Direct approximation: Difference between revisions
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+"problems" section to show why this isn't always a great idea |
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for ratio ''i'' in ''n''-edo. | for ratio ''i'' in ''n''-edo. | ||
== Examples | == Examples == | ||
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Of these intervals, the fifth plays an important role for characterizing [[edo]] systems (as it defines the size of M2, m2, A1). Also, a simple test can show if [[circle-of-fifths notation]] can be applied to a given edo system, because for this the sizes of fifth and octave must be relatively prime. | Of these intervals, the fifth plays an important role for characterizing [[edo]] systems (as it defines the size of M2, m2, A1). Also, a simple test can show if [[circle-of-fifths notation]] can be applied to a given edo system, because for this the sizes of fifth and octave must be relatively prime. | ||
== Problems == | |||
Although direct approximation is perhaps easier to understand than mapping through [[val]]s, it is not always practical in harmony. For example, it is impossible to construct a major triad using the direct approximations of 3/2, 5/4, and 6/5 in [[17edo]] since the step numbers do not add up (5 steps + 4 steps ≠ 10 steps). | |||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Method]] | [[Category:Method]] | ||