I am a 17 year old male. My range is currently E2 to C4 and I am untrained.
My vocal range is narrow, but I want to be able to sing well. I'm wondering if I am still be able to improve my tone and vocal range.
You said you're 17 and male. Your voice may have broken years ago or quite recently, and you might not even have very good control over it yet.
The more you sing the more flexible your voice is likely to become and, to some extent, you should be able to extend your range a bit... but don't force it.
My experience is entirely in singing classical music, where there's great attention paid to timbre and tonal quality of a voice, and being able to sing in a specific tonal quality, and volume, over different parts of your range.
A conductor might want music sung very breathily, or very smoothly or very quietly or very loud or warmly or 'covered' or... and the chances are you won't be able to do that over your entire range even on a good day.
On a bad day - you're tired - the air's too dry - you've got a sore throat... getting notes at extremes of your range, or at points in your voice where eg you change from chest to head voice will be more difficult.
Vocal exercises are often about finding ways to make some of these things easier, or at least give you better control over them.
There are lots of tutorial pages on the web, just as there are lots of singing teachers. I think you'd be best to find a teacher because that way you get advice from someone who hears and sees (and feels, eg your stomach as you do it), whereas watching a tutorial video you won't know if you're doing something the right way. However be aware that different teachers teach different techniques. Unless you climb into a MRI scanner you'll not really know what your vocal cords and muscles, soft palate etc are doing when you think about producing a sound in a particular way. Different teachers may have quite different ways of explaining how to do something and part of the problem is finding a teacher who's on the same 'wavelength' as you, so that when they explain something you understand what they mean.
Keep on practising and work on your vocal exercises.
Let's compare your vocal cords to a rubber band. I'm sure you've done this at some point in your life: if you stretch the rubber band between your fingers (or something else) and strum it, it produces a sound. The harder you stretch the rubber band, the higher the sound becomes.
When you strum the rubber band, you can see it going up and down. This moves the air around it and produces a sound. The distance between the crests and throughs (highest and lowest point) determines the velocity, how loud it is. The time it takes to go from a crest to the next crest is the wavelength (or frequency), how high it is (the note).
A higher frequency means the rubber band vibrates more intensely (it is spun more tightly). See the link below for more details:
Your vocal cords, much like a rubber band, can stretch and contract. As with a rubber band, your vocal cords can be stretched out and spun more tightly to create a higher pitched sound. Of course, there are limits to this; if you stretch it too tight, you might break it when strum. Your vocal cords are pretty touch, and it will hurt when you try to reach too high.
There are a ton of exercises you can do to stretch your vocal cords and start practising to reach higher notes. Another advantage of the exercises and stretching your vocal cords, is that it becomes easier to have more clearer tones as well (must like a warm-up for your muscles makes it easier to maintain a cardio workout). Below is a site that lists some exercises to "warm up" your vocal cords:
But, at some point, you will reach the highest note you can produce with your chest voice. Most people will automatically switch to their head voice, or "falsetto". In this head voice mode, you can produce even higher notes, because your larynx is closing your vocal cords in a specific way, shortening the effective length of the cords.
This means the vocal cords gain in frequency, because the time it takes from a crest to the next is shortened. To get back to the rubber band example: if you strum the rubber band it produces a low note. If you put your finger in the middle of the band and strum it again (without adjusting the tension of the band) it produces a higher note.
One good exercise I find very good (after the regular stretching and warm-up), is using an instrument to produce sound, which you then replicate with your voice. Start at middle C and work up or down, depending on which you want to train. There are a few melodies you can try to make it more interesting, more difficult and even more natural than just plain notes:
I hope this long post helps you understand how things work and what you can do to improve. I'd love to hear from you how things go from here on out! Don't fret it when it won't work the first time; practise is key! Nobody starts out perfect!