Having introduced the Chinese scale to you, we do hope that you now have a clearer picture of the early Chinese works in music.

We have seen that some popular mis conceptions about the Chinese scale (like the lack of an octave, lack of semi tones) do not have a very strong basis to them. Our project has shown that it all boils down to a matter of interpretation, and unless further archealogical evidence can be found, no conclusions can be made to admit, or deny the claims. One thing that is sure, is that the notion that the early Chinese scale is "backward" compared to Pythagoras's work or the Just Innotation should be changed. Especially when we have shown that the Jue-Zeng method can actually be used to generate the Just Innotation.

A possible deduction could be that the early Chinese has already heard a scale which is roughly equivalent to the equal temperament scale of our days. The modern scale took musicians and mathematicans close to two centuries to formulate, with scales of up to 4 semitones being used before that. The Chinese however have managed to devise a scale consisting only of 2 semitones as early as -5th century. This is remarkable. (the benefits of having a scale with as little different semitones as possible require some in depth knowledge of music, which we will not go into here)

Chinese music has evolved to a relatively different form today. Akin to our project, we will not start on a history of the evolution of the Chinese music scene, but instead show the modern scale used in modern Chinese music now. The annontation used now is called the (jian pu).

Different representations

It can be said to be based upon the modern chromatic scale, whereby instead of C, D, E, ... we use the annotations 1, 2, 3, ... ,7. Annotations for the accidentals are the same (ie using '#'and 'b'). The comparisons between the (jian pu) and the modern chromatic scale are too substantial, and too subjective. And rather than being a comparison between two forms of scales, they basically degenerate into a comparison between two different forms of representations for the same kind of scale. Put simply, the two of the representatons are based on the same equal temperament scale.

The author can't but resist the temptation to explain it by :

Sets Model written for fun


Returning to the conclusion, we would also like to include a small explanation on how the sounds for the early Chinese scale were reproduced. To reproduce the sounds, a Chinese stringed instrument called the Gu Zheng was used. Using only 1 string out of the 21 strings on the instrument, we first select a fixed length that corresponds to a C (turns out to be 65.0 cm). We then follow the up and down generation by the fifths to generate the rest of the sounds. The sequences of the scale and the piece Twinkle Twinkle Little Star are then put together on the computer.

A Gu Zheng

This method of reproducing the sound is severely limited. One, to save on file size, the sound files have to be compressed thus they may not sound to be in tune. Second, our instrument of measure is the humble ruler, which poses some difficulty and introduces some errors in our computation for the length of the string. Fourth, we have tuned the Chinese notes based on the current day calibration of 440 as explained earlier. This most probably isn't what the early Chinese based their scales on.

However despite the limitations above, we hope that we have been able to give the reader a rough idea of the general progression of the early Chinese scale as compared to the modern ones.

None of our group members are well trained in western music. A lot of work were done researching and understanding music theory. Besides, the generation of the scales mathematically were totally new to us and at times our sources showed to be beyond our understanding. However, we also tend to disagree with some of the material that we had come across, and thus put forth our own ideas in some cases (like the explanation on how to avoid the comma in the Chinese scale).

We have tried to come up with a site that is easy and understandable to most people, even those without musical background, and as such certain details were ommited. For more information, you may be interested to check out some of the sources listed in the Bibliography...

All said, we hoped that this project has accomplished what we set out to do, to give you an insight into the mathematics behind the early Chinese scale, and understand its intricacies bettter.

We will end this project with this quote we came across, and which we find highly apt. =)

Music is a Science which should have definite rules; these rules should be drawn from an evident principle; andthis principle cannot really be known to us without the aid of Mathematics. Notwithstanding all the experience I may have acquired in music from being associated with it for so long, I must confess that only with the aid of Mathematics did my ideas become clear and did light replace a certain obscurity of which I was unaware of before. - Rameau, 1922