I should have known better...
So I had my DAW main line outputs connected to my powered monitors using really good 1/4" TS cords.
Then, I installed TRS 1/4" to TRS 1/4" and the signal path was much louder with much less noise.
That is because I went from unbalanced to balanced. 
I should have done this years ago!  I got Hosa cables thru Amazon.  They were the least expensive compared to MusiciansFriend or Sweetwater and with Amazon Prime, they got here in 2 days with free shipping.
 
So the lesson is don't skimp on the most basic items in your studio.  I remember all the days I used Radio Shack RCA plugs with 1/4" adapters for everything 'cause most of what I owned didn't have xlr outputs.  Now I only have a few pieces of audio gear that uses xlr and TRS inputs and outputs and I am finally taking advantage of that through the use of good cabling. 
 
I am still learning after decades doing this! 
 
Rimshot

 
 

Good news!
 
:-)

I have experienced similar things.  My new Kurzweil synth has balanced outputs too and for quite a while I was using unbalanced leads to connect it to the mixer thinking the line inputs I was using were unbalanced.  But it turned out the line lnputs were balanced instead.  So I made some quality TRS to TRS leads and installed them.
 
Before with the unbalanced connection I was quite happy with signal level and the quiescent noise was pretty low.  But with the balanced leads the output level shot up 6 dB which was nice of course but the background noise of the machine disappeared and I mean it went totally silent!  I was stoked.  When you lower any background noise from any hardware synth like this it means less work later in terms of noise removal etc.. Some older hardware can be noisy to the point of noticing it. The original Kurzweil K2000 has unbalanced outputs and the background noise is quite high. There are ways to deal with it of course but it has to be dealt with none the less. And if you doing lots of K2000 overdubs you will get a quiescent noise built up too.  Good news is by the time they got to my current model they certainly sorted it big time.  The balanced outs are the opposite now to the unbalanced outs.  Tons of level with no noise present what so ever.
 
I encountered it as well in that a bass player gave me for a while to test a nice Manley front end valve DI and pre for bass.  Very nice sounding thing this. I patched it into a mixdown at one stage and loved the sound of it there as well.  Manley makes beautiful gear and it sounds fat too.  It is excellent between the bass and amp or a mixer.
 
It has a balanced XLR out and an unbalanced jack out as well. At first I was running the unbalanced out with a short lead and it gave reasonable output level with some low level background noise when feeding an amp or mixer.  I thought I would check the XLR out and I experienced the same as the Kurzweil.  A major jump in level with total cancellation of any noise component. I mean it went dead silent as well. For a piece of valve gear it sounded like the signal to noise ratio was huge. 80 to 90 or 100 dB or more.
 
It is too easy to think that the only difference between using unbalanced leads and balanced leads is the change in level. There is often more associated with it and that can be (not always)  major drop in any background ambient or quiescent noise component.  If any output can be connected to an input and they are both balanced it is usually well worth the effort of making or buying the leads to make it happen.
 
I am sure there are many out there who are using unbalanced leads in situations where the balanced connection could be used instead. Many line inputs on many mixers are balanced now. A lot of instruments and synths have balanced outs now as well, not all are taking advantage of it. You have to dig deep usually in the specs and you often find something relating to balanced outs if they are available.
 
It is essential to use balanced outs to your active monitors too. Many audio interfaces feature balanced outs.
Using balanced outs feeding your monitors allows you to get the maximum SPL level from your speakers when being driven hard, if you are ever doing that which we don't do we! (I bloody do and I love it)

Nice post Jeff.  I too can't believe the increase in level and decrease in noise.  I bloody no and I love it too!

My Steinberg UR-44 hooked to my Yammie actives was a total noise machine, using unbalanced cables.  Balanced solved the problem.  I thought something was defective at first, since the interface is new to me.

I've been jamming to Pink Floyd through my UR-44 using the Yamaha amp sim and added stereo reverb DSP.  It sounds r   e   a  l   l  y good.  I've got my master volume on the UR-44 at 9 A.M.  
 

<entering annoying mode... again>!
 
Jeff - a minor correction please - any balanced input should be fed as a balanced input whether the source is balanced or single ended! The benefit is a reduction in noise. The magnitude of the benefit depends entirely on the designed (and executed) of the input stage.
 
To review:
 
A balanced source has equal impedance, with respect to ground, from each of two output pins.
A symmetrical source presents the signal on each of two output pins, and the signal polarity (not phase) is inverted on one of the pins.
A single-ended output has only one signal pin.
 
A balanced input takes the difference between the signal pins. Even if there is only signal on one pin the provides immunity from induced noise because anything that is common to the two signal pins will cancel out (Common Mode Rejection).

IF the signal appears on both pins, and one pin has the polarity inverted, then the difference becomes A - (-B) which is the same as A + B, and that's where the 6dB increase in level comes from.
 
If you have a single-ended output feeding a balanced input there are two ways to maximize S/N ratio:
1) you can connect the shield, through a resistor that is equal to the source impedance of the output to the inverting input pin. You can do this by using a twisted pair. This presents an equal impedance, with respect to ground, to both input pins and allows the difference function to operate properly.

2) If you have a transformer, or more recently the InGenius(tm) chip as the first stage of the input you can simply connect a coaxial cable between the two signal pins.

WHAT????
 
