Harmonic class: Difference between revisions

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'''Harmonic ~~Class~~''' ('''HC''') classifies JI ratios 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 class''' ('''HC''') classifies JI ratios 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.

~~== List~~ of ~~harmonic classes ==~~

[[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.

* HC1 - 1/1, ~~2/1~~

* HC3 - 9/8, 3/2, 4~~/3, 16/9, 3/1~~

* HC5 - ~~10/9~~, 6/5, ~~5/4, 8/5, 5/3~~

* HC7 ~~- 8/~~7~~, 7/6,~~ 9/7~~, 7/5, 10/7, 12/7, 7/4~~

* HC11 - 12/11, 11/10, 11/9, ~~14/11, 11/8, 16/11, 11/7, 18/11, 20/11, 11/6~~

* HC13 -

[[Category:Class]]

[[Category:Overtone]]

[[Category:Limit]]

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-'''Harmonic Class''' ('''HC''') classifies JI ratios 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 class''' ('''HC''') classifies JI ratios 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.
-== List of harmonic classes ==
+[[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.
-* HC1 - 1/1, 2/1
-* HC3 - 9/8, 3/2, 4/3, 16/9, 3/1
-* HC5 - 10/9, 6/5, 5/4, 8/5, 5/3
-* HC7 - 8/7, 7/6, 9/7, 7/5, 10/7, 12/7, 7/4
-* HC11 - 12/11, 11/10, 11/9, 14/11, 11/8, 16/11, 11/7, 18/11, 20/11, 11/6
-* HC13 -
 [[Category:Class]]
 [[Category:Overtone]]
 [[Category:Limit]]