Poetry
noun, の adjective
A poem song is poetry. It's not quite a song but I think you can make the connection.
詩歌 used to be for two kinds of poetry called kanshi and waka, but nowadays it's also used for other traditional Japanese poetry forms like tanka, haiku, senryu, and more.
This is a jukugo word, which usually means on'yomi readings from the kanji. You know these readings, but there's usually an extra い in the middle. Don't worry, しか is totally fine too, but しいか is more common. You got this!
私たちは詩歌の作り方を学んでいます。
We are learning how to write poetry.
最近は詩歌をたしなんでいます。
Lately, I've been enjoying poetry.
これは詩歌を楽しむために作られたラジオ番組です。
This is a radio program created for the enjoyment of poetry.