A scale is "stretched" when the tunings are set so that each interval and octave is larger than 100 Cents or 1200 Cents.
1 – This practice of tuning was initially considered by piano tuners. When a note is played on a stringed instrument, components are produced at the same time but for physical reasons, they are inharmonic (the frequencies of overtones depart from whole multiples of the fundamental frequency). The piano tuner therefore uses his knowledge and ear to correct this effect and ensure that the intervals between the notes retain their consistency by performing a stretched tuning. He can not correct all the beats generated by multiple inharmonic but he draws a soft progression of these stretched intervals for a consistent and musical final tuning.
2 - A piano tuner can also look to have fifths without beating across the whole tessitura. He realizes a tuning said "equal temperament with perfect fifths." It follows from this technique a ratio of 2.003875 between octaves (instead of 2.0 - because they are enlarged 1/7th of Pythagorean comma). The tuning becomes stretched in this case too. http://fr.wikipedia.org/wiki/Temp%C3%A9rament_%C3%A9gal_%C3%A0_quintes_justes
3 - Another reason for a stretched tuning is to adapt the musical instrument to his environment and use. For a solo piano concert, the musician may wish to give a brilliant effect to high notes and also fuller sounding bass notes.
4 - Beyond the physical rules governing string instruments and their use, stretched tuning may have another role that interest musicians and acousticians.
Our ears and brain evaluate the pitch of a sound subjectively. We feel that the high notes sound "flat" and the bass notes sound "sharp".
This psychoacoustic effect is such that the perceived tonality matches the real frequency in the area lower than 500 Hz and not beyond 500Hz. Research on this concept can be done from here: http://en.wikipedia.org/wiki/Mel_scale
There may be other reasons for this tuning technic and any additions or corrections are welcome.
Unlike the piano tuners, Steelpan and Handpan tuners can control the harmonics during the tuning process. The tuner may therefore choose to stretch the tuning for psychoacoustic reasons (N°3 and 4).
I research now what kind of stretched curves produce what kind of perceived effects...