The 'Altered' Scale

'Altered' is a very weak name for a very important scale. It marks a cross-over between different types of music, namely classical or unsentimental, and jazz, popular songs and bitter-sweet. I believe it strikes a deep chord in most people, conjuring up emotions they don't necessarily feel in other harmonies. The reason for this is that it is a remarkably simple scale in construction - as simple as the major scale - even though it can seem to musicians to be horribly complicated.

We need to work up to it from the major scale.

An explanation of the major scale

Why does the major scale comprise the bizarre sequence Tone-Tone-Semitone-Tone-Tone-Tone-Semitone?

Listen to Little Brown Jug, a perfect example of a "3-chord" tune.

Vibrating strings and tubes have a natural resonance at some root frequency and also resonances at frequencies which are simple ratios of the root. The ear likes such simple ratios but regards ratios which are irrational or too close as dissonant.

C________________________F____ _____G________________________C'___
256 341.33 384 512
1 4/3 3/2 2

Take the names C, F, and G as purely arbitrary. C' is 2 times the frequency of C and corresponds to a vibrating C-tuned string touched exactly in the middle, the first overtone of C. This is so perfect harmonically that C' sounds 'the same as' C. G is the second overtone of C and corresponds to the string being touched a third of the way along. C corresponds to the second overtone of F. So G and F are the two notes harmonically closest to C (apart from C').

The triad C-E-G is in the ratios 1:5/4:3/2 (in 'just' tuning) and this simple ratio sounds very pleasing to the ear. So someone experimenting with a stringed instrument would play the notes of that chord and might also play the same notes based on the nearest roots G giving G-B-D and F giving F-A-C. Add all these notes together and you have the major scale:

C_________D_________E____F____ _____G_________A_________B____C'___
1 9/8 5/4 4/3 3/2 5/3 15/8 2
These 7 notes repeated higher and lower plus the three chord triads based on C, F, and G give ample material for making up many pleasing tunes, such as Little Brown Jug.

The triad C-E-G ratio can be better thought of as 4:5:6. Then it can be seen as overtones on a string tuned to 2 octaves below C, touched at a fourth, a fifth, and a sixth of the way along.

Minor scales

In 'just' tuning the minor triad C-Eb-G is 1:6/5:3/2, and this sounds as pleasant as the major triad, if slightly sadder. This could be expressed as 10:12:15, but that would put the fundamental at 1/10 of C, absurdly low. But 6*C=5*Eb=4*G, so these three notes have a common harmonic at G, two octaves higher, which may be what appeals to the ear.

Applying the same logic as before, if you combine Cm triad with Fm triad and Gm triad you get the following:

C_________D____Eb________F_________G____Ab________Bb________C'___
1 9/8 6/5 4/3 3/2 8/5 16/9 2
This is referred to as C melodic minor and contains the same notes as Eb major. So Cm is also referred to as the relative minor of Eb or the Aeolian mode of Eb.

An example is Hawaii 50 (though this modulates to Eb major at the end).

A stronger variant is to combine the Cm, Fm and G major triads, giving:

C_________D____Eb________F_________G____Ab_____________B____C'___
1 9/8 6/5 4/3 3/2 8/5 15/8 2

This is referred to as C harmonic minor and is a different note sequence to any major.

A third variant is to combine the Cm triad with the Gm triad and the F major triad giving:

C_________D____Eb________F_________G_________A____Bb________C'___
1 9/8 6/5 4/3 3/2 5/3 16/9 2

This is also called the Dorian mode of Eb and is used very effectively in Benny Golson's Stolen Moments.

Digression on Inexact tuning

In the derivation of the above scales tones and semitones have no meaning. We have simply used mathematical ratios (but cheated by giving them the names of notes on a full keyboard). But picked out on a guitar string the ratios of the major scale are close to the sequence 2-2-1-2-2-2-1 where a unit is the space between frets. Unfortunately the pure ratios don't cleanly transpose to a new key. If you multiply all the values by 3/2 then you transpose the scale into G as root. But D (9/8) times 3/2 gives a new A=27/16=1.6875. (The old A was 5/3=1.666, i.e just over 1% out). It gets worse with repeated key transposition. There's no perfect solution to this problem and J. S. Bach introduced the compromise of even-tempered tuning (the well-tempered klavier) which tuned keyboards to intervals based on 12 equal semitones, each the 12th root of 2. Effectively this puts the keyboard out-of-tune in every key but by the same amount. It is now almost universally accepted. The mathematical difference from 'just' tuning is shown below:

C____Db___D____Eb___E____F____Gb___G____Ab___A____Bb___B____C'___Note
1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 16/9 15/8 2 Just
1 1.1251.2 1.25 1.333 1.5 1.6001.6671.7781.8752 Just
1.0001.0591.1221.1891.2601.3351.4141.4981.5871.6821.7821.8882.000Even

To show this another way, the green marks on the line are even-tuned, the red marks are the 'just' ratios. (In just tuning Db and Gb are too complicated.)

