}} which tempers out ''m'' in addition to all the commas that are tempered out by ''W'' (thus its [[Rank and codimension|codimension]] is one dimension higher than that of ''W'').
Given a [[rank]]-''r'' [[regular temperament|temperament]] ''W'' and a [[comma]] ''m'' not [[tempering out|tempered out]] by ''W'', the '''interior product''' of ''W'' and ''m'' is the rank-{{nowrap|(''r'' − 1)}} temperament {{nowrap|''W'' ∨ ''m''}} which tempers out ''m'' in addition to all the commas that are tempered out by ''W'' (thus its [[Rank and codimension|codimension]] is one dimension higher than that of ''W'').
<math>
 
\def\vsp{\mathchoice{{}\mkern-6mu}{{}\mkern-5mu}{{}\mkern-3.5mu}{}}
\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right\vert}
\def\wedgie#1{\left\langle\vsp\left\langle\begin{matrix}#1\end{matrix}\right\vert\right\vert}
\def\monzo#1{\left\vert\begin{matrix}#1\end{matrix}\right\rangle\vsp}
\def\bimonzo#1{\left\vert\left\vert\begin{matrix}#1\end{matrix}\right\rangle\vsp\right\rangle\vsp}
\def\trimonzo#1{\left\vert\left\vert\left\vert\begin{matrix}#1\end{matrix}\right\rangle\vsp\right\rangle\vsp\right\rangle\vsp}
\def\wmproduct#1#2{\left\langle\vsp\left\langle\begin{matrix}#1\end{matrix}\,\vert\vert\,\begin{matrix}#2\end{matrix}\right\rangle\vsp\right\rangle\vsp}
</math>
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