OK you have a tone. It's played by a cello. If it's pitched higher it doesn't sound like a cello any more. It sounds more like a violin. There is a connection, therefore between pitch and tonal quality.

They talk about half-tones and whole-tones too which is a pitch designation.

A sine wave can have the same pitch as any other instrument. But it doesn't sound the same so the idea of pitch may be altered as it's perceived. It can be measured in frequencies but it differs in overtones. 440 Hertz remains regardless of what instrument plays it.
But the tonal quality varies. A higher or lower pitch does affect tonal quality. The two are inextricably bound in music.

Frank Hamilton