The mixo b2 b6 bebop dominant scale (here used as an E7(b9b13) chordmode):
scale degrees
1 b2 3 4 5 b6 b7 7 8
chordmode
E F G# A B C DD#E
The mixo #2 #4 bebop dominant scale (here used as an F7(#9#11) chordmode):
scale degrees
1 #2 3 #4 5 6 b7 7 8
chordmode
F G# A B C D EbEF
Although the mixo b2 b6 and mixo #2 #4 bebop dominant scales laid out in the tables above have different starting pitches, they are made up of the exact same notes (in other words, they can be viewed as modes of each other).
In both cases, the added chromatic passing tone corresponds to the major seventh (7) scale degree (as is the case in several of the more “traditional” bebop scales such as the bebop dominant scale, the bebop harmonic minor scale, and the seventh flat 5 diminished scale listed on this Wikipedia page).
Further, the notes they are made up of are the chord tones belonging to two separate dominant chords, whose roots sit a semitone apart (E7 (E G# B D) and F7 (F A C Eb) in our examples). Labeling either of these scales bebop double dominant hence seems quite fitting.
It can be noted that besides the mixolydian b2 b6 (1 b2 3 4 5 b6 b7 8 / E F G# A B C D E) and mixolydian #2 #4 (1 #2 3 #4 5 6 b7 8 / F G# A B C D Eb F) modes, several other 7-note scales are contained within the 8-note bebop double dominant scale presented above:
the double harmonic major scale (1 b2 3 4 5 b6 7 8 / E F G# A B C D# E);
the fourth mode of the double harmonic major scale presented in the previous bullet point, also known as the double harmonic minor scale (1 2 b3 #4 5 b6 7 8 / A B C D# E F G# A);
the harmonic minor scale (1 2 b3 4 5 b6 7 8 / A B C D E F G# A).
Comme le recommande l’édition japonaise du Hanon (voir les références ci-dessous), les gammes doivent être pratiquées entre 60 et 120 BPM. Commencez à 60 et augmentez progressivement le mouvement (pas plus de 2 BPM par 2 BPM). Lorsque vous atteignez un certain tempo un jour donné, commencez votre pratique plus lentement (4 à 10 BPM plus bas) le jour suivant.
Doigtés
Dans l’édition belge/française, les doigtés appropriés, fournis par Alphonse Schotte (qui a révisé et augmenté l’édition originale du Hanon), sont listés à l’exercice 39 pour les gammes majeures et mineures (harmoniques) ainsi que les arpèges, et à l’exercice 43 pour les gammes mineures mélodiques. Dans l’édition japonaise, les gammes majeures et tous les types de gammes mineures sont regroupés au sein de l’exercice 39, tandis que les doigtés pour les arpèges se trouvent à l’exercice 41.
Les gammes sont présentées en suivant le cycle des quintes dans les deux éditions. Il est toutefois intéressant de noter que les tonalités se succèdent en ascendant (do, sol, ré, la…) dans l’édition française, alors qu’elles se suivent en descendant (do, fa, sib, mib…) dans l’édition japonaise.
Remarquez que les gammes mineures ont généralement les mêmes doigtés dans leurs versions harmoniques et mélodiques. Les seules exceptions à cette règle concernent les tonalités de do# et de fa# mineur. Lorsque vous pratiquez les gammes mineures mélodiques, veillez à jouer en mineur mélodique en ascendant et en mineur naturel en descendant, comme indiqué dans le Hanon. Pour un rappel sur la théorie relative aux gammes mineures harmoniques, mélodiques et naturelles, voir cet article.
Routine
Toutes les gammes et tous les arpèges doivent d’abord être pratiqués mains séparées (main droite et main gauche seules), puis mains ensemble, en suivant les étapes suivantes sans interruption :
monter et descendre la gamme sur une octave en noires
monter et descendre la gamme sur deux octaves en croches
monter et descendre la gamme sur trois octaves en triolets (de préférence deux fois pour développer la force)
monter et descendre la gamme sur quatre octaves en doubles-croches (de préférence deux fois pour développer la force)
Enfin, après avoir effectué ces étapes, toutes les gammes peuvent être suivies de ces progressions harmoniques simples également proposées dans le Hanon : IV6-I/5-V7-I pour les gammes majeures et IVmi6-Imi/5-V7-Imi pour les gammes mineures.
Références
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.
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). When you get to a given tempo 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.
La gamme mineure naturelle correspond au mode VI de la gamme majeure, également appelé mode éolien (pour une révision complète des modes, voir cet article). En d’autres termes, elle comporte exactement les mêmes notes que la gamme majeure, mais elle commence et se termine sur le 6e degré de celle-ci.
Par exemple, la gamme de la majeur comporte les notes la si do# ré mi fa# sol# la. Le sixième degré de la gamme est ici la note fa#. On a donc la gamme mineure naturelle suivante : fa# sol# la si do# ré mi fa# (ce qui est identique au mode fa# éolien).
Une autre façon de voir les choses est de penser que la tonique d’une gamme mineure naturelle donnée se trouve une tierce mineure en dessous de la tonique de sa gamme majeure relative.
