Lay the scale along the positive X axis of the number line. For example, the major scale has intervals 2-2-1-2-2-2-1, so the notes would be at points 0, 2, 4, 5, 7, 9, 11 and 12. There are always 12 steps in a scale because the octave of a note is 12 steps higher. This is because the octave of a note is twice the frequency and the 12th power of 1.059435 is 2, so 12 steps doubles the frequency.
Look at how this view of scales and the number line matches scales on fretted stringed instrument, such as the guitar. Zero on the number line corresponds to the open string, and the integers on the number line correspond to the frets on the instrument. The 12th fret on the instrument sounds a note that is an octave higher than the frequency of the open string. The major scale on a stringed instrument can be taken off the scale on the number line. The major scale that starts with the open string goes on to these frets: 2, 4, 5, 7, 9, 11 and 12. These numbers come off the number line.
Find the scales on stringed instruments by making multiple copies with each new coordinate shifted by the distance between the sounds of the different strings. For example, if you make five copies of the X axis and place each copy one unit above the previous coordinate, you have a representation of the six strings of the guitar. Start the numbering on the new coordinates on 5, 10, 15, 19 and 24 to reflect the tuning of the higher strings. With this new coordinate system, it is easy to see how the scales are played on the guitar.