Song 10

  1. Whole-tone Symmetry
  2. The Whole-tone scale
  3. Y2K Blues
  4. Keyboard Chord Voicings
  5. Phrasing - playing "Outside"
  6. Practice - Five Chord Qualities
  7. Session Materials


Song | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | ?? |

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S 10.1 : Whole-tone Symmetry

Symmetric musical elements are intervals, chords and scales which have their component notes spaced at equal intervals over a full octave range.

In the major scale some notes are spaced a whole tone apart (C-D, D-E, etc.) , while other notes are spaced at semitone intervals (E-F, B-C). The major scale is therefore not a symmetric scale.

In the chromatic scale on the other hand all 12 notes are spaced at equally semitone intervals. The chromatic scale is therefore a symmetric scale . (More about this scale in Session 11.)

Symmetric scales and chords have an ambiguous floating quality, as any of the component notes can be the tonic of the scale (or root of the chord). Changing the tonic of the scale changes the pitch levels of the component notes, but not the tonality (type of sound) of the scale.

Whole-tone symmetry is a new musical term defined by me.
It includes all symmetrical music elements which can be formed by dividing the octave (which spans 12 semitones, and therefore 6 whole tones) into an equal number of whole-tone intervals, or multiples of whole tones.
These include three types of elements.

  1. tritone - Audio 10.1
    Dividing the octave (= 6 whole tones) into two, creates two halves of 3 whole tones each. In Jazz these are called tritones.
    In classical terminology these are the augmented 4th or the diminished 5th, such as C-F# or F#-C.
    This is the only interval in music that remains the same (3 whole tones) when inverted.

  2. augmented triad - Audio 10.1
    Dividing the octave into three equal intervals of 2 whole tones each produces the augmented triad. For example C-E-G#.
    When inverting this chord it produces two other tonic chords (E-G#-C, and G#-C-E) with the same notes and the same (augmented triad) quality.

  3. whole-tone scale - Audio 10.1
    Dividing the octave into six equal intervals of 1 whole tone each produces the whole-tone scale. This scale consists of six notes, all spaced at whole tone intervals. Each of the notes in the scale can act as the tonic note for its own whole-tone scale. The tonality of all these six scales (unlike the modes of the major scale) remains the same.

The characteristic features of these three whole-tone symmetrical elements are their bright, almost aggressive sound, combined with a floating quality as a result of their lack of a clearly defined tonal centre. This sets them apart very distinctly from all other music tonalities.

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S 10.2 - The Whole-tone scale

Below the C whole-tone scale.
Starting the same group of notes on D instead of C produces the D whole-tone scale (D E Gb Ab Bb C D). The same applies to any of the other four notes of the scale.

Audio 10.2

The other whole-tone symmetry elements discussed above are also present within the scale.

The C whole-tone scale contains three tritones
C - Gb
D - Ab
E - Bb

The C whole-tone scale also contains two groups of augmented triads
C - E - Ab
D - Gb - Bb

Below the Db whole-tone scale.

Audio 10.3

Together the two groups of notes cover all twelve possible whole-tone scales.

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S 10.3 - Y2K Blues

I imagine that the name "Y2K" will forever remind us of the computer bug which caused so much anxiety rather than the Year 2000 itself.

Y2K Blues is the very last song I wrote in the old millennium.
The song reflects all the anxiety, aggressiveness and uncertainty that has been the standout feature of the entire past Century.
But the song also pays tribute to whole-tone symmetry, which became (at the beginning of the 20th Century) such an important musical tool for Claude Debussy, Olivier Messiaen and other modern composers, who used it to forge the course of Western music into totally new directions.

The Jazz pianist and composer Thelonius Monk was also very fond of symmetric elements and used them in many of his compositions. Y2K Blues will therefore probably remind you of some of his music.

