Tetrachord

in b locrian: - - - (b-a-g-f) .]]

progression creates a descending tetrachord bassline: - - - . Phrygian half cadence: i-v6-iv6-V in c minor (bassline: c -b -a -g) .]]

Traditionally, a tetrachord is a series of four tones filling in the interval of a perfect fourth, a 4:3 frequency proportion. 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, originally in reference to harp-like instruments such as the lyre or the kithara, with the implicit understanding that the four strings must be contiguous. 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 (or 249 cents). This characteristic interval is usually slightly smaller (approximating to 200 cents), becoming a whole tone. Classically, the diatonic tetrachord consists of two intervals of a tone and one of a semitone. ;Chromatic :A chromatic tetrachord has a characteristic interval that is greater than half the total interval of the tetrachord, yet not as great as four-fifths of the interval (between 249 and 398 cents). Classically, the characteristic interval is a minor third (approximately 300 cents), 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 (greater than 398 cents). 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.

History

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.

Permutations

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. (same hypate and mese for the ancient Greeks) ;Dorian mode :A rising scale of tone, semitone and tone, C D E♭ F, or D E F G (E to a for the ancient Greeks). ;Phrygian mode :A rising scale of a semitone followed by two tones, C D♭ E♭ F, or E F G A (D to G for the ancient Greeks).

(The extents of the Greek system are from Chalmers, Divisions of the Tetrachord. )

Pythagorean tunings

Here are the traditional Pythagorean tunings of the diatonic and chromatic tetrachords:

Diatonic hypate parhypate lichanos mese 4/3 81/64 9/8 1/1 | 256/243 | 9/8 | 9/8 | -498 -408 -204 0 cents

Chromatic hypate parhypate lichanos mese 4/3 81/64 32/27 1/1 | 256/243 | 2187/2048 | 32/27 | -498 -408 -294 0 cents

Since there is no reasonable Pythagorean tuning of the enharmonic genus, here is a representative tuning due to Archytas:

Enharmonic hypate parhypate lichanos mese 4/3 9/7 5/4 1/1 | 28/27 |36/35| 5/4 | -498 -435 -386 0 cents

The number of strings on the classical lyre varied at different epochs, and possibly in different localities – four, seven and ten having been favorite numbers. Originally, the lyre had only five to seven strings(see also the Kithara, a larger form), so only a single tetrachord was needed. Larger scales are constructed from conjunct or disjunct tetrachords. Conjunct tetrachords share a note, while disjunct tetrachords are separated by a disjunctive tone of 9/8 (a Pythagorean major second). Alternating conjunct and disjunct tetrachords form a scale that repeats in octaves (as in the familiar diatonic scale, created in such a manner from the diatonic genus), but this was not the only arrangement.

The Greeks analyzed genera using various terms, including diatonic, enharmonic, and chromatic, the latter being the color between the two other types of modes which were seen as being black and white. Scales are constructed from conjunct or disjunct tetrachords: the tetrachords of the chromatic genus contained a minor third on top and two semitones at the bottom, the diatonic contained a minor second at top with two major seconds at the bottom, and the enharmonic contained a major third on top with two quarter tones at the bottom, all filling in the perfect fourth of the fixed outer strings. However, the closest term used by the Greeks to our modern usage of chromatic is pyknon or the density ("condensation") of chromatic or enharmonic genera.

{| class="wikitable" |Didymos chromatic tetrachord |16:15, 25:24, 6:5 |- |Eratosthenes chromatic tetrachord |20:19, 19:18, 6:5 |- |Ptolemy soft chromatic |28:27, 15:14, 6:5 |- |Ptolemy intense chromatic |22:21, 12:11, 7:6 |- |Archytas enharmonic |28:27, 36:35, 5:4 |}

This is a partial table of the superparticular divisions by Chalmers after Hofmann.

