Utilities

	Interval
	Chord-Clock
	Circle Of Fifths
	Position
	Transposing

Intervals

Latin intervallum space between ramparts, interval, from inter- + vallum rampart. Intervals describe the distance of two tones.

Distance in half notes	interval name	Symbol
0	unison	0
1	minor 2nd	b2
2	major 2nd	2
3	minor 3rd	b3
4	major 3rd	3
5	perfect 4th	4
6	diminished 5th	b5
7	perfect 5th	5
8	augmented 5th	b6
9	major 6th	6
10	minor 7th	b7
11	major 7th	7
12	octave	8

Pure, Minor and Major Intervals

We differentiate pure and minor / major intervals.

Pure Intervals
Unison, Fourth, Fifth and Octave. These intervals are in the basic form pure intervals.

Minor / Major Intervals
Second, Third, Sixth and Seventh. These intervals appear in two basic forms.

Diminished and Augmented Intervals

Diminished Intervals
Pure and minor intervals are diminished by lowering the above tone or by heightening the lower tone.

Augmented Intervals
Pure and major intervals are augmented by heightening the above tone or lowering the lower tone.

Consonant and Dissonant Intervals

Consonant Intervals
Melodious intervals are denoted as consonant intervals.
Unison, Octave, Fifth, Fourth, Major and Minor Third.

Dissonant Intervals
These intervals sound chafing, odd and disharmonious.
Minor Second, Major Second, Diminished Fifth, Augmented Fifth, Seventh.

Description of the Consonant and Dissonant Intervals

Minor Second	Squeaking and sharp, very dissonant like sharp mustard and full of suspense.
Major Second	Dissonant but less than minor second, mild mustard.
Minor Third	Sad, tearful, responsible for rapid sale of tissue and the minor characteristic.
Major Third	Is responsible for the major characteristic, simply nice and lovely.
Fourth	Quite harmonic.
Augmented Fourth (Tritone)	Simple wicked and was called "diabolus in music" (devil in music)! Located exactly in the middle of the scale and sounds absolutely brutal! Has great importance in atonal music.
Fifth	Neutral, sobering, harmonic and strict
Augmented Fifth	Almost as blatant as the augmented fourth and causes sleepless nights!
Sixth	Neither fish nor bird more major oriented.
Seventh	Suspenseful but not strange, happy end sober, the reliving resolution to the next root note.

Chord-Clock

Latin Accordare = together sounding

With this tool all chords of a score can be decoded! It serves to translate the sometimes complicated chord symbols into notes. For that the chord symbols are first replaced by a numbering structure.
On the utilities-wheel the numbers are arranged in a circle and show you the notes on the background that are contained in the sought chord.

Symbol	Full name	Structure
C	Major triad	1 3 5
Cm	Minor triad	1 b3 5
C4 (Csus)	Suspended 4th without 3rd	1 4 5
C+ (C 5+)	Augmented triad	1 3 5+
Cm- (Cm5b)	Diminished triad	1 b3 b5
C6	Sixth	1 3 5 6
Cm6	Minor sixth	1 b3 5 6
C7	Dominant 7	1 3 5 b7
Cm7	Minor with minor seventh	1 b3 5 b7

Altered chord

Symbol	Full name	Strucure
Cmaj7	Major seventh	1 3 5 7
C0 (C verm.)	Diminished seventh chord	1 b3 b5 6
C9 (C7/9)	Major ninth chord	1 3 5 b7 9
Cb9 (c7/b9)	Minor ninth chord	1 3 5 b7 b9
C9+	Major triad with blue notes	1 3 5 b7 9+
C11	Eleventh chord	1 3 5 b7 9 11
C13	Thirteenth chord	1 3 5 b7 9 11 13
Cadd9	Add=additional without 7	1 3 5 9

Altered chord

Adjusting root note	reading off altered chords

Chord	Notes	Structure
D7#11	1 3 5 b7 9 #11	D F# A C E G#

What is a chord?

A chord is the sound of three or more notes together. An exception are the so called power chords that contain only two notes (triad without third). The note sequence of a chord is variable (called inversion).

Whether C E G or E G C or G C E, it is always the same chord. Also allowed is the expansion of a chord with an octave with one of the chord notes (e. g. C E G E). It still is a triad! 

Chord Structure

Normally chords consist of layers of thirds on top of each other. Rare are fourth chords that are built from diminished and augmented fourths or fifth chords that are built from layering fifths.

