Introduction to music theory by Bernard Holden

 

Most of the illustrations are taken from screen shots from the iPhone app “jazz practice”  which I developed and published as an interactive music theory and practice app .The main purpose of the app is not only to provide a practice tool but also to demonstrate, using computer science, both visually and audibly, how major and minor modes and chords sequences are created. I wish I had something like this when I was at music college. For that reason I set about creating the app which I continue to use on a regular basis . If you have an iPhone or iPad I recommend you download JAZZ PRACTICE  from the App Store to use in conjunction with this web page as you will be able to hear the scales and chords being played and try out the practice regimes. Although it works well on both iPad and iPhone please note you will only find it under  iPhone apps.

http://itunes.apple.com/gb/app/jazz-practice/id470174568?mt=8

Examples can be seen and heard by clicking where shown blue ( as in altered scale) or you tube clips as above.

 

image001-5

The above illustration includes a guitar fretboard indicating where you would place your finger to play the note E. As you move your finger up the fretboard the string producing the sound gets shorter resulting in a corresponding higher note. This is much the same as playing the notes on a xylophone as the smaller notes produce a higher note than the longer ones. On the illustration three of the strings have two Es which are what is known as an octave apart. Although one E is higher than the other they sound the same harmonically. The reason is that one has exactly double the frequency of the other because you are halving the length of the string when you play the high E . Each octave is divided by 12 frets and the interval between each fret is called a semitone or half step. By the same token the space between every other fret is called a tone. There are therefore six tones (whole steps) in an octave comprising what is called the Whole Tone  scale . You can play whole tone scales from either E or F, the next fret up or anywhere else for that matter although you are then repeating yourself. Whatever instrument you play there are only two whole tone scales to learn from whichever note you chose. The whole tone scales are  easy to see on piano as one is the two black notes together followed by four whites together (F G A B ), and the other the three blacks together follow by the 3 whites together ( C D E ).

image003

..C D E  F   G  A B C D  E F G A B   C D E  F G A

The piano keyboard above with a note marked in red  is also the note E. Assume you are playing that note followed by the white note to its right called F followed by the next black note called F sharp (#) followed by the next white note called G . That is the same as moving up each guitar fret.  You are ascending in semitones playing what is called chromatically. The interval between E and F# is a tone . The white notes are named A to G and the black notes has the same letter as its adjacent white note with the addition of a sharp or flat . Put another way F# can equally be Gb .

image007

 

There are 12 semitones (half steps) in an octave which derives from the Latin “Octo” for 8 number of notes in a major scale. It follows a major scale, has 7 intervals which do not divide equally into 12 because the seven intervals in a major scale are not all the same . They are always tone,tone, semitone, tone ,tone, tone, semitone (whole step,whole step,half step,whole step,whole step, whole step,half step)

The letters of the alphabet A to G are used ascending in alphabetic order.  Where C is located on the keyboard a semitone below the pair of black notes count out tone, tone, semitone, tone,tone,tone, semitone, to obtain the C major scale .

 

 

image008 click C Major scale

..C D  E F  G A B C

Notation

This relates to how music is written. Each type of note in the table below has a different time value starting with four beats for a semibreve or whole note. CLICK BLUE ABOVE.

Click on diagram to enlarge

image015

 

Where you are reading a note which has more than two beats it is better to get used to not to counting  the first beat  when you are reading it . For example if you are playing a dotted minim which has three beats play the note then count “two” “three”. If you were to play the note and count “one” at the same time you are using your brain for an unnecessary function and sight reading is hard enough to master without over burdening your brain. You would however count all the beats of a note if it was being held over from a previous bar . For note values of one beat or less it is best  to learn play them without counting at all so that aspect becomes automatic . With on beat ” rests” it is preferable to count every beat including beat “one” .

Where music is “syncopated” some suggest counting in quavers or eight-notes so four to the bar becomes eight beats “one and two and three and four and”

 

Triplets mean a group of three notes played inside the length of two of its note types, as in this example

 

image001

 

The pitch of each note is determined by its location on the stave either on a line or the space between the lines. These are set out below for both treble and bass clef.

Click on diagram to enlarge

image014

 

 

Now to continue with major scales and to examine the circle in the illustration below known as the cycle of fifths. Starting from C move anti clockwise to the next note G.

Let’s do the same exercise as we did for C counting the intervals tone,tone,semitone, tone,tone,tone, semitone (whole step,whole step,half step,whole step,whole step, whole step,half step) for a major scale from G and we get G A B C D E F# G. See below how the sharps are written on the stave.

.image015

 

image017

 

Repeat this for the next note D and we get D E   F#G A   B C#D

image021

image019

 

Note that every space and line is used on every major scale

 

Then

 

 

Aimage023image025

 

Eimage027image029

 

Bimage033image031

Now let’s go clockwise from C to  F

and we get F G A Bb C D E F

 

Fimage035image037

 

Bbimage039image041

 

Ebimage044image046

 

Abimage048image050

 

Db

image005image062

Gb

image058image009

 

You will have noted that progressing round the cycle of fifths in this way we either add a sharp (#) or a flat (b). You may wonder why some keys are in sharps and some flats . This is done simply to facilitate reading and writing of notes on the five lines with four spaces of the music stave. F# is the same note as Gb but occupies a different position on the stave. G is a sharp key because it has an F# as well as a G . It would be confusing if you notated it as Gb since you would then have two notes in the same position on the stave.

