The Scale Revisited

 

Recall that the modern chromatic scale is an equal temperament scale. It consist of only one type of semi tone. For the purpose of discussion, we will look at the scale generated by the Lu-Shi Chun-Qiu method. This choice is justified by the fact that we do now yet know the exact chromatic sequence generated by the Jue-Zeng method and that 3 of the 4 possible scales from the latter method are actually isomorphic to the Lu-Shi Chun-Qiu scale.

The animation above demonstrates the rough reproduction of the Chinese scale. (Note the limitations of our reproductions in the concluding section). Compare that with the reproduction of the modern day scale below.

 

A person trained in music would cringe on hearing the Chinese notes above as they are "off-key". Though we have assigned the rough equivalences of the Chinese notes to their modern day equivalences like (Huang-Zhong to "C"), each of the sounds actually differs from the scale we know today. Our observation is that the notes from the Chinese scale are generally flatter (ie. lower frequency) than the modern notes. This however does not show us that the Chinese scale is way off. The intervals between the notes of the Chinese scale sound similiar to that of the modern notes. This can be seen from our observation that the notes in the Chinese scale all tend to be "flatter" by the same amount than their modern equivalents.

One explanation for this is of course the inaccuracies in our reproduction of the Chinese notes. Another explanation is that the Chinese scale could have been measured in a different calibration from what we are using now. Modern day tuners allow musicians to tune notes according to calibrations ranging from 438 Hz to 445 Hz typically. The Chinese could have defined their scale in a calibration that we do not use today, ie. > 445 Hz, which explains why the notes all differ from their modern equivalences by a fixed amount.

To demonstrate that the Chinese scale so generated bear a strong resemblance to the modern day scale, try the two sound samples below. We built these two sound samples (a short extract from "Twinkle Twinkle Little Star") based on the Chinese notes and modern notes we have obtained from the Chinese zither.

 

Though the "Chinese version" sounds off key, a strong resemblance exists between it and the modern version. This is perhaps one of the most substantial and clear way through which to present the similiarities between the two scales.