Into the first year of iPad, the typical iOS music app had far too much latency to be a viable music instrument (music instruments must be in the 10ms of latency range... 1/100 of 1 second touch to audio response; at a time when 100ms was the norm.). Mugician and Geo Synthesizer were widely regarded as some of only a handful of iOS instruments which could be played at the actual speed that real musicians could throw at it. (Much of this was achieved by avoiding UIKit in favor of OpenGLES2 up until the real-time issue became less of a problem.)
In addition to mobile apps, I did some experimentation on Microsoft Windows with large touchscreens, in this case using OSC protocol rather than standard MIDI:
Compare with Minor
Compare with Phrygian
As chord progressions change, the bottom half of the scales (tetrachords) define the notes in use. Usually the scale isn't defined rigidly across the entire octave. The idea is to string together shorter partial scales. In this way, many melodic runs will be full of accidentals, while still having a clear tonal character.
Note that if rooted on note 1, it's the harmonic minor tetrachord.
Now, go to Maqam World and read about Ajnas
More generally, the pentatonic core is stable; and other notes tend to move around to suit the circumstances. Note that in none of this have you seen an actual quartertone (1 fret) interval. The harmonics on a string generally dictate where notes will lie, and there isn't a useful second interval much smaller than a half tone (2 fret - small step).
This is another generic shape that arises, which is roughly centered around a Rast tonality. This scale is practically impossible to resolve with non-quartertone instruments playing along though.
Notice that harmonic 5 is slightly flat of the nearby fret. This is why when playing a maj third interval between two strings, bend the bottom note up a little bit until the timbre of the chord cleans up (and the beating goes away). This narrows the distance between the two notes.
Similarly harmonic 6 is slightly sharp of the nearby fret. So when playing minor third intervals between two strings, bend the top note up a little bit until the timbre of the chord cleans up (again, eliminates beating). This stretches the distance between the two notes.
Other intervals like a semitone (ie: an E and F played together) can be made just by bending the F up a little bit to clean up the chord. The locations of the harmonics make it clear what the pattern of adjustments for intervals is going to be.
Maqam is closely tied to Pythagorean tuning, where scales can be roughly thought of as a span of perfect fifths. A span of 53 perfect fifths comes so close to closing into a circle, that as far as this drawing goes, it doesn't matter whether we literally draw a scale created by spanning 53 perfect fifths or using 53 equal temperment. See how well the more important harmonics line up with fret locations.
The fret widths drawn were automatically generated based on how close they are in the perfect circle of fifths. Many instruments only include a subset of these frets, using a span of 22 fifths. That leaves a pattern where whole tones are cut into 9 equal parts, where whole tones (from fret 0 to fret 9, a pitch difference of 9/8) have no exact semitone. There is a semitone at either 4 or 5, for high or low semitones. Usually, the large semitone is used, as it more closely matches actual harmonics. When moving from note to note, there are temporary chords of a semitone going on.
In this system:
As a side-note about a common definition of "Sruti", a span of 22 perfect fifths will cause a scale that is very close to 12et to arise; except every note other than the root and fifth will have a doubled partner very close by (roughly distance 81/80 away). Similarly, a span of 17 perfect fifths gives a Pythagorean intonation where sharps and flats are distinct, like split black keys. Then spanning only 12 gives the true Pythagorean piano tuning, with its wolf interval among an otherwise fantastic intonation. Spanning 7 gives a purely intoned diatonic scale, and spanning 5 gives a purely intoned pentatonic scale.
Using this diagram, you can calculate explicitly how to reach a 53et fret by navigating in terms of only fourths, fifths, maj third, min third. The given ratios are just the more obvious equivalent ratios at that location. The point of this diagram is to show that 12et is an approximation of this Sruti span of 22 perfect fifths. And even though it's defined in terms of "3-limit" (pure fifths), it actually contains some "5-limit" (including Just Intonation thirds). And finally, the 53 equal temperment encompasses them both. To some degree, this whole system exists as a side-effect of people playing string instruments with the strings tuned fourths and fifths apart; where the 81/80 pitch drift depending on melodic path is an issue that must be explicitly dealt with. 12et simply equates these close note pairs to make them go away in theory, but this issue still exists physically in the sound; creating a tension between clean chorde timbre (ie: beating) versus having distinct instruments playing from the same pitch set.
Other equal temperments are possible. For practical reasons, 31 equal temperment might be a reasonable upper limit for most fretted and keyed instruments. Just for the sake of completeness, I will include it here. It is well known for being a great choice for triads (major and minor chords). It also doesn't have the 81/80 problem, as it is theoretically derived from a Just circle of major thirds. But note that it's not a great fit for Pythagorean intervals, which is important to support in maqam.
The important pitch ratios are in this (large) image as an octave equivalent ratio oriented pitch wheel.