The minor in music history allows you to infuse music into whatever major you pursue, and regardless of career path. This allows you to personally customize your education, letting you grow as you discover new interests and expand your intellectual journey. This signals to your prospective employers that you have engaged in a formal academic inquiry in more than one area and help to distinguish you from other job candidates without the minor.
For example, a journalism and new media major who minors in music history would help prepare you for work in music criticism. A business major with a music history minor helps prepare you for a career in businesses that are involved in the arts. A child study major who minors in music history develops a background that can be used when teaching music in the classroom.