User:Akselai/On the infinite division of the octave: Difference between revisions
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== Properties == | == Properties == | ||
∞edo, by this construction is a flexible object. Some have defined ∞edo as simply the union of all edos, which is actually supported by this construction. At the ''h''-th height of the chain with ''m''edo, we only need to adjoin (''mh'')edo to obtain the (''h''+1)-th height, and we would have encompassed all integer factors along the tower and hence all edos. (Though, the | ∞edo, by this construction is a flexible object. Some have defined ∞edo as simply the union of all edos, which is actually supported by this construction. At the ''h''-th height of the chain with ''m''edo, we only need to adjoin (''mh'')edo to obtain the (''h''+1)-th height, and we would have encompassed all integer factors along the tower and hence all edos. (Though, the intervals of an arbitrary subset edo do not follow a val mapping.) | ||
On the other hand, ∞edo can also be built from, say 5<sup>''n''</sup>edos. Then it would not contain 2edo, among other edos that are not powers of 5. | On the other hand, ∞edo can also be built from, say 5<sup>''n''</sup>edos. Then it would not contain 2edo, among other edos that are not powers of 5. | ||