This chart illustrates that the mathematical coincidence of Eb, E, and G (the other notes are dependent) falling on twelfth root of 2 boundaries is not so startling - they miss by a visible (and audible) amount.

This sample plays a just-tuned triad changing into an even-tuned triad halfway through.

The change is perceptible but not catastrophic.

Permuting the major and minor triads

Deriving the major and minor scales in this way suggests that we should try all 8 combinations of major and minor triads for C G and F and indeed some interesting results emerge. (Minor triads are shown in red for clarity.)

C triadG triadF triadCombined Notes Same as
C E GG B DF A CC D E F G A B CC major
C E GG B DF Ab CC D E F G Ab B CC harm maj
C E GG Bb DF A CC D E F G A Bb CF major
C E GG Bb DF Ab CC D E F G Ab Bb CE7alt
C Eb GG B DF A CC D Eb F G A B CB7alt
C Eb GG B DF Ab CC D Eb F G Ab B CC harm min
C Eb GG Bb DF A CC D Eb F G A Bb CBb major
C Eb GG Bb DF Ab CC D Eb F G Ab Bb CEb major

We see that 4 scales out of the 8 have the same notes as a major scale. Every time you change one of the three triads from major to minor you add a flat, so we have scales in C, F, Bb, and Eb. The last of the 8, for example, is properly called C melodic minor but it has the same notes as Eb major, rotated by 2. At the simplest level I am taking scales which contain the same notes as being the 'same', although obviously the starting note or root has a big effect on what we hear.

The second scale is called C harmonic major and 'pairs' with the sixth, C harmonic minor. These sound essentially 'classical' to me. They differ from the other six in that it's not easy to find a single chord which encompasses all seven notes (see later). It's easy to find two chords (D diminished plus either C major or C minor) which can accompany the scale, but in any event the result is non-jazzy.

Scales 4 and 5 are the shock. They are versions of the same scale, called 'Altered'. So this simple table proves that the altered scale/chord is not an esoteric side-shoot of music but as easily derived as the familiar major and minor scales. I would contend that this is why it is easy and appealing to listen to. Unfortunately it is not so easy to play, having a peculiar complexity all of its own.

The Altered Scale

This is certainly the most important jazz scale and is responsible for making popular music sound evocative and for generally producing 'a lump in the throat'. This is a snippet of Tania Maria singing Besame Mucho.

This goes from Em through E7alt to Am, through F#m7-5 and B7alt back to Em, and then again through E7alt to Am.

"Every note added to a chord costs you a member of the audience."

It is certainly true that many jazz players make horrid sounds in the hope of sounding clever. But the altered scale does not fall into that category. Because of its simple derivation it sounds nice. On slow numbers Bill Evans, the king of altered scales, could be regarded as the best cocktail pianist there ever was because he played beautiful, tuneful music.

The altered scale is listed in Wikipedia in different inversions as 'altered', 'acoustic', 'adonai malakh mode' (suspect), 'half-diminished', 'lydian augmented', and 'melodic minor' (also suspect).

So the confusing thing about this scale is how many different flavours it has. The recognised way to derive a C7alt chord is to take a C7 chord (C E G Bb), augment the G to G#, add the flat ninth (Db), flatten the tenth E to Eb and the fifth G to Gb. That seems absurdly complicated although the resulting chord does indeed sound like a C chord, and it obviously resolves to F or Fm.

C C# D# E F# G# A#

Here is a few bars of Tangerine using this flavour of C7alt and D7alt.

CONFUSION ALERT: There now follows a list of inversions of the alt scale and their uses:

Based on C

The following is what we derived by combining Cmajor, Gminor and Fminor.

C D E F G G# A#

This doesn't feel much like a C scale and it is not called C7alt. Wikipedia calls it C-adonai malakh but that confuses it with another Jewish scale (C C# D D# F G A A#). It could be called C7+ since it is clearly a C7 scale with the addition of an augmented 5th. However that is confusing in that in C+ (C augmented) the Ab normally replaces the G, whereas in our scale the Ab replaces the A. So I shall call it Cjazz as it has an essentially jazz flavour.

