As recommended in the Japanese edition of the Hanon (listed under the references section below), the scales are to be practiced between 60 and 120 BPM. Start at 60 and increase incrementally (no more than 2 BPM by 2 BPM). If you get to a certain BPM on a specific day, begin your practice 4 to 10 BPM slower on the next day.
Fingerings
The proper fingerings, provided by Alphonse Schotte (who revised and expanded the original edition of the Hanon), are listed under exercise 39 for major and (harmonic) minor scales and arpeggios, and exercise 43 for melodic minor scales in the French/Belgian edition. In the Japanese edition, major and all types of minor scales are grouped together under exercise 39, while fingerings for the arpeggios can be found under exercise 41.
The scales are listed in order following the circle of fifths in both editions. Interestingly however, the different keys ascend through the cycle (C, G, D, A…) in the French edition, whereas they descend (C, F, Bb, Eb…) in the Japanese edition.
Note that minor scales usually have the same fingerings in their harmonic and melodic versions. The only notable exceptions are in the keys of C# and F# minor. When practicing melodic minor scales, make sure to play melodic minor ascending and natural minor descending, as indicated in the Hanon. For a review of the theory behind harmonic, melodic, and natural minor scales, see this post.
Routine
All scales and arpeggios should be practiced hands separate first (right hand and left hand on their own) and then hands together, going through the following steps without interruption:
up and down the scale over one octave in quarter notes
up and down the scale over two octaves in eighth notes
up and down the scale over three octaves in triplets (preferably twice to build strength)
up and down the scale over four octaves in sixteenth notes (preferably twice to build strength)
Finally, after performing these steps, all scales can be followed with these simple harmonic progressions also provided in the Hanon: IV6-I/5-V7-I for major scales and IVmi6-Imi/5-V7-Imi for minor scales.
References
Hanon, Charles-Louis. Le pianiste virtuose en 60 exercices. Bruxelles, Paris : Schott Frères, 1923-1929.
Hanon. The Virtuoso Pianist. Tokyo: ZEN-ON Music Co., Ltd. 1955.
The natural minor scale corresponds to mode VI of the major scale, also known as Aeolian (for a comprehensive review on modes, see this post). In other words, it has the exact same notes as the major scale, but it begins and ends on the 6th scale degree of the major scale.
For example, the A major scale has the following notes: A B C# D E F# G# A. The sixth scale degree here is the note F#. F# natural minor is thus: F# G# A B C# D E F# (the same as the F# Aeolian mode).
Another way to look at this is to think that the tonic in any given natural minor scale is to be found a minor third below the tonic of its relative major scale.
For example, the relative minor scale of C major (C D E F G A B C) is A minor (A B C D E F G A). Indeed, there is an interval of a descending minor third between the two tonics, C and A (for a comprehensive review of intervals, see this PDF).
Harmonic minor
Most music students know that harmonic minor is “natural minor with a raised seventh.” But why do we call it harmonic minor? What exactly is harmonic about it?
Consider this: the chord built on the fifth scale degree in natural minor is a minor seventh chord (Emi7 in the key of A minor). To get a dominant-tonic relationship akin to the one we have in major keys (G7 to C for instance, with the tritone F & B resolving to the notes E & C), that minor third in the V chord needs to be raised by a half step. Vmi7 now becomes V7: a dominant chord with a major third (which is called the leading tone because it resolves up a half step to the tonic). With the scale reflecting this change in the V chord, we now have harmonic minor. That is: A B C D E F G# A in the key of A (here, the G# is both the leading tone of the A harmonic minor scale and the major third of its fifth degree, the E7 chord). Does that make sense? I hope so! And if it does, we can now move on to melodic minor…
Melodic minor / jazz minor
In the harmonic minor scale, the raised seventh creates an interval of an augmented second, a melodic “gap” so to speak, between the sixth and seventh scale degrees (some might say this results in an “exotic” or “Middle-Eastern” feel). This “gap” can be somewhat discomforting, particularly to a Western ear that expects a series of major and minor seconds, i.e. whole steps and half steps (as is the case in the major and natural minor scales).
