a guitarist's notebook

Mon - December 22, 2008

Diminished Scale Voice Leading

Upper partial triads of the tonic and dominant diminished scales with resolutions to the tonic chord. Specifically, voice leading to three note quartal fragments of the tonic chord.

Criteria

The examples are limited to those progressions which best meet the criteria that the penultimate "triad" fragment and subsequent quartal fragment (1) have few or no common tones, (2) are in close proximity, and (3) demonstrate contrary motion in voice movement.

The Tonic Diminished Scale

For the key of A major the grand quartal chord is:
G# - C# - F# - B - E - A - D

and the constituent three note "4th" chords which may represent an Amaj chord (sans "D"):
G#4, C#4, F#4, B4
(see previous post on quartal chord voicings here)

The tonic diminished scale in A is:
A - B - C - D - D# - F - F# - G# - (A)

and the constituent triads of the diminished scale are:
D, Bm, B, G#m, Ab, Fm, F , Dm, (D)

Technically speaking, the grand quartal chord for the diminished scale is comprised of alternating P4 and dim4 (M3):
A - D - F# - B - D# - G# - C - F - (A)
Therefore, the subsequent upper partial triads are likewise, in a sense, derivative quartal chords.

Cycle of alternating perfect and diminished fourths

Examples

Page 1
Page 2
Page 3

Download PDF file here

The Dominant Diminished Scale

The Dominant Diminished Scale in E is
E - F - G - G# - Bb - B - C# - D - (E)

and constituent triads are:
C#m, C#, Bbm, Bb, Gm, G, Em, E, (C#m)

Alternating cycle of dim4 and P4
E - G# - C# - F - Bb - D - G - B - (E)

Cycle of alternating diminished and perfect fourths

Examples

Page 1
Page 2

Download PDF file here

Posted at 08:43 AM

Fri - December 19, 2008

The Diminished Scale - Part One

Chords from the Octatonic Symmetric Scale

In preparation for a forthcoming post, I started to brainstorm and came up with a number of harmonic possibilities which can be extracted from the diminished scale.

Generally, the examples posted below are in order of consonance - from triads to altered dominant chords.

Page 1
Page 2
Page 3
Page 4
Page 5
Page 6

Click here for the PDF file

Relevant and interesting Wikipedia article here

Posted at 08:52 AM

Mon - December 1, 2008

the melodic minor pentatonic scale

Functional applications for this pentatonic scale: C - D - Eb - G - A - C

Substitution Reference
Table one demonstrates applications where pairs of MmP scales might be used over common chord progressions. Two illustrates progressions where the melodic minor pentatonic (min 6/9), the minor major seventh and augmented major seventh chord tones may be interchanged*. Page three lists the usual places where one might otherwise use the modes of the heptatonic melodic minor scale.

page 1
page 2
page 3

download pdf here

* compare with these previous posts on augmented patterns
ambiguous augmented arpeggios (12/02/03)
More Augmented Patterns (08/08/08)

Applications
Melodic minor pentatonic lines in various contexts.

page 1
page 2
page 3

pdf here

Points of Interest
- Structure in semitones: 2 - 1 - 4 - 2 - 3
- Scale tones = the "minor 6/9" chord (C - Eb - G - A - D)
- In fifths: C - G - D - A - Eb (see A4 voicings/inversions listed in the post on quartal chords here and here)
- Classification: Hemitonic Pentatonic
- Pattern 1158 in Slonimsky's Thesaurus**

Similar
Akin to the South Indian Raga Sivaranjani (alternate sp.: Shivaranjani, Shivarangani)
listen here
podcast on Raga Sivaranjani part one and part two from the wonderful site Raagarasika

Also a transitional tuning (rare) for the Japanese Koto:
- Kurama Jishi to Hirajoshi = C - D - Eb - G - A - (etc) to C - D - Eb - G - Ab - (etc). (transposed)
In Sen

Nomenclature
On a cursory search I've come across one other scale which has been christened "melodic minor pentatonic." In fact, I can think of at least four other scales to which the name could reasonably fit:

C - D - Eb - F - G - A - B
C - D - Eb - F - G - A - B
C - D - Eb - F - G - A - B
C - D - Eb - F - G - A - B

So, here is my argument for using the name "melodic minor pentatonic" for this particular scale:

1. The relative similarities in scale tone structures with the pentatonic as compared with the heptatonic forms:

Major : Melodic Minor
C - D - E - F - G - A - B : C - D - Eb - F - G - A - B
[1 - 2 - 3 - 4 - 5 - 6 - 7] : [1 - 2 - b3 - 4 - 5 - 6 - 7]

vis - á - vis

Major Pentatonic : Melodic Minor Pentatonic
C - D - E - G - A : C - D - Eb - G - A
[1 - 2 - 3 - 5 - 6] : [1 - 2 - b3 - 5 - 6]

2. The multiple uses of this pentatonic scale are likewise analogous to the seven note melodic minor scale. Additionally, compared to other pentatonics, this scale contains the greatest number defining chord tones (3rd and 7th) and upper partials (15) of chords usually associated with the parent heptatonic scale.

