It is very important to practise scales in thirds, particularly for aspiring jazz musicians. Melodic patterns based on thirds have been used by composers and improvisers for hundreds of years. Moreover, since chords are constructed primarily from intervals of a third, playing scales in thirds lays the foundation for an understanding of harmony. The pdf attachment shows six exercises, which you should eventually be able to play in every major and minor key:
Exercises 1 & 2
This is the basic exercise, for less experienced players, which you should start to play as soon as you are able to play a scale in one octave. The examples here are in G major and E minor. Note that the E minor exercise is in the harmonic minor. Try to sing the exercise first, and then play it slowly on your instrument. It is important to be aware of whether each third is major or minor.
This is for intermediate to advanced players. As your technique develops you should extend the pattern to cover the full range of your instrument. This example is for the saxophone, encompassing the range from low B to high E. Start and end on the key note, which in this case is G.
Here the thirds are played in triplets, which creates an interesting rhythmic effect.
Here every other third is inverted.
This is a combination of Exercises 4 and 5: thirds in triplets with every other one inverted!
Scales in thirds – Score