Variations

Persian

Persian music divide the tetrachord differently than the Greek. For example, Farabi presented ten possible intervals used to divide the tetrachord : {| |Ratio: |align=center|1/1 |align=center|256/243 |align=center|18/17 |align=center|162/149 |align=center|54/49 |align=center|9/8 |align=center|32/27 |align=center|81/68 |align=center|27/22 |align=center|81/64 |align=center|4/3 |- |Note name: |align=center|c |align=center| |align=center| |align=center| |align=center| |align=center|d |align=center| |align=center| |align=center| |align=center|e |align=center|f |- |Cents: |align=center|0 |align=center|90 |align=center|98 |align=center|145 |align=center|168 |align=center|204 |align=center|294 |align=center|303 |align=center|355 |align=center|408 |align=center|498 |}

Since there are two tetrachords and a major tone in an octave, this creates a 25 tone scale as used in the Persian tone system before the quarter tone scale. A more inclusive description (where Ottoman, Persian and Arabic overlap), of the scale divisions is that of 24 tones, 24 equal quarter tones, where a quarter tone equals half a semitone (50 cents) in a 12 tone equal-tempered scale (see also Arabian maqam). It should be mentioned that Al-Farabi's among other Islamic treatises also contained other division schemes and provided a gloss of the Greek system as Aristoxenian doctrines where often included.

Uses

's Suite for Piano, Op. 25 .]]

Milton Babbitt's serial theory extends the term tetrachord to mean a four-note segment of a twelve-tone row.

Allen Forte occasionally uses the term tetrachord to mean what other theorists call a tetrad, and what Forte himself also calls a "4-element set"—a set of any four pitches or pitch classes .

Sources

BEWARE! These videos with playing examples are meant to be used in succession, and with a introducing chapter I havent done yet. You are still welcome do the exercises though:-) And see my video on "practicing the major scale, tips and tetrachords", its posted as video reply to this lesson. The Major tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, whole step, half step. Here is Pattern 1, 4 notes on 1 string, A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Phrygian tetrachord bass fingering patterns

Duration: 3:00
Published: 2010-07-08
Uploaded: 2010-08-27
Author: MarloweDK

The phrygian tetrachord scale (1 b2 b3 4) Half step, whole step, whole step.

Lydian tetrachord bass scale practice , the Lydian Major scale

Duration: 1:18
Published: 2010-07-09
Uploaded: 2010-08-27
Author: MarloweDK

An example of using the Lydian tetrachord (1 2 3 #4) and the Major terachord (1 2 3 4) for simple imro over the Lydian Major scale The C Lydian scale can be looked at as two tetrachord scales: a C lydian tetra chord (C 2 3 #4) and a G Major tetra chord (GABC) This not art , just a simple scale demonstration;-) This scale / mode is very "spanish" sounding with the 1 , b2 b3 scale degrees

Lydian tetrachord bass pattern 1

Duration: 0:42
Published: 2010-07-10
Uploaded: 2010-09-08
Author: MarloweDK

The Lydian tetrachord (1 2 3 #4) Whole step, whole step, whole step. Pattern 1, all notes on a single string

Minor Tetrachord bass scale practice , the Dorian minor scale

Duration: 1:19
Published: 2010-07-08
Uploaded: 2010-08-27
Author: MarloweDK

An example of using the minor tetrachord for simple imro over the dorian minor scale, see the previous "Minor Tetrachord" videos on fingering pattern for the minor tetrachord scales. This not art , just a simple scale demonstration;-)

Lydian tetrachord bass pattern 2

Duration: 0:32
Published: 2010-07-10
Uploaded: 2010-09-08
Author: MarloweDK

The Lydian tetrachord (1 2 3 #4) Whole step, whole step, whole step. Pattern 2, 3 notes on start string, 1 note on next string

Phrygian Tetrachord bass scale practice , the Phrygian minor scale

Duration: 1:35
Published: 2010-07-08
Uploaded: 2010-08-27
Author: MarloweDK

An example of using the phrygian tetrachord (1 b2 b3 4) for simple imro over the phrygian minor scale The C Phrygian scale can be looked at as two phrygian tetrachord scales: a C phrygian tetra chord (C Db Eb F) and a G phrygian tetra chord (G Ab Bb C) This not art , just a simple scale demonstration;-) This scale / mode is very "spanish" sounding with the 1 , b2 b3 scale degress

Lydian tetrachord bass pattern 3

Duration: 0:29
Published: 2010-07-10
Uploaded: 2010-09-08
Author: MarloweDK

The Lydian tetrachord (1 2 3 #4) Whole step, whole step, whole step. Pattern 3, 2 notes on start string, 2 notes on next string

Major tetrachord, pattern 2

Duration: 1:24
Published: 2010-06-28
Uploaded: 2010-10-11
Author: MarloweDK

Here is Pattern2, 3 notes on start string, 1 note on next string The Major tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, whole step, half step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Major tetrachord, pattern 3

Duration: 1:08
Published: 2010-06-28
Uploaded: 2010-10-16
Author: MarloweDK

Here is Pattern 3, 2 notes on start string, 2 notes on next string The Major tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, whole step, half step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Major tetrachord, pattern 4

