A. Absolute pitch of the 66 tones of the 33 bells in the 2nd tier of the 65 bells of Marquis Yi (433 B.C.) | |||||||||||||||

in Cent deviations relative to the western standard scale based on A4 = 440 Hz | Back to main page |
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D | D# | E | F | F# | G | G# | A | A# | B | C | C# | D | D# | ||

Set I | |||||||||||||||

Octave D6-C7, 3 bells | -40 | (+14)* | -18 | -42 | (+25)* | (+35)* | |||||||||

Octave D5-C6, 3 bells | -52 | -62 | -10 | -38 | -29 | -16 | |||||||||

Octave D4-D#5, 5 bells | -41 | -40 | -18 | -50 | -35 | -59 | -64 | -60 | -42 | -60 | |||||

Set II | |||||||||||||||

Octave D6-C7, 3 bells | -11 | -15 | -18 | -16 | -60 | -23 | |||||||||

Octave D5-C6, 3 bells | -41 | -58 | -21 | -36 | -51 | -40 | |||||||||

Octave D4-D#5, 6 bells | -53 | -63 | -34 | -13 | -47 | -46 | -44 | (+12)* | -74 | -35 | -27 | -46 | |||

Set III | |||||||||||||||

Octave D5-C6, 4 bells | -24 | -39 | -15 | -38 | -16 | -25 | -58 | -38 | |||||||

Octave D4-C5, 3 bells | -50 | -50 | -22 | -42 | -41 | -15 | |||||||||

Octave G3-D#4, 3 bells | -32 | -21 | -18 | -26 | -24 | -28 | |||||||||

Total mean | -39.0 | -46.7 | -19.5 | -25.5 | -35.4 | -40.5 | -41.3 | -58.0 | -52.0 | -31.6 | -31.0 | -44.7 | |||

Standard deviation (SD) | 14.7 | 17.1 | 6.9 | 17.7 | 12.3 | 7.8 | 15.1 | 29.9 | 14.9 | 9.6 | 16.0 | ||||

Variance | 214.9 | 291.2 | 48 | 150.8 | 227.6 | 222 | |||||||||

Weighed variance of CGDAE: 217.3 | |||||||||||||||

Variance of F vs. weighed variance of CGDAE: p < 0.05 (F-test, 2-tailed, F=4.527, df1=39, df2=7) | |||||||||||||||

Series of fifths, intervals in Cent, absolute pitch in Cent deviations from A440 | |||||||||||||||

The six main tones in fifths | F | 687.9 | C | 696.2 | G | 696.4 | D | 697.8 | A | 694.5 | E | mean C-E: | 696.2 | ||

Mean absolute pitch | -19.5 | -31.6 | -35.4 | -39.0 | -41.3 | -46.7 | |||||||||

Conclusions: | |||||||||||||||

a) Due to the significantly small variance, F appears to be the norm tone, from which D and then | |||||||||||||||

via temperated fifths GC and AE are derived. See also outstanding precision of D-F thirds below. | |||||||||||||||

b) All fifths in the series CGDAE are equally tempered for the sake of improved thirds. | |||||||||||||||

B. Relative pitch of the 66 tones of the 33 bells in the 2nd tier of the 65 bells of Marquis Yi (433 B.C.) | |||||||||||||||

All intervals, in Cent, of the thirds and fifths in main chord D-F-A-C of the scale DEFGAC | |||||||||||||||

Set | I | II | III | Better than piano | |||||||||||

Octave | 6 | 5 | 4 | 6 | 5 | 4 | 5 | 4 | thirds in % | ||||||

Interval | |||||||||||||||

D - F | 322 | 342 | 323 | 293 | 320 | 319 | 309 | 327 | 75 | ||||||

F - A | (443) | 381 | 359 | 358 | 370 | 390 | 390 | 381 | 50 | ||||||

D - A | (765) | 723 | 682 | 651 | 690 | 709 | 699 | 708 | |||||||

A - C | (310) | 313 | 299 | 337 | 311 | 309 | 287 | 326 | 62.5 | ||||||

F - C | (753) | 694 | 658 | 695 | 681 | 699 | 677 | 707 | All 24 thirds: 62.5 | ||||||

Conclusion: The tuning reflects an orientation towards pure thirds, | |||||||||||||||

not towards pure fifths. 15 of 24 thirds are more exact than the modern piano thirds, which have | |||||||||||||||

300 instead of 316, and 400 instead of 386 Cent. | |||||||||||||||

( )* 4 of 66 tones are possibly mistuned. Chroma affiliation was done according to bell | |||||||||||||||

inscriptions. However, musical practice is uncertain. Values excluded from calculations in A. |