Tim Crawford has an on-going discussion about the warble effect that has baffled many flutemakers and players.
He begins with this simple description of a very complicated phenomenon.
[The Warble is a “natural vibrato” effect occurring in some flutes when the fundamental (all holes covered) is played. Some folks find this to be a pleasing attribute and others do not.]
Read more... And, browse the hundreds of pages of information related to Native American culture.
http://www.snowwowl.com/naartmusictimcrawford2.html
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To hear the warble effect being played go to "each" page of the site of Dr. Oliver W. Jones, Jr.
Don't miss the Flute Gallery of rare and interesting flutes while there.
http://www.wildhorsemtnflutes.com/