According to historians, the taiko drums have been brought into Japan from China, during the Yayoi period (500 BC - 300 AD).
But according to Japanese mythology, the inventor of taiko music was Ame no Uzume, the Goddess of dawn and revelry:

According to the myth, Amaterasu-ōmikami, the Sun Goddess, upset by her brother, locked herself into a cave, leaving the world without the sun.
To bringing her out, Ame no Uzume started to dance, beating the rhythm in a wooden tub (or sake barrel, according to other versions).
And that way, the taiko music was born…

You can read the rest of the myth here or here

Photo from the Kumagaya Uchiwa Matsuri:

Kumagaya Uchiwa Matsuri, Kumagaya, Saitama

EXIF Info:

Yesterday’s Japan Photo: Massha Mitomo Jinja