It still needs to be stabilized from digital noise. Some people use RC if Vref is attached to Vcc. Others use a separate Vref device ((reference chip or another regulator). If Vref is not very stable then the output data won't be either.

He's lucky that he get to throw away the LSB since the MIDI data is only 7-bit (assuming standard controller data). But I don't know if his problem "38, 39, 38, ..." is before or after throwing away the LSB.

Also he might not have a problem at all, just a matter of deciding what data is relevent or not.