Raising the sixth a half step (from F to F# in the key of A) makes the augmented interval disappear and “smooths out” the scale from an intervallic point of view. The result is what we call melodic or jazz minor. In A, we have: A B C D E F# G# A.
Looking at the scale from a different angle, one might notice that a given melodic minor scale would feature all the same notes as its parallel major counterpart, except for the third, which, of course, has to be minor (lowered by a half step when going from the parallel major scale to the melodic minor scale).
Summary
Name
Example (in A)
Remarks
Natural minor
A B C D E F G A
Equivalent to the Aeolian mode. Relative of C major (both scales share all of the same notes).
Harmonic minor
A B C D E F G# A
Presence of the leading tone (raised seventh), which creates harmonic tension and yields the V7-Imi progression.
Melodic minor
A B C D E F# G# A
Equivalent to playing the parallel A major scale with a lowered third (minor instead of major).
These three different types of minor scales are commonly found in the Western tonal system. There are, however, myriad other minor sounding modes (Dorian, Phrygian, Aeolian, and Locrian for example) and scales (such as the Hungarian minor scale or the minor pentatonic).
The blues as a musical genre is characterized by an ambiguous tonality, constantly oscillating between major and minorÂą. In order to render such an ambivalent quality when playing the blues, two distinct (though related) scales are commonly used: the major and the minor blues scales, which quite simply derive from the major and minor pentatonic scales respectively. In each case, a “blue” note is added to the five tones that form the basic major/minor pentatonic sounds. The major and minor blues scales can therefore be considered hexatonic scales, each being comprised of six distinct notes.
From major pentatonic to major blues scale
As presented in this short article, the major pentatonic scale is comprised of scale degrees 1 2 3 5 6. In the key of C for example, that’s C D E G A.
Reflecting the feeling of major-minor ambiguity discussed above, the blue note of choice here is indeed #2 (or, enharmonically, b3): with this addition to the basic tones of the major pentatonic scale, both the augmented second (or, enharmonically, the minor third) and the major third are included in the major blues scale. Note that the blue note creates chromaticism in the scale, dividing the whole-tone interval originally present in the pentatonic between scale degrees 2 and 3 into two semitones. Adhering to widely accepted principles of music notation, we’ll refer to this blue note as #2 in the context of an ascending melody, and as b3 in the context of a descending melody. Hence the formula:
The minor pentatonic scale is comprised of scale degrees 1 b3 4 5 b7. In the key of A, that’s A C D E G. As explained in the article already mentioned above, A minor pentatonic and C major pentatonic are relatives. As such, they both feature all the same notes (the only difference being their “starting point” or root: A in the former case, C in the latter).
Quite simply, each minor blues scale also happens to be the relative minor of its major counterpart, hence featuring all the same notes as the latter, but played starting a minor third below its root:
C major blues scale
C D D# E G A C ascending
C A G E Eb D C descending
A minor blues scale (A is a minor third below C)
A C D D# E G A ascending
A G E Eb D C A descending
Notice that the blue note is the same tone in both scales: #2/b3 in the context of the major blues scale becomes #4/b5 in the context of the minor blues scale². So the general formula for the minor blues scale is:
As I always tell my students: “in music, there are no hard and fast rules” (Mark Levine actually expressed the idea of musical freedom in jazz using this very wording a few decades ago in his Jazz Piano Book). Pretty much anything goes, as long as you’re honest with what you’re hearing in your mind’s ear. But the notion of infinite possibilities can be daunting… Not to worry though: that’s where the pentatonics and the blues scales step in! They’re a natural, fun, versatile way to begin your journey with improvisation, and will surely prove to be instrumental in developing your inner ear and exploring musical ideas. If you’re wondering over what chords these scales can be played, here’s a very general way of thinking about it to get you started:
the major pentatonic/blues scale works on dominant (C7, C7(#9)…) and major chords (C6, Cma7) built on the same root as the scale;
the minor pentatonic/blues scale works on dominant (C7, C7(#9)…) and minor chords (Cmi, Cmi6, Cmi7…) built on the same root as the scale;
the minor pentatonic/blues scale also works on dominant and minor chords built on a root located a fourth above the tonic of the scale (F7, Fmi7) or a fifth above the tonic of the scale (G7, Gmi7).