Without wishing to add unnecessary confusion at this stage you may have also worked out that the scale of Gb with six flats has the same notes as the scale of F# with six sharps but would be written differently. On the treble clef one would start on the first space and the other the second line up.

The diagram below shows there are flat and sharp equivalents for every note but at this stage probably just worth noting for reference purposes. It is probably of more relevance to classical musicians than jazz musicians.

Click on diagram to enlarge

keysignatures8

Cycle of Fifths

I have already said the circle in the illustration is called the cycle of fifths. The reason you may have noticed is that moving anti clockwise from C the next note G, is the fifth in the C scale. The next note D is the fifth of G and so on. If you move in the other direction clockwise, C is the fourth of G and F the fourth of C . For this reason it is also known as “The Cycle of Fourths” I have seen examples of the cycle moving in both directions. My preference, rightly or wrongly, was to adopt the cycle whereby a 2 5 1 cadence, discussed later, was moving “forward” in a clockwise direction rather than backward in an anti clockwise direction.

Chords

Although by no means  all songs but many songs written over the years utilize the Cycle of Fifths as a basis for their underlying harmonic progression. Although melodies usually consist of single notes, the addition of other notes in the form of a chord sequence whether played on a guitar or perhaps the left hand by a pianist will provide the essential additional colour.

For the moment we will confine ourselves to three chords , major 7th(∆), minor 7th and dominant 7th . They are each defined by the 3rd and 7th of the chord which are a perfect fifth apart for the major 7th(∆) and  minor 7th and a tritone apart for the dominant 7th making it a less stable chord than the other two. 

I will start by describing the notes that go making up these chords in relation to the major scale .

For a major seventh chord(∆) we take the first note in the scale (root) shown in red plus the third, fifth and seventh . C major seventh chord illustrated below is therefore

image060 click C∆7

.C E  G B

It is worth noting here that if we remove the B we will get a straightforward C major chord C E G sometimes called a major triad. This is a perfectly valid chord, which depending on the type of music could well be more appropriate .

image062 click C maj

.C E G

Other than a major 7(∆), 7th implies flat 7. C7 chord therefore has the 7th note B flattened by a semitone. C7 therefore becomes

image064 click C7

.C   E G Bb

 

The fundamental difference between a major and minor is the 3rd of the chord is flattened to create a minor sound.  A minor seventh chord therefore has the third note flattened as well as the 7th so C minor 7th becomes

 

image066 click Cm7

.C Eb G Bb

It is interesting to note that if you remove the root note C you are left with Eb major triad. That is because C is the relative minor of Eb major which I will discus later. It follows that if you were improvising  over an Eb chord you could achieve the same result thinking C minor which might seem less daunting even though you are in same relative key .

 

Another frequently used chord is the augmented whereby the fifth is raised a semitone or half step. This is often used where a tune moves from a 1 to 5 chord but the five chord has a raised fifth by a semitone. “Do you know what it means” and “I’m Gonna sit right down and write myself a letter” spring to mind. A Whole Tone scale referred to in the opening  paragraph can be used to good effect over this chord.

image043

C   E  G#

It is worth noting there are only four augmented triads

1 2 3 4
C E Ab G B Eb F A Db Bb D Gb
E Ab C B Eb G A Db F D Gb Bb
Ab C E Eb G B Db F A Gb Bb D

 

Each interval is a major third part which is also the basis for the harmonic progression of “Giant Steps” and the bridge of “Have you met Miss Jones” described later.

Harmonic Movement Around Cycle

I mentioned earlier that many melodies “move ” around the Cycle of Fifths (click to hear what programming this produces)

To understand how this works we need first to look at “modes” of the major scale discussed in next paragraph in more detail. For simplicity as it has no sharps or flats, we will consider C major . Starting on C “mode one” or Ionian mode this is the normal major scale. However what happens if we play the same scale from D to D. As we discussed earlier, the major scale of D has two sharps at C and F. However , as we are playing the scale with no sharps the effect is to flatten the 3rd and 7th to create a minor seventh scale known as  Dorian mode. Moreover , if we create a chord based on the 1st 3rd 5th and 7th notes of the  Dorian mode we get a minor seventh chord Dm7. As the root of this chord is D is the second note in the C major scale it sometimes referred to as the 2 chord when playing in the key of although it is more usual to express this in Roman numerals. Note the location of 2 in red on the cycle of fifths

D Dorian scale

image068                                                   image070 Click Dorian

..D F   A C                                                                                     D E F G A B C D

For this exercise let’s move round the cycle to the  fifth note in C scale ie G to G playing all “white” notes . Now, the 7th note in the major scale of G has an F# but as we are playing an F natural we are flattening the 7th and playing what is known as the mixolydian mode. A chord based on the 1st 3rd 5th and 7th is therefore a G7 chord or “5” chord  when playing in C

G Mixolydian

G7image074 Click Mixolydian

It follows that there are also “3 chords”, “4 chords”and “7 chords” but, continuing round the cycle, we will just stick to one more for now a “6” chord that is  Am7 below.

