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Phrasing changes too Getty Ritter 7 years ago
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6262 \h1{One-Third-Comma Meantone}
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64 Quarter-comma meantone was by far the most common variety of meantone temperament after it was first proposed in the 16th century, but it was far from the only one proposed or used. One of the first rigorous mathematical descriptions of quarter-comma meantone comes from the 16th-century music theorist and organist \link{https://en.wikipedia.org/wiki/Francisco_de_Salinas|Francisco de Salinas}. In his writing, he \em{also} described a different meantone system with a similar motivation: instead of trying to build a meantone system that accomodates perfect major thirds, what if we built a meantone system that accomodates perfect \em{minor} thirds?
64 Quarter-comma meantone quickly became the most common exemplar of meantone temperament after it was first proposed in the 16th century, but it was also far from the only one proposed or used. One of the first rigorous mathematical descriptions of quarter-comma meantone comes from the 16th-century music theorist and organist \link{https://en.wikipedia.org/wiki/Francisco_de_Salinas|Francisco de Salinas}. In his writing, he \em{also} described a different meantone system with a similar motivation: instead of trying to build a meantone system that accomodates perfect major thirds, what if we built a meantone system that accomodates perfect \em{minor} thirds?
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6666 A perfect minor third corresponds to a ratio of \tt{6:5}, which has a slightly more dissonant, haunting sound than most of the ratios we've been working with. A perfect minor third sounds like this:
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