A tremolo harmonica is, in the part of the world of which I am most familiar -- Topeka, Kansas, U.S.A. -- not very commonly known. Far more often here, a "harmonica" is an instrument with ten or twelve holes in a single row, two notes (one blow, one draw) per hole, by some called a "standard diatonic". So much more common is this ten- or twelve-hole instrument that, upon pulling out one or more my tremolos, I have received that silent "what in the world..." look from at least three professional harmonica players. Tremolo is different in that there are two parallel rows of holes (usually 16, 21, or 24 holes per row), where each hole has only one reed (either blow or draw), and where each vertical pair contains one reed tuned right on the note, and one reed tuned just slightly off. I have heard that the off-tuning is about four cents, but this does varies by model, by individual instrument, and even by note. This setup leads to the term "tremolo", which is shorthand -- not really an accurate term -- for the "beating" one hears with the two slightly-offtuned reeds played together.
Over my time with harmonication, I have found that the composite timbre of the tremolo works much better when playing with vocals, and when playing deeply embedded within ensembles. When playing chords or in close ensemble of any sort, the "beating" effect is almost completely cancelled out, and is directly replaced with a plethora of wonderful overtones, both low and high. And a plethora of overtones is exactly what one wants when playing with vocals, or in close integration with other musicians. Ever tried to sing along to a solo flute, or play a piano with a pipe-organ as a duet? The flute and many tones on pipe-organ have almost no overtones, which means that they produce almost singular sine wave tones, and their tones therefore clash easily without other instruments. Tremolo, in contrast, works very well for both solo and ensemble, because it brings its own big set of carefully tuned overtones. And also, for many, tremolo is actually quite a lot easier to play, because the notes are much more physically separated.
I started tremolo myself because a very nice Brelli tremolo harmonica happened to be the instrument my wife bought for herself more than thirty years before, and never used very much. She pulled it out of an old box when we were cleaning up, and handed it to me without a single word. I looked at it from various angles, thought "Well, there has to be a scale in there somewhere," and was amazed to find that in two weeks I was playing familiar tunes singably. But only one week passed by before I wanted another instrument, as a reserve, or a backup: as a carry-it-into-all-storms. So I bought a Hohner Blues Band, a very very common ten-holer, which had been recommended to me by various usually reliable sources. I was shocked at how much harder it was to play. I couldn't isolate notes the same way, or do chords the same way, and all of the output was much more muddled. So I went back to my Brelli for a while, and then a while after that I was at my brother-in-law's place for a party, and was asked to play, and had none except another ten-holer of his which was lying around. So I tried hard. I was able to do my notes and chords acceptably, and better over time, without the special tone quality.
Eventually, after I had my sweet Brelli in my hands again, and especially after a microgig or two, I understood the situation much better. I could get good at ten-holer if I wanted to do so, but tremolo was where I needed to be, because of the results of that tone quality. The next instrument I bought (also on advice) was a Hohner 32/64; and although I had good times with this instrument, I learned from it what Richter tuning is (see the review of the Hohner Double Echo), and why I don't want it. (I don't, but I should bear witness that there are lots of tremolo folks who do lots of good with Richter tuning. I need my scales and my range. More in other writing!) After taking much more time for learning about which tremolo and where, I sent the bucks for a Tombo 1521 in Eb (I had a dire need for Eb and in that year I found no others available by mail- or web-order), and I found what I was needing all along. I now often use my Swan Professionals, Hohner Echo Celestes, Suzuki Humming Tremolos, and Tombo 1521s and 3121s. More recently, since the Forum went up, many excellent folks have contributed additional instrument reports, and whenever some of mine wear out, I am looking forward to the new directions!
Today I play regularly at our church, occasionally at other churches, principally with our church's band which admits of many genre, especially modern high-test worship music. The tremolo is definitely the harmonica I need. I have tried others; but others do not blend so well in ensemble, probably because of the lack of the broad overtones which the tremolo provides. Regardless, I am very happy to have my instruments, and I play them whenever He makes it possible!