5-limit: Difference between revisions

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== Syntonic comma pairs ==

A significant interval in 5-limit JI is [[81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. ~~81/80~~ is tempered out in [[12edo|12EDO]], [[meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely 12edo musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, ~~etc~~. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). '''Bold''' fractions are simplest for this interval category.

A significant interval in 5-limit JI is [[81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. The syntonic comma is tempered out in [[12edo|12EDO]], [[meantone]], and many other related systems, meaning that those 5-limit and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely 12edo musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, and so forth- however, perhaps a handful in the Xenharmonic community are at least starting to take the idea of such a distinction more seriously. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). '''Bold''' fractions are simplest for this interval category.

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 == Syntonic comma pairs ==
-A significant interval in 5-limit JI is [[81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. 81/80 is tempered out in [[12edo|12EDO]], [[meantone]], and many other related systems, meaning that those 5- and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely 12edo musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, etc. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). '''Bold''' fractions are simplest for this interval category.
+A significant interval in 5-limit JI is [[81/80]], the syntonic comma or Didymus' comma, which measures about 21.5¢. Although it rarely appears as an interval in a scale, it represents the difference between many 5-limit intervals and a nearby [[3-limit]] (Pythagorean) interval. The syntonic comma is tempered out in [[12edo|12EDO]], [[meantone]], and many other related systems, meaning that those 5-limit and 3-limit distinctions are obliterated and one interval stands in for each. Living in a largely 12edo musical culture from birth, we are not accustomed to distinguishing two different major thirds, two different minor seconds, and so forth- however, perhaps a handful in the Xenharmonic community are at least starting to take the idea of such a distinction more seriously. Below is a list of some common intervals involving 3 and 5 which are distinguished by 81/80. The next column modifies intervals by another 81/80, for a total of 6561/6400 (43 cents). '''Bold''' fractions are simplest for this interval category.
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