Modes:  You may hear terms like "Mixolydian" or "Dorian" in relation to scales or patterns used in improvisational music.  These terms come from ancient Greece and are a part of modern music as well.  Although the names are the same as in ancient Greece the sequence of intervals varies from the original Greek modes.  These modes are very easy to figure out since they start on the white keys of the piano keyboard starting with C and moving up to B playing only the white keys.  The series of intervals created by doing this defines each mode, and using this sequence each mode can be played starting on any note.  W=whole step, h=half step.

Mode White Key Sequence
Ionian C W-W-h-W-W-W-h
Dorian D W-h-W-W-W-h-W
Phrygian E h-W-W-W-h-W-W
Lydian F W-W-W-h-W-W-h
Mixolydian G W-W-h-W-W-h-W
Aeolian A W-h-W-W-h-W-W
Locrian B h-W-W-h-W-W-W

As we can see the Ionian mode the the same as the C major Scale and the Aeolian the the same as the A minor scale.
The Dorian mode has a minor feel due to the minor 3rd from D to F.  This mode is used in both in jazz and pop music.  Miles Davis, the Beatles and Simon and Garfunkel all used this mode in songs like Eleanor Rigby, Scarborough Fair and Milestones.
The Phrygian mode is related to the natural minor Aeolian except the second note is a half step lower.  Modern use of this mode is the Phrygian Dominate Scale, or the Spanish Gypsy Scale.  In this scale the 3 note is raise a half step.  Starting on E you would play G# instead of G natural.  this mode is used in jazz and classical music.
The modern Lydian mode is a major scale with the 4th raised a half step.
The Mixolydian mode has the same series of half steps as the major scale except the seventh degree is a half step lower.  This mode is used in many musical styles including blues, pop and bluegrass.  The Locrian Mode is the only mode that results in a diminished chord from the tonic.  this mode has been used sparingly by Rachmaninov, Sebelius and others.

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