This example, Killer Joe, is based on alternating C9 and Bb9 chords but uses the same Cjazz scale on both chords.

Based on E

How does Cjazz relate to C7alt? Our sequence is an inversion of E7alt:

E F G G# A# C D

This matches E7+5-9-10-12 (!!) which is what E7alt is short for.

This run down is E7alt resolving to Am (as in the Tania Maria sample).

Based on F

F G G# A# C D E

This is strongly minor and fits wherever Fm69 is called for, for example on the first chord of You Don't Know What Love Is.

Based on D

The Portuguese 'Fado' is cited as differing from other Western music by using sequences such as Gm7-5 C7 Fm7-5 Bb7 instead of Gm7 C7 Fm7 Bb7. In fact the widespread m7-5 scale is yet another inversion of the altered scale. Dm7-5 is

D E F G G# A# C

This is a few bars of Gentle Rain in Fm.

It follows the sequence

Dm7-5 G7alt Cm7-5 F7alt Bbm7-5 C7alt Fm

Arguably all these chords (except the final Fm) are alts, though the m7-5 sound is so strong and distinctive that one would never call it an alt chord in a fake book.

Based on Bb

This can be used in The Girl from Ipanema, played here in Ab.

To round this section off, here is a snippet of Bill Evans playing Autumn Leaves.

It's from Portraits in Jazz recorded in December 1959 and is packed with alt chords.

The Diminished Scale

No discussion of the altered scale would be complete without a mention of the diminished scale, which can sound very similar. If you take alternate intervals of a semitone and a tone you produce a scale with lots of character, the Diminished or Octatonic scale. There are only three such scales, so scale practice is four times easier than for major or minor scales.

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

Contrast this with C7alt:

C C# D# E F# G# A#

In chord notation the root of C-diminished is C, or D#, or F#, or A, but not the other notes.

The other two scales are C# D E F G G# A# B and D D# F F# G# A B C.

This example is a blues in C base on the chord sequence:

C7 F7 C7 C7 F7 F7 C7 A7 D7 G7 C7 C7

All accompanying chords are simply 3rd and 7th, and all the melody notes are on the diminished scales of the appropriate root. Note that the same run is used on the A7 as the preceding C7, since C and A have the same diminished scale.

I believe the diminished scale is a 'contrived' scale and as such does not appeal emotionally, only intellectually, and the reason for this is that it cannot be derived from addition of triads as the altered scale can.

Sample Chords for the Most Important Scales

I've been treating the words 'scale' and 'chord' often as if they were the same thing. To justify this it is an interesting exercise to find a single chord that cover all notes of a scale. Since this involves 7 or 8 notes it is helpful to split the chord into a left-hand and a right-hand half and this acts as an aide-memoire for the notes of the scale.

Major

F against Em7

This contains all the notes of C major, i.e. all the white notes, though it's obviously an F chord.

This is a snippet of Blue Moon:

It plays the last 4 bars of the middle 8 of Blue Moon (in F) where the final chord is F# against Fm7, and covers the notes of C# major.

Melodic Minor

Fm against Ebmaj7

This contains all the notes of C melodic minor (same as Eb major) though it's based on Fm

Blue in Green starts and ends on that chord, but based on D minor.

Harmonic Minor

Am against Ddim

As I said earlier, this doesn't really work, but it is used here at the beginning of The Summer Knows:

Diminished Scale

Ebdim against G#dim

This example would be for D, F, Ab, or B diminished scale. The upper chord is a tone higher than the lower.

Two Sleepy People gives an example on its second chord, with the run-down being a D diminished scale.

If you make the upper chord a semitone above the lower, the result is less agreeable, but still acceptable.

Altered

Bb7 against C7

This is only one of number of flavours of the alt chord. It is used here in the fourth chord of Mood Indigo.

Of course harmonising which such heavy chords as the above is not good practice. Bill Evans is happy with three or perhaps four notes. Imagine we are called on to play Db7alt. The following 4 inversions are scored here in C key signature. Typically the bass would be playing G or Db. This is a perfect example of why alt chords appear so difficult because this would normally be written in 5 flats with accidentals.

Bill Evans uses the first of the four all the time, sometimes leaving out the A. He rarely (if ever) uses the second and fourth inversions, and I think this must be a matter of habit since they don't sound so bad. He frequently uses the third inversion, and this has a 'sweeter' sound than the others.

