Music students start a day with ‘Ear Training Class’ in the morning at music colleges & universities.
Great musicians have excellent ears. The reason of singing off key is nothing to do with your vocal folds or thoracic diaphragm, or any other parts of your body/instrument but it is to do with your ears that is in charge of your listening ability. The reason you are singing off key is that 'your ears are not trained well yet'.
So what is the solution for this problem? Learning to play piano can be very helpful because piano has definite pitch. Musical keyboards are laid out horizontally, so you can easily see what you are playing and by playing it you are training your ears. Also singing along the keyboard helps correct your listening skill. Play just one key at a time and sing along with the note that you are playing can be very helpful to correct your ears.
And having an experienced vocal coach who can monitor whether you are singing too low or too high and also can show you how to fix your specific issue of singing off key will be very helpful to improve your pitch/singing quickly. So yes, you will be able to sing on key by improving your ears & listening skills first.
In the next lesson we'll talk about 'the importance of sipping water while singing'~
Big Cheers & Much Love XXOO, Sunghee