Playing the Baroque Flute

I'm not an "expert" on the Baroque flute (also called Traverso.) I was trained on the concert flute and that is where a lot of my skill comes from. But I've been playing Baroque flute for a couple of decades now and I believe I have enough experience to share some tips. In many ways, information about any transverse flute, modern or ancient, can be transferred to the others. But they do have their personal quirks which is what makes them so interesting (and frustrating) to play. Fingerings, tone, volume, range, chromatic notes, basically everything shifts for each flute. This is what gives them their unique sounds.  

-There are several books on Baroque flutes, old and new, out there and I do suggest taking a look at one or more of them. "Method for the One-Keyed Flute" by Boland has some great advice for ANY wood flute, care instructions and some technique exercises. Treat the fingerings as a starting suggestion (this applies to any fingering chart really). Each flute is a bit differently and different fingerings may work better than others. Most of these books assume you already play the modern flute or have a teacher and do not include much basic how-to-get-a-sound-out stuff. If you are starting from scratch you may want to talk to, or take lessons from, a flute teacher to get those basics down.
-Now, another approach is to get an instruction book for the Irish flute. Irish flutes are basically historical flutes of one type or another and these books often have more absolute beginner info in them. These books tend to emphasize Irish trad. playing styles which are different from Baroque/Classical styles so keep that in mind. Comparing the two styles is quite a good idea for anyone regardless of which style you want to play; there are lots of insights into both styles you can get that way.
-When looking for advice and tips, keep in mind that there are several different Baroque flutes out there. The flute went through a radical redesign at the beginning of the Baroque era (1600-1750) and then continued to change without any one style becoming standard. Some of the changes included the shape of the bore (inside of the tube), adjusting the tuning and adding a key. Then they added a couple more keys. Then they added yet more keys.  Then they argued about which keys were useful, which were "decadent" and which got in the way. Some keys closed holes when they were pressed and others opened them. The only key they all more or less agreed on was that first one for the right hand pinky. After that, it was anyone's guess which keys an instrument maker would use or a player would prefer. Plus, some Baroque flutes can be taken apart into 3 pieces, some come in 4 pieces, some have multiple different sized middle sections and the foot joint can sprout a telescoping extension that is almost steampunk looking.
There are reasons for all these apparently conflicting designs; they sound different and some music works better on one and some on an other. Baroque music was not uniform by any practical definition (this is the era of J. S. Bach, Barbara Strozzi and Turlough O'Carolan; the era when opera was invented and folk music began crossing the Atlantic Ocean) and musicians and audiences alike loved variety so naturally there was a wide range of instruments to go with all the different musical styles.

In spite of all that, tips for one style of Baroque flute can generally be applied to the others. But it helps tremendously to know exactly what kind of Baroque flute a person is talking about.
I play a one-keyed, four-piece Baroque flute. It is one of the simpler (though not simplest) styles. It has some of the most limits on chromatics and scales unless you are comfortable with half-hole fingerings. It is one of the last flutes that could be held to either side of the body though it was usually held to the right so the flute section wouldn't knock into each other too often.

Baroque flute in action. Photo by STL Photovisions

Baroque flute in pieces. Maple wood.

Now here are my three main tips (plus one extra);
1) Work with tuning and modes.
2) Try to improvise on the flute you are learning.
3) Finally play the flute regularly even if you don't sound the way you want yet.
Extra; Consider learning the pennywhistle.

1) Tuning on the Baroque flute is not the same as the concert flute. Not just because of the reduced chromatic notes either. The internal scale is tuned a bit differently than a modern flute and it takes time to adjust. Any tuning work on any flute will help so if tuning the Baroque flute gets too frustrating, do some tuning exercises on another flute for a bit. This improves your ear which WILL help your tuning on the Baroque flute eventually. Remember, as your ear improves, you hear the flaws in your playing more and it can feel like you are getting worse. You aren't. Your hearing and your playing are just improving at different rates.
In general, typical tuning issues on the concert flute are magnified on the Baroque flute. For example, the 3rd and 7th degrees of the major scale need attention. And any note in a chord that needs tweaking on the concert flute likely will need very careful adjusting on the Baroque flute. The trick is that you may or may not need to adjust in the same direction or the same amount.
Closely related to tuning is playing in modes. These are scales that use different patterns than major or minor. Playing in a mode is often easier than trying to play in many major or minor scales other than the scale the flute is tuned to. (That's what all those keys are for-chromatics and shifting keys.) This is why you will find quite a bit of older music and folk music that uses modes. It fit the instruments better (or the instruments fit the music better if you prefer). 
What's more, playing in a mode makes you listen to your tuning differently. You will notice that some modes are easier to play in tune than others. This is partly a result of how you are listening to and adjusting your tuning. Each scale rearranges your hearing and tuning sense whether you notice it or not. A note that sounds fine in one mode may sound badly out of tune in another. This teaches you a lot about the tuning of your instrument.
This takes time and work, no way around it. But here's the good thing; if you keep at it, you eventually will develop a more instinctive understanding of how to adjust on the Baroque flute. You will always need to pay attention but it will become more natural, at least on some scales. This link is a short introduction to the modes if you want to know more about them.

