Due to historical confusion, Lydian mode can refer to two very different musical modes or diatonic scales.
Greek Lydian mode
The Lydian mode is named after the ancient kingdom of Lydia in Anatolia. In Greek music theory it was based on the Lydian tetrachord: descending (the way the Greeks always wrote about it), a series of falling intervals of a semitone followed by two whole tones. Applied to a whole octave, the Lydian mode was built upon two Lydian tetrachords separated by a whole tone. This is identical to the modern major mode: C D E F | G A B C (ascending, in the modern reckoning). Placing the two tetrachords together, and the single tone at bottom of the scale produces the Hypolydian mode (below Lydian): F | G A B C | (C) D E F. Placing the two tetrachords together, and the single tone at the top of the scale produces the Hyperlydian mode (above Lydian), which is effectively the same as the Hypophrygian mode: G A B C | (C) D E F | G. Confusingly, the Greek Lydian mode is the same as the mediaeval and modern Ionian mode or major mode.
Mediaeval and modern Lydian mode
The early Christian church developed a system of eight musical modes (called the octoechos), which mediaeval music scholars related to the ancient Greek modes. However, due to misinterpretation of the Latin texts of Boethius, mediaeval modes were given the wrong Greek names. In mediaeval and modern music, the Lydian mode is a major scale with the fourth scale degree played a semitone higher than it would be in the major scale. The mediaeval and modern Lydian mode is the same as the Greek Hypolydian mode.The Lydian mode has the formula 1, 2, 3, #4, 5, 6, 7. Its tonic chord is a major triad.
A Lydian scale based on the note C consists of the notes C D E F# G A and B. Alternatively, if we start on the note F, the scale consists of the notes F G A B C D E. This scale can be played on the white notes of a piano without the use of any sharps or flats (black keys) only if started on the note F (F G A B C D E).
A rare evocation of the Lydian mode in the Classical repertoire comes from the third movement of Ludwig van Beethoven's String Quartet No. 15 in A minor, Op. 132 (1825). (See Common practice period.) It is titled by the composer "Heilige Dankgesang eines Genesenen an die Gottheit, in der lydischen Tonart" ("Holy Song of Thanksgiving by a Convalescent to the Divinity, in the Lydian Mode").
The theme tune for The Jetsons is written in the Lydian mode. The theme for The Simpsons is sometimes cited as being in the Lydian mode, and this is certainly true for the first few bars. However, later passages in the theme include a minor 7th, along with other notes characteristic of the Lydian mode, and that thus places those passages in the Lydian dominant scale, which is sometimes thought wrongly to be another mode, or related to the modal system.
Modern usage of the Lydian mode is often implied by certain chord spellings. For example, the chords D/C or Cmaj7#11 imply a C Lydian harmony. (D/C7 or C7#11 would both imply the Lydian dominant scale, which is the same as Lydian but with a flat 7th note)
Notable songs in Lydian mode
Care must be exercised in identifying songs or pieces based in Lydian mode. It is common for listeners to confuse Lydian mode, particularly at the beginning of a piece, with an extended section based on the IV chord of a major key (or, less commonly, a flat VI chord in a minor key).A good example of this ambiguity of Lydian mode can be found in the song "Maria" by Leonard Bernstein and Stephen Sondheim from the musical West Side Story; the opening measures of the main theme (E-flat, A, B-flat) could indicate E-flat Lydian mode, but the following four measures clearly establish B-flat major. By the time the E-flat-A-B-flat motive appears again in measure six, we are clearly hearing a IV chord in B-flat major rather than a chord built on the tonic of E-flat Lydian.
That said, the main theme and the song do cadence clearly to an E-flat major chord - although, in both cases, an A-flat (rather than the defining Lydian A-natural) is prominently featured in the penultimate chord.
On the other hand, it could be argued that a piece of music that follows this sort of pattern is actually fluctuating between Lydian mode and major tonality. For instance, in "Here Come My Girl" by Tom Petty each verse alternates between a D-flat major and E-flat major chord, with a D-flat pedal tone maintaining the impression that D-flat is tonic, and a repeated guitar lick frequently hitting the essential raised fourth scale degree--G-natural, in this case. This gives the verses a distinctly Lydian flavor. But in the chorus sections of the song, the tonality clearly shifts to A-flat major. This pattern is fairly common in pop music. Whether to say these songs are shifting between Lydian and major tonality, or simply extending the IV chord in major tonality, is somewhat open to interpretation.