Am7image078 click Aeolian

………..A C E  G                     A Aolian mode

Try  playing a 6 chord followed by a 2 followed by a 5 followed by a 1 chord which in effect is playing round the cycle of fifths which results in  Am7  Dm7  G7  C

Many  tunes will fit eg “Mack the knife”, “All the things you are” , “Fly me to the moon”

Equally play in order of 1 6  2. 5 for “I’ve got rhythm” or “Blue Moon”,  “These foolish things” or “The way you look tonight. Alternatively,  2 5 1 6 for “Autumn leaves”, “Fools rush in where angels fear to tread” and many more too countless to mention

Check out this video on YouTube: (Please excuse my piano playing)

It will become apparent that many famous songs use this harmonic  progression  for the obvious reason that it flows in such a melodic way. This is because, as can be seen in the 11 V 1 diagram below, the consecutive chords progressing round the cycle are interlocking with common chord tones.

 

11  Dm7 D F A C
V G7 G B D F
1 C C E G B

 

It follows that if you learn to play this cadence in all keys you will have a covered quite a bit of ground. Not only that with so many note choices open to you it’s possible to create your melodic lines giving both scope for composing new melodies or perhaps improvising a jazz solo. What makes it easier is that if you are for example playing a solo over a 6 2 5 1 in the key of C provided your note choices are all from the  C major scale you can’t go far wrong. That is not to say every note has to be in the scale as there are exceptions which will work also.

Looking at the 11 V 1 diagram above, it is worth noting that the interval between the 3rd and 7th of “11” and the “1” chord is a perfect fifth whereas for the “V” chord its a tritone.. This is what makes the V chord unstable making it want to resolve to the one chord. Tritones are discussed later.

Can I learn to improvise?

Many of the early jazz musicians would have known little or nothing about the cycle of fifths . That is also probably true of many exponents of the art today, relying on “playing by ear” to what flows instinctively to a natural flowing harmony. Many others however, find it a more difficult task to improvise by ear. Although clearly not all, this often applies equally to many highly skilled and talented professional classical musicians . They would  however find it easy to play jazz solos of famous jazz musicians transcribed into written music  or  countless licks from tuitions books of phrases which work over selected chord patterns . In Mozart’s time it was common to leave gaps for the pianist to improvise over cadenzas. In this sense improvising is not confined to jazz. Moreover many classical compositions follow the same harmonic principles discussed in this book . I remember once hearing an operatic piece by an early Italian composer on classical FM . I was surprised to hear the harmony appeared to closely resemble “All the things you are” even though the theme was nothing like it . ” Jesu Joy of man’s desiring” springs to mind as a classical composition  that represents a 3 6 2 5  1 harmony . “Air on a G” string by Bach follows similar cadences as does for that matter, “Whiter shade of pale” by Procol Harum, in of course, a completely different genre.

We have discussed so far modes and chords round the cycle of fifths . It might be an idea to focus on a tune called Mack the Knife which is based on a repeating 6 2 5 1 progression. I have written out the tune in C followed by the arpeggios followed by the modes A Aolian   D Dorian     G Mixolydian       C Ionian

image079

If you can download the jazz practice app so much the better as you can set it to V1-V1-11-11-V-V-1-1 and use it as a backing track . Once you played it through a few times try making up your own melody or improvisation using any note in the key of C . You could get one friend to play the melody another the arpeggios and another the mode scale all at the same time perhaps taking turns to try soloing in the key of C.

If you want something really challenging, set the app to 11-V-1-1 descending in whole tones. The middle section of a tune called “Cherokee” is based on this progression and is among the most challenging to play as it progresses though some keys which are not the easiest to play. Have  look at the YouTube video “Giacamo Smith plays the bridge of Cherokee”  below

Another similarly challenging middle section of a tune is the bridge of “Have you met Miss Jones” by Richard Rogers . However, instead of descending in whole tones with a 11 V 1 , it descends twice in two whole tones ( major thirds) then back up once two whole tones . This is very similar to John Coltrane’s “Giant Steps” which I talk about in greater detail further on.  Set the app to play a 11 v 1 progression  to move either up or down in major thirds.

Modes

We have already discussed why playing the scale of C from the second degree of its scale creates a Dorian mode with a flat 3 and flat 7 because the major scale of D has two sharps. It follows if we do the same thing from the fourth degree F you get a raised fourth as the major scale of F has a Bb in it as its fourth note. Each mode therefore has its own unique characteristic regardless of which key which you can hear by clicking below.

