Tanaka was an early advocate of 53 equal temperament as a means of closely approximating 5-limit just intonation.
First proposed in the 18th century by Leonhard Euler, this model was also used by Hugo Riemann in his theory of harmony.
Tanaka also suggested what would now be called a Fokker block as a way of viewing the pitch classes of 53 equal temperament.
Tanaka proposed a set of harmonic cadences designed to reflect a traditional Japanese aesthetic, acknowledging pentatonic scales and incorporating suspended tones in the manner of the chords played by the shō.
He had Johannes Kewitsch, of Berlin, construct a 5-octave version and in 1891 he demonstrated it to Anton Bruckner in Vienna, who was impressed with its potential.