This means you can play over a whole blues using just one scale! C minor pentatonic/blues indeed sounds great over C7, F7, and G7 (degrees I, IV, and V of a C blues respectively). Play the scale against each of these chords and listen carefully: you’ll notice the different shades it takes…
Conclusion
That’s all there really is to it! A common misconception is to think that there is only one blues scale. Thinking in terms of having two distinct blues scales (which are, in fact, each other’s relatives) at one’s disposal is indeed a simpler and more fruitful approach.
As I mentioned briefly in this post’s opening paragraph, the added notes (#2/b3 in the case of the major blues scale, and #4/b5 in the case of the minor blues scale) are often called “blue notes.” There is quite some controversy in musicological circles around those so called blue notes… But I tend to agree that the ones mentioned here do indeed largely contribute to giving a bluesy feel to your basic pentatonics, and are indeed the most common. So play around with them, and you’ll see… They sound great!
Notes
Âą In “Blue Note and Blue Tonality,” William Tallmadge writes about “neutral” pitches (quarter-tones), and particularly “neutral” thirds in the context of the blues: singers and instrumentalists traditionally inflect the third in the blues scale, which as a result sounds somewhere in between the tempered minor and major thirds (hence the term “neutral”). On many instruments however (such as the piano), it is impossible to play neutral thirds (you’d have to go in between the keys!). Jazz and blues pianists have no choice but to use either minor or major thirds, or to play around with both.
² For further reading on the topics of pentatonic scales and the blues, I suggest referring to chapters 9 and 10 in Mark’s Jazz Theory Book.
References
Levine, Mark. The Jazz Piano Book. Petaluma: Sher Music Co., 1989.
Levine, Mark. “Chapter Nine: Pentatonic Scales.” In The Jazz Theory Book, 193-218. Petaluma: Sher Music Co., 1995.
Levine, Mark. “Chapter Ten: The Blues.” In The Jazz Theory Book, 219-236. Petaluma: Sher Music Co., 1995.
Tallmadge, William. “Blue Note and Blue Tonality.” The Black Perspective in Music, Autumn 1984 (pp. 155-165).
The term “pentatonic” comes from the Greek language: the prefix penta-, “five,” and the word tonos, “tone,” are associated to bring forth the idea of a five-tone scale.
There are of course many five-tone scale possibilities within the twelve-tone equal temperament system. We’ll focus on the most common pentatonic scale here and call it the “global” pentatonicÂą (this particular scale is indeed encountered in the musics of many cultures around the world).
[1] The global pentatonic is based on a succession of ascending fifths: C G D A E.
[2] Reordered within the range of a single octave, we have: C D E G A.
[3] The intervals formed by the tones of this scale relative to its root (C) are as follows:
a major second between C and D;
a major third between C and E;
a perfect fifth between C and G;
a major sixth between C and A .
Since all the intervals in this scale are major (except the perfect fifth), it is often referred to as the major pentatonic. What I call the scale’s “formula,” based on Arabic numerals² representing its scale degrees (as opposed to Roman numerals commonly used to represent chords that are built on each scale degree), is: 1 2 3 5 6.
[4] Just like the diatonic seven-note major scale (C D E F G A B), the major pentatonic’s relative minor scale can be built by playing all the notes that comprise the major pentatonic, beginning on the tone located a minor third below the latter scale’s root: A C D E G.