 

1 Ionian 1 2 3 4 5 6 7 8
11 Dorian 1 2 b3 4 5 6 b7 8
11 Phrygian 1 b2 b3 4 5 b6 b7 8
lV Lydian 1 2 3 #4 5 6 7 8
V Mixolydian 1 2 3 4 5 6 b7 8
V1 Aolian 1 2 b3 4 5 b6 b7 8
V11 Locrian 1 b2 b3 4 b5 b6 b7 8

 

Minor Harmony

I have already explained that the fundamental difference between a major and minor chord is that with the latter the third is flattened. Minor chords occur even in music written in a major key. With some music the whole melody is in effect written in a minor key. For this purpose every major key has what is known as its relative minor. Both of these have the same key signature or number of sharps and flats . See diagram below from which it will be seen E minor has a key signature of one sharp F which is the same as its relative major G

Click on diagram to enlarge

image081

If you play an Eb instrument such as alto sax this diagram could also be used to tell you your key relative to concert pitch .

The minor key starts three semitones below its relative major or, expressed another way,  the major key  is the minor third of its relative minor . For example A minor is the relative minor of C and C is a minor third of A.

C major pentatonic has the same notes as A minor pentatonic, its relative minor as A minor pentatonic is the 5th mode of C  major pentatonic ( A major pentatonic scale consists of five notes which is a major scale without the 4th and 7th,  constructed as whole step, whole step,minor third, whole step)

Although minor chords occur in music written in a major key, some are tunes fundamentally in minor key . They modulate from minor to major or major to minor generally  resolve to a minor cadence  . “Blue skies” for example in a minor key as well as “Autumn leaves” which is partly major but resolves to the minor . “Green sleeves” is entirely minor . “Summertime” is in a minor key but briefly modulates to major for one bar just before the last four bars

Extensions

We have discussed in earlier chapters how harmony moves round the cycle of fifths . A development which took place in the 1950’s from the likes of Bill Evans, was for the pianist to play more complex rootless chords leaving the bass player to emphasise root movement of the chords. That is not to say root position chords are no longer acceptable. We have looked at chords made up from the root, 3rd, 5th and 7th . However this can be extended to 9th, 11th, and 13th in effect adding  another triad on top. When using the 11 this works when playing minor chords which have a flat third as it will be a tone away. There is however a clash with the major third with major and dominant chords as there would be only a semitone interval. For this reason 11 is used for minor and 11# used  for major so we add a major triad for major and a minor triad for a minor chord. Let us illustrate this with a II  V  I in C the top three notes being the extensions.

B 13 E 13 A 13
G 11 C# 11# F# 11#
E 9 A 9 D 9
Extension triad Em A D
ii V I in C Dm7 G7 C

 

Although I play mostly jazz, I have just started playing in local blues band on Saxophone. When something was in a minor key I tried playing a riff based on a minor triad a tone up which seemed to work well. In other words if it was in A minor I played a riff using a B minor triad. Alternatively, if you are playing a jazz standard in a minor key . Take “Softly in a morning sunrise” in C minor . In your solo try adding a descending D minor triad arpeggio and see how effectively it is .

 

Some examples of extended rootless chord voicings for piano are listed below for major 2 5 1 cadences.  Note how the finger movement from one chord to the next is minimal.

Even if you are not a piano player try playing the following sets of four notes in the right hand column with your right hand with the corresponding root notes D G and C in your left.

image007

Left Hand right hand  Voicings
11-V-1 Root
C MAJOR Dm9 D C,E,F,A (b7,9,b3,5)
C MAJOR G7 9 13 G B,E,F,A (3,13,b7,9)
C MAJOR C∆9 C B,D,E,G (∆7,9,3,5)
11-V-1 Root
C MAJOR Dm9 D F,A,C,E (b3,5,b7,9)
C MAJOR G7 9 13 G F,A,B,E (b7,9,3,13)
C MAJOR C∆9 C E,G,B,D (3,5,∆7,9)

 

The emergence of Bebop at the end of the 1930s associated with the likes of saxophone player Charlie Parker and trumpet player Dizzie Gillespie saw the frequent use of the #11.  initially it was referred to as Flat 5 which is the same note an octave apart. See example of this note added to a C7 chord. Its use in phasing jazz improvisation was a defining initial distinction between Early Jazz (or Traditional Jazz) and “modern Jazz” .

.C   E G Bb     F#

image017

C7#11

 

This chord is used also to great effect in compositions such as the 3rd and 4th bars of “On a Clear Day” or “Take the A Train” by Duke Ellington. The flat five interval is by no means limited to jazz and is used extensively in rock and blues playing. You will note the interval between C and F# is 3 tones .The tritone interval, as it is known, is also used extensively in classical music although, because of its dissonant sound, it was banned at one time from Renaissance church music as signifying evil. ( Click C7#11 )

As discussed earlier in relation to the 11 V 1 cadence , the interval between the 3rd and 7th of the “V” chord is a tritone which is what makes it unstable wanting to resolve to the “one” chord.

Its worth noting that if you play Dominant chords around the cycle of fifths as in the B section of “Rhythm Changes” the 3rd and 7th guide tones descend in semi tones ( half steps). It follows if two musicians wanted to provide a simple backing to a solo on this B section this method works as they would be playing the guide tones to the harmony while remaining a tritone part. Try this out by setting the app to play Dominant 7 clockwise every two bars.