Which Altered Scale Should You Use?

We have 5 flavours of the altered scale associated with C. The first, Cjazz, is just a name for what I see as the easiest way to derive the scale, and you won't find this in a fake book. The m7-5 is very common and is not confusing. When you see m7-5 simply play the jazz scale based on the tone below (Dm7-5 becomes Cjazz). The m69 should be unambiguous. Don't play the altered scale against Fm7 or Fm9. Do play it (Cjazz) on Fm69 or Fmnatural7 but be aware that the E natural may sound discordant to some listeners (though Bill Evans played it all the time).

But what about all the C7, C9, C7-9, C7-3, etc. chords? Can these be altered scales? There is no clear-cut answer to this and your ear has to tell you. The altered chord/scale always wants to resolve so it's rarely going to be correct to play it on a static chord, for instance the first F in Girl from Ipanema. But the second chord, G7-5, is more dynamic. We have two flavours of altered chord, both major and both involving the seventh. Which should we use? For this G7-5 the answer is clearly the Ajazz flavour, not the Ebjazz. The next chords are Gm7 and then C7 (possibly written as F#7-5). For this C7 you have to use the alt flavour (Abjazz, not Djazz).

Here is the example of 'The Shadow of Your Smile' by Johnny Mandel with the altered scale used fairly frequently. It uses the three flavours, alt, 7-5, and m7-5.

This is how it appears in the first Real book with the original nicely understated chords. Let's take it bar by bar:

Bar 1. F#m7. Minor 7ths and 9ths are best left alone. They give the listener a base from which to understand the harmony of the song. Too many rarefied chords and he can easily 'lose' the key.
Bar 2. B7 becomes B7alt=Gjazz. This is moving strongly towards Em and the alt chord always begs to be resolved.
Bar 3. Em. We could deliberately distort Mandel's intentions and turn this into Em-natural7, i.e. Em with D#. Then we could use the Bjazz scale on it. But this is a good way to alienate your audience. Leave it as Em.
Bar 4. A7 becomes A7-5=Bjazz=Eb7alt. The D# (flat fifth) against an A7 chord is much easier on the ear than the D# against Em, as the same scale would have been in the previous bar.
Bar 5. Am7.
Bar 6. D7 becomes D7alt=Bbjazz. This is moving strongly towards the G.
Bar 7. Gmaj7. As is. Natural 7th scales are very similar to their relative minor sevenths.
Bar 8. Cmaj7. As is (but use F# rather than F in the scale).


Bar 9. F#m7-5. Any m7-5 chord can be covered by the appropriate alt scale, here Ejazz=Ab7alt. Country Music afficionados won't like the G#, but then they shouldn't have come to a jazz club.
Bar 10. B7 becomes B7alt=Gjazz as in bar 2.
Bar 11. Em.
Bar 12. Em7.
Bar 13. C#m7-5. Use Bjazz=Eb7alt.
Bar 14. F#7 becomes F#7alt=Djazz. The ear expects a following B chord.
Bar 15. F#m7. As is. The expected B7 is preceded by the gentler F#m7.
Bar 16. B7. You could turn it into B7alt=Gjazz. But the next chord is going to be F#m7, not Em, so it's probably wiser to leave this as an unadorned B7.


Bar 17. F#m7.
Bar 18. B7 becomes B7alt=Gjazz.
Bar 19. Em.
Bar 20. A7 becomes A7-5=Bjazz=Eb7alt.
Bar 21. Am7.
Bar 22. D7 becomes D7alt=Bbjazz.
Bar 23. Bm7-5. Use Ajazz=Db7alt.
Bar 24. E7alt. This cries out for a strong E7alt=Cjazz scale.


Bar 25. Am7.
Bar 26. Cm7 followed by F7-5=B7alt=Gjazz.
Bar 27. Bm7.
Bar 28. E7 becomes E7alt=Cjazz.
Bars 29 and 30. A7 Eb7 Am7 D7. The following is a nice close-moving sequence:

Bar 31. G.

Bar 32. B7.

Here is a very stylised (and quite irritating) rendering of the song with those chords. Wherever a jazz scale appears it is played as a pure scale. When there's no jazz scale the bar is left empty.

