The scale is a melodic structure that includes a group of musical pitches (i.e. musical tones). It is a set of ascending or descending melodic intervals. The scale exists in the horizontal dimension of music. Usually, musical pitches that are included in a scale are also called scale degrees. Nowadays, the most useful scale is the Heptatonic scale. Sometimes it is named Diatonic. "Hepta" means seven so this type of scale has seven degrees (seven pitches): tonic, supertonic, mediant, subdominant, dominant, submediant, leading tone (or subtonic). Tonic is the tonal center and resolution tone. The leading tone is the most dissonant and it resolves to the tonic.
The construction of the scale is related to the so-called circle of fifth. If we will stack fifths from F we will get next progression: F-C-G-D-A-E-B-F. That progression is called the circle of fifth. The last fifth in it will be diminished. This set of pitches forms seven musical modes: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Locrian. They are named Gregorian modes because the prime usage of them was to write Gregorian chants and other liturgical musical compositions.
Natural major has the same structure as Ionian mode. There are four perfect intervals in the scale: unison, fourth, fifth and octave. All rest intervals are major: second, third, sixth and seventh. Major intervals sound more stable than all the others that is why the scale usually associated with a joyful feeling. Each major scale has a relative minor and vice versa.
You can build the natural major scale using the following pattern: Tone - Tone - semitone - Tone - Tone - Tone - semitone.
The major scale can be harmonic or melodic as well as the minor scale. However, these types of scales are rarely used. The use of harmonic minor is due to functional harmony. While harmonic major can only play a decorative role.
In the pattern of harmonic major attention should be paid to an augmented second: Tone - Tone - semitone - Tone - semitone - Tone and semitone - semitone.
And melodic scales complement harmonic ones. In the harmonic major, the sixth degree is lowered. In the melodic major sixth and seventh degrees are lowered.
The pattern of the melodic major scale: Tone - Tone - semitone - Tone - semitone - Tone - Tone.
Natural minor has the same structure as Aeolian mode. In addition to four perfect intervals in the scale: unison, fourth, fifth and octave; it has three minor intervals: third, sixth and seventh; and also major second. Natural minor does not have a leading tone. Instead of that, it has subtonic. But functional harmony demands the tension to resolve. That is where you need the harmonic minor.
The pattern of the natural minor scale will be as follows: Tone - semitone - Tone - Tone - semitone - Tone - Tone.
In the harmonic minor, the seventh degree is raised to get the leading tone. So in comparison with the natural minor, it has a major seventh. Chord progressions can not be built without the harmonic minor. In melodic figuration, you can use natural minor for descending movement but for ascending movement neither natural nor harmonic minor is enough. The problem is that you still need major seventh for the leading tone and there will be an augmented second between sixth and seventh degrees.
A noticeable difference in the pattern of the harmonic minor scale is the presence of an augmented second: Tone - semitone - Tone - Tone - semitone - Tone and semitone - semitone.
To solve the problem you need to use the melodic minor. In this musical scale, both and seventh and sixth degrees are raised. In addition to four perfect intervals, the melodic minor also has three major intervals: second, sixth and seventh; and minor third. Sometimes this scale is used to build chord progressions too.
The ending of the melodic minor pattern resembles the natural major scale: Tone - semitone - Tone - Tone - Tone - Tone - semitone.
The chromatic scale contains twelve musical pitches. The distance between degrees in the scale always equals to a semitone (a half-step). As a symmetrical scale, it has neither center no tonic. Like any other scale, the chromatic scale can be ascending or descending. With the ascending motion, we raise the current pitch by one semitone to get the next scale degree. In this case, the scale notated with sharp signs. With the descending motion, we lower the current pitch by one semitone to get the next degree. The scale notated with flat signs. Primarily, this scale is used in melodic figuration.
Previously, we got one diminished fifth in our circle of fifth. To get the full circle of fifths we need to continue stacking: F-C-G-D-A-E-B-F♯(G♭)-C♯(D♭)-G♯(A♭)-D♯(E♭)-A♯(B♭)-F. Let's look at the end of the progression. Technically A♯ and B♭ are equal pitches with the same frequency. Note name and accidental sign depend on the start pitch and movement direction. A♯ is an ascending fifth from D♯. B♭ is a descending fifth from F.