This is in the spirit of the What is a Word™/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.
If a word conforms to a certain rule, I call it a Asymphonic Word™. Use the following examples to find the rule:
$$ % nonstandard template, do not reuse % \def\Pad{\P{0.0}} \def\Title{\textbf{Asymphonic }} \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\ \def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words }^™\Pad}\def\NT{\Pad\textbf{Non-}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2017.02.04}\S{6px}{0} \begin{array}{cc}\Pad~\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad~\T&\NT\\\hline % \text{CACHE}&\text{CRICKET}\\ \hline \text{CIRCLE}&\text{CROCODILE}\\ \hline \text{CANCER}&\text{COCK}\\ \hline \text{GRUDGE}&\text{GANG}\\ \hline \text{GEOGRAPHY}&\text{GEOLOGY}\\ \hline \text{GRAPHOLOGY}&\text{GEMOLOGY}\\ \hline \text{GAUGE}&\text{GAG}\\ \hline \text{CROTCH}&\text{CHARACTER}\\ \hline \end{array}$$
CSV version:
CACHE, CRICKET
CIRCLE, CROCODILE
CANCER, COCK
GRUDGE, GANG
GEOGRAPHY, GEOLOGY
GRAPHOLOGY, GEMOLOGY
GAUGE, GAG
CROTCH, CHARACTER
Not only these but many such words exist.