I am a novice to this and probably have a 'budget' sax. I when I test the notes using an app downloaded to my iPhone all the notes are fine except the G which plays as an A (flat). I assume because all the other notes are okay, I have something wrong with the G key as opposed to a tuning problem?
Rather late I know but it sounds as if the Ab key is being held slightly open. This is usually due to the LH pinky keys being mis-aligned. There needs to be a slight gap between the tabs on the C# & B keys & the Ab touchpiece. Any technician will be able to sort this quickly.