What Pi "Sounds like" depends on what correspondence you make between the irrational number Pi and notes on an instrument. In this video, we (1) expanded Pi in base 12, which would give us digits from 0 to 11 (using two extra digits a=10 and b=11 ---not to be confused with the notes with the same names!), then played the following notes for the digits:
0=C
1=D Flat
2=D
3=E Flat
4=E
5=F
6=F#
7=G
8=A Flat
9=A
a=B Flat
b=B.
This is clearly arbitrary, and the tune sounds just as arbitrary.
To create some interest, we added the tune an octave lower, staggered by one measure, and then repeated the tune (32 notes, more or less) a fifth higher.
(Note you get a more pleasing melody if you use base 7, and just the notes of the diatonic scale. You could use just the notes of the pentatonic scale, if you expand the number base 5.)
For your information, Pi (π) in base 12 is approximately
3.184809493b918664573a6211bb151551a05729290a7809a49274214
and, in case you're interested, in base 7 it is approximately
3.0663651432036134110263402244652226644...
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