Greatness rhymes with:
lateness, abruptness, absoluteness, acuteness, alertness, appropriateness, astuteness, bluntness, brightness, compactness, completeness, correctness, cuteness, directness, earnestness, eyewitness, faintness, fastness, fitness, flatness, forthrightness, gauntness, hartness, inertness, jointness, lateness, lightfastness, lightness, neatness, politeness, quietness, remoteness, rightness, robustness, separateness, shortness, softness, steadfastness, stoutness, sweetness, swiftness, tartness, tightness, unpleasantness, vastness, wetness, whiteness, witness, witness'
Greatness sounds like:
garden's, gardenias, gardening, gardens, gardini's, gerding, girding, gordon's, gradations, grading, graduating, graduations, grating, greeting, greetings, gretna's, gritting, grouting, guardian's, guardians, guarding, gyrating, gyrations, gyrodynes