Par exemple, la gamme mineure relative de do majeur (do ré mi fa sol la si do) est la gamme de la mineur (la si do ré mi fa sol la). En effet, il existe bien un intervalle d’une tierce mineure descendante entre les deux toniques, do et la (pour une révision des intervalles, voir ce PDF).
Mineur harmonique
La majorité des étudiants en musique savent bien que le mineur harmonique correspond au “mineur naturel avec une septième élevée d’un demi-ton”. Mais pourquoi la dénomination de mineur harmonique ? D’où vient le caractère harmonique de la gamme ?
Considérez ceci : l’accord construit sur le cinquième degré de la gamme mineure naturelle est un accord de septième mineure (Emi7 dans la tonalité de la mineur). Pour obtenir une relation dominante-tonique semblable à celle qui existe dans les tonalités majeures (G7 à C par exemple, avec le triton fa et si se résolvant vers les notes mi et do), la tierce mineure de l’accord V doit être augmentée d’un demi-ton. L’accord Vmi7 devient alors V7 : un accord de dominante avec une tierce majeure (appelée note sensible parce qu’elle se résout un demi-ton plus haut vers la tonique). La gamme reflétant ce changement dans l’accord V devient mineure harmonique. C’est-à-dire que l’on a : la si do ré mi fa sol# la (ici, le sol# est à la fois la note sensible de la gamme mineure harmonique de la et la tierce majeure de l’accord construit sur le cinquième degré de cette gamme, E7). Vous me suivez ? J’espère que cela prend sens ! Puisque vous êtes avec moi, passons maintenant à la gamme mineure mélodique…
Mineur mélodique / jazz
Dans la gamme mineure harmonique, la septième majeure crée un intervalle d’une seconde augmentée, un “interstice” mélodique pour ainsi dire, entre le sixième et septième degré de la gamme (certains penseront que cela donne une impression “exotique” ou “moyen-orientale”). Cet “intervalle” peut s’avérer gênant pour une oreille occidentale qui s’attend à une série de secondes majeures et mineures, c’est-à-dire à des tons et des demi-tons (comme c’est le cas dans les gammes majeures et mineures naturelles).
En élevant la sixte d’un demi-ton (de fa à fa# en la mineur), on fait disparaître l’intervalle de seconde augmentée ; on “lisse” donc la gamme du point de vue des intervalles. Le résultat est ce que l’on appelle le mineur mélodique (ou encore jazz minor en anglais). En la, nous avons donc : la si do ré mi fa# sol# la.
En regardant la gamme sous un angle différent, on remarque qu’une gamme mineure mélodique donnée comporte toutes les mêmes notes que la gamme majeure qui lui est parallèle (donc basée sur la même tonique), à l’exception de la tierce, qui, bien sûr, doit être mineure (abaissée d’un demi-ton lorsque l’on passe de la gamme majeure parallèle à la gamme mineure mélodique en question).
Attention : en musique classique, la gamme mineure mélodique prend deux formes distinctes, ascendante et descendante. Les compositeurs avaient en effet coutume de privilégier l’une ou l’autre selon que leurs lignes mélodiques allaient dans telle ou telle direction. La forme ascendante (avec la sixte et la septième majeures) correspond à ce que l’on appelle simplement mineur mélodique en jazz, tandis que la forme descendante correspond à la gamme mineure naturelle (sixte et septième mineures). On a donc, en la mineur : la si do ré mi fa# sol# la sol fa mi ré do si la.
Résumé
Nom de la gamme
Exemple en la
Remarques
mineure naturelle
la si do ré mi fa sol la
Équivalente au mode éolien. Relative de la gamme de do majeur (les deux gammes partagent toutes les mêmes notes).
mineure harmonique
la si do ré mi fa sol# la
Présence de la note sensible (septième élevée d’un demi-ton), créant une tension harmonique et permettant d’avoir la progression V7-Imi.
mineure mélodique
la si do ré mi fa# sol# la
Équivalente à la gamme majeure parallèle (la majeur) avec une tierce abaissée d’un demi-ton (mineure au lieu de majeure).
Ces trois types de gammes mineures se retrouvent couramment dans le système tonal occidental. Il existe cependant une myriade d’autres modes et de gammes ayant une sonorité mineure (tels que les modes dorien, phrygien, éolien, locrien, ou encore la gamme mineure hongroise et la pentatonique mineure).
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).
A note of caution: in classical music, the melodic minor scale is viewed as having distinct ascending and descending forms. Indeed, composers used to have recourse to one or the other, depending on the direction of their melodic lines. The ascending form (with both the major sixth and major seventh scale degrees) corresponds to what we simply call melodic minor — or jazz minor — in the jazz world. The descending form, on the other hand, corresponds to the natural minor scale (with its minor sixth and minor seventh). Thus we have, in A minor: A B C D E F# G# A G F E D C B A.
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 minor¹. 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
¹ 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).
Review of Word Out’s concert at Le Barbizon in Paris (January 2023) on Jazz à bâbord. French critic Bob Hatteau’s blog features album reviews, artist interviews, and covers live jazz shows occurring in and around Paris.
🇫🇷 “Jim Funnell’s Word Out mixe tradition et modernité dans un néo-bop mélodieux et enjoué.”
🇬🇧/🇺🇸 “Jim Funnell’s Word Out’s melodious and playful neo-bop blends tradition with modernity.”
