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 natural 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 the TV theme to Hawaii50 (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 natural 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.

CONFUSION ALERT: There now follows a list of inversions of the alt scale and their uses, that's to say we are going to take ONE scale and see how it sounds when we use different notes in the bass.

That scale is going to be B7alt, which, referring to the table, was made up from three triads, Cminor, Fmajor, and Gmajor.

C D Eb F G A B C

We can also see this as the 4th item in the table (transposed) as Gmajor, Cminor, and Fminor.

Don't worry that this 'B' scale starts on C. This is the easy way to derive an alt scale. Go up a semitone and use melodic minor scale, ascending or descending.

B7alt (based on B)

B C D Eb F G A B

This inversion is B7alt and is what is normally meant by 'alt' in the fake books.

This matches B7+5-9-10-12 (!!) which is what B7alt is short for.

This run down is B7alt resolving to Em (similar to the Tania Maria sample).

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

B7alt/C=Cm69

C D Eb F G A B C

This is strongly minor and fits wherever Cm69 is called for, for example on the first chord of Cry Me a River (played in Cm).

B7alt/D and B7alt/Eb

These two roots aren't much use. The F triad on top of Eb is an attractive chord but it doesn't fully fit the alt scale and it starts sounding nasty if you include the B natural. So it should be regarded as it's 'own' chord.

B7alt/F=F7-5

This is probably the sexiest use of the alt scale

F G A B C D Eb F

It can be used in most cases when F7-5 is written. It's used here in the second chord of The Girl from Ipanema, played in Eb.

B7altG=?

G A B C D Eb F G

This does not seem to have any name in the fake books, but it's quite useful and can give a 'spooky' sound.

This example, Killer Joe in G, is based on alternating G9 and F9 chords and uses the same B7alt/G scale on both chords.

B7alt/A=Am7-5

The Portuguese 'Fado' (and hence Brazilian music) is cited as differing from other Western music by commonly using sequences such as Gm7-5 C7 Fm7-5 Bb7 rather than Gm7 C7 Fm7 Bb7. In fact the widespread m7-5 scale is yet another inversion of the altered scale. Am7-5 is

A B C D Eb F G A

This is a few bars of Gentle Rain in Cm.

It follows the sequence

Am7-5 D7alt Gm7-5 C7alt Fm7-5 Bb7alt Eb

Arguably all these chords (except the final Eb) 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.

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.

B C D Eb F Gb Ab B

Contrast this with B7alt:

B C D Eb F G A B

In chord notation the root of B-diminished is B, or D, or F, or Ab, but not the other notes.

The other two scales are C Db Eb E Gb G A Bb C and Db D E F G Ab Bb B Db.

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.

Some Sample Chords

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.

B7alt

B7+ against Dm7

B7alt/C=Cm69

Cm6 against G7

B7alt/F=F7-5

F7 against Eb+

B7alt/G

No easy one-chord solution here. (Any suggestions?).

B7alt/A=Am7-5

Am7-5 agains G7

Of course harmonising which such heavy chords as the above is not good practice. Bill Evans is happy with three or perhaps four notes and he never played the root note of a chord, leaving that to the bass or the imagination, even on solo piano.

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.

The following is a useful sequence of close chords:

An Exercise for the Reader

When enumerating the flavours of the B7 Altered scale I stated that:

B7alt = Cm69 = F7-5 = B7alt/G = Am7-5

I.e. they all use the same scale notes, though they sound very different. I'm going to omit the B7alt/G alternative which doesn't have a name, then here is that equivalence tabulated for all 12 roots:

Dm7-5 E7alt Fm69 Bb7-5
Ebm7-5F7alt Gbm69B7-5
Em7-5 Gb7altGm69 C7-5
Fm7-5 G7alt Abm69Db7-5
Gbm7-5Ab7altAm69 D7-5
Gm7-5 A7alt Bbm69Eb7-5
Abm7-5Bb7altBm69 E7-5
Am7-5 B7alt Cm69 F7-5
Bbm7-5C7alt Dbm69Gb7-5
Bm7-5 Db7altDm69 G7-5
Cm7-5 D7alt Ebm69Ab7-5
Dbm7-5Eb7altEm69 A7-5

What this means is that if you find e.g. B7alt in a fake book, then you can consider playing the 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.

