User:Frostburn/Geometric algebra for regular temperaments: Difference between revisions
→Decomposition: Add some decomposition examples and hand waving. |
→Decomposition: Add TODO indicating that the hand waving is bad. |
||
| Line 61: | Line 61: | ||
== Decomposition == | == Decomposition == | ||
In equal temperament it is obvious that the building block of any musical interval is a single scale step, it's not immediately obvious what intervals in higher rank temperaments are made out of. We can wedge two vals together but the factorization is not unique. What we need are two vals that are as simple as possible. | In equal temperament it is obvious that the building block of any musical interval is a single scale step, it's not immediately obvious what intervals in higher rank temperaments are made out of. We can wedge two vals together but the factorization is not unique. What we need are two vals that are as simple as possible. '''TODO''': Scrap this and translate the algorithm from [[Wedgies and multivals]] to Geometric algebra. | ||
Let's return to three dimensions (or two thinking projectively). Meantone can be decomposed into: | Let's return to three dimensions (or two thinking projectively). Meantone can be decomposed into: | ||