2) Now, improvising is a WONDERFUL way of getting to know an instrument, in my humble opinion. Chasing down a melody in your head will really teach you what an instrument is capable of in your hands. Additionally, playing a wide range of music helps you find out what works on a specific instrument faster than almost anything. I suggest looking at older music that was written when these flutes were commonly played (though some of these may prove a bit challenging!) or folk music (those books on Irish flutes I mentioned often have Celtic tunes in them that work well). This music is often written with some awareness of which chromatics are difficult to handle. Take these tunes as leaping off points; ornament them, add notes and let the tunes lead you into improvised melodies that explore the flute's sound. But don't stop there. Experiment with music you like that is outside the typical style for the Baroque flute. Some pieces will work, some will sound dreadful and others will sound oddly transformed. This is all useful when getting comfortable with a new instrument.
You also need time to develop the tone you want and improvising is a great tool for that too. The tone of a wooden Baroque flute will naturally be different than a metal concert flute (this is why many people like it.) But there is a wide range of possible sounds within that wood tone. Listen to your sound, the sound of other players and see if you can change your sound to match others. Experiment to find out just how many changes you can make to your tone. Not every change will create a "pleasant" tone and this is ok for our purposes. The more tone options you have, the easier it is to create a tone you like or that fits a specific performance. It is nearly impossible to describe in words just HOW a person changes their tone. We tend to resort to "relax your throat" or "let the air pour out" or "make it sound like melted chocolate" to cause students to change embouchure shapes. The control of those tiny muscles develops almost subconsciously the longer you play and listen to others. Which makes playing for fun (and I think improvising is wildly fun) one of the best tone exercises around.

3) Don't be discouraged if you don't sound like a virtuoso right away. Just keep at it. Playing/practicing in short, regular sessions is the key. Five minutes once a day will bring about improvement. Fifteen minute sessions each day or every other day are plenty long enough when starting out. You don't want to exhaust yourself and regular practice rather than long is what keeps you from forgetting what you've learned.
And if you miss a day (or three) don't beat yourself up. You won't forget everything THAT fast! Besides, breaks are good both for your playing and for your enthusiasm. I firmly believe that having one scheduled day a week that you do not practice (unless you just feel like it) keeps you from getting overwhelmed and frustrated. You need that down time to remember how much you enjoy playing, to find and listen to recordings you want to sound like and to get some rest.

Whatever you do, make sure you have fun! Perfection is not the goal of music; delight and joy is.

P. S. 
It recently occurred to me that learning the pennywhistle is tremendously useful for learning the Baroque (or any period) flute. Whistles use a 6-hole fingering pattern that is basically the same as the Baroque flute AND uses cross-fingerings most people don't mention with period instruments. The cross fingering are not always transferable but sometimes they are. Add to that, you get to hold the whistle in front of you and PUT YOUR ARMS DOWN! Trust me, the chance to rest your arms and keep playing is fantastic. Not to mention whistles are a great deal of fun all on their own. For more on this idea, see my post 6 Holes-Where Traversos and Whistles Meet.
Just make sure you get a pennywhistle with a tone you like! You don't have to go to the most expensive or fancy whistle (though you can; I sprang for a wooden whistle and couldn't be happier). But do ask to hear a sound clip or try the whistle out first to see if you like it. I suggest Elf Song Whistles (the Jasper Whistle) or Tilbury Whistles as fairly good starting points without spending large amounts of cash. There are cheaper whistles but they can be inconsistent. That doesn't mean all bad-some professional players use $15 whistles to this day-it just get trickier to find a good one. (By the way, the word "tweaked" next to a cheap whistle means "someone has modified this whistle from the original". This is usually good and means various issues have been cleaned up a bit.)
Or look up the "Wandering Whistler" on-line and check out his whistle reviews.

Second P. S.
Tone advice; Since I can't comment or reply to my own posts (a tech issue I hope is resolved soon), I'm including a reply to a question on tone here.
All the tone exercises concert flute players learn are great for the Baroque flute too. Slow but beautiful tunes are good when you've gotten bored with the long tones. Octave jumps can help since the more your upper and lower octaves match in tone, the more likely you are to have a good (or better) tone. Listen to other players and compare your tone to theirs. You may not like their tone but that's ok. You want your ear to process that Baroque sound so you can hear yourself as accurately as possible. Wood instruments often sound "softer" or "darker" or "airier" than metal flutes and that can take getting used to. Try to change your tone intentionally. The more changes you can make to your tone, the more control you will have over it.
And try to play the Baroque flute fairly regularly (daily, every other day or every third day if possible) so your embouchure muscles remember all the new things your trying to do. Keep at it and good luck!