Lydian mode

The modern Lydian mode is a seven-tone musical scale formed from a rising pattern of pitches comprising three whole tones, a semitone, two more whole tones, and a final semitone.
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 7/4
 c4^\markup { Modern C Lydian scale } d e fis g a b c2
</score>
Because of the importance of the major scale in modern music, the Lydian mode is often described as the scale that begins on the fourth scale degree of the major scale, or alternatively, as the major scale with the fourth scale degree raised half a step. This sequence of pitches roughly describes the scale underlying the fifth of the eight Gregorian (church) modes, known as Mode V or the authentic mode on F, theoretically using B but in practice more commonly featuring B. The use of the B as opposed to B would have made such piece in the modern day F major scale.
Ancient Greek Lydian.
The name Lydian refers to the ancient kingdom of Lydia in Anatolia. In Greek music theory, there was a Lydian scale or "octave species" extending from "parhypate hypaton" to "trite diezeugmenon", equivalent in the diatonic genus to the medieval and modern Ionian mode (the major scale).
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 7/4
 e4^\markup { Greek Lydian tonos (diatonic genus) on E } fis gis a b cis dis e2
</score>
In the chromatic and enharmonic genera, the Lydian scale was equivalent to C D E F G A B C, and C C E F F A B C, respectively, where signifies raising the pitch by approximately a quarter tone.
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 7/4
 e4^\markup { Greek Lydian tonos (chromatic genus) on E } f gis a bes cis dis e2
</score>
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 7/4
 e4^\markup { Greek Lydian tonos (enharmonic genus) on E } feh gisih a aih cisih disih e2
</score>
Medieval Lydian mode.
In the Middle Ages and Renaissance, this mode was described in two ways. The first way is the diatonic octave species from F up to F an octave above, divided at C to produce two segments:
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 5/4
 f4^\markup { Medieval Lydian mode on F } g a b c
 \time 4/4
 \parenthesize c d e f
</score>
The second is as a mode with a final on F and an ambitus extending to F an octave higher and in which the note C was regarded as having an important melodic function. Many theorists of the period observed that B is used more typically than B in compositions in Lydian mode.
Modern Lydian mode.
The Lydian scale can be described as a major scale with the fourth scale degree raised a semitone, making it an augmented fourth above the tonic, e.g., an F-major scale with a B rather than B. This mode's augmented fourth and the Locrian mode's diminished fifth are the only modes to have a tritone above the tonic.
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 7/4
 f4^\markup { Modern F Lydian scale } g a b c d e f2
</score>
In Lydian mode, the tonic, dominant, and supertonic triads are all major. The subdominant is diminished. The triads built on the remaining three scale degrees are minor.
Notable compositions in the Lydian mode.
Classical (Ancient Greek).
The "Paean and Prosodion to the God", familiarly known as the Second Delphic Hymn, composed in 128 BC by Athénaios Athenaíou is predominantly in the Lydian "tonos", both diatonic and chromatic, with sections also in Hypolydian.
Medieval.
The 12th-century "Hymn to St. Magnus" from the Orkney Islands, referencing Magnus Erlendsson, Earl of Orkney, is in Gregorian mode or church mode V (F white notes), extending from the E below to the octave above, with B's throughout, in two-part harmony of mostly parallel thirds. The Sanctus, Agnus Dei, and Ite, missa est of Guillaume de Machaut's "Messe de Nostre Dame" feature extensive use of F and B, as well as F and B.
Romantic.
A rare, extended use of the Lydian mode in the Classical repertoire is Simon Sechter's 1822 "Messe in der lydischen Tonart" (Mass in the Lydian Mode). A more famous example from around the same time is the third movement of Ludwig van Beethoven's String Quartet No. 15 in A minor, Op. 132 (1825), titled by the composer "Heiliger 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 alternating passages in F use the Lydian scale with sharp fourth scale degree exclusively.
Charles-Valentin Alkan's "Allegro barbaro" (Étude Op. 35, No. 5, published in 1848) is written strictly in F Lydian, with no B's present at all .
Anton Bruckner employed the sharpened fourth of the Lydian scale in his motet "Os justi" (1879) more strictly than Renaissance composers ever did when writing in this mode.
Modern.
In the 20th century, composers began once again to exploit modal scales with some frequency. George Enescu, for example, includes Lydian-mode passages in the second and third movements of his 1906 Decet for Winds, Op. 14. An example from the middle of the century is the scherzo movement of Carlos Chávez's Symphony No. 3 (1951–54). The movement opens with a fugue subject, featuring extremely wide leaps, in C Lydian with following entries in F and G Lydian. Alexei Stanchinsky wrote a Prelude in Lydian Mode earlier in the 20th century.
Jazz.
In "Lydian Chromatic Concept of Tonal Organization", George Russell developed a theory that became highly influential in the jazz world, inspiring the works of people such as Miles Davis, John Coltrane, Ornette Coleman, and Woody Shaw.