[5] The intervals formed by the tones of this new scale relative to its root (A) are as follows:
a minor third between A and C;
a perfect fourth between A and D;
a perfect fifth between A and E;
a minor seventh between A and G.
Since all the intervals in this scale are minor (except the perfect fourth and fifth), it is often called the minor pentatonic. Its “formula” is: 1 b3 4 5 b7.
To sum up, here are the important formulas again below (accompanied by examples with the note C as the tonic in both cases, for ease of comparison):
Major pentatonic
1 2 3 5 6
C D E G A
Minor pentatonic
1 b3 4 5 b7
C Eb F G Bb
Notes
Âą This terminology is used by Michael Hewitt in his book Musical Scales of the World (see Hewitt 2013).
² More accurately speaking, these are the numerals commonly used in Europe that stem from the Hindu-Arabic numeral system.
References
Hewitt, Michael. “Section 5: Pentatonic Scales.” In Musical Scales of the World, 125-134. The Note Tree, 2013.
The “dominant shape” is extremely versatile. It can be used to voice chords that are derived both from major harmony, and from melodic minor harmony. The degrees on which each chord mentioned here functions are indicated in the captions below each example. Some of those chords work better in modal contexts (or when one has a vertical approach on each particular chord within a tonal context), and some also sound fitting in various tonal contexts. Let your ear be your guide!
Transposable formulas (specific arrangements of chord tones and tensions, e.g. “3 13 b7 9”) are also given in the captions for each chord (in each caption, position B is listed first and position A second to be consistent with the music notation). By position A/B, it is meant “dominant shape (voicing used for the V chord) extracted from the major II-V-I progression in position A/B.”
The dominant shape is comprised of the following intervals (listed from the bottom to the top of the voicing): major third, major second, perfect fourth in position A / perfect fourth, minor second, major third in position B.
Use cases
The mixolydian (dominant) chord is listed first, since it is, naturally, the one from which the thought of using the dominant shape to play other chords comes from. Then we have the altered chord, and it is interesting to note that there is a sub V (tritone substitution) relationship between the mixolydian and the altered dominant chords. Eb7 and A7alt, for example, indeed share the same guide tones (G and Db/C#), and their roots are indeed a tritone apart. As a result, one chord can be substituted for the other following the tritone substitution rule.
Works on degrees: V (major), IV (melodic minor). Position B: 3 13 b7 9; Position A: b7 9 3 13.Works on degrees: VII (melodic minor). Position B: b7 #9 3 b13; Position A: 3 b13 b7 #9.
I have then chosen to list the locrian and minor 6/9 chords, since they are also widely used. In fact, a minor II-V-I can be played entirely using the dominant shapes presented here (e.g. Emi7(b5) = E A Bb D, A7alt = G C Db F, Dmi6/9 = F A B E).
Works on degrees: VII (major), VI (melodic minor). Position B: 1 11 b5 b7; Position A: b5 b7 1 11.Works on degrees: I (melodic minor), II (major). Position B: 6 9 b3 5; Position A: b3 5 6 9.
Next up are the lydian and phrygian sounds, which also come in handy, albeit arguably more sporadically than the ones mentioned previously.
Works on degrees: IV (major), bIII (melodic minor). Position B: #11 7 1 3; Position A: 1 3 #11 7.Works on degrees: III (major), II (melodic minor). Position B: 5 1 b9 11; Position A: b9 11 5 1.
The mixolydian b13/aeolian sound is probably the least common of all (moreover, it is rather tricky to find an adequate chord symbol for it, so the space has been left blank).
Works on degrees: V (melodic minor), VI (major), Position B: 9 5 b13 1; Position A: b13 1 9 5.
