Melodic Phrasing
The solo's next statement is a soaring melodic phrase that connects both the "A" and "B" harmonic minor fingerings we've been discussing:
Melodic Phrase   -   (228.05KB MP3)
m.6                m.7                m.8
-----------------|------------------|-12-11-14-11-15-14p12
-----------------|---------13-12p10-|---------------------
--------9-8-11-9-|-12-11p9----------|---------------------
-7-9-10/---------|------------------|---------------------
-----------------|------------------|---------------------
-----------------|------------------|---------------------
 d u d  d u d  u   d  u    d  u       d  u  d  u  d  u
               m.9                                    m.10
----12-14-15-|-/20-19-17-19----17-------------------|-----
-15/---------|--------------20----19-20-17-19-16-17-|---16
-------------|--------------------------------------|-19--
-------------|--------------------------------------|-----
-------------|--------------------------------------|-----
-------------|--------------------------------------|-----
 d  d  u  d        u  d  u  d  u  d  u  d  u  d  u    d u
----------------------------------------------------------
----------------------------------------------------------
-19-17p16----17-16----------------------------------------
----------19/------19-17-16h17p16h17p16-/\----------------
----------------------------------------------------------
----------------------------------------------------------
 d  u     d  d  u  d  u  d
If this phrasework is completely improvisational, it only enhances my respect for Yngwie's brilliant sense of melody. Measures 6-8 are an attractive ascending line built on the "B", or "sword" harmonic minor fingering used in the solo's opening statement. This line caps with a dramatic slide in measure 9 which takes us up to the "A" fingering where the solo started. By staggered stepwise motion, the line eventually comes to rest at the base of the "A" fingering with a trill on the 16th fret of the D string.

As we saw in the opening statement, Yngwie's approach to picking descending lines often employs legato to simplify complex passages. In this passage, we can see that Yngwie's picking technique for ascending lines is even richer, employing not only alternate picking and legato, but also a key third ingredient: sweeping.

Scalar Sweeping
Yngwie's use of sweeping to play arpeggios is so widely imitated at this point that it has become a shred cliche. But the truth is that the vast majority of Yngwie's sweeping happens in his scale playing. The essential concept is that downstrokes are simply extended whenever possible through the next higher string. This economizes pick motion and makes fast passages easier to play. For this reason, sweeping in a scalar context is often called economy picking. In reality, sweeping is sweeping is sweeping.

In the melodic passage above, you'll find downward sweeping right in the first measure. The passage begins with three alternate-picked notes on the D string. The third alternate picked note -- a downstroke -- is used to bridge the gap between the D and G strings:
Ascending Scalar Sweeping   -   (139.28KB MP3)
m.6
----------------------------------------------------------
----------------------------------------------------------
--------9-8-11-9------------------------------------------
-7-9-10/--------------------------------------------------
----------------------------------------------------------
----------------------------------------------------------
 d u d  d u d  u
Although the picking notation beneath the D-to-G string change indicates consecutive "d"s, remember that these are not separate downstrokes. The initial downstroke is simply pushed through the next higher string, sounding two fretted notes with one motion.

Scalar sweeping occurs again in measure 8, connecting the B string with the E string. The sweep is followed by a striking legato slide from the 15th to the 20th frets (also confusingly notated by a "/", but hey) which is the dramatic apex of the phrase:
Sweep + Legato Slide   -   (179.68KB MP3)
m.8                                 m.9
-12-11-14-11-15-14p12----12-14-15-|-/20-19----------------
----------------------15/---------|-----------------------
----------------------------------|-----------------------
----------------------------------|-----------------------
----------------------------------|-----------------------
----------------------------------|-----------------------
 d  u  d  u  d  u     d  d  u  d        u
What's so cool about the legato slide is that it is not only the most exciting moment in the lick, but also the precise thematic midpoint. On the way up, Yngwie climbed by way of descending seconds -- two-note fragments where a higher note is followed by the next lower note in the same scale. Immediately after the slide, Yngwie descends by way of ascending seconds. Again, if this lick is entirely improvisational (which it may very well be), you have to respect the powerful creativity:
Descending-Ascending Seconds   -   (150.91KB MP3)
m.9                              m.10
-17-19----17-------------------|--------------------------
-------20----19-20-17-19-16-17-|----16--------------------
-------------------------------|-19-----------------------
-------------------------------|-------------------------
-------------------------------|-------------------------
-------------------------------|-------------------------
 d  u  d  u  d  u  d  u  d  u    d  u
The final scalar sweep happens in measure 10 at the tail end of the run. It connects the D string to the G string by way of the now-familiar downward (i.e. ascending) sweep:
Final Sweep   -   (148.46KB MP3)
m.10
----------------------------------------------------------
----------------------------------------------------------
-19-17p16----17-16----------------------------------------
----------19/------19-17-16h17p16h17p16-/\----------------
----------------------------------------------------------
----------------------------------------------------------
 d  u     d  d  u  d  u  d

Mechanics
Since the distance from one string to the next is small, about a half inch or so, Yngwie typically executes the sweeping motion by pushing the pick across the gap with his right-hand thumb and forefinger. The wrist gets involved again to continue alternate picking on the new string. And so on. This combination of movements has a distinctly different appearance than the pure wrist or elbow motions of alternate picking, and has led various observers to theorize that Yngwie might be using some [dubious] esoteric right-hand motion like circular picking. Nope, it's just sweeping.

Ultimately, the source of the motion is not super important. Sweeping earned its economy picking nickname because there is minimal motion involved, so finding the fastest possible way to move your hand is not necessary when practicing sweep licks. The hard part is keeping constant time. Sweeping motions have a tendency to rush once you get them going. When you combine alternate picking and sweeping in the same lick, you run the risk of smearing the swept sections and laboring the picked ones.

A great lick for practicing Yngwie's deft combination of alternate and sweep picking occurs as another stop-time fill at 2:51 of Now Your Ships Are Burned. It's an ascending scale in E harmonic minor, played at -- you guessed it -- the "A" fingering. The lick changes strings exclusively with sweep picking:
Stop-Time Ascending Fill   -   (131.93KB MP3)
----------------------------15-17-19----------------------
-------------------16-17-19/------------------------------
----------16-17-19/---------------------------------------
-16-17-19/------------------------------------------------
----------------------------------------------------------
----------------------------------------------------------
 d  u  d  d  u  d  d  u  d  d  u  d
The speed at which Yngwie plays this particular lick is simply terrifying, and the heavy muting he uses only serves to accentuate its aggressiveness. Downward sweeps are used to execute the string changes, while alternate picking is used to connect them to the middle note on each string. This is an extremely common pattern in shred and should definitely become part of your sweeping practice regimen. It's particularly difficult to play this lick evenly because the swept notes actually outnumber the alternately-picked notes 2 to 1. Practicing at a speed where you can be sure all the notes are played evenly, and making sure to stay as relaxed as possible in the right hand, is the way to go.