The ancient Chinese musical system depends on very ancient mathematics used to determine sound frequencies. The easiest way to explain it is to work through a real example.
ð ɪ WORD_BOUNDARY eɪ n t̠ʃ ə n t WORD_BOUNDARY t̠ʃ aɪ n iː z WORD_BOUNDARY m j uː z ɪ k ə l WORD_BOUNDARY s ɪ s t ə m WORD_BOUNDARY d ɪ p ɛ n d z WORD_BOUNDARY ɔ n WORD_BOUNDARY v ɛ ɹ i WORD_BOUNDARY eɪ n t̠ʃ ə n t WORD_BOUNDARY m æ θ ɪ m æ t ɪ k s WORD_BOUNDARY j uː z d WORD_BOUNDARY t ə WORD_BOUNDARY d ɪ t ɜː m ɪ n WORD_BOUNDARY s aʊ n d WORD_BOUNDARY f ɹ iː k w ə n s i z WORD_BOUNDARY ð ɪ WORD_BOUNDARY iː z i ɪ s t WORD_BOUNDARY w eɪ WORD_BOUNDARY t ʊ WORD_BOUNDARY ɛ k s p l eɪ n WORD_BOUNDARY ɪ t WORD_BOUNDARY ɪ z WORD_BOUNDARY t ə WORD_BOUNDARY w ɜː k WORD_BOUNDARY θ ɹ uː WORD_BOUNDARY ʌ WORD_BOUNDARY ɹ iː ə l WORD_BOUNDARY ɛ ɡ z æ m p ə l WORD_BOUNDARY