Category Archives: FunJazz Piano Lessons

comment pratiquer les gammes et arpèges majeurs et mineurs au piano

🇬🇧 → how to practice major and minor scales and arpeggios on the piano


Tempo

Comme le recommande l’Ă©dition japonaise du Hanon (voir les rĂ©fĂ©rences ci-dessous), les gammes doivent ĂŞtre pratiquĂ©es entre 60 et 120 BPM. Commencez Ă  60 et augmentez progressivement le mouvement (pas plus de 2 BPM par 2 BPM). Lorsque vous atteignez un certain tempo un jour donnĂ©, commencez votre pratique plus lentement (4 Ă  10 BPM plus bas) le jour suivant.

Doigtés

Dans l’Ă©dition belge/française, les doigtĂ©s appropriĂ©s, fournis par Alphonse Schotte (qui a rĂ©visĂ© et augmentĂ© l’Ă©dition originale du Hanon), sont listĂ©s Ă  l’exercice 39 pour les gammes majeures et mineures (harmoniques) ainsi que les arpèges, et Ă  l’exercice 43 pour les gammes mineures mĂ©lodiques. Dans l’Ă©dition japonaise, les gammes majeures et tous les types de gammes mineures sont regroupĂ©s au sein de l’exercice 39, tandis que les doigtĂ©s pour les arpèges se trouvent Ă  l’exercice 41.

Les gammes sont prĂ©sentĂ©es en suivant le cycle des quintes dans les deux Ă©ditions. Il est toutefois intĂ©ressant de noter que les tonalitĂ©s se succèdent en ascendant (do, sol, rĂ©, la…) dans l’Ă©dition française, alors qu’elles se suivent en descendant (do, fa, sib, mib…) dans l’Ă©dition 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 ĂŞtre pratiquĂ©s mains sĂ©parĂ©es (main droite et main gauche seules), puis mains ensemble, en suivant les Ă©tapes 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 prĂ©fĂ©rence deux fois pour dĂ©velopper la force)
  • monter et descendre la gamme sur quatre octaves en doubles-croches (de prĂ©fĂ©rence deux fois pour dĂ©velopper 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.

how to practice major and minor scales and arpeggios on the piano

🇫🇷 → comment pratiquer les gammes et arpèges majeurs et mineurs au piano


Tempo

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.

les trois types de gammes mineures (harmonie tonale occidentale)

🇬🇧 → the three kinds of minor scales in Western tonal harmony


Mineur naturel

La gamme mineure naturelle correspond au mode VI de la gamme majeure, Ă©galement appelĂ© mode Ă©olien (pour une rĂ©vision complète des modes, voir cet article). En d’autres termes, elle comporte exactement les mĂŞmes notes que la gamme majeure, mais elle commence et se termine sur le 6e degrĂ© 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 donnĂ©e 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 rĂ© mi fa sol la si do) est la gamme de la mineur (la si do rĂ© 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 rĂ©vision des intervalles, voir ce PDF).

Mineur harmonique

La majoritĂ© des Ă©tudiants en musique savent bien que le mineur harmonique correspond au “mineur naturel avec une septième Ă©levĂ©e d’un demi-ton”. Mais pourquoi la dĂ©nomination de mineur harmonique ? D’oĂą vient le caractère harmonique de la gamme ?

ConsidĂ©rez ceci : l’accord construit sur le cinquième degrĂ© de la gamme mineure naturelle est un accord de septième mineure (Emi7 dans la tonalitĂ© de la mineur). Pour obtenir une relation dominante-tonique semblable Ă  celle qui existe dans les tonalitĂ©s majeures (G7 Ă  C par exemple, avec le triton fa et si se rĂ©solvant vers les notes mi et do), la tierce mineure de l’accord V doit ĂŞtre augmentĂ©e d’un demi-ton. L’accord Vmi7 devient alors V7 : un accord de dominante avec une tierce majeure (appelĂ©e note sensible parce qu’elle se rĂ©sout un demi-ton plus haut vers la tonique). La gamme reflĂ©tant ce changement dans l’accord V devient mineure harmonique. C’est-Ă -dire que l’on a : la si do rĂ© mi fa sol# la (ici, le sol# est Ă  la fois la note sensible de la gamme mineure harmonique de la et la tierce majeure de l’accord construit sur le cinquième degrĂ© de cette gamme, E7). Vous me suivez ? J’espère que cela prend sens ! Puisque vous ĂŞtes avec moi, passons maintenant Ă  la gamme mineure mĂ©lodique…

Mineur mélodique / jazz

Dans la gamme mineure harmonique, la septième majeure crĂ©e un intervalle d’une seconde augmentĂ©e, un “interstice” mĂ©lodique pour ainsi dire, entre le sixième et septième degrĂ© de la gamme (certains penseront que cela donne une impression “exotique” ou “moyen-orientale”). Cet “intervalle” peut s’avĂ©rer gĂŞnant pour une oreille occidentale qui s’attend Ă  une sĂ©rie de secondes majeures et mineures, c’est-Ă -dire Ă  des tons et des demi-tons (comme c’est le cas dans les gammes majeures et mineures naturelles).