Finally, if the same voicing (G C Db F in position B / Db F G C in position A) were to be played over an Ab root (tonic of the Ab major scale), the “avoid note” Db might stand out and create havoc, particularly in a tonal context… In a modal/vertical context however, the voicing can be used and sounds quite unique and intriguing.
Practice tip
Internalize both shapes by taking them through the cycle of fifths (using different roots in the left hand for example; that way you’ll get the different sounds described above). It’s fine if you have to think about the formulas at first, but try and gradually shift towards using your ears and muscle memory exclusively. It is without question a challenging exercise… But trust yourself in the process: it will be way more fun!
The excerpt above is a transcription of Herbie’s short solo on the A section, right before Wayne Shorter states the latter two thirds of the closing melody, coming in on the bridge (B) and going into the final A and coda. The inspired introduction is another spot in this version where the piano is featured. Listen closely to the form throughout: A (9 measures), B (9 measures), A (9 measures). That’s three sections of nine measures eachÂą. A cool and unusual form…
Notes
Âą And I somehow can’t help but think about Nikola Tesla’s obsession with 3, 6, and 9… These numbers are indeed often seen as representing the non-physical realm. Is there a connection with the idea of the soul of a newborn infant (the eyes are “the window to the soul”) entering the physical world through incarnation?
References
Shorter, Wayne. Speak no Evil. Blue Note/Decca 744042. 2021 (originally released in 1966, recorded 1964).
Piano being a polyphonic instrument, pianists naturally have access to playing several notes on the keyboard at once, which is definitely an advantage when trying to develop harmonic consciousness. Guitarists also have a fretboard suited to playing and hearing both simple and complex chords, and vibraphonists, with two pairs of sticks, are often seen playing four notes at once — a perfect number if you’re focusing on chord tones only! But what about you melodic instrumentalists out there? How does a flute player, a trumpet player, or a double bass player go about hearing a tune’s harmonic framework?
Having taught a few people who play such melodic instruments (as opposed to pianists which typically make up the bulk of my students), I have found that going through a tune arpeggiating its chords is a worthwhile exercise. It gives the player a deeper awareness of the changes, which later enables him or her to be more connected to the tune when improvising (and when playing/embellishing the melody).
Arpeggiating is easily achieved for most chords: play the chord tones first (root, third, fifth, and seventh) then move up to the tensions (ninth, eleventh, and thirteenth)¹. Once you’ve reached the top, just make your way back down from the thirteenth to the root. That works really well for major and minor chords with ninths, elevenths, and thirteenths, and also for most dominant chords with tensions. But altered chords (a specific kind of dominant chord) can be a bit of a challenge because of the inner workings of the altered mode: it indeed appears to have two ninths (one flat and one sharp), and can be apprehended as having two fifths as well (a diminished and an augmented fifth). This can all be quite confusing… So let’s try and see through the fog so that you know what to play when you get to those last four bars of the tune Footprints for example².
First, it is important to know that the altered chord’s parent mode, the altered mode, comes from the melodic minor scale (also called jazz minor). Play C melodic minor for instance (C melodic minor is equivalent to the C major scale with a minor third instead of a major third). Now play all the same notes as in C melodic minor, but starting and ending on the note B. This is the B altered mode (B C D Eb F G A B), mode VII of melodic minor (the altered chord is thus the VIIth degree of melodic minor). Now, let’s attribute scale degrees (notated using Arabic numerals accompanied by flats and sharps when necessary) to the notes of the B altered mode:
B
1
root
C
b9
flat ninth
D
#9
sharp ninth
Eb (= D#)
3
major third
F
b5 / #11
diminished fifth or sharp eleventh
G
#5 / b13
augmented fifth or flat thirteenth
A
b7
minor seventh
If you look closely, you might notice that we seemingly have two different kinds of thirds in this mode: a minor third (D), and a major third (Eb or, spelled enharmonically, D#). Theoretically, D natural can also function as a #9 on a chord whose root is B. And since we cannot have two thirds in a given chordmodeÂł, scale degrees 3 and #9 can logically be attributed to D# (Eb) and D respectively.
