There may be many reason why a note can sound so good.
An important one is the overtones of a particular note of fundamental frequency f to be slightly more than x2 f, x3 f, x4 f .., etc so that it sound correct and pleasing to ear brain.
Great pianos, orchestras (each individual instrument), pipe organs do this.
But sometimes very few specimens of very cheap electronic instruments can do this. One example is the Casio MA-100. Not only does each note sound nice, (for example the voice Street Organ) but but each note is tuned so that high octaves sound correct to ear brain by having the right amount increase of frequency from "equal" temperament.
In summary the wrong amount of inhamonicity (lower or higher frequencies than needed by the human ear brain) sounds bad. What is wishfully called harmonicity (exact x2, x3, x4, x5 frequency,...) sounds appalling. The right amount of inharmonicity sounds perfect. For example the great large Steiway grand pianos. Other example is the very high instrument notes of the song I've had the time of my life from the Dirty Dancing soundtrack.
References:
Ear brain octave vs engineering octave - euroelectron
Octaves and pitch - Lindqvist-Gauffin, Sundberg
Octave Stretch - Terhardt
http://www.mmk.ei.tum.de/fileadmin/w00bqn/www/Personen/Terhardt/ter/top/octstretch.html
http://historicaltuning.com/StretchingOctaves.html
Bibliography:
Musical Acoustics - Donald Hall
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