Tetrachords

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory. It literally means four strings. ( see the Wikipedia tab for a more detailed explanation )

Using C as the root here are some types of tetrachords.

Major tetrachord

tone - tone - semitone
C - D - E - F ( 1 2 3 4 )
G - A - B - C ( 5 6 7 8 )

Minor tetrachord

tone - semitone - tone
C - D - Eb - F ( 1 2 b3 4 )
G - A - Bb - C ( 5 6 b7 8 )

Phrygian tetrachord

The Phrygian scale

semitone - tone - tone
C - Db - Eb - F ( 1 b2 b3 4 )
G - Ab - Bb - C ( 5 b6 b7 8 )

Tetrachord are a great way to get started with improvising and creating your own melodies and solos.

Applying to Ukulele

With tetra chords containing only four notes. It is easier to just know the notes of the neck and have some fingering principles for navigating the notes.

WidipediA: Tetrachord

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory. It literally means four strings. Ancient Greek music theory distinguishes three genera of tetrachords. These genera are characterised by the largest of the three intervals of the tetrachord:

Diatonic

A diatonic tetrachord has a characteristic interval that is less than or equal to half the total interval of the tetrachord. Classically, the diatonic tetrachord consists of two intervals of a tone and one semitone.

Chromatic

A chromatic tetrachord has a characteristic interval that is greater than half the total interval of the tetrachord. Classically, the characteristic interval is a minor third, and the two smaller intervals are equal semitones.

Enharmonic

An enharmonic tetrachord has a characteristic interval that is greater than four-fifths the total tetrachord interval. Classically, the characteristic interval is a major third (otherwise known as a ditone), and the two smaller intervals are quartertones.

As the three genera simply represent ranges of possible intervals within the tetrachord, various shades (chroai) of tetrachord with specific tunings were specified. Once the genus and shade of tetrachord are specified the three internal intervals could be arranged in six possible permutations.

Modern music theory makes use of the octave as the basic unit for determining tuning: ancient Greeks used the tetrachord for this purpose. The octave was recognised by ancient Greece as a fundamental interval, but it was seen as being built from two tetrachords and a whole tone. Ancient Greek music always seems to have used two identical tetrachords to build the octave. The single tone could be placed between the two tetrachords (between perfect fourth and perfect fifth) (termed disjunctive), or it could be placed at either end of the scale (termed conjunctive).

Scales built on chromatic and enharmonic tetrachords continued to be used in the classical music of the Middle East and India, but in Europe they were maintained only in certain types of folk music. The diatonic tetrachord, however, and particularly the shade built around two tones and a semitone, became the dominant tuning in European music.

The three permutations of this shade of diatonic tetrachord are:

Lydian mode

A rising scale of two whole tones followed by a semitone, or C D E F.

Dorian mode

A rising scale of tone, semitone and tone, C D E♭ F, or D E F G.

Phrygian mode

A rising scale of a semitone followed by two tones, C D♭ E♭ F, or E F G A.

Curt Sheller • All Things `Ukulele and Jazz Guitar