and in Greek theory it would fail to exclude the other tetrachords. The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers: τόνος may refer to a pitch, an interval, a "key" or register of the voice, or a mode. Shades or tunings The diatonic tetrachord can be "tuned" using several shades or tunings. Aristoxenus (and Cleonides, following his example; see also Ptolemy's tunings) describes two shades of the diatonic, which he calls συντονόν (syntonón, from συντονός) and μαλακόν (malakón, from μαλακός). Syntonón and malakón can be translated as "tense" ("taut") and "relaxed" ("lax, loose"), corresponding to the tension in the strings. These are often translated as "intense" and "soft", as in Harry Partch's influential Genesis of a Music, or alternatively as "sharp" (higher in pitch) and "soft" ("flat", lower in pitch). The structures of some of the most common tunings are the following: The traditional Pythagorean tuning of the diatonic, also known as Ptolemy's ditonic diatonic, has two identical 9:8 tones (see major tone) in succession, making the other interval a Pythagorean limma (256:243): hypate parhypate lichanos mese 4:3 81:64 9:8 1:1 | 256:243 | 9:8 | 9:8 | -498 -408 -204 0 cents However, the most common tuning in practice from about the 4th century BC to the 2nd century AD appears to have been Archytas's diatonic, or Ptolemy's "tonic diatonic", which has an 8:7 tone (see septimal whole tone) and the superparticular 28:27 instead of the complex 256:243 for the lowest interval: hypate parhypate lichanos mese 4:3 9:7 9:8 1:1 | 28:27 | 8:7 | 9:8 | -498 -435 -204 0 cents Didymus described the following tuning, similar to Ptolemy's later tense diatonic, but reversing the order of the 10:9 and 9:8, namely: hypate parhypate lichanos mese 4:3 5:4 9:8 1:1 | 16:15 | 10:9 | 9:8 | -498 -386 -204 0 cents Ptolemy, following Aristoxenus, also described "tense" and "relaxed" ("intense" and "soft") tunings. His "tense diatonic", as used in Ptolemy's intense diatonic scale, is: hypate parhypate lichanos mese 4:3 5:4 10:9 1:1 | 16:15 | 9:8 | 10:9 | -498 -386 -182 0 cents Ptolemy's "relaxed diatonic" ("soft diatonic") was: hypate parhypate lichanos mese 4:3 80:63 8:7 1:1 | 21:20 | 10:9 | 8:7 | -498 -413 -231 0 cents Ptolemy described his