We have now identified three of our chord tones: the root (B), the major third (D#), and the minor seventh (A), which indeed outline a dominant seventh chord in skeletal form. It’s now time to add some flesh to those bare tones! Before moving on to tensions, we have to make a choice for our last chord tone: the fifth. We can either use a diminished fifth (the note F in our example) or an augmented fifth (G).
Altered arpeggio using b5 as a chord tone
If we decide that the b5 will function as the fifth of the altered chord for our purpose of arpeggiating it, we have the notes B, D#, F, and A in the lower part (chord tones) of the arpeggio. The remaining notes of the chordmode are C (b9), D (#9), and G (b13). They form the upper part (tensions) of the arpeggio. And we have:
B
D#
F
A
C
D
G
D
C
A
F
D#
B
1
3
b5
b7
b9
#9
b13
#9
b9
b7
b5
3
1
Notice that the tensions (C, D, and G) form a quartal triad that can be notated C2, D7sus(omit 5), or Gsus depending on its inversion. In this case, there is an absence of eleventh in the chordmode due to the presence of b5.
Altered arpeggio with b5 going through the circle of fifths
Altered arpeggio using #5 as a chord tone
If we decide that the #5 will function as the fifth of the altered chord for our purpose of arpeggiating it, we have the notes B, D#, G, and A in the lower part (chord tones) of the arpeggio. The remaining notes of the chordmode are C (b9), D (#9), and F (#11). They form the upper part (tensions) of the arpeggio. And we now have:
B
D#
G
A
C
D
F
D
C
A
G
D#
B
1
3
#5
b7
b9
#9
#11
#9
b9
b7
#5
3
1
The tensions (C, D, and F) do not form any specific tertial nor quartal triad here, and in this second scenario, there is an absence of thirteenth in the chordmode due to the presence of #5.
Altered arpeggio with #5 going through the circle of fifths
So there you have it: two different ways of arpeggiating altered chords in full (i.e. entire chordmodes with four chord tones and three tensions). Don’t forget to practice both examples a) and b) in all twelve keys! As always, I recommend following cycle five root motion, starting at different points in the cycle every time you pick up your instrument to practice (I’ve started with B7alt in the audio examples above since this is the chord we’ve been concerned with throughout the article).
Finally, to further illustrate my point, allow me to offer a recording of Footprints for your consideration, wherein I used seven-note voicings extensively in the keyboard part (stacked thirds for the most part and the altered voicings discussed above for E7alt and A7alt in the 10th measure of each chorus). The track features soloists Corey Wallace (trombone) and Philippe Lopes De Sa (soprano saxophone), as well as a rhythm section comprised of Akiko Horii (percussion), Hiroshi Fukutomi (electric guitar), and myself (keyboard and keyboard bass). Enjoy!
Notes
Âą These kinds of voicings are often referred to as “stacked thirds” (Levine 2014:3)
² The chords in this four bar progression are F#mi7(b5), F7(#11), E7alt, A7alt resolving to Cmi7. Listen to Wayne Shorter’s version on Adam’s Apple.
Âł A chordmode is an indivisible entity that arises when a given chord sounds in unity with the scale from which it derives. “The complete sound of a chord is its corresponding mode within its parent scale.” (Russell 2001)
References
Levine, Mark. “Chapter One: The Menu.” In How to Voice Standards at the Piano: The Menu, 1-22. Petaluma: Sher Music Co., 2014.
Russell, George. “Part One: The Theoretical Foundation of the Lydian Chromatic Concept of Tonal Organization.” In Lydian Chromatic Concept of Tonal Organization – Volume One: The Art and Science of Tonal Gravity, 1-53. Brookline: Concept Publishing Company, 2001.
Shorter, Wayne. Adam’s Apple. Blue Note 7464032. 1987 (originally released in 1966).
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