Cassandra triads: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 568515141 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 568515307 - Original comment: ** |
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There is an ambiguity in how we compute harmonic entropy for triads, depending on whether we use utonal or otonal approximations. The common major triad is otonally a 4:5:6 and utonally a 1 / (10:12:15). Because the otonal form is simpler, it dominates over the utonal form. For the minor triad, the situation is reversed; the minor triad is primarily a utonal 1 / (6:5:4) and secondarily an otonal 10:12:15. | There is an ambiguity in how we compute harmonic entropy for triads, depending on whether we use utonal or otonal approximations. The common major triad is otonally a 4:5:6 and utonally a 1 / (10:12:15). Because the otonal form is simpler, it dominates over the utonal form. For the minor triad, the situation is reversed; the minor triad is primarily a utonal 1 / (6:5:4) and secondarily an otonal 10:12:15. | ||
The subminor triad is primarily an otonal 6:7:9 and secondarily an otonal 1 / (14:18:21). The supermajor triad is primarily an otonal 14:18:21 and a utonal 1 / (6:7:9). | The subminor triad is primarily an otonal 6:7:9 and secondarily an otonal 1 / (14:18:21). The supermajor triad is primarily an otonal 14:18:21 and secondarily a utonal 1 / (6:7:9). | ||
The consonance of otonal chords comes primarily, I believe, from the fact that they share a common fundamental frequency; by the same token, utonal chords share a common overtone. Because these are two different mechanisms, it may be a good idea when calculating harmonic entropy to evaluate the two components //separately//. | The consonance of otonal chords comes primarily, I believe, from the fact that they share a common fundamental frequency; by the same token, utonal chords share a common overtone. Because these are two different mechanisms, it may be a good idea when calculating harmonic entropy to evaluate the two components //separately//. | ||
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There is an ambiguity in how we compute harmonic entropy for triads, depending on whether we use utonal or otonal approximations. The common major triad is otonally a 4:5:6 and utonally a 1 / (10:12:15). Because the otonal form is simpler, it dominates over the utonal form. For the minor triad, the situation is reversed; the minor triad is primarily a utonal 1 / (6:5:4) and secondarily an otonal 10:12:15.<br /> | There is an ambiguity in how we compute harmonic entropy for triads, depending on whether we use utonal or otonal approximations. The common major triad is otonally a 4:5:6 and utonally a 1 / (10:12:15). Because the otonal form is simpler, it dominates over the utonal form. For the minor triad, the situation is reversed; the minor triad is primarily a utonal 1 / (6:5:4) and secondarily an otonal 10:12:15.<br /> | ||
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The subminor triad is primarily an otonal 6:7:9 and secondarily an otonal 1 / (14:18:21). The supermajor triad is primarily an otonal 14:18:21 and a utonal 1 / (6:7:9).<br /> | The subminor triad is primarily an otonal 6:7:9 and secondarily an otonal 1 / (14:18:21). The supermajor triad is primarily an otonal 14:18:21 and secondarily a utonal 1 / (6:7:9).<br /> | ||
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The consonance of otonal chords comes primarily, I believe, from the fact that they share a common fundamental frequency; by the same token, utonal chords share a common overtone. Because these are two different mechanisms, it may be a good idea when calculating harmonic entropy to evaluate the two components <em>separately</em>.<br /> | The consonance of otonal chords comes primarily, I believe, from the fact that they share a common fundamental frequency; by the same token, utonal chords share a common overtone. Because these are two different mechanisms, it may be a good idea when calculating harmonic entropy to evaluate the two components <em>separately</em>.<br /> | ||