1. A game apparatus operable to execute a game music generating program stored on a storage medium, said game apparatus comprising: a phrase data storage area that stores different kinds of a plurality of phrase data, based on a musical characteristic, wherein said phrase data designate a length and a pitch of a pronunciation of a tone color; a rhythm-pattern storage area that stores at least one kind of rhythm pattern data, constructed of rhythm data, that designate a length in performance for performing a phrase, and a timing of said phrase; game music-data reproducing programmed logic circuitry that reproduces game music data constructed of at least one part; a tone storage area that stores data of a sound output according to said music data; a continuous counter for counting the number of times the same phrase has been selected; and sound outputting programmed logic circuitry that outputs a sound according to the music data reproduced by said music-data reproducing programmed logic circuitry, wherein said game music generating program is capable of being executed by a processor of said game apparatus to perform the steps of: randomly selecting one kind of the phrase data stored in said phrase data storage area including incrementing said continuous counter when the phrase data selected last time and the phrase data selected this time agree and re-selecting the phrase data when a count value of said continuous counter is larger than a predetermined value; selecting one rhythm data from one kind of the rhythm pattern data stored in said rhythm-pattern storage area according to a predetermined rule; and generating the music data from the phrase data selected by said randomly selecting one kind of the phrase and the rhythm data selected by said selecting one kind of rhythm data.