Harmonic class: Difference between revisions
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'''Harmonic class''' ('''HC''') classifies JI | '''Harmonic class''' ('''HC''') classifies [[JI]] [[ratio]]s based on the highest [[prime interval|prime]] they contain in either the numerator or denominator. HC tells us that the ratio must contain the prime of whatever class it falls into and will contain no higher prime. | ||
[[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist. | [[Harmonic limit]] refers to the highest prime allowed in the ratios and includes all simpler ratios of lower limit, but HC only contains those which contain that prime. For example, while 5/4 falls into the 7-limit, it is not considered a HC7 interval because the highest prime it contains is 5 not 7. Therefore, HC7 must contain a 7 and no higher prime. 9/7 however would be considered HC7 because 9 is not prime but rather a multiple of 3. Therefore, HC9 does not exist. | ||
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It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the [[2.3-equivalent class and Pythagorean-commatic interval naming system|2.3-equivalent class]] may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]]. | It has been criticized by some schools that the sound of JI is not well characterized by this classification system. Specifically, it is believed that each harmonic class lacks a consistent sound quality. Rather, [[primodality]] classifies intervals by their common denominator, and meanwhile, the [[2.3-equivalent class and Pythagorean-commatic interval naming system|2.3-equivalent class]] may be used as an enhancement suitable for traditional JI and/or [[regular temperament theory]]. | ||
[[Category: | [[Category:Prime limit]] | ||
[[Category: | [[Category:Interval complexity measure]] | ||