It is also possible to have what is known as altered chords whereby a b9 and b13 can be added to a dominant chord. An example of this is shown later under 11 V 1 minor voicings.  An altered scale comprises a major scale with every note flattened except the root note.  I explain later under minor two five ones how the altered scale is derived from the seventh mode of the jazz melodic minor. The altered scale is

half, whole, half , whole , whole , whole , whole –

part diminished scale followed by part whole tone scale .

It works over dominant chords . Try playing C7 without the 5th (C E and Bb ) with left hand and a scale of all the black notes plus C and E with right.  In relation to the dominant chord it is root, b9, #9, 3rd, #11, #5 , b7. The same notes are obtained by playing Db melodic minor. Most jazz musicians wishing to play the altered  scale over  dominant scale  will think in terms of the melodic minor starting from the flat two of the chord. So, you would play a Db melodic minor scale over C7 as it has the same notes as C altered scale.

Guitar

The notes on the guitar also move round the cycle of fifths or fourths depending on which direction you are going. From the lowest to highest left to right we have E A D G B E which coincidentally happens to be the notes in the G major pentatonic scale and its relative minor E minor pentatonic scale. Hence pentatonic scales can be played on a guitar as bar chords with one finger across the fret.

image083

 

Selection of chords using “Jazz Practice” app

 

C majorimage085

 

C minorimage087

 

 

 

Cm7image090

 

 

C∆7image091

 

Cm∆7image093

 

 

C ∆7#5image096

 

C7 #11(9)image106

 

Cm6image099

 

C6 9image110

Cm7(9)image104

 

C7 #11(9)image106

 

 

 

C∆ 6image108

 

 

 

Cm6 9image110

 

 

C7 (9)image112

 

 

 

 

C7 (13)image114

 

 

 

 

 

C7 (b9)image116

 

 

 

 

 

C7 (b13)image118

 

 

 

 

C ∆7 (9)image120

 

 

 

C ∆7 (6)image122

 

 

 

 

C dimimage124

 

 

 

 

C7image126

 

 

 

 

 

 

Cm7b5image128

 

 

C sus       image064

I am not a guitarist but it will no doubt be obvious that the key can be changed  by moving the same shape up and down the fret. The strings marked with x are muffled so that they do not sound. Having said that there are chords which can be played in open position in the low fret position to play basic chords. A capo can be used to play the same chords in different keys . I always thought using a capo was cheating until I saw a video of Paco de Lucia using one.

Substitution chords

Jazz musicians often talk about substitution chords and I will make brief reference to the chord often substituted for the “5” chord in a 2 5 1 cadence . As discussed the standard major 2 5 1 progression has a bass line that moves round the cycle of fifths . An alternative substitution is to change the 5 chord so that the bass line instead descends chromatically . In other words instead of say Dm7 G7 C we get Dm7 Db7 C . In this context the Db7 can be either described at a flat 2 (b-11) or  by what is know an a flat 5 substitution for the V chord . In this example G7 is the V chord which has D as it’s 5th and therefore Db as it’s flat 5th . Hence “flat 5 substitution”.

If you are a horn player set the app to play a 11 V 1 in C ie Dm G7 C. But over the V chord G7, try playing a Db7 chord . The “flat 5 substitution”  works as you are in effect playing the 3rd,, 7th,#11 and b9 of G7 .

The 3rd and 7th always define the quality of a chord and the 3rd and 7th of Db7 and G7 are both the same notes and a tritone apart just as the root notes are a tritone apart. This applies to all tritone substitutions of dominant chords .  Db7 would normally be based on Db mixolydian but better still sharpen the 4 to G by playing Db Lydian Dominant

It is common practice to play either a tritone substitution or an altered chord over a V dominant chord and as can be seen, in terms of note choices,  they are similar.

To illustrate this let us look at the modes of a   2 5 1 in F      Gm7 C7 F . However for C7 tritone substitute Gb Lydian Dominant . It will be seen below that but for the F natural, it is similar to  C altered scale. Gb7#11 is essentially the same chord a C alt.

Gb Lydian Dominant

Gb Lydian Dominant

 

The diagrams below illustrate the relationship Gb with C alt and C mixolydian scales

 

C mixolydian

C7 C D E F G A Bb
Gb b5 b6 b7 ∆7 b9 b9 3

 

C alt

C alt C Db Eb E Gb Ab Bb
Gb b5 5 13 b7 R 9 3

 

Below is a blues sequence showing  11 V tritone substition chords  in bar 4

 

C7 F7 C7 C#m7 F#m7

(Gm7   C7)

F7 F7 C7 C7
Dm7 G7 C7 C7

 

Minor Two Five Ones

Another development which took place was the emergence of a cadence when resolving to a minor chord which enabled the bassist to play a line which like the major 2 5 1, also moved  round the cycle of fifths . For example a minor 2 5 1 cadence to Cm would be

Dm7b5 (D half diminished or DØ9)  to G7b13 to Cm .

The examples of how they could be played are set out below

Ø indicates a m7b5 chord otherwise known as  half diminished.