Scale Notes

For the construction of chords usually notes from the own scale are used. For the chords of the C major scale only the notes C, D, E, F, G, A and B are available. This is also the reason that either minor or major thirds come up. Chords that contain none scale notes are called altered chords.

Triads

The simplest chord is a triad. It is built by piling up thirds and contains 3 notes, the root, the third and the fifth (second third). Minor and major thirds produce 4 combinations of piling up thirds with the C Major scale.

Root	+	Major Third	+	Minor Third	=	Major Triad	C, F, G
Root	+	Minor Third	+	Major Third	=	Minor Triad	Dm, Em, Am
Root	+	Minor Third	+	Major Third	=	Diminished Triad	Bdim

The fourth combination is not part of the C major scale triads.

Root

+

Major Third

+

Major Third

=

Augmented Triad

Triads of the C Major Scale

Recipe for the construction of a triad.

Root + next but one note + next but one note

Example C Triad

C

D

E

F

G

A

B

Scale	C	D	E	F	G	A	B
Degree	I	II	III	IV	V	VI	VII
Notes	C E G	D F A	E G B	F A C	G B D	A C E	B D F
Chord	C	Dm	Em	F	G	Am	Bdim

Seventh Chords

A seventh chord is triad that is extended by an additional third. The chord consist of the root, a third, a fifth and a seventh and is called therefore a seventh chord.

Recipe for the construction of a seventh chord

Root + next but one note + next but one note + next but one note

Example C Seventh Chord

C

D

E

F

G

A

B

Here are the resulting seventh chords from the scale notes of the C major scale

Scale	C	D	E	F	G	A	B
Degree	I	II	III	IV	V	VI	VII
Notes	C E G B	D F A C	E G B D	F A C E	G B D F	A C E G	B D F A
Chords	Cmaj7	Dm7	Em7	Fmaj7	G7	Am7	Bm7b5

Maj7, j means that the major seventh is contained in the chord.
7 means that the minor seventh is contained in the chord.
b5, 5- means that the diminished fifth is contained in the chord.

The most used chord is the dominant seventh chord. It consist of a major triad and a minor seventh (e. g. G7)

Expanded Chords 7 9 11 13

A diatonic expanded chord has five, six, or seven notes. The seventh chord and therefore the characteristic of the chords (major, minor, dominant7) is unchanged. An expansion adds also an accent or a different sound color. By piling up additional thirds five note chords (ninth chords), six note chords (eleventh chords) or seven note chords (thirteenth chords) can be formed.

Those expanded chords a rarely used in their entire form. Most common is to play the base triad (with or without fifth) with the additional ninth (minor/major), eleventh (minor/major) or thirteenth (minor/major).

Suspended Chords

You have might seen the chord Csus4. It is called a suspended chord (suspended fourth) and contains a fourth instead of the third. The chord Csus9 has a D instead of a C.

Csus4, C4	C F G
Csus9	C E G D

Altered Chords

Altered chords are used in Jazz to produce more tension. This tension is produced by none scale notes. The fifth (5) and the ninth (9) are decreased or increased by half a tone. The fourth (4 or 11) are increased by half a tone and the thirteenth (13) is decreased by half a note. Alterations are indicated by the symbols (+ or -) or with the sign (# or b).
Here are some examples:

Chord	Note Sequence	Chord name	Alteration
C+, C5+, C5#, Caug	C E G#	Augmented triad	Augmented fifth
Cmb5, Cm-,	C Eb Gb	Diminished triad	Diminished fifth
C7+, C75#	C E G# Bb	Aug. Dom7 chord	Aug. fifth
C7b5	C E Gb Bb	Dim. Dom7 chord	Dim. Fifth

Of course for the altered chords the Diminished Whole Note scale fits. It is located on the Dom7 color circle.

Diminished Chords

Two minor thirds piled up result in a diminished triad.

Root

+

Minor third

+

Minor third

+

Diminished triad

Three minor thirds piled up result in a diminished seventh chord. It is also a diminished triad with a minor seventh. With the first minor third the chord already has a minor character.

Root

+

Minor third

+

Minor third

+

Minor third

+

Diminished seventh chord

Possible Chord Symbols:

Cº

Cdim

The suitable diminished scale also called the Whole Note – Half Note scale is located on the minor color circle (Diminished scale, beginning with W-step).

