The harmonic major scale has just one tonally effective mode which is named after its parent prime.
It is spelled in numerical form (relative to the major scale):
So if the tonic is c, then the scale consists of the following notes and chords:
|c||d||e||f||g||a||b||Hear these notes|
|C||d0||e||f||G||A+||b0||Hear these chords|
It has semitones between its 5th and 6th degrees and between its 7th and 8th degrees. It has three types of second - major, minor and augmented, making it less melodically smooth than the diatonic scales.
It is, however, very effective tonally, with the tonic on I being very decisive and quite unambiguous.
Indeed this scale is often substituted for the major scale as it can strengthen the tonality. It is from this scale that perhaps the two most common chromatic chords in the major scale are derived - the minor subdominant (iv) and the diminished supertonic (iio).
The harmonic major scale is not usually used for an extended period of time because of its melodic and harmonic deficiencies compared to the major scale. But outside of the stylistic conventions of common practice music which avoid augmented seconds and prefer major and minor triads to augmented and diminished it can be very effective as a medium for tonally centred expression.