No, there is no maximum income limit for a traditional IRA. Anyone can contribute to a traditional IRA. While a Roth IRA has a strict income limit and people with incomes above it can't contribute at all, that rule doesn't apply to a traditional IRA. However, this doesn't mean that your income doesn't matter at all.
If your income is within the phase-out range, you'll divide the portion of your contribution directly into a Roth IRA and the part into a traditional, non-deductible IRA that you'll convert. Under the pro rata rule, IRA conversions are taxed in proportion to the amount of taxable contributions in all IRA balances. Roth IRAs allow you to save money that grows tax-free, but the Internal Revenue Service imposes income limits on those who can contribute to a Roth IRA. With a clandestine Roth IRA, a person makes a non-deductible contribution to a traditional IRA and then converts that account into a Roth IRA.
At Charles Schwab, for example, the account closing process is done daily, but allows 16 months of inactivity before closing an IRA if the customer has another open and funded IRA account. You save the most if you don't have pre-existing traditional IRA balances that need to be included in your tax bill, or if your employer's qualifying plan allows deductible IRA balances to be reinvested.