Online singing lessons can be every bit as effective as singing lessons in person. To qualify this more, singing lessons using Skype, Google, or FaceTime can be as effective as the teacher or vocal coach is effective. Granted, the quality of sound is slightly less than in person, but it is better than a phone by a long shot.
What does the vocal coach need to hear? EVERYTHING, but it is not necessarily dependent upon sound quality, per se. Everyone does not perceive pitch the same way. Everyone does not hear at the same "depth and breadth" of sound, either. A vocal coach with a developed relative pitch can be very good. A vocal coach with perfect pitch has an excellent level of sound and pitch perception.
Knowing what was sung and knowing precisely what is heard is totally necessary for helping identify the source of a singer's pitch problems. Is it incorrect melodic intervals or is it a weak "harmonic ear" causing a singer to sing out of tune? Singers who also play a piano or guitar oftentimes have a more highly developed "ear" but not always.
Most singers seem to not want to spend the time and effort with ear training--except for the excellent ones. Ear training especially for singers is almost nonexistent, which is why I have taken the time to develop singer-specific exercises.
Whether online or in person, the exercises I have developed are as effective equally. The much neglected musical "ear" is the key factor in singers singing out of tune (Pitchy, off key). It isn't hard to handle and also doesn't require months to make it better.
Online singing lessons can be used for the various other factors for better singing, if the vocal coach is competent.
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