Ionian/Lydian Gapped Scales and Hybrids
The Lydian scale is the same as the Ionian scale except that its fourth note is sharpened by a semitone. The Lydian scale has a major third and is thus, together with the Ionian and Mixolydian scales, a major scale. To convert an Ionian to a Lydian key signature add a sharp to, or remove a flat from, it. Likewise, to convert a Lydian to an Ionian key signature, add a flat to, or remove a sharp to, it. Note, however, that, although the above is theoretically correct, heptatonic Lydian scales are virtually unknown in Celtic, Anglo-American and English folk melodies.
07 Barbara Ellen (Cecil J. Sharp, 1916, One Hundred English Folk Songs)
Tune Analysis: E Ionian key signature but no A (4th). If the A were natural the scale would be Ionian, if sharp Lydian. Hexatonic E Ionian/E Lydian gapped scale, Authentic.