Chords
Cm7b5	Cº , Cdim

Chords and their Scales

Chords	Scales
MAJOR	MAJOR-SCALES
C, Cmaj7, Cmaj9, C6	C-Major, C-und G-Pentatonic, C-BeBop, C-Lydian, C-Blues
Cmaj7#11	C-Lydian
MINOR	MINOR-SCALES
Cm, Cm7, Cm9, Cm11	C-Dorian, C-Pentatonic, C-BeBop, C-Blues, C-Harmonic, C-Natural, F-und B-Major Pentatonic, Es-Major BeBop
Cm, Cm6	C-Melodic, C-Dorian, C-Pentatonic, C-BeBop, F-und B-Major Pentatonic, Es-Major BeBop
Cm-maj7	C-Melodic, C-Harmonic, Es-Major BeBop
Cm7b6	C-Natural, As-Major Pentatonic
Cm7b9	C-Phrygian
DOMINANT	DOMINANT-SCALES
C7, C9, C13	C-Mixolydian, C-Major Pentatonic, C-Lydian, C-BeBop, C-Blues
C7sus, Csus, C11	C-Mixolydian, F-Major Pentatonic, C-Sus-Pentatonic (see Minor-Pentatonic)
(Half-) DIMINISHED	DIMINISHED-SCALES
C7#11	C-Lydian (Dominant)
C7alt, C7#9, C7#9#5	C-Altered (Diminished Whole Tone), F-Minor Melodic, F-Minor Harmonic,
C7b9, C7b9b5	C-Diminished begin with H-step (Half Tone - Whole Tone scale), F-Minor Harmonic, F-Minor Melodic
C7aug, C7+, C7#5	C-Whole Tone (Whole Tone scale)
Cm7b5	C-Locrian, C-Locrian (#2)
Cdim7	C-Diminished begin with W-step (Whole Tone - Half Tone scale)
Cphryg	C-Phrygian, C-Phrygian (#6), C-Spanish
Cmaj7#5	C-Lydian Augmented, C-Major BeBop
C7susb9	C-Phrygian, C-Phrygian (#6)

Circle of Fifths

On the circle of fifths you can find the chromatic scale in an altered note sequence. The interval between two neighbouring notes is called pure fifth.

C

G

D

A

E

B

F#

Db

Ab

Eb

Bb

F

Application #1, Parallel Major and Minor Scales

The Natural Minor scale and the Major scale are Parallel scales and contain the same notes and key signatures. The Natural Minor scale is always a minor third lower than the Parallel Major scale. Here are the Parallel Minor and Major scales with their key signatures:

Major scale

C

G

D

A

E

B

F# Gb

Db

Ab

Eb

Bb

F

Natural Minor scale

A

E

B

F# Gb

Db

Ab

Eb

Bb

F

C

G

D

Key signature

1#

2#

3#

4#

5#

6# 6b

5b

4b

3b

2b

1b

The parallel key of each major key is built by playing the same notes but instead starting with the sixth note of the major scale. That leads to the following rule.

The VI degree of a Major scale is the root tone of the Parallel Minor scale. The III degree of the Minor scale is the root tone of the Parallel Major scale.

Example:

Major scale	C D E F G A B
Minor scale	A B C D E F G

Parallel Major and Minor Pentatonic

The same rule can be applied for the Parallel Pentatonic scales, too.

The VI degree of the Major Pentatonic is the root note of the Parallel Minor Pentatonic. The III degree of the Minor Pentatonic is the root note of the Parallel Major Pentatonic.

Example:

Major pentatonic	C D E G A
Minor pentatonic	A C D E G

Application #2, Key Signatures

Also the key signatures follow the law of the circle of fifths, then between neighbouring key signatures the interval is a fifth, too.

F# - Fifth - C# - Fifth - G# - Fifth etc.

F#, C#, G#, D#, A#, E#, B#

Major

Minor

Key Signature

C

Am

G

Em

F#

D

Brn

F#

C#

A

F#m

F#

C#

G#

E

C#m

F#

C#

G#

D#

B

G#m

F#

C#

G#

D#

A#

F#

D#m

F#

C#

G#

D#

A#

E#

C#

A#m

F#

C#

G#

D#

A#

E#

B#

Bb, Eb, Ab, Db, Gb, Cb, Fb

Major

Minor

Key Signature

F

Dm

Bb

Bb

Gm

Bb

Es

Eb

Cm

Bb

Es

As

Ab

Fm

Bb

Es

Ab

Db

Db

Bbm

Bb

Es

Ab

Db

Gb

Gb

Ebm

Bb

Es

Ab

Db

Gb

Cb

Cb

Abm

Bb

Es

Ab

Db

Gb

Cb

Fb

 

Progression

Cadere, lat. = falling — A progression is a sequence of chords from scale notes (diatonic). The progression helps to build up suspense (Dominant) and the dissolution to the root chord (Tonic). Here is a table of the chord degrees of the Major scale. 

