Another way to write scale formulas is relative to the major scale.
If we assign a number to each note in the major scale, starting with 1, we have: 1, 2, 3, 4, 5, 6, 7
We can then raise or lower the notes with sharps or flats to write formulas for other scales relative to the major scale.
For example, another common type of scale is the natural minor scale (sometimes simply called the minor scale), which has a major-scale-relative formula of: 1, 2, 3♭, 4, 5, 6♭, 7♭.
To figure out the notes of the C minor scale, for example, using the major-scale-relative formula above, we can take the notes of the C major scale (C, D, E, F, G, A, B) and flattening degrees 3, 6, & 7, giving us: C, D, E♭, F, G, A♭, B♭.