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Superparticular number
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Superparticular number

Superparticular numbers, also called epimoric ratios, are improper rational fractions of the form

Superparticular numbers were written about by Nicomachus in his treatise "Introduction to Arithmetic". They are useful in the study of harmony: many musical intervalss can be expressed as a superparticular ratio.

Ratio Name Related musical interval
2:1 duplex diapason (P8)
3:2 sesquialterum diapente (P5)
4:3 sesquitertium diatessaron (P4)
5:4 sesquiquartum ditonus (M3)
6:5 sesquiquintum semiditonus (m3)
9:8 sesquioctavum tonus (M2)
18:17 (super)sesquiseptimus decimus semitonium (m2)

See also

External links