Y2K Blues uses the embellished blues chord progression in the usual 12 bar format.
The song is in the concert key of Bb, but I discuss it here again in the "easy key" of C. This makes it probably easier to follow.

Audio 10.4

Y2K Blues uses two types of scales not commonly used for the blues.
In the first 8 bars of the song I have used the C Lydian dominant scale (C D E F# G A Bb C) over the C7 chord, and the F Lydian dominant scale (F G A B C D Eb F) over the F7 chord. (These scales were already introduced in Session 8 for the song "Cruisin'".)
The F# and B natural (shown in green) identify these scales.

Audio 10.5

Also present in the first 8 bars of the melody are several tritone intervals.
These tritones also represent the essential chord tones for the C7 chord (3=E , b7=Bb) and for the F7 chord (3=A , b7=Eb).
The two green notes also infer tritone intervals with the root tones of their respective chords (F# with C, and B with F).

The melody in bars 9 to 12 consists entirely of whole-tone scale notes.
The G whole-tone scale (G A B Db Eb F G) and F whole-tone scale (F G A B Db Eb F) use the same notes. The C whole-tone scale (C D E Gb Ab Bb C) uses the remaining 6 notes of our Western music system.

Audio 10.6
(Only flats are used in the above line to make for easier reading, but the Db over the G7 chord and the Gb over the C7 chord (instead of C# and F#) still produce the bright 'augmented 4th sound'.)

The melody uses a pattern of augmented triads to spell out the scale.
The non chord-tone notes of the scale do not clash with the chord but simply add more colour.

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S 10.4 - Keyboard Chord Voicings

Y2K Blues provides a good opportunity to play skeleton chords as left hand accompaniment using the essential chord tones (3 and b7) only. This fits in with the angular Monkesque sound of the song.

Invert the tritone for the F7 and G7 chords, with the b7 at the bottom and the 3rd on top. This provides smooth transitions from chord to chord as shown below.

Audio 10.7

The tritone formed by the 3rd and b7th of the dominant 7th chord is probably largely responsible for the unstable, tensional nature of the chord.
Being a symmetric interval, the tritone interval remains the same when inverted. This means that there are two different dominant chords that share the same essential chord tones.
For example :

Chord 3 b7

The six tritone intervals within the octave represent therefore the essential chord tone combination (3 - b7) for all 12 dominant 7th chords.
When played in
Circle of Fifths order, these skeleton chords (= chords with one or more chord tones omitted) are simply a series of tritones that move in semitone steps downwards.

Audio 10.8

Practising the above provides you with smooth skeleton chord voicings for all twelve dominant 7th chords. These are ideal for use over the blues in any key.

Tritone Substitution
In Jazz harmonies the above principle is also used as the basis for chord substitution.
In the progression Gm7 - C7 - Fmaj7 the C7 chord can be replaced by the Gb7 chord.

This changes the original Circle of Fifths progression to a chromatic progression Gm7 - Gb7 - Fmaj7.
This principle is called Tritone Substitution.

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S 10.5 - Phrasing : playing "Outside"

Using Lydian dominant scales (over the first 8 bars) and whole-tone scales (over the last 4 bars of the blues) for improvisation provides a quirky sound that is in part "outside" the usual tonalities for blues improvisation.

The melody for Y2K Blues is a good example of how to bring out such tonality effectively.
Focus on the tritones, the unusual augmented 4th and the outside notes of the whole-tone scale (Db and Eb over the G7 chord, B and Db over the F7 chord).
Note also the root notes of the chords are not emphasised in this song. They only occur fleetingly as quavers in the melody.

Audio 10.4

The #4 used in the Lydian dominant scale is not the same as the b5 in the blues scale. They are of course the same note but the contexts in which they occur are quite different.

In the C Blues scale ( C Eb F Gb G Bb C) the Gb functions as a transition between the G and the F. It mimics the bending of notes typical of blues singers right from the early beginning of blues development.
The Gb is one of the three blue notes in the blues scale : Eb, Gb and Bb (b3 - b5 - b7). Together they create the characteristic mellow sound in the blues.

