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I am not a musician, just a dilettante. I am interested in the traditional Chinese music system, which is supposed to be a pentatonic scale.

According to Wiki, one way to get a pentatonic scale is to take five consecutive pitches from the circle of fifths and put them into one octave. For example, we take C, G, D, A, E and put them in one octave as C, D, E, G, A. That sounds good, as according to my references, the traditional Chinese system consists of the following pitches separated by perfect five (7 semitones).

Now comes what I need help understanding. As I read about the pentatonic scale, I should take C, D, E, G, and A and then go to the next octave, retaking C. I.e., the same notes but the next octave. However, if I keep taking seven semitones, it should be C, G, D, A, E, and then B, F#, and so on! These notes are not in the octave-based pentatonic scale but appear when I keep taking seven semitones; it makes me think I am missing something.

UPD: To clarify the question. I have a book claiming that the traditional Chinese acoustic system was based on twelve notes separated by perfect fifths, seven semitones. So, as far as I see, it does not correspond to the standard pentatonic (C-D-E-G-A) as soon as we go outside an octave?

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  • You don’t keep taking seven semitones. You just get the five notes and then play them in any octave. Commented Mar 27 at 10:43
  • @ToddWilcox Thanks! I have updated the question to make it more clear.
    – Arastas
    Commented Mar 27 at 10:52
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    You might be running into the fact that to say "chinese" and "traditional" is to reference several millennia of history, and many shifting and overlapping subcultures. You might start with a deeper dive using some truly historical and reputable source; I suspect it's something more nuanced then "over all those thousands of years and diverse genres, cultures, and practices, 'Chinese music was pentatonic.'" Commented Mar 27 at 13:49
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    Wikipedia turns up Shi'er lü, but the timeline for it seems to overlap with the sentence "Around or before the 7th century BC, a system of pitch generation and pentatonic scale was derived from a cycle-of-fifths theory." Commented Mar 27 at 13:50
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    @Arastas the 12-note scale is also not closed unless you temper the fifths or let one of them be rather smaller than a 3:2 ratio, or some other compromise.
    – phoog
    Commented Mar 27 at 16:53

2 Answers 2

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Sixteenth-century Chinese music theorists were apparently the first to calculate 12-tone equal temperament with high precision, so they must have known that equal temperament was a fairly close approximation to twelve tones derived from the just fifth (3:2 frequency ratio). Some Chinese music also uses, fairly prominently but not exclusively, a five-pitch pentatonic scale of the type described in the question. The derivation of the pentatonic scale from four perfect fifths was known from the 7th century or earlier.

We can infer that Chinese theorists also recognized octave equivalence, and that they, or at least some of them, knew these facts, which are not mutually exclusive or contradictory:

  • one can derive the pentatonic scale described in the question from five pitch classes separated by a fifth.
  • if you keep going until you have twelve pitch classes, the next one you generate will be fairly close to the one you started with.
  • if you temper the fifths, you can spread the out-of-tune-ness around so nothing sounds that bad.
  • you can use the 12 pitch classes you end up with to create other scales with more than five pitch classes per octave; each scale with fewer than twelve pitch classes is a subset of the full twelve-member set of pitch classes. (The Indian seven-tone scale was used for a time from the sixth century but later abandoned.)

So at some point at least, somebody recognized that the pentatonic scale was five adjacent pitches in the circle of fifths. Or maybe they didn't think of extending the circle to the twelfth tone until much later. In any event, when you have a melody in the pentatonic scale, you don't generally play the notes in circle-of-fifths order, and the jump from E to G is the same as the jump from A to the upper C as you wrap around the octave.

It's very unlikely that Chinese music started by noticing you could generate scales by using notes a fifth apart and then just decided to stop after five notes. Rather, the theorists noticed (as Greek theorists also did) that the notes of the scale they'd already been using could be related to one another through recursive application of the 3:2 ratio.

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  • "Ancient Chinese music theorists apparently theorized about the 12-tone scale and knew that equal temperament was a fairly close approximation to twelve tones derived from the just fifth." Apparent how? Source?
    – Aaron
    Commented Mar 27 at 16:55
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    @Aaron I've added some sources and corrected the timeline.
    – phoog
    Commented Mar 27 at 17:09
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A pentatonic scale has five notes. Once you have establisehed five notes by whichever method you choose then you stop and repeat those notes in the other octaves.

If you keep adding notes by your perfect fifth method then you end up with the notes of a seven-note major scale, and if you add even more then you end up with a twelve-note chromatic scale. Both of these are useful, but neither of them is a pentatonic scale.

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  • Thanks! So, we either take the first five steps of the perfect-fifths-sequence to get a (major?) pentatonic, or keep adding notes getting something else.
    – Arastas
    Commented Mar 27 at 14:16
  • No seven note major scale, but a lydian scale!
    – Lazy
    Commented Mar 27 at 14:18
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    @Lazy It depends where you start, lydian is just a mode of the major scale.
    – PiedPiper
    Commented Mar 27 at 14:28
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    Sure, but by this argument you get a minor scale as well. The reasonable assumption is that the starting tone is the root, by which it would be lydian. Of course, if you assume that the second note obtained that way was the root, then it would be a major scale. But I’d claim it makes more sense to use the first note upon which everything else builds on as the root.
    – Lazy
    Commented Mar 27 at 14:52
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    @Lazy it really doesn't matter here: call it whatever you like. It contains the notes of a major scale, so that's what I'm calling it.
    – PiedPiper
    Commented Mar 27 at 15:45

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