There are thousands of web sites & forms, official institutions, banks etc, that do not agree with your definition...
Example: Kentucky labor laws - .... While semi-monthly employees are paid on the 15th and at the end of each month..
Example on
http://www.payroll.com/resources/newhire/new_payperiods.html
The third step is to determine the length of your payroll periods. A payroll period may cover one day, one week, two weeks, half a month, one month, one quarter, or one year. Respectively, these periods are referred to as daily, weekly, bi-weekly, semi-monthly, monthly, quarterly, and yearly.