Shí-èr-lǜ Shí-èr-lǜ Shí-èr-lǜ (, , "12 pitches") (twelve-pitch scale) was a standardized gamut of twelve notes. Also known, rather misleadingly, as the Chinese chromatic scale, it was one kind of chromatic scale used in ancient Chinese music. The Chinese scale uses the same intervals as the Pythagorean scale, based on 2:3 ratios (8:9, 16:27, 64:81, etc.). The gamut or its subsets were used for tuning and are preserved in bells and pipes. Unlike the Western chromatic scale, the shí-èr-lǜ was not used as a scale in its own right; it is rather a set of fundamental notes on which other scales
Diatonic scale Pythagorean tuning: Six of the "fifth" intervals (C–G, D–A, E–B, F–C', G–D', A–E') are all = 1.5, but B–F' is the discordant tritone, here ≈ 1.423828125. Extending the series of fifths to eleven fifths would result into the Pythagorean Chromatic scale. It would add pitches for the five "piano black key" notes, for instance A–E–B–F–C–G–D–A–E–B–F–C–G. A and G are commonly thought of as being the same note, but as worked out in this way, G is higher pitch than A by about 1.01364 (, the Pythagorean comma, about 24% of a semitone, = ). Depending on whether one chooses A