You wrote: "I have found this 'additional' part in the net. I believe, originally Wu Yuxiang transmitted this text to his followers. It complements Da Shou ge (Song of pushing/hitting hands). It looks quite unusual to me since primarily talks about sounds (during pushing/hitting hands)."
That is a strange document. There is a commentary in Shen Shou’s 1991 compendium, _Taijiquan pu_ (pp. 54-55). I will attempt here a rough translation of the Wu Yuxiang text and Shen Shou’s commentary. As you say, the text consists of words that are primarily sounds, rather than meaningful terms (with the exception of peng). The tone designations are classical tones, which are not the same as the tones in modern Mandarin. The last three terms have no tone designations. Here’s my attempt:
The let-out and release of hitting hands
Peng: rising level tone
Ye: entering tone
Yi: rising tone
Hai: entering tone
Hu: rising tone
If this document were put in terms equivalent to more modern language, it would perhaps be called “The eight qi methods of issuing in push hands.” The eight “sound words” in the text are used in association with the issuance of jin in push hands, so that when one issues jin, one employs the release of a sound as a way of giving vent to tension (tu3qi4), in order to increase its explosive force, and to raise the actual level of the fajin’s result. Just as Yang Chengfu left a transmission, “The three qi methods of releasing jin in push hands” (tuishou fangjin san qi fa), these are in accordance with three different directions of fajin: upper, middle, and lower, and selectively applying one of the “sound words” Heng, Hai, or Ha, in order to accompany the release of tension in the fajin (yi peihe fajin tuqi). The above mentioned “three qi methods” are no doubt strongly related to “the eight qi methods” [of this text]. The three qi [sounds] Heng, Hai, Ha, if compared with this document, in fact [correspond to] Hang, He, and Ha [that is, the final three sounds].