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

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

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

Any alt scale can be though of as a melodic minor a semitone up. So 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) where the line in red below the fake book chords tells you which melodic minor to play.

Autumn Leaves in Bb

Cm7 F7-5 Bb E7-5EbAm7-5D7alt Gm69 G7alt
Cm7F#m melBb Bm melEbCm melEbm melGm melAbm mel
Cm7 F7-5 Bb E7-5EbAm7-5D7alt Gm69 Em7-5
Cm7F#m melBb Bm melEbCm melEbm melGm melGm mel
Am7-5 D7altGm69 G7altCm F7altBb E7-5Eb
Cm melEbm melGm melAbm melCmF#m melBb Bm melEb
Am7-5 D7altGm C7-5Am7-5D7alt Gm69 G7alt
Cm melEbm melGmGm melCm melEbm melGm melAbm mel

Which Altered Scale Should You Use?

We have 5 flavours of the altered scale associated with B. The second of our 5, Cm69(=B7alt/C) should be unambiguous. But don't play the altered scale against Cm7 or Cm9. Do play it on Cm69 or Cmnatural7 but be aware that the B natural may sound discordant to some listeners (though Bill Evans played it all the time).

The fifth, Am7-5=(B7alt/A) is very common and again is not confusing. When you see m7-5 simply play the alt scale based on the tone above (e.g. Dm7-5 fits with E7alt).

But what about all the B7, B9, B7-9, B7-3, B7-5, 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 A7alt/G flavour, not the Eb7alt. The next chords are Gm7 and then C7 (possibly written as F#7-5). For this C7 you can use C7alt, though F#7alt will fit just as well.

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. B7 Lead-in.

Bar 2. 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 3. B7 becomes B7alt. This is moving strongly towards Em and the alt chord always begs to be resolved.
Bar 4. Em. We could deliberately distort Mandel's intentions and turn this into Em-natural7, i.e. Em with D#. Then we could use the Ebalt/E scale on it. But this is a good way to alienate your audience. Leave it as Em.
Bar 5. A7 becomes A7-5=Eb7alt/A. 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 6. Am7.
Bar 7. D7 becomes D7alt. This is moving strongly towards the G.
Bar 8. Gmaj7. As is. Natural 7th scales are very similar to their relative minor sevenths.
Bar 9. Cmaj7. As is (but use F# rather than F in the scale).


Bar 10. F#m7-5. Any m7-5 chord can be covered by the appropriate alt scale, here G#7alt/F#. Country Music afficionados won't like the G#, but then they shouldn't have come to a jazz club.
Bar 11. B7 becomes B7alt as in bar 2.
Bar 12. Em.
Bar 13. Em7.
Bar 14. C#m7-5. Use D#7alt/C#.
Bar 15. F#7 becomes F#7alt. The ear expects a following B chord.
Bar 16. F#m7. As is. The expected B7 is preceded by the gentler F#m7.
Bar 17. B7. You could turn it into B7alt. 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 18. F#m7.
Bar 19. B7 becomes B7alt.
Bar 20. Em.
Bar 21. A7 becomes A7-5=Eb7alt/A.
Bar 22. Am7.
Bar 23. D7 becomes D7alt.
Bar 24. Bm7-5. Use C#7alt/B.
Bar 25. E7alt. This cries out for a strong E7alt scale.


Bar 26. Am7.
Bar 27. Cm7 followed by F7-5=B7alt/F.
Bar 28. Bm7.
Bar 29. E7 becomes E7alt.
Bars 30 and 31. A7 Eb7 Am7 D7. The following is a nice close-moving sequence:

Bar 32. G.

Bar 33. B7.

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

Shadow of Your Smile:

And here is the score for that sample:

Conclusions

The 'Altered' scale/chord is as easily derived as the major or minor scales, and, in C, is simply the addition of Cmajor, Gminor and Fminor triads (E7alt), or the Cminor, Gmajor and Fmajor triads (B7alt).

It appears unnecessarily complex in the literature because the particular name B7alt applies to a scale/chord derived by no less than 4 modifications to B7. In contrast, going up a semitone and taking the melodic minor scale (Cm mel) is far easier to think of.

The choice of root against an alt chord changes its flavour strikingly, so that it can sound like a B7 that wants to resolve to E or Em (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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