Shadow of Your Smile:

And here is the score for that sample:

An Exercise for the Reader

When enumerating the flavours of the Altered scale I stated that:

Cjazz = Dm7-5 = E7alt = Fm69 = Bb7-5

I.e. they all use the same scale notes, though they sound very different. Here is that equivalence tabulated for all 12 roots:

Cjazz Dm7-5 E7alt Fm69 Bb7-5
DbjazzEbm7-5F7alt Gbm69B7-5
Djazz Em7-5 Gb7altGm69 C7-5
EbjazzFm7-5 G7alt Abm69Db7-5
Ejazz Gbm7-5Ab7altAm69 D7-5
Fjazz Gm7-5 A7alt Bbm69Eb7-5
GbjazzAbm7-5Bb7altBm69 E7-5
Gjazz Am7-5 B7alt Cm69 F7-5
AbjazzBbm7-5C7alt Dbm69Gb7-5
Ajazz Bm7-5 Db7altDm69 G7-5
BbjazzCm7-5 D7alt Ebm69Ab7-5
Bjazz Dbm7-5Eb7altEm69 A7-5

What this means is that if you find e.g. B7alt in a fake book, then you can play the Gjazz=Am7-5=B7alt=Cm69=F7-5 scale on top of it. Of course you can't change the root without endangering the essential feeling of the piece, so this aide-memoire is for pianists, guitarists, and front-line soloists rather than for bass players. A reasonable objection to the table is that it makes a complicated situation even worse by adding the first column, Cjazz etc., which is a notation that never appears in fake books. However it does seem to me that there's a need for such a name (witness the example of Killer Joe which really does use that inversion). And thinking of the Cjazz scale as being a C7 scale with the modification of A to Ab is the easiest of all the ways of deriving the 'altered' scale.

To get into the spirit of things play the sequence Gm7 C7alt F D7alt (e.g. the beginning of Tangerine) as

Gm7 Abjazz=Bbm7-5=C7alt=Dbm69=Gb7-5 F Bbjazz=Cm7-5=D7alt=Ebm69=Ab7-5

round and round, thinking of the different inversions each time.

Now here is an example of the chords of Autumn Leaves written as they would appear in a fake book (but including some passing chords and some Gm69s) together with the 'jazz' equivalent below in red. The exercise is to busk a chorus thinking in every case of the 'jazz' scale, rather than the fake book equivalent.

Autumn Leaves in Bb

Cm7 F7-5 Bb E7-5EbAm7-5D7alt Gm69 G7alt
Cm7GjazzBb GbjazzEbGjazzBbjazzDjazzEbjazz
Cm7 F7-5 Bb E7-5EbAm7-5D7alt Gm69 Em7-5
Cm7GjazzBb GbjazzEbGjazzBbjazzDjazzDjazz
Am7-5 D7altGm69 G7altCm F7altBb E7-5Eb
GjazzBbjazzDjazzEbjazzCmDbjazzBb GbjazzEb
Am7-5 D7altGm C7-5Am7-5D7alt Gm69 G7alt
GjazzBbjazzGmDjazzGjazzBbjazzDjazzEbjazz

Conclusions

The 'Altered' scale/chord is as easily derived as the major or minor scales, and is simply the addition of Cmajor, Gminor and Fminor triads (Cjazz), or the Cminor, Gmajor and Fmajor triads (Gjazz).

It appears unnecessarily complex in the literature because the particular name C7alt applies to a scale/chord derived by no less than 4 modifications to C7. In contrast the Cjazz inversion can be derived from C7 with a single modification.

The choice of root against an alt chord changes its flavour strikingly, so that it can sound like a C7 that wants to resolve to F or Fm (the normal use), or it can sound like a minor69, a m7-5, or a 7-5 chord.

The use of alt chords in a harmonisation has a profound effect on the flavour of the piece. Used in country music, for example, or in a hymn, they would sound totally anachronistic, and destroy the spirit of the tune entirely. But without them popular music and jazz would lose much of their tension and soulfulness. Latin music would be flat and pointless.

When listening to second-rate accompanists, there is a sharp divide between those that have assimilated the alt chord and those that have not. The former sound far more sophisticated. I'm drawing a distinction here between players who play some added notes, e.g. a flattened ninth or an augmenthed fifth, or who always play m7-5 chords in their simplest form, and those who are at ease with the whole altered scale. Yet the 'altered' scale is not so difficult to master if you start from an inversion which is the simple sum of three triads.

Finally, here is a chorus of Bill Evans playing I Should Care:

The opening backing chords of every half chorus are a descent, Gb7alt F7alt E7alt Eb7alt D7alt G7alt C7alt F7. The solo line is too varied to present simple altered scales but the feeling is there throughout.

Comments? Email Chris Paradine

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