A woman in the Harem in Constantinople would be trained and educated in all the fine arts. She could even sell her work, to raise money for anything she wanted, including buying her freedom. However, a palace trained wife was also sought after, as not only would the woman be educated and talented, she would have political knowledge of the Seray.
The above picture is a 16th century turban cover. A turban was worn like a hat, having been sewn together then placed on the head when needed as a solid object. When not in use, it would be covered up, to protect them. Many of these clothes are quite heavily embroidered.
This is a 18th century sampler, at the Fitzwilliam Museum. What is noticeable is the traditional ottoman embroidery elements of asymmetrical flowers etc are interspersed with Western elements like the beribboned flower sprays.
If interested, please look through the Museum page, which has links to Museums and their online collections or possibly check out your local Universities or State Libraries. However, there are books for sale about Ottoman embroidery from Borders Australia, The Nile Australia and Amazon.
Flowers of Silk and Gold– a permanent exhibit at the Textile Museum.
The Ottomans.org– embroidery page.
Turkish Cultural Foundation– Turkish embroidery.
Bazaar to Piazza By Rosamond E. Mack on Google Books.