Maths Sequences In Music

Anyone who starts exploring music theory will start to see mathematical patterns in music – they’re all over the place! In this article I’d like to share with you some ideas on using numerical patterns applied to scales – I call them Melodic Sequences and they’re super useful, often sound great and are awesome technical exercises to help your fingers break out of the tired old patterns. 

You will find that the things you practice are the things you play when you improvise and so running scales up and down can be a dangerous thing to practice too much – they rarely sound cool in an improvisation.

However, melodic sequences can sound really musical and are in my opinion a much more fun and useable thing to practice – and the king of them all is “3rds”. Chords are constructed in stacked 3rds, and so if you are improvising and find yourself on a good note, there’s an extremely high chance that the note up a 3rd will also sound great, so it’s a very good thing to drill into our fingers, so they do it quite naturally.

As a number pattern 3rds would look like: 1 3, 2 4, 3 5, 4 6, 5 7, 6 8 etc. I describe it as play a note, miss a note and then come back to the one you missed. Repeat.

You can apply the number sequence to any scale (or group of notes) but applying it to the major scale would be the best place to start. Just number the notes of your Major Scale and then apply the sequence and off you go! 

Try it in Pattern 1 of the Major Scale, and you should find it falls fairly easy under the fingers. Try it in Pattern 2, and you’ll find you hit some interesting fingering problems that will help you develop your technical guitar problem-solving. You’ll find lessons on The Major Scale in 3rds across all five patterns on my website, along with problem-solving hints!

<< Tab of Major Scale P1 in 3rds >>

Each Melodic Sequence in each Scale Pattern will present new challenges for fingering, picking, dexterity and concentration, so you are guaranteed a solid workout! Try applying the 3rds patterns to Minor Pentatonic Scales! Yes, theory pedants, it’s not really intervals of 3rds anymore (a mixture of 4ths and 3rds), but it sounds super cool!

<< Tab of Min Pent P1 in 3rds >>

But you can have a lot more fun than this – the concept is a big one, and there are loads to explore. One that I really like is reversing every second pair of 3rds, so: 1 3, 4 2, 3 5, 6 4, 5 7, 8 6 – this sounds awesome applied to the major scale or a pentatonic!

You might like to try other number sequences like 1234, 2345, 3456, 4567, 5678 – which I call 4-in-a-line. Or 123, 234, 345, 456, 567 etc which is 3-in-a-line.

You can try using other intervals like 4ths: 1 4, 2 5, 3 6, 4 7, 5 8 etc. or 5ths: 1 5, 2 6, 3 7, 4 8, 5 9 etc. or 6ths or even 7ths! Reversing every second pair is almost always a fun idea too. You can change them up any way you like in fact, and you’ll find plenty of examples of the great Baroque composers using patterns like 1 3 2 1, 2 4 3 2, 3 5 4 3, 4 6 5 4 – you can get as creative as you like!
I would encourage you to take this idea and run with it – it’s challenging yet fun, creative but logical and both musical and technical – a great blend. I wouldn’t go overboard with it – but a few 5-minute sessions of sequences applied to different scales will be well spent! Hope that gives you something fun to explore and see you for more soon! Safe travels! J.

Food For Thought