Subgroup monzos and vals: Difference between revisions
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== Conversion == | == Conversion == | ||
In order to convert a subgroup monzo to a standard monzo (without converting it to a rational number), look at the monzo for each basis element of the subgroup monzo. For example, 2.3.13/5 [1 -1 1⟩: | |||
2 = [1 0 0 0 0 0⟩ | |||
3 = [0 1 0 0 0 0⟩ | |||
13/5 = [0 0 -1 0 0 1⟩ | |||
Now, we take each of these monzos and multiply each of the entries by the corresponding entry in the subgroup monzo. | |||
[1 0 0 0 0 0⟩ * 1 = [1 0 0 0 0 0⟩ | |||
[0 1 0 0 0 0⟩ * -1 = [0 -1 0 0 0 0⟩ | |||
[0 0 -1 0 0 1⟩ * 1 = [0 0 -1 0 0 1⟩ | |||
Now, we add all the entries together vertically, to get: | |||
26/15 = [1 -1 -1 0 0 1⟩. | |||
Mathematically speaking, if '''m'''<sub>''G''</sub> is an smonzo of the subgroup ''G'', and if ''S'' is a [[subgroup basis matrix]] whose columns form a basis for the subgroup ''G'', then the corresponding monzo '''m''' is given by | |||
$$\vec m = S\vec m_G$$ | $$\vec m = S\vec m_G$$ | ||