Playing sheet music by pattern recognition
Playing sheet music by pattern recognition is a trick that makes sight reading music much easier.
The notes found in music are not random, they often fall into patterns. With a bit of experience you can learn to read music by recognising these patterns, without needing to care about the individual notes.
For example, you may see something like the following:

Literally it shows the notes G, A, G, d, e, d, but there is another way of viewing it. This is two repetitions of a simple pattern:
- Play a note.
- Play the note one step higher in the scale.
- Play the starting note again.
We will be exploring some of these common patterns, and how you can make use of them for reading music.
Scale runs
The most basic pattern you'll see in sheet music is a scale run, a sequence of adjacent scale notes in ascending or descending order:

Most often, scale runs are 3 or 4 notes long. There are a number of them in the first part of 'Jim ward's jig', which have been marked with slurs below:

The frequency that these patterns are found in music is why practising scales is useful. It develops a connection between the adjacent notes, allowing you to play them at sight.
Arpeggios
Arpeggios are another pattern that shows up all the time in melodies, and so learning to recognise these patterns helps with reading sheet music.
An arpeggio is the notes of a chord played sequentially. For example, the C major arpeggio contains the notes 'C, E, G', and the octave has also been shown:

The Donegal Lass begins on an ascending A Major arpeggio in its first part, and there are a number of other arpeggio fragments which have been marked with slurs:

It is important to note that the order of the notes in an arpeggio can change. For example, you can take the notes of the C major arpeggio, 'C, E, G', and put the low C at the top, leaving you with 'E, G, c'.
Reordering the notes of an arpeggio is called an 'inversion', and triads have two of these. The 'name' of the chord is always the note at the top of the largest gap:

Inversions allow a given chord tonality to be referenced by a melody, while allowing the notes to remain within a given range, maintaining the desired melodic flow. An example can be seen in bar two of 'Langstrom's pony', from the previous heading.
A second inversion A major arpeggio is used. Note that the 'A' note is repeated twice, and also that the bar returns to A following the high C:

Learning to play arpeggios by pattern recognition, it helps to practice playing the 3 note arpeggios within the range of your ocarina, and an example exercise for C major has been provided below:

I'd also recommend practising the inversions of the triads in the same way.
Diatonic intervals
An interval is the distance between two notes, and within sheet music, a given diatonic interval is always represented by the same number of positions on the staff.
Learning to recognise intervals allows you to make arbitrary movements within a scale relative to another note, without caring which notes you are moving between.
Seconds
In sheet music a second is the interval between any adjacent line and space. The second is the smallest diatonic interval.

Thirds
Thirds are easily recognised as they are the interval between any two adjacent lines, or any two adjacent spaces. They are very commonly seen as arpeggios are based on thirds.

Fourths
A fourth is a movement of three staff positions. That is, the from a line to the space above the line above, or from a space, to the line above the space above.
Fourths are often seen as it is the interval between the fifth of a chord and the octave. Fourths also exist within inverted arpeggios.

Fifths
A fifth is the distance between 3 adjacent lines or 3 adjacent spaces. It is also the same as two thirds added together.

Sixths
A sixth is the interval between three lines plus one, or three spaces plus 1.

Sevenths
A seventh is four lines or four spaces on the staff.

Octaves
The interval between four lines plus one, or four spaces plus 1 is an octave.

Identifying and performing diatonic intervals
Making use of diatonic interval patterns when playing sheet music comes down to learning to identify the intervals at sight, and learning to navigate the notes of your ocarina by interval.
Learning to identify intervals at sight
Identifying intervals at sight is pretty easy:
- Get some music paper.
- Ask a friend to draw notes at different intervals for you to identify.
- Start with 3 or 4 intervals initially, and adding more as you gain experience.
There are also music practice apps that will generate random intervals in notation, and allows you to practice identifying them in the same way.
Learning to navigate your ocarina by interval
Navigating the notes on your ocarina by interval is what diatonic interval exercises teach you. For example, here are the diatonic fifths within the range of an alto C ocarina:

You can find diatonic interval exercises for an alto C ocarina in the exercises section. Diatonic intervals for ocarina.
Common figures
There are also a number of figures which show up frequently in sheet music. Consequently, learning to recognise them helps with reading sheet music using pattern recognition. A few examples of such figures are shown below.

Many of these patterns have been discussed in the section Using melodic patterns to play by ear, and there is a great article about it online, 'The 24 universal melodic figures', which gives many examples of these in popular music.
Putting it into practice, playing sheet music by pattern recognition
Lets return to the first part of Jim ward's jig, and try playing this sheet music by pattern recognition.

- Following the starting G is an ascending scale run from G to B.
- The first two notes second bar forms a descending scale run, starting from the B in the previous bar, and then drops by a third.
- Bars 3 and 4 can be read using seconds and thirds.
- Bars 5 and 6 are almost the same as 1 and 2, but bar 6 finishes on an ascending scale run.
- Bar seven includes a descending E minor arpeggio.
You may notice that this tune includes a figure descending by a second followed by a third, or a third followed by a second.

Both of which can be considered 3 note 'slices' of a pentatonic scale, and are also common melodic figures worth learning. They are discussed in 'The 24 universal melodic figures'.
Once you can read by pattern recognition, one of the things you one can do with the skill is to transpose music at sight, or read music onto ocarinas in different keys at written pitch.
You disassociate the note positions from fixed fingerings, and instead associate them with relative movements in a scale. Transposing is then just a matter of substituting one scale for a different one.