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When swinging and playing fairy bells, for example, playing downward scales to imitate peals of bells, both hands must grip the sides of the instrument. If the instrument is placed on a table then both arms and hands (and thumbs) are much freer. But how much freer? The same issue confronts a player of the 18th century bell harp/English harp when played on a table rather than held in the air.
There is an interesting contrast with a similar instrument, the salterio or plucked dulcimer. On that instrument, played with plectrums attached to fingers too, the arms move over all the strings. But this 22-string fairy bells, or a bell harp is different. Firstly the hands and thumbs are only moving in one plane, left-right or right to left. On a dulcimer the player is playing all over the instrument, left, right, near to the player,further away from the player. Secondly, these FRAS instruments are designed with a definite left-hand side (or territory) and a similar right hand side. The design strongly suggests that the left hand is covering the left territory and the right hand, the right territory... and no more than that. But, with the hands freed from actually gripping the instrument, it's possible for each hand to visit each other's territories: the left hand can reach over and play on the right side and vice versa. The instrument becomes more like a salterio; not only would the player be able to have a simple bass line accompanying a melody, sequences of thirds and sixths would be possible too.
As far as playing an 18th century bell harp/English harp on a table is concerned there is simply no evidence to go on but I think it unlikely that bell harp players were influenced by salterio playing. The salterio came to prominence in the 18th century, but not in Britain and there is no evidence that it was even known in Britain. I suspect that bell harp players stuck to playing notes on the left hand side with the left hand and the right hand notes with the right hand and this manner of play is indicated in the admittedly less than reliable definitions in dictionaries of the time.