The Major 3rd Interval
The Major 3rd interval defines the sound of Major in anything it is in, chords, scales and arpeggios. Because it is so definitive most people find it fairly easy to recognize.
The easiest way to play a Major 3rd is to just go up 4 frets (so there will be three 'empty' fret between the note you start on and the one you end on) and you can also step back one fret back and onto the next string down.
Cross onto or over String 2 (B string) you need to jump the top note up a fret, so in this case it will mean the Major 3rd from String 3 to String 2 will be in the same fret - the guitar is tuned in Perfect 4th intervals except String 3 to String 2 which is a Major 3rd.
There are quite a few possible song references you can use for the Major 2nd, we're looking for the first two notes of the melody to use the interval jump of a Major 2nd (Tone).
I usually recommend Oh When The Saints because that seems to be a well-recognized melody, but most important is that you find a song that you relate to and that you know very clearly in our musical mind.
Oh When The Saints Go Marching In
Major Arpeggio (common in vocal exercises)
Blister in the Sun (Violent Femmes)
Ob-la-di Ob-la-da (The Beatles)
While Shepherds Watched Their Flocks by Night
Dr Justin prescribes 5 minutes a day of singing a Major 3rd (on top of your 5 mins of Play What you Hear). So 10 minutes a day of Ear Training if you can afford it!
1. Start with playing the interval on the guitar and singing along to get used to the sound and feel of the interval. Imagine your Song Reference while you are doing so, and sing the words if it helps. If you're still struggling with singing you can always hum!
2. Play and sing a root note, then stop playing and sing the interval jump and then check it on the guitar so you're sure you are getting it right and in tune.
I would recommend at least a week singing the one interval and using shapes all over the neck so that you get familiar with it everywhere - if there are parts of the neck you find a lot harder - work more on them. Play and sing this until you feel that you can sing it from anywhere and play the interval from any note! Then move onto the next interval!