	I	II	III	IV	V	VI	VII
C	C	Dm	Em	F	G	Am	B º
G	G	Am	Bm	C	D	Em	F# º
D	D	Em	F#m	G	A	Bm	C# º
A	A	Bm	C#m	D	E	F#m	G# º
E	E	F#m	G#m	A	B	C#m	D# º
B	B	C#m	D#m	E	F#	G#m	A# º
F#	F#	G#m	A#m	B	Gb	D#m	E# º
Gb	Gb	D#m	Bbm	F#	Db	A#m	F º
Db	Db	A#m	Fm	Gb	Ab	Bbm	C º
Ab	Ab	Bbm	Cm	Db	Eb	Fm	G º
Eb	Eb	Fm	Gm	Ab	Bb	Cm	D º
Bb	Bb	Cm	Dm	Eb	F	Gm	A º
F	F	Gm	Am	Bb	C	Dm	E º

• Major chords = Capital letters, • Minor chords = Lower case letters

The chord degrees can be assigned into 3 groups.

Degree	Chord Type
I , VI	Tonic
IV, ii	Subdominant
V, iii, vii	Dominant

Major Progression

The major progression and herewith the most used major progression has the following structure:

Structure	Degree	Chord
T - S - D - T	I - IV - V - I	C - F - G - C

More major progressions:

Major

ii – V - I

V – ii - I

V – IV - I

iii – IV - I

iii – ii - I

• T = Tonic • S = Subdominant • D = Dominant

Minor Progression

In comparison with the major progression there are three basic minor progressions with the following structure:

Natural, pure minor	t – s – d - t
Harmonic minor	t – s – D - t
Melodic minor	t – S – D - t

While the minor progression of the Harmonic scale with the major triad as dominant is the most important one, the progression of the Melodic Minor scale is rarely used.

Structure	Degree	Chord
t - s - D - t	i – iv – V - i	Cm – Fm - G - Cm

More minor progressions :

Harmonic Minor: V – iv - i

Here is a table of the chord degrees of the Harmonic Minor scale:

	I	II	III	IV	V	VI	VII
C	Cm	Dm-	Eb+	Fm	G	Abm	Bm-
G	Gm	Am-	Bb+	Cm	D	Em	F# m-
D	Dm	Em-	F+	Gm	A	Bbm	C# m-
A	Am	Bm-	C+	Dm	E	Fm	G# m-
E	Em	F#m-	G+	Am	B	Cm	D# m-
B	Bm	C#m-	D+	Em	F#	Gm	A# m-
F#	F#m	G#m-	A+	Bm	Gb	Dm	F m-
Gb	Gbm	D#m-	A+	F#m	Db	Dm	F m-
Db	Dbm	A#m-	E+	Gbm	Ab	Am	C m-
Ab	Abm	Bbm-	B+	Dbm	Eb	Em	G m-
Eb	Ebm	Fm-	Gb+	Abm	Bb	Bm	D m-
Bb	Bbm	Cm-	Db+	Ebm	F	Gbm	A m-
F	Fm	Gm-	Ab+	Bbm	C	Dbm	E m-

Position

You probably came already across the magic word II-V-progression. Evil minds allege that Jazz consists only of such progressions since the Realbook is full of it (e. g. Recordame by Joe Henderson)!

Chord degrees is a topic that you should get familiar with it. Here the SacleTwister is a very useful tool, too.

If within a major scale 4 thirds are piled up the result will be seventh chords for each degree. They can be numbered with roman letters and then are called positions. In C major that means with the II-V-progression the chords Dm7 and G7 (Dominant) are to be used. 

Do you ask yourself sometimes how the great musicians get their countless chords and scales and create from them the most beautiful improvisations? You too can double your repertoire all at once! The magic word is substitution.

A substitute means that a chord is played instead of another chord. In that way new possibilities arise to expand a harmony. The same is true for arpeggios or scales. Also an improvisation can be made more interesting or difficult scales can be even made simpler.

Chords of a family can be substituted at will with each other.

Following example with the C major scale:

• Family II: II = Dm7 und IV = Fmaj7
• Family V: V = G7 und VII = Bm7b5
• Family I: I = Cmaj7 und III = Em7 und VI = Am7

Chord and Mode Substitution in Major and Minor

Trough the substitution of chords or modes/scales new possibilities open up to expand an improvisation or to sometimes simplify an improvisation.

