22 Shruti Tuning is a ancient, sophisticated, microtonal system of tuning. In every octave, there are 7 Swars. Of these, 2 are ‘Achal’ or ‘Immovable’ - Shadja (Sa) and Pancham (Pa). The remaining 5 notes (Re, Ga, Ma, Dha and Ni), called ‘Chala’ or ‘Movable’ Notes, have two variants each - a low and a high. This is how we get the 12 notes (5*2 + 2) in an octave. But, in a 22 Shruti system, each of 10 ‘Chala’ notes are further subdivided into 2 Shrutis - a low and high variant, giving a total of 22 (2*10 + 2) Shrutis. Thus for each of the 5 Notes (Re, Ga, Ma, Dha and Ni), we have 4 variants called ati-komal, komal, shuddha and teevra.. For each of the 10 ‘Chala’ notes, there is a region of pitch movement that is allowed in Hindustani Classical Raga Music that is demarcated by its corresponding two Shrutis. There are no such regions for Sa and Pa, which are fixed points in the octave. Although the difference between consecutive Shrutis is very small, when appropriate shrutis are used, it can subtly enhance consonance in a Raga's soundscape.
Gandhar Tuning is a tuning system based on the concept of the ‘Swayambhu’ (Self Manifested) Gandhar that can be heard in a perfectly tuned Tanpura. It is a system of 12 notes where there is a self-consistent relationship between notes. These 12 notes are a subset of the 22 Shrutis. In Gandhar Tuning, all the Shuddha Notes are tuned precisely using the Shadja :: Swayambhu-Gandhar :: Pancham ratios. Sa :: Ga :: Pa, Ma :: Dha :: Sa and Pa :: Ni :: Re are all the same ratios. Once the ratios of Shuddha notes are fixed using the above relationships, one can extend them to find the ratios of the remaining Komal and Teevra notes.
Equal Temperament is an invention of Western Music that enables playing chords in many scales. Since a Gandhar / 22-Shruti Keyboard cannot be used for any other pitch than it was originally tuned for, these can’t be used for chromatic melodies that span multiple pitches. Equal Tempered Notes split the octave in 12 ‘Equal’ parts. Now, the frequencies in an octave follow a power of two relationship, i.e. a note in the higher octave is 2 times the frequency of the same note in a lower octave. This means that the 12 parts are not at equal frequency intervals. Rather, ratios of subsequent notes are a ‘12th root of 2’ factor apart. Except for Sa, all others are irrational numbers, therefore dissonant with the Sa. In fact, only ratios that are simple rational fractions are harmonic with the Sa. Sa-Ga-Pa, Ma-Dha-Sa and Pa-Ni-Re chords (major chord) on an Equi Tempered keyboard are somewhat dissonant, while on a Gandhar Tuned / 22-Shruti keyboard, they are perfectly consonant. Equi-Tempered Tuning should be only used for multi-pitch melodies; it is unsuitable for Hindustani Classical Music.