What Japanese songlike poetry form uses an unrhymed 7-7-7-5 structure? The answer is dodoitsu. Dodoitsu is a Japanese folk-song and poetry form made of four lines with a moraic pattern of 7-7-7-5, for 26 morae in total, and it normally does not rhyme.
The form developed toward the end of the Edo period from popular song traditions rather than the courtly literary culture associated with waka and tanka. Dodoitsu verses were often sung or recited for entertainment, sometimes with shamisen accompaniment. Their subjects commonly include love, work, everyday life, and humor.
Dodoitsu is easy to confuse with better-known Japanese forms. Haiku or hokku is associated with a 5-7-5 pattern, while tanka uses 5-7-5-7-7. Sedōka has a different six-line 5-7-7-5-7-7 structure. The key clues here are the four-line 7-7-7-5 design and its songlike, frequently comic character.
In English descriptions, the units are often called syllables, but Japanese verse is more precisely counted in morae, or sound units. That distinction matters because Japanese mora counts do not always match English syllable counts.