With the II-V-I progression are here possible substitutions listed.

Chord Substitution in Major

Chord Substitution in Major with example

Degree	Harmony	Position of the Substitution	Substitution
II	_ m7	Minor third ascending	_ maj7
V	_ 7	Major third ascending	_ m7b5
I	_ maj7	Major third ascending Minor third descending	_ m7 _ m7

Degree	Harmony	Position of the Substitution	Substitution
II	D m7	Minor third ascending	F maj7
V	G 7	Major third ascending	B m7b5
I	C maj7	Major third ascending Minor third descending	E m7 A m7

Mode Substitution in Major

Degree	Harmony	Primary Mode	Interval	Substitution
II	_ m7	_Dorian	_ + minor third	_ Lydian
V	_ 7	_Mixolydian	_ + major third	_ Locrian
I	_ maj7	_ Ionian (major)	_ + major third _ - minor third	_ Phrygian _ Aeolian

Chord Substitution in Minor

Degree	Harmony	Position of the Substitution	Substitution
II	_ m7b5	Minor third ascending Tritonus * ascending -+ descending	_ m7 _ maj7
V	_ 7	Major third ascending	_ dim
I	_ m (maj7)	Minor third descending	_ maj7#5

*Tritonus (tritonus, lat./ greek = three tone step)

The Tritonus compromises 3 whole note steps and correlates to an augmented fourth. The Tritonus was in the past considered the "diabolus in musica", "the devil in the music“. The use of the interval was forbidden and didn't fit the composition method at that time.

Example:

Degree	Degree	Position of the Substitution	Substitution
II	D m7b5	Minor third ascending Tritonus * ascending -+ descending	F m7 Ab maj7
V	G 7	Major third ascending	B dim
I	C m (maj7)	Minor third descending	Eb maj7#5

Mode Substitution in Minor

Degree	Degree	Primary Mode	Interval	Degree
II	_ m7b5	_ Locrian	_ + minor third _ + Tritonitus	_ Dorian _ Lydian
V	_ 7	_ Harmonic Dominant	_ + major third	_ Locrian
I	_ m7	_ Harmonic Minor	_ + minor third	_ Ionian

Transposition

Transponere, lat. = transpose
With many instruments the transcribed notes don't match the actual sound.

The tenor sax for example is tuned in Bb and by playing the transcribed note C the note Bb sounds. In the following table are a few instruments with their corresponding tuning listed.

Realbooks and lead sheets are mostly transcribed in C and for instruments that are not tuned to C the scores have to be rewritten. With ScaleTwister this is a cakewalk. Here are some useful examples:

Tuning of the Instruments
Tuning	Instrument	Tone C is noted:
C C C C C C	• Piano • Guitar • Contrabass • Trombone • Violine • Flute	C C C C C C
Bb Bb Bb Bb Bb	• Trumpet • French Horn • Clarinette • Soprano Sax • Tenor Sax	D D D D D
Es Es Es Es Es	• Alto Sax • Horn • Eb-Trumpet • Baritone Sax • Bass Clarinette	A A A A A

Transposing of a Score in C to Tenor Sax Score (Bb)

Just simply imagine that the color circle displays your tenor sax notes and the background of the ScaleTwister shows the notes of the lead sheet.

Leadsheet C

C

C#

D

D#

E

F

F#

G

G#

A

Bb

B

Tenorsax Bb

D

D#

E

F

F#

G

G#

A

Bb

B

C

C#

Transposing of a Tenor Sax Score (Bb) to a Alt Sax Score (Eb)

Now just imagine that the background of the ScaleTwister are your tenor sax notes and on the wheel are the alto sax notes. Since the note C is noted as D with the tenor sax and A with the alto sax, turn the A of the wheel to the position D of the background and then you can read all the notes.

Tenorsax Bb

D

D#

E

F

F#

G

G#

A

Bb

B

C

C#

Altosax Es

A

Bb

B

C

C#

D

D#

E

F

F#

G

G#

Transposing of a Score by any Interval Step

In the initial position the pointer of the wheel points to 12 o'clock. It points to the note C on the background. The background of the ScaleTwister corresponds again to the score you would like to transpose. If you want to step up a score by a major third for example, turn the wheel until the desired interval (major 3rd) is on the 12 o'clock position. Now you can read the notes.

Score

C

C#

D

D#

E

F

F#

G

G#

A

Bb

B

Major third

E

F

F#

G

G#

A

Bb

B

C

C#

D

D#