回答
Yes, it makes sense, but not completely. “When I played” is in the past tense (演奏した). “I should play” is in the present (演奏すべきです). Let me assume that you meant the present tense (ラルゴの曲を演奏するときには、ゆっくり演奏すべきです).
When I play a piece of music in largo, I should play it slowly.
(1) “A musical piece” usually means a piece from a musical show (ミュージカル). Did you actually mean it? If so, it is good; otherwise, we say, “a piece of music.”
(2) When we talk about tempo, we usually say, “in largo,” “in moderato,” “in allegro,” "in presto," and so on. It is not correct to say, "with largo," but you can say, "with the tempo marking of largo." Music teachers might explain tempo markings to beginning students like this.
When you play a piece of music with the tempo marking of largo, you should play it slowly.
(3) In classical music, “largo” does not mean “slowly.” It means “broadly.” We play slowly for sure, but we add more broadness to our notes. In Japanese, “largo” is 幅広く or ゆったりと. If you are a music student, you might want to learn the meanings of “lento,” “largo,” and “adagio.” They are similar but different. They are not only tempo markings but also indications of style.
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