A scale formula is the arrangement of intervals from one tone to the next that defines the structure of the scale. Each scale such as major, natural minor, whole tone, etc, has it's unique formula. As an example, the whole tone scale is structured with a whole step between each of the adjacient tones. There are different methods used to describe this formula. Three different ways to say the same thing are shown for the Whole Tone scale:
Notice that the first two methods show the distance between adjacient tones (containing 6 elements) whereas the third method is shows the distance between the root and the other notes of the scale (containing 7 elements, including the starting 0, root). The first two methods tell you how far to the next adjacient note. The third method doesn't tell you how far to the next adjacient tone (you'd have to do the math). Instead it tells you what distance (in half steps) that note is from the root reference (0).
This page will use the third method to describe scale structures. Using that method the page is for practicing common scale structures (and for experimenting with other structures). The numbers represent half step increments across the 12 tone per octave system. The box labeled '0' represents the root (first note) of the scale and box labeled '12' represents the octave of the scale, they will always be included in the scale.
If you want to test your understanding of the major scale formula (or several others from the menu), click on the boxes labeled with numbers to select the appropriate location to create that scale formula (to unselect a number box, click it again). Your task is to select the 2nd, 3rd, 4th, 5th 6th and 7th notes of the major scale structure (or whatever scale is selected from the menu). When completed with your choices of the scale structure, click the 'Evaluate My Choices' button. (When evaluating be sure that the scale you are creating is also the scale selected in the Scale Type menu.) To hear your choices played click the 'Play My Choices' button.
You can experiment with other structures and hear them using the 'Play My Choices' button.
Scale Type: Volume:(white and black key layout when first note is C)
(click on the numbers that represent the structure of the scale selected in the Scale Type menu.)