Duration: 1:18
Published: 2010-06-28
Uploaded: 2010-10-16
Author: MarloweDK

Here is Pattern 4, 1 note on start string, 3 notes on next string The Major tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, whole step, half step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Minor tetrachord, pattern 1

Duration: 0:33
Published: 2010-06-30
Uploaded: 2010-08-27
Author: MarloweDK

The minor tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, half step, whole step. Here is Pattern 1, 4 notes on 1 string, A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Major tetrachord , All 4 Patterns

Duration: 0:50
Published: 2010-06-28
Uploaded: 2010-10-16
Author: MarloweDK

All 4 Major tetrachord patterns played in succession. The Major tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, whole step, half step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Minor tetrachord, pattern 2

Duration: 0:22
Published: 2010-06-30
Uploaded: 2010-08-26
Author: MarloweDK

Here is Pattern 2, 3 notes on 1 string, 1 note on next string The minor tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, half step, whole step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Lydian tetrachord for bass - all 4 fingering patterns

Duration: 0:52
Published: 2010-07-10
Uploaded: 2010-09-08
Author: MarloweDK

The Lydian tetrachord (1 2 3 #4) Whole step, whole step, whole step. All 4 fingering patterns in sequence

Minor tetrachord, pattern 3

Duration: 0:24
Published: 2010-06-30
Uploaded: 2010-08-26
Author: MarloweDK

Here is Pattern 3, 2 notes on 1 string, 2 notes on next string The minor tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, half step, whole step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Lydian tetrachord bass pattern 4

Duration: 0:33
Published: 2010-07-10
Uploaded: 2010-10-18
Author: MarloweDK

The Lydian tetrachord (1 2 3 #4) Whole step, whole step, whole step. Pattern 4, 3 notes on start string, 1 note on next string

Minor tetrachord, All 4 patterns

Duration: 0:32
Published: 2010-06-30
Uploaded: 2010-08-27
Author: MarloweDK

Here are all 4 patterns played in succession. The minor tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, half step, whole step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

Minor tetrachord, pattern 4

Duration: 0:26
Published: 2010-06-30
Uploaded: 2010-08-26
Author: MarloweDK

Here is Pattern 4, 1 note on 1 string, 3 notes on next string The minor tetrachord is a four note scale that can be played with 4 different patterns/fingerings, you should practice them all. Pattern formula is whole step, half step, whole step. A method/series to learn the modes and common scales by dividing an eight note scale into 2 four note scales (the brain has an easier time remembering 1234 1234 than 12345678) You only need to learn 4 different tetrachords to be able to play all 7 modes : Ionian Major, Dorian minor, Phrygian minor, Lydian, Mixolydian Major, Aolian minor, Locrian half diminished.

tetrachord

Duration: 0:52
Published: 2010-10-09
Uploaded: 2010-10-10
Author: houstonbiker

etude #6? tetrachord

tetrachord lesson by Swanney

Duration: 3:26
Published: 2009-03-02
Uploaded: 2010-08-27
Author: skitzofingers

Introduction to tetrachord scales for the guitar by Swanney. In this lesson there are 4 different type tetrachords. Major, Minor, Diminished, and Whole Tone. This example shows one of the fingerings that can be used to play the different type tetrachords. Once you learn the patterns and the sound of each tetra, it is a good idea to practice playing each tetrachord thru all 12 keys. Here is a link to the tab: www.andersonhall.com/tab/tetra-lesson-chart.jpg

Everyday I Love You By Stewart - The Tetrachord

Duration: 3:25
Published: 2010-11-16
Uploaded: 2010-11-16
Author: ekltsang

Live at Castaway Piano Bar, Star Pisces

1 octave Lydian Major scale with tetrachords, pattern 1

Duration: 0:58
Published: 2010-07-10
Uploaded: 2010-09-11
Author: MarloweDK

The C Lydian scale can be looked at as two tetrachord scales: a C lydian tetra chord (C 2 3 #4) and a G Major tetra chord (GABC) Pattern1

1 octave Lydian Major scale with tetrachords, pattern 2

Duration: 0:35
Published: 2010-07-10
Uploaded: 2010-08-27
Author: MarloweDK

The C Lydian scale can be looked at as two tetrachord scales: a C lydian tetra chord (C 2 3 #4) and a G Major tetra chord (GABC) Pattern 2

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Major tetrachord, pattern 1