equal, and it is held to include all the possible distinctions of pitch within an octave, deriving this reputation doubtless from the circumstance that to Chinese ears it appears as the limit of the derivation by fifths.[1] For were a thirteenth pipe constructed, its note would fall theoretically 24 cents, or the eighth of a tone above the octave of the initial note; and practically, it may be presumed, would be considered by a primitive instrument maker to be that octave. The powers of the process to engender a series of notes within an octave would therefore, we may suppose, be held to have exhausted themselves in the sequence of twelve just given.[2] To these the Chinese give the following names in the order of the series of fifths: (1) Huang-chung, (2) Lin-chung, (3) Tai-tsu, (4) Nan-lu, (5) Ku-hsi, (6) Ying-chung, (7) Jui-pin, (8) Ta-lu, (9) I-tse, (10) Chia-chung, (11) Wu-i, (12) Chung-lu. Arranged in order of pitch upwards within the octave the sequence becomes: Huang-chung, Ta-lu, Tai-tsu, Chia-chung, Ku-hsi, Chung-lu, Jui-pin, Lin-chung, I-tse, Nan-lu, Wu-i, and Ying-chung.
But it was not alone the method of deriving these twelve sounds, the interval order which they should embody, which was fixed by their inventors. Their absolute pitch was determined also by the choice of a standard intonation for Huang-chung, the note of generation. This Ling-lun made by one account to coincide with the murmur of the spring whose bamboos furnished the first Lu, and which proved to be the source of the Hoang-ho river. Under successive dynasties various prescriptions of the most elaborate and exact character as to
- ↑ Amiot, pp. 64, 87.
- ↑ If we carry on the fifth progression by taking account of the small interval of 24 cents above the octave of the initial note brought in by the twelfth fifth, no further interval of different size will be introduced until the seventeenth fifth is reached, which gives a note 66 cents below the octave of the starting-point. An extension of the progression to include sixteen fifths was employed by the Arabian theorists of the fourteenth century and earlier, and gives their seventeen step octave (Helmholtz, Tonempfindungen, 4 edn., p. 458). This more complex theoretical construction was, according to Mr. Ellis (fr. of Helmholtz, p. 281), a mathematical determination of an already existing interval order. The lutist Zal-zal (ninth century) had introduced certain new notes into the scale, produced apparently by the trisection of the quarter of a string; and approximations to these were yielded, it proved, by this exclusion of the fifth progression.
