The human voice is the original musical instrument.
It is also the most difficult instrument (in my experience) to master.
Every bit has to be sculpted:
Every volume change
Every emotional nuance
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For those lucky enough to be born with beautiful tone, singing might be a bit easier. But as with any instrument it can take years to get to a "professional level".
There are a few tricks and tips, however, that can speed up the process.
1. Understanding the anatomy
a) The vocal chords are similar in some ways to a violin string. Each point on the vocal cord corresponds to a SPECIFIC note.
When attempting to sing a note using the wrong part of the vocal chord, it is certainly possible to produce the correct note. However, the strain involved results in a raggedy tone, and can eventually injure the voice.
b) When singing a high note (using the thinner front part of the vocal cords), the thicker parts of the vocal cords towards the back can vibrate due to air pressure issues and cause bad tone and raggediness.
To solve this problem, you have to physically hold the back part of your vocal cords down.
While this seems totally "out there", remember that your vocal cords have muscles attached to them. AND they are muscles you can control (just like lifting a finger). If you "look inside" your body, you'll figure out how to do this.
2. Air flow
a) Everyone knows you have to control your breathing from the diaphragm. You have to prepare your air BEFORE each note or phrase.
b) What not everyone knows is that it is important to keep the airway clear and open. Too many people constrict the throat especially when attempting high notes.
Yawn. Yes, go ahead and yawn. You'll notice (if you look in the mirror) that your throat expands.
This is called the "Big Throat". Learn to expand your throat without yawning.
When singing (or playing any wind instrument), the big throat will allow you to have a large clean clear tone (as opposed to a weedy constricted tone).
Fear is a huge factor, especially when singing high notes. To leave the fear behind simply "think low" on high notes. By "thinking low" when singing high, you can expand your range up to half an octave immediately.
a) In the same way as any instrument, you have to practice phrases over and over again until they sound "just right". In many cases you'll have to practice ONE SYLLABLE over and over again to get it right and THEN go back to insert it into the phrase you're working on.
Then practice it enough to where it becomes subconscious reflex.
b) The vocal cords are contolled by muscles. If you sing every single day, your muscle control will increase - just like body building.
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Once you understand that the voice is simply an instrument like any other, you can begin to master it methodically like the other instrument(s) you play.