Combine Enum and Class for Extended functionality

EnumClassSample.cs

// The  idea is to collect this kind of parsing nearest possible to the enum itself
// Why? Because the enum is the reason to the Method and are  easy to find and modify
// Also it's natural to extend with other kind of parsing. Just insert more methods.

// The main drawback, is that I have to state the enum more explicit (i.e. Something.TypeOf)
// Also the code design appears no standard and would apply if the enum was for internal use in the class.

// So, the question
// How would you do this more nice? I tried abstract, base inheritance, partial. None of them apply.
// This is a shortened down and renamed sample of a code that should be better coded.

    public static class Something
    {
        public enum TypeOf : short
        {
            Minute = 2, Hour = 3, Day = 4, ........
        }

        public static long GetTicks(Something.TypeOf someEnum)
        {
            long ticks = 0;
            switch (someEnum)
            {
                case Something.TypeOf.Minute:
                    ticks = TimeSpan.TicksPerMinute;
                    break;
                case Something.TypeOf.Hour:
                    ticks = TimeSpan.TicksPerHour;
                    break;
             ....
            }
            return ticks;
        }
    }


        // This class is called from anywhere in the system.
        public static void SomeMethod(string dodo, object o, Something.TypeOf period)
        {
            // With the design above
            long ticks = Something.GetTicks(period);

            // Traditional,
            if (period == Period.Day)
                ticks = TimeSpan.FromDays(1).Ticks;
            else if (period == Period.Hour)
                ticks = TimeSpan.FromHours(1).Ticks;
        }