Imho the "king of waveforms" is the pulse wave. It can go from a "hollow" but powerful square (pulsewidth 50%, odd harmonics only), to more full-bodied sounds with a nice mix of odd and even harmonics, to nasal/spiky sounds at extreme pulsewidth settings (close to 0 or 100%). And pulsewidth modulation is just so pleasing to the ear, despite it being such a simple process.
Single hramonic (1): sine wave All harmonics (n): sawtooth (ramp) wave Odd harmonics (without even harmonics) (2n+1) (n - 2n)): meanderic (square) wave Even harmonics (without odd harmonics) (2n) (n - (2n+1)): double sawtooth wave Singled triodd harmonics (multiples of three plus one harmonics) (without multiples of three plus two harmonics and simple multiples of three harmonics) (3n+1) (n - (3n+2) - (3n+3)): triatonic wave Shifted singled triodd harmonics (multiples of three plus two harmonics) (without multiples of three plus one harmonics and simple multiples of threeharmonics) (3n+2) (n - (3n+1) - (3n+3)): shifted triatonic wave Triple harmonics (multiples of three harmonics) (without multiples of three plus one harmonics and multiples of three plus two harmonics) (3n) (n - (3n+1) - (3n+2)): triple sawtooth wave Doubled triodd harmonics (without multiples of three plus two harmonics) ((3n+1)+(3n+2)) (n - (3n+2)): tercitonic wave Shifted doubled triodd harmonics (without multiples of three plus one harmonics) (3n+(3n+2)) (n - (3n+1)): shifted tercitonic wave Shifted doubled triodd harmonics (without multiples of three harmonics) (3n+(3n+1)) (n - 3n): shifted tercitonic wave
Imho the "king of waveforms" is the pulse wave. It can go from a "hollow" but powerful square (pulsewidth 50%, odd harmonics only), to more full-bodied sounds with a nice mix of odd and even harmonics, to nasal/spiky sounds at extreme pulsewidth settings (close to 0 or 100%). And pulsewidth modulation is just so pleasing to the ear, despite it being such a simple process.
Single hramonic (1): sine wave
All harmonics (n): sawtooth (ramp) wave
Odd harmonics (without even harmonics) (2n+1) (n - 2n)): meanderic (square) wave
Even harmonics (without odd harmonics) (2n) (n - (2n+1)): double sawtooth wave
Singled triodd harmonics (multiples of three plus one harmonics) (without multiples of three plus two harmonics and simple multiples of three harmonics) (3n+1) (n - (3n+2) - (3n+3)): triatonic wave
Shifted singled triodd harmonics (multiples of three plus two harmonics) (without multiples of three plus one harmonics and simple multiples of threeharmonics) (3n+2) (n - (3n+1) - (3n+3)): shifted triatonic wave
Triple harmonics (multiples of three harmonics) (without multiples of three plus one harmonics and multiples of three plus two harmonics) (3n) (n - (3n+1) - (3n+2)): triple sawtooth wave
Doubled triodd harmonics (without multiples of three plus two harmonics) ((3n+1)+(3n+2)) (n - (3n+2)): tercitonic wave
Shifted doubled triodd harmonics (without multiples of three plus one harmonics) (3n+(3n+2)) (n - (3n+1)): shifted tercitonic wave
Shifted doubled triodd harmonics (without multiples of three harmonics) (3n+(3n+1)) (n - 3n): shifted tercitonic wave