I've seen and attempted to play multiple songs on the piano that include chords that are tenths or sometimes even elevenths or twelfths (rarely), and these chords have four or five notes.
If I were to come across a chord like this, as I can only reach a 9th, what would be the best way to play it? (e.g., inversions, skipping notes, etc.)
The following general principles/techniques for handling large chords are given below:
Many pianists learn to play on our fingertips. This requires a significant curve to the hand, which makes it harder to open the hand to its full span. Flattening out and playing closer to (or even directly on) the pads of the fingers makes it easier to achieve wide spans.
For additional details with photos see this post.
One common error when playing large chords it to play too close to the edge of the keys. When playing with a flatter hand, it's fine for the long fingers, but can leave the thumb and pinky hanging off in space, then requiring twisting to bring them closer to the keys. Shifting the hand away from the body brings the thumb and pinky closer to the keys without sacrificing the natural hand position.
Some related discussion, with photos, can be found here.
Sometimes, the layout of the chord will allow a single finger to play two notes. A classic example of this comes from Chopin's Prelude in A Major, Op. 28 No. 7. Measure 12 includes the following right-hand chord, which is played (and often notated) with the thumb covering both the A# and C#.
X:0
T:Chopin Op. 28 No. 7, m. 12
M:None
K:None
L:1/2
[^A^ce^a^c']
The header is self-explanatory. For a large right-hand chord, see if one or more notes can be played by the left hand, and vice versa.
Example
In Rachmaninoff's arrangement of Rimsky-Korsakov's "Flight of the Bumblebee", there are left-hand chords spanning a 10th. For a pianist will a smaller hand-span, or who has difficulty locating the chord quickly enough at high speed, it's straightforward to shift the topmost note of the left hand to the right hand.
mm. 10-11 (SOURCE: view the "Arrangements and Transcriptions" tab.)
Especially in large left-hand chords, the bass note can be played alone, followed immediately by the remainder of the chord. This can work in the right hand as well, but is especially common in the left because of the emphasis it gives to the bottom note of the chord.
In the Chopin example below, it is not uncommon to hear the chords not marked for arpeggiation played in this way. In the first measure of the example, the second left-hand chord might be played with the F# treated as a grace note, preceding the rest of the chord.
The grace-note portion is not limited to a single note. In the second measure of the Chopin excerpt, the second chord could be played in two parts: the lower E-B followed by the upper E-B.
A very common solution is simply to play the chord as a very rapid arpeggio. This way the entire chord need not be spanned simultaneously, and the hand can shift to maintain a natural position.
Example
In the B section of Chopin's Nocturne in C Minor, Op. 48 No. 1, there are written left-hand chords that span as much as a twelfth. Many of the large chords are marked to be rolled, but others are not. However, note the measure in which all chords are marked as rolled. This suggests that Chopin intended the unmarked chords are to be played as block chords.
Valentina Lisitsa in the below recording rolls nearly all the left-hand chords. When she rolls the left hand, she sometimes rolls the right hand and sometimes does not.
Often in large chords, one or more notes will be doubled. (Keep in mind to consider both hands when looking for doublings.) In general, the highest and lowest notes in a chord (both hands included) are the most important, so inner notes are a safer bet.
Using the above Chopin chord as an example, the low A# could be left out, since it's doubled an octave above.
X:0
T:Chopin Op. 28 No. 7, m. 12
M:None
K:None
L:1/2
[^ce^a^c']
In some situations, a good result can be obtained by shifting the octave of a note, or changing the relative positions of notes.
For me there is confusion in your using the word "best": There are no strict rules in music.
What I usually do, as an amateur pianist/composer, is to select the notes which have the most distinctive color (can be the 13th you name it), choose a pair of other notes from the chord that either push toward the classic triad, or on the contrary on the triad coloration notes.
Then with the help of left hand bass, I choose on the right hand the one conformation which is more or less the easiest (on which I do not stumble too often), while preserving the color tones I have selected.
For having the easiest conformation, I heavily use inversions.
Five stars for Aaron's answer. Personally I am not a slave to notation and if something doesn't fit my hand, I don't force it. An injury can put you out of commission for a long time. My teacher couldn't reach tenths but used to do stretching exercises to reach them and she blew out a tendon on her thumb. It took two years to heal. My general rule of thumb is to avoid using the abductors as much as possible. Using them with the flexors creates a dual muscular pull which leads to all sorts of issues.
