arithmetic mean of the string lengths (if one wishes to think in terms of frequencies, rather than string lengths or interval distance down from the tonic, as the example below does, splitting the interval between the frequencies 4:3 and 5:4 by their harmonic mean 31:24 will result in the same sequence of intervals as below): hypate parhypate lichanos mese 4:3 31:24 5:4 1:1 |32:31 |31:30 | 5:4 | -498 -443 -386 0 cents This method splits the 16:15 half-step pyknon into two nearly equal intervals, the difference in size between 31:30 and 32:31 being less than 2 cents. Rhythmic genera The principal theorist of rhythmic genera was Aristides Quintilianus, who considered there to be three: equal (dactylic or anapestic), sesquialteran (paeonic), and duple (iambic and trochaic), though he also admitted that some authorities added a fourth genus, sesquitertian. References Sources Further reading Ancient Greek music theory Byzantine music theory Greek music Musical scales Melody types