And I will write the sentence in a cover letter for job application.
If I write "I have both a bachelor's and master's in music", the sentence will give employer an impression that I got 1 BA degree in Music and 1 MA degree in Music.
However, when he looks at my CV, he will know my MA degree is Music tech, but not music.
Then you need to repeat. I have a master's degree in Music Tech(nology? - spell out the full name) to complement my bachelor of arts degree in Music.
Most poeple would not make a big distinction between Music and Music Tech, but if the job you are applying to is in the music field, then you should be as specific as possible.