Different types of scales?
In the field of mathematics, scale is very important because it is used in measurement. It has four types; (1) the nominal or the scale that differentiates the two items, (2) ordinal scale that allows for rank orders, (3) interval scale that is in the degree of difference of items, and (4) the ratio type used in the estimation of the ratio of the continuous quantity.
C, C#, D, D#, E, F, F#, G, G#, A, A#, B. Since E# = F natural, there is no extra "E#" but instead F natural, which would have been there anyways. Same for B# and C. There are 7 different white-key scales and 5 black-key scales, totaling 12 scales. Each of those 12 different notes on the keyboard have 4 different types of scales, of which one of each is the major scale.
There are major scales in all twelve keys. Same with minor but their are three different types of minors which include harmonic, melodic, and natural. There are also the modes of scales including Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. Finally there are "Blues" scales used in Jazz. This includes the root, minor third, fourth, flat fifth, fifth, and flat seventh.