1a minor 11Ø-V-1 MINOR

 

left hand right hand Voicings
11Ø-V-1 Minor Root
F melodic min 11 chord DØ9 D C,E,F,Ab (b7,9,b3,b5)
Ab mel minor V chord G7 b13 b9 G B,Eb,F,Ab (3,b13,b7,b9)
C melodic min 1 chord Cm7 9 C Bb,D,Eb,G (7,9,b3,5)
left hand right hand
11Ø-V-1 Minor Root voicings
F melodic min 11 chord DØ9 D F,Ab,C,E (b3,b5,b7,9)
Ab mel minor V chord G7 b13 b9 G F,Ab,B,Eb (b7,b9,3,b13)
C melodic min 1 chord Cm7 9 C Eb,G,Bb,D (b3,5,7,9)

The theory however was a bit more complex as the chords were based on modes of what is known as the jazz melodic minor. This is a major scale with a flattened 3rd e.g.

image130

….C D Eb F G A B C

To make matters more complicated it involves three different melodic minors . In the  examples above and below

Dm7b5 is the chord  based on 1st 3rd 5th and 7th of the 6th mode of F jazz melodic minor known as D locrian # 2 scale or half diminished scale.

G7b13 based on the 7th mode of  Ab melodic minor scale known as G altered so called as it is the same as a  major scale with all the notes flattened except the root.

Cm based on Mode one of C melodic minor

When taking my jazz harmony exams I remembered the respective melodic minor scales by the fact they make up a minor triad which is probably more coincidence than anything to do with minor harmony. The example above for instance is     F Ab C        an F minor triad.

Click Minor modes for 11 V 1

11    D Half Diminished Scale

V     G Altered Scale

1      C Melodic Minor Scale

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Scales

 

The most important scales in jazz to concentrate on are the twelve major  scales from all degrees of those scales, the melodic minor scale, the three half diminished scales and the two whole tone scales . These will be enough to play over any chord sequence . The melodic minor scale is useful as played from the flat b2 of a dominant chord becomes the altered scale. For example Db melodic minor has exactly the same notes as C altered scale.  The altered scale contains the basic guide tones of a dominant chord i.e.  root, third and b7  but in addition  b9, #9, #11,and #5. The diminished scale over a dominant chords give root, b9,#9,3rd, #11, perfect 5th, 6th and b7. The whole tone scale gives root,  9, 3rd, #11,  #5 and b7.

To describe all scales that exist in detail would require a book in itself. For reference purposes, I will illustrate below some additional more commonly used scales limiting the examples to C root.

Blues scale

image140image146

 

 

image144image142 Major Pentatonic

 

image146image148Minor Pentatonic

 

 

image150image152 Whole tone

 

 

image154image013Half whole dim scale.   This scale  is  formed by chromatically approaching each of the diminished arpeggio notes as in  DIM 1 ,  DIM 2 and  DIM 3.

As there are only 3 diminished arpeggios it follows there can only be 3 diminished scales. Example of one  below which has same notes whether starting from B, D, F or Ab.

B C Db D Eb E F Gb G Ab A chromatic scale
C Eb Gb A dim apegegio
B C D Eb F Gb Ab  A Dim scale

 

image158image160Harmonic Minor

 

The Whole Tone scale

As explained in the opening paragraph there are only two whole tone scales to learn, made even easier as they each have only six notes . Very easy on guitar as you simply play every other fret . Piano also easy as most of the scale is two black notes together followed by three whites or three blacks together followed by two whites . As well as augmented triads with a #5 they work over any dominant chord preferably without the perfect as that would clash with the b5 and #5.

Set the app to play the whole tone scale either moving in semi tones or clockwise round the cycle of fifths . On saxophone and clarinet for each register, I tend to think of one scale as “black notes” lower half and “white” the top half reversing this for the second scale if that makes sense. In other words think of the saxophone register as C to C on the piano since it’s much easier to visualize the two whole tone scales on piano .

The use of the altered scale was an important post 1960’s development in modern jazz as it gives you the flat 9 sharp 9, major third sharp 11, sharp 5 and flat 7.  If you are improvising over a dominant chord you get the altered scale by playing the melodic minor scale from  the flat two of the chord. e.g. Db melody minor over C7.  A simpler alternative  is learning the whole tone scale as it contains 5 of notes contained in the altered scale with one additional note the “nine” . The only two notes missing therefore are the flat 9 and sharp 9. So, a reasonable compromise given there are only two whole tone scales to learn so they become part of your automatic “muscle memory” . Very useful therefore to add to your improvising vocabulary .

