Origin
On the guqin, the left end of the dotted scale is a mirror image of the right end. The instrument is played with flageolet tones (harmonics) as well as pressing the strings on the wood. The flageolets appear on the harmonic positions of the overtone series, therefore these positions are marked as the musical scale of this instrument.
The flageolet positions also represent the harmonic consonant relation of the pressed string part with the open string, similar to the calculations Pythagoras did on his monochord. The guqin has one anomaly in its scale. The guqin scale represents the first six harmonics and the eighth harmonic. The seventh harmonic is left out. However this tone is still consonant related to the open string (otherwise it would not be a harmonic) and has a lesser consonant relation to all other harmonic positions. This is the main reason all the ratios of the sevenths family (7:1, 7:2, 7:3, 7:4, 7:5 and 7:6) also often are not present in other musical scales like for instance the just intoned major and minor scale or the major scale in the Pythagorean tuning.
Read more about this topic: Scale Of Harmonics
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