Tonight, as a result of Sibylle’s ordering a set of E-Z Scale Blocks for her studio, I learned a neat trick for “calculating” the notes of a Major scale.
Major scales are comprised of two tetrachords separated by a half step. A tetrachord is four notes. So a C Major scale is: C D E F G A B C. The first tetrachord is C D E F and the second is G A B C. The second C is one octave higher than the original C.
If you start with: C D E F G A B, leaving the repeated C out, you can easily find the notes of the next scale by taking the first four notes (the tetrachord) and moving them to the end of the string. Once you’ve done that add a sharp to the last note. The result (starting from C Major) is G Major: G A B C D E F#.
Start with G Major: G A B C D E F#, and move the first four notes, and add a sharp gives you: D E F# G A B C#, or D Major.
Start with D Major: D E F# G A B C# and you get A Major: A B C# D E F# G#. And so on.
As a visual person, seeing the pattern with lettered blocks was amazing. Knowing a formula for figuring out the progression of scales is even cooler.