Gig Performer’s note naming convention is the MIDI Note Standard - middle C is always note 60. Always. Unfortunately, there is no set standard for octave notation, which is what you are describing. This topic comes up regularly in this Community. You can read my last response to one of the topics about it HERE which is a good description of the issue, and the problem the post was trying to solve. In your particular case, I would recommend you consider the standard to be the MIDI notation and the variable to be what any individual piece of hardware is using/sending, and create your solution accordingly.
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