 

You may like to compare below the relationship between C altered scale, Gb Pentatonic scale and Db melodic minor scale

 

C ALT C Db Eb E Gb Ab Bb C Db Eb
Gb pent Gb Ab Bb Db Eb
Db mel mi Db Eb E Gb Ab Bb C Dd

 

It has to be stressed not all music from classical to jazz and pop flows in a regimented way around the cycle of fifths since otherwise music would be very boring. Some forms of music for example jazz fusion will just consist of one chord played throughout the piece or maybe two chords perhaps a semi tone apart known as “modal jazz”. Miles Davis with much acclaimed composition uses this in “So What” consisting of a  repeated riff which remains on one chord except for an eight bar section in the middle which is the same chord raised a semitone. John Coltrane’s famous jazz composition “Giant Steps” takes one major scale but divides it equally into three major thirds descending an octave in two one third steps down one back, then ascends in three one third steps to arrive back where you started taking what I suppose could be said to be “giant one third steps” . It is worth noting the movement uses an augmented triad described earlier.The mathematical division of six whole tones or whole steps of a major scale into three is simple arithmetic . The tricky part is having to play in the more difficult keys in the improvisation process. Set the app playing 11 V 1 1 descending then ascending in major thirds to simulate something close to the harmonic movement of “Giant Steps”.  Each step arrives on a major 7 chord.

Not all music forms move clockwise round the cycle, including pop songs and the 12 bar blues structure which starts on the one chord, moves to 4 chord, back to the one then the five chord resolving to the one. If you download the app you will see there is a version commonly used by blues musicians. You can play a C blues scale over the whole sequence for a blues in C. I have also included an example in the App Jazz practice” “4 chord  pop song” . Below is a  YouTube video of  “Axis of Awesome ” It had a huge number of hits in which an Australian band of that name play something like 100 apparently well known pop songs to the amazement of the audience without changing the chord  structure . They even throw in the first four bars of “Waltzing Matilda  “the structure they are using is

1                               5                                     6                           4           in the key of E major

Eimage162 B7        image164          C#m7image166 A       image168

Check out this video on YouTube:

 

Blues Harmonica

Why chose the next one round the cycle eg C if you are playing in G? In other words why is the choice the fourth note in scale you want to play in?

It’s because you suck the C harp to get the G “1 chord” in which the blues is being played then blow to get the IV chord C in which the harp is pitched . The chart below shows the notes for a standard 10 hole blues harp in C .

RIGHTER TUNING (blow reeds at top)

C E G C E G C E G C
1 2 3 4 5 6 7 8 9 10
D G B D F A B D F A

The 10 “blow holes” are ascending major triads in C but as can be seen not the “suck holes” . The major scale of C can be played using holes 4 to 7 alternately blowing and sucking to get  C D E F G A B C.

The first 3 holes produce a C major triad when blown and a G major triad  chord when sucked .

 

The Jazz Practice app includes the ability to play a  basic 12 bar blues sequence in all keys which for G is programmed as follows

G  C. G. G. C. C. G. G  D C G C

To play along on a blues harp tuned in C you suck holes 123 for the 1 chord G,  blow holes 123 for the 1V chord C and suck hole 1 for the V root D .

 

Other notes which take practice known as “note bending” are produced by changing the shape of the players mouth .What I did see was interesting  was that although all the blow notes were a series of major triads the suck notes include the flat 7 and 9. This must make it possible on C harp to produce a

G7 9 chord when sucking without even “bending” a note .

Diminished Harmony

I have so far not mentioned diminished harmony which again has little connection with cycle of fifths. It features however in much classical music as well as jazz particularly early jazz and a number of well known songs. Some examples you can no doubt check on You tube include the introduction to “Dipper Mouth Blues” played by Louis Armstrong Hot Five, or the second chord of “Deep Purple” by Peter De-Rose , “Till there was You”  made famous by the Beatles or “If I loved you” by Richard Rogers.

I started off by pointing out that there are 12 semitones or half steps in a major scale. Dividing this exactly in four we get 4 minor thirds each with 3 semi tones to create the diminished chord. Because the chord is divided equally in this way all the notes in the chord for example C diminished (Co7) are the same in Ebo, Gbo and Ao. So when you learn to play the arpeggio up and down your instrument it’s the same for all three arpeggios. The other good news is the same applies to F diminished and G diminished so there are only three arpeggios you need to practise. It is clearly called a diminished chord because if you take a 7th chord say C7 all the notes are flattened or “diminished” except the root note so that C7 ie C E G Bb becomes Co7 ie C Eb Gb A.( Not to be confused with half diminished chord where the 7th is not flattened ie C Eb Gb Bb )

 

Illustration showing the three diminished arpeggios. Click blue 1 2 and 3 to hear sound

DIM 1                            DIM 2                      DIM 3

 

Co7                                Fo7                            Go7

image019         image027          image036

Ebo7                             Abo7                           Bbo7

image021          image029       image037

Gbo7                                Bo7                           Dbo7

image023          image031           image039

 

Ao7                                 Do7                           Eo7

image025           image033           image041

The diminished arpeggios is used frequently in early jazz over a diminished chord but can also be used  over a dominant chord a semitone up as a C diminished  arpeggio is very similar to B7 with addition of a b9.

The use of the diminished scale is also very effective . It is basically formed by chromatically approaching each of the diminished arpeggio notes. So for Co7 we have

Arpeggio        C     Eb    Gb       A

Dim scale   B C D Eb F Gb Ab A

Just as there are only three diminished arpeggios, there are also only three diminished scales and the above scale has the same notes starting from any note of the arpeggio F, Ab,  B  or D.

