Are two melody strings louder than one?
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What a great discussion!
Sometimes our ears interpret a richer or fuller sound as a 'louder' sound. As Dusty said, a decibel measuring instrument should be able to technically answer whether two melody strings are actually louder than one. It's how technicians measure the loudness of machinery or traffic noise. But there are so many more qualities to sound than simply decibels.
I like Randy's point about the two strings being struck a fraction of a second apart... However when we play two notes or two open strings a half-second apart while normally playing a tune, does that make those notes louder? If not, then why should the same action be louder if the time between striking two strings is shortened to a smaller fraction of a second as with two melody strings? Unless some sort of sympathetic vibration effect does something, as Robin mentions.
I would think it must be true- Nate's point about extra strings producing more tension on the top- and that might increase volume overall. But I can't imagine that adding one thin melody string tuned to the same pitch would do enough to hear any difference. I suppose if one added two heavy drone strings, or tuned all the strings to a higher pitch that might increase top tension enough to hear it.
As Wally mentioned, musicians often tune strings to create 'beats' that play off each other in a pleasing way. The beats of two adjacent strings tuned not quite in unison can produce an intentionally pleasing sound quality. Classical violinists do this very intentionally. Sophisticated electronic tuners make this easier to achieve nowadays whereas it used to be attempted by ear long ago.
Lastly, if you place the dulcimer on a wooden table to play, you get an immediate and very noticeable increase in sound volume. I call that 'the music box effect', and it's common practice in playing traditional dulcimer antecedents such as epinette, hummel, langspil, langelik...