Does anyone know of an appointment scheduling app for small businesses, suitable for a business that has lots of appointments, like music lessons or massage/spa businesses?

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It should have the following features.

In addition to scheduling appointments on a calendar, it should avoid duplicate scheduling of employees/workers.

Allow workers to set unavailable time periods.

Allow customers to cancel appointments online.

Allow appointments to be moved, so that employees won't get double-paid and customers won't get double-billed for make-up appointments.

If requested, send out reminders to workers and clients ahead of appointments. (I already know that patio11 has an Appointment Reminder app.)