This scale also know as the half whole (half whole step) diminished scale can also be played over the C7b9 or for that matter any dominant chord. An example of this would be the first part of “Caravan” by Duke Ellington.

Given there are only three half diminished scales to learn this is one of the most important scales to practice so they become automatic . The reason is the scale comprises root , flat 9, sharp 9, major 3rd,  #11, perfect 5th, 6th and b7. It will therefore work over any dominant, diminished, dominant #11, or dominant b9 chord.

 

Sus Chords

 

As this is an introduction I will make brief reference to sus chords, short for “suspended”. In essence this involves removing the 3rd and replacing it with a 4th ( eg C sus4) or 2nd (C sus 2) sus 4 is perhaps most used both in classical music , early jazz , modern jazz and pop music. For this reason if you see C sus this implies it is C sus4. In early jazz it is usually a “passing chord” whereas in modern jazz it can be an underlying harmony such as in ”Maiden Voyage” by Herbie Hancock which contains mostly 9sus chords throughout.

C sus 4    or C sus

image058

…………G             C              F

C sus 2

image060

…….C D         G

 

 

 

 

image054

 

………C                  G   Bb         D       F

……….1                    5   b7         9        4

 

image055

 

Autumn Leaves

I have previously discussed and shown examples of 11 V 1 major and  minor voicings and talked about relative major and keys .

To demonstrate the above I have written out the previous voicings shown in the treble clef for a section of “Autumn Leaves” as this song consists almost entirely of major and minor 11 V 1 passages alternating every four bars in the same relative key. Note the 4 chord in fifth bar. I have written the basic melody in the bass clef adding the notes for the melody. Even if you are new to keyboard this should not be too difficult to master as I have written it out in A minor the relative key of C. The main reason for this is to demonstrate the quality of the harmony deriving from using “extended” chords discussed earlier.

 

aaaaaa tm leaves

Click       Autumn Leaves MOV

 

Right hand
Autumn Leaves
11 Major Dm9 C,E,F,A (b7,9,b3,5)
V major G7 9 13 B,E,F,A (3,13,b7,9)
1 Major C∆9 B,D,E,G (∆7,9,3,5)
4 Major F∆9 A,C,E,G (3,5,∆7,9)
11 Minor Bm7b5 A,Db,D,F (b7,9,b3,b5)
V Minor E7 b9 b13 G#,C,D,E (3,b13,b7,b9)
1 Minor Am7 9 G,B,C,E (7,9,b3,5)

image068

Why are not all wind instruments tuned to C like the piano

The answer is probably two-fold . One is to do with making certain instruments easier to play in keys other than C and the other to do with size . The standard size clarinet is pitched in Bb so that when you play a C  that is the same as Bb on the piano a tone higher.  Therefore if you were playing a piece in Eb concert you would play in the key of F which is much easier to get your fingers round. If you were playing something in A major you would have to play in B which has 5 sharps so more difficult . So in this case it would be much easier to play a clarinet pitched in A as you would be playing in C. For this reason classical players usually have  both a Bb and an A clarinet .

 

The A clarinet is little longer than  the Bb clarinet .In the opening chapter I talked about the length of a guitar string affecting its pitch. Pythagoras is best known for the theorem that bears his name about squares of a right angled triangle . However one day he was walking past a blacksmith and heard the relative pitch of the two pieces of metal the blacksmith was hitting with his hammer. He offered the blacksmith a sum he could not refuse for the hammer and two bits of metal. He then went away to research the relative pitch of different size pieces of metal.

 

Getting back to wind instruments, some are pitched in C such as the flute but then why are some saxophones pitched in Bb and some in Eb . The answer is to do with the relevant size of the various saxophones . Assuming a baritone saxophone is twice the size of an alto they can both be in Eb as one will be an octave below the other. However , a tenor is roughly in the middle of these two sizes so would have to be pitched half way between the two Eb notes ie.  Bb. The Bass saxophone is four times the size of a soprano saxophone and twice the size of a tenor and they are all for this reason pitched in Bb. In total there are eight  saxophones a sub contra bass Bb,contra bass Eb, Bass Bb,   Baritone Eb, tenor Bb, alto Eb, soprano Bb, sopranino  Eb .

 

Slash Chords

These are triads over a bass note to give a particular sound wanted by the composer for example Eb/C (which happens in this instance to be Cm7)

It follows that if a bass player chooses to play something different from that intended this can completely change the harmony of the piece of music. Remove C from C maj 7and you get an Em triad . Remove C from C+ (C augmented) and you get an E major triad . By the same token Cm7b5 has the same notes as Ebm6 but sounds different if played “first inversion”ie root in the bass.

There is a slightly amusing story about an English jazz band leader called Ken Collier no longer with us, who played an early style of jazz trumpet. He had the same bass player for many years but when the drummer forgot to bring his bass drum he heard the wrong notes the bassist was playing for the first time. He asked the bass player if he always played like that following which, it is said, he sacked him on the spot. By all accounts it seems he played a slap style of double bass which had little connection with the harmony that was being played and got away with it for years.