Fokker block: Difference between revisions
if this Todo is not showed to the viewer, people will get wrong ideas of what the properties of Fokker blocks are |
→Duodene and 12 equal temperament: Fix sign of diesis. add intermediate step determinant |
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Let's take [[5-limit]] just intation, and pick the [[128/125|diesis]] (128/125) and the [[syntonic comma]] (81/80) as our chromas. | Let's take [[5-limit]] just intation, and pick the [[128/125|diesis]] (128/125) and the [[syntonic comma]] (81/80) as our chromas. | ||
The octave equivalent lattice is generated by fifths and just major thirds. | The octave equivalent lattice is generated by fifths and just major thirds. | ||
The diesis | The diesis is the difference between an octave and three major thirds, so it has coordinates <math>(0, -3)</math>. | ||
The syntonic comma is reached by stacking 4 fifths and going down a major third, so it has coordinates <math>(4, -1)</math> | The syntonic comma is reached by stacking 4 fifths and going down a major third, so it has coordinates <math>(4, -1)</math> | ||
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:<math> | :<math> | ||
\begin{vmatrix} | \begin{vmatrix} | ||
0 & 3 \\ | 0 & -3 \\ | ||
4 & -1 | 4 & -1 | ||
\end{vmatrix} | \end{vmatrix} | ||
= (0 \cdot -1) - (-3 \cdot 4) | |||
= 12 | = 12 | ||
</math> | </math> | ||