To normalize is to make the wave form a similar level so that one word isn't louder than another.
actually, that is not what normalization does. normalization maintains the relative volumes across whatever region is being normalized, but it increases the gain of everything in the region by a uniform amount.
it does it by searching for peaks and taking the value of the highest one. so, if the loudest part is at, say, -4.1 dB, then it will add 4.1 dB of gain to everything. the loudest part is now at 0 dB, but not everything will be at 0 dB. it does the exact same thing as pushing up the fader 4.1 dB.
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what you've described is what a compressor is for -- reducing the dynamic range of a signal. i've yet to find a compressor plug-in i like for voice, but there are some hardware compressors which are good. or amazing. but they cost.
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so here's the best news: you can do what you want for free. before i apply any compression to a lead vocal (or would apply to a VO, if i recorded those anymore), i gain-ride the track. by that, i mean that i adjust the volume curve according to the performance, to smooth it out.
i don't use GB, so i don't know if you can automate volume across a track, but all the other DAWs allow it. it's tedious work, but it sounds the best. you go through the peformance, phrase by phrase, word by word, sometimes syllable by syllable, and make the too quiet parts louder, and the too-loud parts quieter, just by drawing the appropriate curve.
i'll sometimes apply (hardware) compression afterwards, but i do that more for tone than to adjust dynamics.
hope that helps.