Who invented the cabin chime? What aircraft was the first to use it?
I can't definitively identify the true origin of the chimes; but the earliest reference to them I can find is in:

ARINC Characteristic 715-3 Airborne Passenger Address Amplifier (PA AMP)
This standard describes the characteristics of a PA AMP designed for
installation in commercial aircraft. Its function is to amplify control voice,  music and internally generated chime audio signals to drive the aircraft cabin  loudspeaker system.

The original ARINC 715 was published in 1978.
The standard they defined is in section 3.4 of the document:

3.4 Chimes
The PA Amplifier equipment should include a chime generator capable of
providing two tones in the four remote controlled sequences that may
be deployed through either the auxiliary or main amplifier utilizing
aircraft strapping. Internal controls shall be provided to adjust the
individual tone levels for balancing the related outputs.
3.4.1 Tone Frequencies
The high tone should be 587 Hz (musical Note D) and the low tone
should be 494 Hz (Musical Note B) signals of a pleasant sounding
musical nature.
3.4.2 Tone Harmonics
The chime tone harmonics should be minimized with the second harmonic
level at least 30 dB below that of the fundamental and each succeeding
harmonic should be a further 3 dB below the preceding harmonic.
3.4.3 Tone Decay
The single high and low tone levels should decay to a level 30 ±6 dB
below the peak level within 900 milliseconds from the peak. The second
tone of the high/low combination should begin 900 ± 100 milliseconds
after the peak of the first tone.
3.4.4 Sequence Control
Five tone sequence control lines should be provided to actuate
individual or two tone sequences as follows:
a. Passenger Call (High Tone)
b. Attendant Call (High/Low Tone)
c. Attendant Emergency Call (High/Low Tone Repeated Three Times)
d. Seat Belt Sign (Low Tone)
e. Smoking Sign (Low Tone)