Cm: 1 - b3 - 5 - 9 - 13;
Am7b5: 1 - b3 - b5 - b7 - 11 (the locrian pentatonic scale)
F7: 3 - 5 - b7 - 9 - 13;
B7: 3 - +5 - b7 - b9 - #9;

** (The Thesaurus of Scales and Melodic Patterns; Pentatonic Scales, pg. 162, 1158; Slonimsky; Charles Scribner's Sons; 1947)

Posted at 09:05 AM

Wed - November 19, 2008

The Hyper-Lydian Sequence

Not to be confused with the hyperlydian mode, the term hyper-lydian sequence is employed here to describe an imaginary sequence* of alternating major and minor thirds.

The name seems appropriate because the first six notes are identical to that of the Lydian arpeggio (C - E - G - B - D - F# - A) but, instead of resolving at C', the pattern of alternating thirds continues until the cycle is complete after seven octaves.

Larger illustration here

Breakdown
7 octaves
24 notes: 12 major thirds and 12 minor thirds apart.
12 major triads; all Lydian upper extensions available.
12 minor triads; all Dorian upper extensions available.
2 parallel cycles of perfect fifths.

page 1
page 2
click here for pdf file

Characteristics
The sequence lends itself to harmonic progressions reminiscent of sixteenth century and more recent folk music forms but with one important difference: its potential to gradually slip into distant tonalities via stepwise progressions (see the triadic progressions pages below).

I doubt that Mclaughlin had this sequence in mind when he composed A Lotus on Irish Streams but, nonetheless, the tune stands as an excellent example of the harmonic colors available.

For the score to A Lotus on Irish Streams [J McLaughlin, 1971; Chinmoy Music, Inc (BMI); LP Columbia 31067] click here

download pdf file here

Triadic Progressions Explored
page 1
page 2
page 3
page 4
page 5
page 6

click here for pdf file

*a "synthetic" arrangement of notes made practical through 12 tone equal temperament

Posted at 10:41 PM

Mon - November 3, 2008

Quartal Chords

three and four note quartal chords for guitar

Here is the complete set of practical, accessible and (on good days) playable three and four note quartal chords for guitar.

Criteria
1. Only three and four note chords derived from sequences of perfect fourths - and their inversions - are considered here.
2. Only those chords which are possible on the guitar are considered.
3. While some of the inversions are very challenging, chords with extremely large stretches are not presented (i.e.: not playable by me).
4. Intervals greater than an octave between adjacent notes occur only from the lowest note. Other voicings are not listed.

Arrangement
Each set of three note permutations are divided into four groups a minor third apart - there are a total of three sets.
Each set of four note permutations are divided into three groups a major third apart - there are a total of four sets.

For example, the three note quartal chords:
4(mutually exclusive chords) X 3(number of notes per chord) = 12 tones
4(mutually exclusive chords) X 3(sets) = 12 mutually exclusive chords

Three note quartal chords

page 1
page 2
page 3

download PDF file here

Four note quartal chords

page 1, 2, 3
page 4, 5, 6
page 7, 8, 9
page 10, 11, 12

download PDF file here

The 12-Tone-Row Game
three note quartal version

Objectives:
1. A fun way to create 12 tone rows employing elements of quartal harmonies which gradually progress through familiar tonal areas.

Rules:
1. The player may start on any "4th" chord outlined on the graph above.
2. Choose any of the 4th chord permutations within that 4th chord group.
3. The player will then write down the three notes of the chord - arpeggiated as desired.
4. Chromas (notes of the same letter name) outside of the chord "shell" are permitted as are transposition of the entire chord to another octave.
5. Proceed in either a clockwise or counterclockwise direction to the adjacent 4th chord and repeat the process above.
6. Continue this process until all four chords have been completed.
7. Infuse rhythms, stir in harmonies, salt and pepper to taste. Enjoy your new 12 tone-row while it is still fresh.

Strategies:
1. In general, avoid frequent large leaps.
2. Strive for traditional melodic shapes (e.g.: smaller intervals at the beginning of the line, larger leaps toward the end; highest and/or lowest pitches toward the end of the line)
3. As per the "rules" of the game, by selecting chords from adjacent pools the player will, in effect, be selecting notes which overlap familiar tonal areas.
ex: F#4 + A4 = E - F# - G - A - B - D - E (E minor hexatonic)
4. This game may be played using either of the two other 4th chord sets.

Posted at 08:20 AM

Phrygian Dominant Hexatonic

The Minor Hexatonic Scale

More Augmented Patterns

Wes Montgomery - part three

Ed Bickert - part two

The Augmented Scale Harmonized

Changes - part three

Hexatonic Scales - Continued

Slonimsky - part two

Changes - part two

Changes - part one