No, no heresy here... shields do nothing to reduce induced magnetic fields, they are only effective at radio frequencies, and even that can be tricky. Typical noise energy most studios is in the power line range, and the only way to reduce that is a twisted pair feeding a true differential input. So the shield and the center conductor are exposed to the same noise, and happily the same noise voltage will be induced on both. Freakish, and only recently understood, and yeah, you really have to see it to believe it.

So... if you have a balanced (or more accurately differential) input you will benefit by connecting (correctly) to both signal pins. I am pretty sure the usual references have been posted here recently, and I am feeling lazy, so I'll just suggest reading the app notes at Jensen and Rane as a great start to understanding this stuff better.

I think the combination jacks that are wired to work as either a balanced or unbalanced input contribute to mixed experiences.
 
A well designed unbalanced input circuit isn't nearly as bad as one that is kludged in to a connector and input circuit that is designed to be optimized for a balanced signal.
 
In other words, devices with combo jacks make it seem as if you are directly comparing the broader concepts of balanced vs unbalanced connections but in reality you are not actually comparing circuits that have been optimized for both. You are more likely comparing a circumstance that has been optimized to a circumstance that has been kludged.
 
If unbalanced were inherently terrible, it would have been put out to pasture a long time ago.
 
Having said that, most of my gear has balanced interconnections. I have purchased it so that I can enjoy the benefits of balanced connections. The few pieces of gear I have that were designed primarily for unbalanced interconnection seem to integrate very nicely with the studio as a whole.
 
 
best regards,
mike

Combination jacks are not really the problem...
 
When you use a combination jack you tie tip/pin2 to "+", ring/pin3 to "-", and sleeve/pin1 to common. You could, in theory tie the ring to common as well, but not all of the jack assemblies allow you to split out the TRS from the XLR.
 
Anyway, if you insert a TS plug in you tie the ring and sleeve together anyway, which immediately defeats any benefit from a differential (balanced) input.
 
Anyway, the general consensus amongst folks that would be identified as authorities on the topic of electronic noise reduction is that single-ended inputs are inherently bad when applied to professional and/or commercial applications. This does not apply to single-ended sources (outputs) - these can be made to work with differential inputs.

But here is where it gets tricky...
 
Not everyone understands how a balanced input works - and there are some heroically BAD implementations of balanced inputs out there. Further, the only way to truly balance a source is a transformer. Cross-coupled outputs are probably about as close as your are going to get to an electronically balanced output, and they have all sorts of problems - not the least of which is if you accidentally tie one side to ground you can burn up the output stage.

Tascam, when it was known as Teac, was the big proponent of single-ended interconnections for studios. BUT, if you read the manual for the Model 10 console or 80-8 tape deck you'll discover that they knew EXACTLY what the trade-offs were, and what users needed to do to take advantage of the benefits. Benefits? Yes, the biggest benefit of a single-ended interconnection is that it is easier (and less expensive) to design well. The single-ended connections on the old Teac gear took everything into account, including landing the shields on the chassis, not the circuit board.

It remains a demonstrable fact that a (well designed) balanced source feeding a (well designed) balanced input using a twisted pair with a braided or reussen shield is a measurably better technique than any other combination. The difference between electronically balanced inputs and transformer balanced inputs has become minimal, but a top quality transformer will perform slightly better.

The next best solution is a single-ended source feeding a balanced input, again assuming both are well designed, and the cable is a twisted pair, with braided or Reussen shield. Modifying the source to be impedance balanced (which is redundant<G>) provides a measurable benefit in a noisy environment.

Anything else is a compromise.

That said, it might be a compromise you can live with. I have set up studios using only single-ended inputs and outputs, and I've used coaxial cable, and with a little attention to detail I've been able to get the noise floor to a reasonable level.

It all depends on what you are trying to accomplish!!!

BUT, if the option to use balanced (differential) inputs arises, you really do want to take advantage of it!

I guess what I was trying to say is along these lines; the extra 6dB you get with the balanced connection when you use all the wires is a direct comparison to when you use the same connections with only 2 of the wires.
 
If you had two discrete sets of connections, one that is unbalanced and one that is balanced you may find the comparison more favorable. Yes, there will probably be a a small amount of noise added to the SNR of the unbalanced send, and yes there may be a small amount of noise entering on the cable run, but you may, possibly, find a lot less additional noise than when you simply throw out half your signal by not using the extra wire on a connection that is designed to use one and then use make up gain to get to the nominal levels.
 
Part of this idea includes the consideration that it is rare to run the device doing the sending at such a hot level that it is at the threshold of a SNR problem. If the device has a unbalanced send that was made to sound good at a comparable level as some balanced send we refer to then the differences in perceived results will be much slighter than if we simply throw half the signal away as in the examples cited in the first few posts.
 
In general, I agree with everything you say about the benefit of balanced connections. :-) I'm just making a very small point about how the experience of observing a large difference in one circumstance does not lead to an absolute conclusion that the two technologies always provide such different results. 
 
 
 
 
 
And now because I can't resist: :-)
 
"Anyway, the general consensus amongst folks that would be identified as authorities on the topic of electronic noise reduction is that single-ended inputs are inherently bad when applied to professional and/or commercial applications. This does not apply to single-ended sources (outputs) - these can be made to work with differential inputs."
 
I agree 99.9% but I can't help but think of the many times I have experienced huge SPL in commercial venues with low noise playback on a large PA system being fed by an iSomething and its unbalanced "1/8" output connection into the "tape in" on a Pacific rim mixer.
 
 
all the best,
mike