In the C Lydian dominant scale (C D E F# G A Bb C) on the other hand, the F# replaces the F natural in the scale. This creates the bright and aggressive sound so typical of all Lydian tonalities.
Therefore when playing the the C Lydian dominant scale make sure to avoid playing any F naturals (accidentally), for it would destroy the intended effect!!

Below the three scales for improvisation over Y2K Blues in the ('Easy key') key of C.
Use the whole-tone scale for bars 9 and 10 over both the G7 and F7 chords.

Audio 10.9

You can also experiment by using the G Lydian dominant scale over the G7 chord (G A B C# D E F G), and occasionally with the C whole-tone scale (C D E Gb Ab Bb C) over the C7 chord. But use the whole-tone sound only sparingly, this way it is (like salt on your meal) the most effective.

Again included two practice tracks swapping twos in the Concert key of Bb (C for Bb instruments, G for Eb instruments).

C instruments use these notes for improvisation :

  1. Over Bb7 : Bb C D E F G Ab Bb
  2. Over Eb7 : Eb F G A Bb C D Eb
  3. Bars 9 - 10 : F G A B Db Eb F

Bb instruments use these notes for improvisation :

  1. Over C7 : C D E F# G A Bb C
  2. Over F7 : F G A B C D Eb C
  3. Bars 9 - 10 : G A B Db Eb F G

Eb instruments use these notes for improvisation :

  1. Over G7 : G A B C# D E F G
  2. Over C7 : C D E F# G A Bb C
  3. Bars 9 - 10 : D E F# G# A# C D

Tracks for swapping twos

  • On Y2K Blues 1 I play every first two bars of each 4 bar phrase, you play the last two bars.
    On this track you only play over one chord : Bb7 (C7 for Bb instruments, G7 for Eb instruments).

  • On Y2K Blues 2 I play every last two bars of each 4 bar phrase, you play the first two bars.
    Now you cover all three tonalities.

  • On Y2K Blues 3 you can listen to the combined result.

Feel free to also use the traditional ("inside") tonalities for improvisation over Y2K Blues, such as the minor pentatonic scale, blues scale or the Mixolydian modes. One approach for example would be to alternate "outside" and "inside" choruses.

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S 10.6 - Practice : Five Chord Qualities

Practise the five 7th chord qualities as arpeggios (broken chords) in all keys.
Play each arpeggio over a 2-octave range. Play either straight or swing quavers.
The chord sequence for each root note is :

Major 7th - Dominant 7th - Minor 7th - Half diminished - Diminished 7th

Audio 10.10

If you can not reach comfortably two octaves up from the chord root, loop the arpeggio over a 2-octave range.
For example play the G chords on a saxophone from the low G up to high D, then all the way down to low D, finally back up to your starting point low G.

The play-a-long track provided plays every chord quality for 4 bars in each key (4 bars Cmaj7, then 4 bars C7, then 4 bars Cm7, etc.).
The track follows the Circle of Fifths (starting on C concert).
The bass plays walking bass over all major 7th, dominant 7th and minor 7th chords.
The bass plays in 2s over all half diminished and diminished 7th chords.

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S 10.7 - Session Materials

ItemMidi filesSheet music
Y2K BluesDemoP-a-L C instr. Bb instr. Eb instr.
Embellished Blues in BbSlowFast
Easy Key for C instr. (C) E-Pal 1 Bb instr.for Keyboard
Easy Key for Eb instr. (C) E-Pal 2 Bb instr.
7th Chords Practice Demo P-a-L p.1 p.2
Swapping Twos Y2K Blues 1 Y2K Blues 2
Swapping Twos (Demo) Y2K Blues 3

(You can also use the Embellished Blues in Bb tracks for this song.)

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© 2003 Michael Furstner (Jazclass)