Some of my greatest joy in teaching comes from the sight-singing groups I lead. All a cappella, we concentrate on tuning, not according to any absolute pitch, but as they did it in the old days--until the late Baroque era, at least--just according to where the voices lie.
Not only do I derive great joy from these groups, but so do the people who sing in them, some of whom have had quite a bit of musical training, others not at all. The point is that the essence of melody lies in the tension of linear motion against harmonics and that anyone can learn to tune the harmonics of tones.
Some of these people report back to me that when they tell musician friends that they are taking a class in sight-singing the musicians groan and commiserate: "Oh, you poor thing!" or "Why on earth would you want to do that!"
I blame over-emphasis on the piano, an entirely unvocal pitch source, for these negative responses.