Compound techniques refer to techniques that require a consistent application or coordination of the breath, tongue, and fingers all at once. As such, these techniques tend to take more effort to get into a consistent playing form.
Circular breathing (循环换气 or xunhuan huanqi) is one of the more difficult compound techniques that exist today. A brief description was described in the diaphragm control article. There are two main uses of circular breathing: legato or double tonguing.
Circular breathing in legato is the most traditional means of using circular breathing. It can be a difficult compound technique because there are two different cycles that need to be taken care of, namely the circular breathing cycle as well as the natural rhythm that the part is going. Parts that require circular breathing will have the Ⓥ annotated at where the composer might suggest a [circular] change of breath, while the entire segment that needs to be played in legato be highlighted. An example can be seen below (extracted from《幽兰逢春》by 赵松庭):
╭─────────────────────────────────────────────────────╮ ╭³╮ 7 565 ┊ 65 65 Ⓥ ┊ 65 65 ┊ = === ┊ == > == > ┊ == ⩀ == ╭───⁹───╮ v ┊ サ ˙╰6 - ˙˙˙╰3 - ┊ ˙˙╰3 - ˙˙╰3 - ┊ ˙˙╰3 - ˙˙╰356123567 ┊ ˙ ˙ ┊ ˙ ˙ ┊ ˙ ≡≡≡≡≡≡≡≡≡ ┊ ˙˙˙
The key thing behind circular breathing in legato is to ensure that the transition from cheek to lungs and lungs to cheek is seamless. While many texts suggest learning how to circular breathe [in legato] by the use of a straw in water to learn how to coordinate the buccal cavity and the lungs by trying to keep a continuous stream of bubbles going in the water, I suggest a slightly different approach---focus more on how to maintain the embouchure shape while trying to puff out the air pocket stored in the cheeks.
Seamlessness is obtained when there is no detectable change in the pitch and timbre of the played note, and this translates to having the right jet stream speed and angle from the embouchure. This also means that one must learn how to puff out the pocket of air using only the cheek muscles without altering the embouchure in anyway. It is much harder than it seems because this is an action that one would not normally perform. Once this is done, the other part of coordinating the transfer of air between lungs to buccal cavity and vice versa is much easier.
The focus on an unchanging embouchure while puffing out the air into a jet stream is the cornerstone of the second use of circular breathing: circular breathing double tonguing.
Circular Breathing---Double Tonguing
In standard double tonguing (双吐 or shuangtu), there will come a point in time where there is a need to grab a mouthful of air to continue. Usually this happens at a natural break in the piece of music.
In 1989, 莫凡 wrote《绿洲》, which consisted of a section of sixteenth notes in staccato with no obvious pauses on where breathing can be done since the entire section had a consistent movement that a pause for breath would break the artistic vision. And thus, the 循环换气双吐 or xunhuan huanqi shuangtu technique was born. There is no specific notation for this other than a line that says to use 循环换气双吐 or 循环双吐.
The best way to describe this technique is to first start with T TK pattern of staccato (i.e. 三吐 or santu). In this pattern, a breath is taken between the first T and the next T, thus allowing the pattern to carry on in perpetuity. Note that in this santu pattern, the breath is obtained through the mouth.
We now explain how to progressively build our way to xunhuan huanqi shuangtu. We start with the same T TK santu pattern, but instead of stealing a breath with the mouth, we do so through the nose. Once we are comfortable with doing that, start to store an air pocket in the buccal cavity after the first T, and puff it out while we are breathing in through our nose, without changing our embouchure.
And that's all there is to circularly breathed double tonguing.
As noted before, if the tempo of the staccato part is too high, there will be a need to pace out the breathing parts so that one does not hyperventilate. As yet, I have not seen pieces that demand non-stop double tonguing at high speed with no breaks that will require this refinement, but the future is always an unknown.
This might seem funny at first blush. Why are harmonics considered a compound technique when we talked about it on tongue position at rest?
The simplest way of understanding this is to realise that the tongue position when blowing across the embouchure hole (or chuikong) is only one half of the equation of playing a note by harmonics. The fingering itself is just as important. Harmonics itself are notated with a o written on top of the note sound we are expecting. Here are a couple of examples (assuming tongyin as 5̣):
o o 2̇ 3̇
Harmonics (泛音 or fanyin) are better characterised by equating the ``orthodox'' fingering with the harmonics equivalent. While the dizi itself can have many harmonics, we usually refer to the third and fourth one for this particular compound technique. Also as a result of the acoustics of the dizi, only the uncovering of the right hand holes (i.e. 1--3) play an active role in generating the fanyin.
The fingering pattern charts article shows the pitches of fingering charts given the excitement of the first four harmonics relative to the tongyin, and should be consulted for more details.
Always remember that the note annotated under the fanyin symbol is the actual pitch that one is supposed to hear.