Yeah, I'm one of the ones that has only one bodily sensation, or in my case it's that way; for me:
sound has taste, touch, smell, sight
sight has taste, touch, smell, sound
taste has sound, touch, smell, sight
touch has sound, taste, smell, sight
smell has sound, sight, taste, and touch
but my case may be a whole lot more advanced than most synesthetes. Just means I have sensory overload sometimes and withdraw in order to pray, but often just to have a quiet space to defrag my mental drive. It's not a handicap of any kind. Often it allows the greatest creativity in the world's eyes because the synesthete isn't in the "typical" perfectionist kick, but they're wanting things that sound, look, taste, touch, and smell right to them; for they themselves.
I've not been enough of a student of Mozart to be sure if there's corroborating biographical "hints" along these lines, but Mozart's music is such a piece of art that is well pleasing to absolutely all of the senses and even in moments of all of the senses being aware all at once, that I have a sneaky suspicion that his music came out of a mind that was likely as synesthetic as mine. Not a note out of place, even to a synesthete! No degree of logic, education, training, I.Q., or anything else is going to produce music that's such a pleasure to either a synesthete that's simply got every molecule of both sets of neurons working -- those in the cranium and the 50,000+ neurons behind the heart -- or with those like idiot savants that have one half of the brain working at 100% mental capacity, productivity, activity, etc.
And when a synesthete is able to appreciate the art of an artist that's not a synesthete, then you probably got one of the better reviews of your art that you could possibly get, EVER, if not THE absolute best critical review you could have ever gotten, 'cause they're looking at something whether musically or with painting or photography, cooking, design, fashion, or whatever from many, if not all, levels all at once.