 In the "octave duplex" piano by Hoerr of Toronto, each note had four strings, of which two, three or four could be struck by the hammer depending on the depression of any of four pedals.Steinway’s duplex scale was inspired a half-century earlier by an experiment conducted by the German piano maker Wilhelm Leberecht Petzoldt, in which a small bridge was placed behind the standard larger one with the intention of maximizing the potential additional resonance of a sympathetically vibrating additional length of string.The following table
 
shows the created resonating overtones on the koto for various positions on a stopped string (the proportion being between the "played" portion of the string and resonant portion, the remaining length of the string).