the ornamental turner cuts a pattern on the object, one complete revolution.
the ornamental turner then rotates the object some pre-determined direction and number of degrees (say, 15° clockwise)
the ornamental turner repositions the cutting head a pre-determined distance (say, 0.050" towards the lathe headstock)
the ornamental turner then cuts the same pattern on the object, one complete revolution.
Steps 2-4 are repeated until the object is completed.
Jon Magill authored an article titled, "Phasing Fundamentals" that describes phasing in better details. That article was published in the AAW's magazine, "American Woodturner" in Summer 2008, pages 62-63.
Indexing wheels like the yellow one shown to the right can be made with 3D printers, or they be purchased. I purchased an aluminium one from Alisam Engineering.
Spiral Fluting an Ornament on a Rose Engine
This video shows a number of things, including the use of an Alisam index wheel (around 2:35 into the video).
Disclaimer : eMail comments to me at OTBookOfKnowledge @ Gmail.com. The process of woodturning involves the use of tools, machinery and materials which could cause injury or be a health hazard unless proper precautions are taken, including the wearing of appropriate protective equipment.