I like the sound of the wound bass drone with the doubled high drones a lot!

Robin, double drone is very underrated in my opinion. I like the richness of the bass tone a lot. Some lute and baroque guitars as well as other older instruments have all strings doubled except the melody strings. This may have been for practical reasons (thinner strings were probably harder to make/more costly) but I do think it allows the melody strings to stand out more clearly from the drone.

Depending on string strike timing/forces used, it's all about the waveform spectrum and the phase interplay between the pitches & the harmonics produced from this. Even slightly out of phase components between the two will cancel slightly. Conversely in-phase will reinforce, the end effect is an altered sound spectrum which won't sound like 2 pure pitches played together. This the "fullness" that is heard but not louder.

Interestingly because wave prorogation/ pressure level is governed by the square root rule to make your Dulcimers twice sound as loud as all the others you'll need to strike the strings with 4 times the force of the others players.

I think slashed fingers/broken strings would be the order of day if you tried that

Some months ago, I was just messing around with string configurations.  Doubled melody vs. doubled drone vs. 4 equidistant.    It was cool to hear the differences.  

Thanks all for the additional context and food for thought. My starting point was assuming that two melody strings are louder, because the fuller more pronounced tone has always made it seem louder. The first time I heard the thing about the two speakers next to each other, it was really un-intuitive to me.
The more I think about it, it makes sense to me that if two strings were tuned exactly the same, the effect of paired melody strings would be less noticeable, and the tone would not be noticeably fuller.
I also think the sympathetic resonance of the two strings off each other must help with sustain, which might feel like more volume, since the note retains its full volume for longer before fading.

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...

Sound pressure (SP) is measures in force per unit area, i.e. psi. Loudness is typically measured in decibels (DBA). The relationship between them is logarithmic, but also involves the base (atmospheric) pressure or AP. The SP is very much less than the AP. The math gets very messy.

If we assume that two strings double the sound pressure then I think we are talking about the log of [SP / (SP + AP)] versus the log of [2*SP / (SP + AP)] and you can't hear the difference, although it can be measured with a very, very sensitive sound meter.

I intentionally tune my double melody strings to slightly different frequencies to produce beat, not loudness. In the organ world the effect is called "vox celeste" or "vox humana."

Go with your ears, that's what music is about. 

Whether tuned perfectly together or slightly apart in pitch, doubled strings should not be louder than one.  The sound waves mesh together perfectly (or nearly perfectly) like fingers interlacing.   The slight wave interferences are perceived as 'richness' of tone  not increased volume.  

I'm reminded of how subjective "loudness" is. When I was thinking about slight difference in timing and pitch two things came to mind.The first is a choir: a Google search suggests that a choir of twenty of forty people may only be perceived as twice as loud as one person, but the tonal characteristics are very different.

Another thing that came to mind is that with an extra string, more tension is applied to the instrument, and by doubling the amount of force on the melody end of the bridge, that might increase the amount of force being applied to the soundbox in that spot, making it louder.

Dusty, I am definitely not someone who has an educated guess on the topic, but intuitively I would think if you had two strings of different gauges, overall it would only be as loud as the louder string.

Also, I am not knowledgeable about subjective loudness but Im aware that our ear doesn't perceived the loudness of noise in a linear way, whereas a piece of software might show 1.5x as big of a spike, as best as I understand it, that would not correspond to 1.5x perceived loudness. I personally would not know how to interpret the data in a meaningful way.

Could it be some sympathetic vibration is in play with the doubled strings-- especially since, as Randy indicated, one string is struck a tiny fraction of a second before the other? 

In a related yet unrelated matter, I play a doubled high drone and a single melody string.  (String array: wound bass tuned an octave below doubled high drones then a melody string tuned either a 4th or 5th above the bass.)  If I just un-double that high drone and play the same style (noter)  with 4-equidistant strings, the sound is just not the same.  It is fuller with the doubled high drone.   

Interesting stuff to think about, at least for us dulcimer geeks.

It is not just the timing that is variable, as Mr. Adams suggests, but it is impossible to actually tune two strings to exactly the same pitch, despite our best efforts.  So in practice, we have two strings not plucked at exactly the same time and not tuned to exactly the same pitch.  The sum total of all of that would be an increase in sound, whether you call that volume or "fullness" or whatever.  

This should not be hard to test, Nate.  Turn on some kind of recording device or software and watch the input needles.

What if the two melody strings were not the same gauge?  What if one were .010 and the other .014?  Would the difference in tension result in greater volume?

That's an interesting question and a good point, Randy. I don't know the answer to that but I would  intuitively think that playing two strings slightly out of sync that are the same gauge length and tension would not be any louder than one, but I would imagine that is why the sound is fuller.

Hey Nate. So what if one of the two speakers received a signal a portion of a second slower than the other? Perhaps a better analogy for two melody strings?

Hey folks, I've heard it said that having two speakers of the same power directly next to each other is not perceivably louder than one. They are exciting the same air with the same level of energy, so the second speaker basically does nothing.

I was wondering if a similar thing applies to doubled melody strings. If both strings are at the same tension, channeling vibration into the same place on the bridge, is the second string not actually adding any volume? It can be really hard to tell by listening, since a second string changes the tone. It definitely 'feels' louder, but ears are very easy to trick.

Thanks for any info

Nate