En Ă©levant la sixte d’un demi-ton (de fa Ă  fa# en la mineur), on fait disparaĂ®tre l’intervalle de seconde augmentĂ©e ; on “lisse” donc la gamme du point de vue des intervalles. Le rĂ©sultat est ce que l’on appelle le mineur mĂ©lodique (ou encore jazz minor en anglais). En la, nous avons donc : la si do rĂ© mi fa# sol# la.

En regardant la gamme sous un angle diffĂ©rent, on remarque qu’une gamme mineure mĂ©lodique donnĂ©e comporte toutes les mĂŞmes notes que la gamme majeure qui lui est parallèle (donc basĂ©e sur la mĂŞme tonique), Ă  l’exception de la tierce, qui, bien sĂ»r, doit ĂŞtre mineure (abaissĂ©e d’un demi-ton lorsque l’on passe de la gamme majeure parallèle Ă  la gamme mineure mĂ©lodique en question).

Attention : en musique classique, la gamme mineure mĂ©lodique prend deux formes distinctes, ascendante et descendante. Les compositeurs avaient en effet coutume de privilĂ©gier l’une ou l’autre selon que leurs lignes mĂ©lodiques allaient dans telle ou telle direction. La forme ascendante (avec la sixte et la septième majeures) correspond Ă  ce que l’on appelle simplement mineur mĂ©lodique en jazz, tandis que la forme descendante correspond Ă  la gamme mineure naturelle (sixte et septième mineures). On a donc, en la mineur : la si do rĂ© mi fa# sol# la sol fa mi rĂ© do si la.

Résumé

Nom de la gammeExemple en laRemarques
mineure naturellela si do ré mi fa sol laÉquivalente au mode éolien. Relative de la gamme de do majeur (les deux gammes partagent toutes les mêmes notes).
mineure harmoniquela si do rĂ© mi fa sol# laPrĂ©sence de la note sensible (septième Ă©levĂ©e d’un demi-ton), crĂ©ant une tension harmonique et permettant d’avoir la progression V7-Imi.
mineure mĂ©lodiquela si do rĂ© mi fa# sol# laÉquivalente Ă  la gamme majeure parallèle (la majeur) avec une tierce abaissĂ©e 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 sonoritĂ© mineure (tels que les modes dorien, phrygien, Ă©olien, locrien, ou encore la gamme mineure hongroise et la pentatonique mineure).

the three kinds of minor scales in Western tonal harmony

🇫🇷 → les trois types de gammes mineures dans l’harmonie tonale occidentale


Natural minor

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

NameExample (in A)Remarks
Natural minorA B C D E F G AEquivalent to the Aeolian mode. Relative of C major (both scales share all of the same notes).
Harmonic minorA B C D E F G# APresence of the leading tone (raised seventh), which creates harmonic tension and yields the V7-Imi progression.
Melodic minorA B C D E F# G# AEquivalent 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).

building on pentatonics: the major and minor blues scales

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:

1 2 #2 3 5 6 1 (ascending) / 1 6 5 3 b3 2 1 (descending).

In the key of C, that is:

C major blues scaleC D D# E G A C ascendingC A G E Eb D C descending

From minor pentatonic to minor blues scale

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 scaleC D D# E G A C ascendingC 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 ascendingA 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:

1 b3 4 #4 5 b7 1 (ascending) / 1 b7 5 b5 4 b3 1 (descending).

C minor blues scaleC Eb F F# G Bb C ascendingC Bb G Gb F Eb C descending

Which scale fits what chord?

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).

pentatoniques : les bases

🇬🇧 → pentatonics: the basics


Le terme “pentatonique” nous vient de la langue grecque : le prĂ©fixe penta-, “cinq”, et le mot tonos, “ton”, y sont associĂ©s pour Ă©voquer l’idĂ©e d’une gamme Ă  cinq notes.

Il existe bien entendu de nombreuses possibilitĂ©s d’Ă©chelles de cinq sons au sein du système tempĂ©rĂ© (division de l’octave en douze intervalles Ă©gaux, dits chromatiques). Nous porterons ici notre attention sur la gamme pentatonique la plus usitĂ©e et l’appellerons la pentatonique “globale”Âą (on retrouve en effet cette gamme dans les musiques de nombreuses cultures de par le monde).

[1] La pentatonique globale est fondée sur une succession de quintes ascendantes : do sol ré la mi.

[2] Une fois ces notes rĂ©arrangĂ©es au sein d’une seule octave, nous avons : do rĂ© mi sol la.

[3] Les intervalles formés par les notes de cette gamme par rapport à sa fondamentale (do) sont :

  • une seconde majeure entre do et rĂ© ;
  • une tierce majeure entre do et mi ;
  • une quinte juste entre do et sol ;
  • une sixte majeure entre do et la.

Comme tous les intervalles de cette gamme sont majeurs (mis Ă  part la quinte juste), elle est souvent baptisĂ©e pentatonique majeure. Ce que j’appelle sa “formule”, qui associe des chiffres arabes² Ă  chacun de ses degrĂ©s (contrairement aux chiffres romains communĂ©ment utilisĂ©s pour reprĂ©senter les accords construits sur chacun des degrĂ©s d’une gamme), est la suite de nombres : 1 2 3 5 6.

[4] Exactement comme pour les échelles majeures diatoniques à sept sons (do ré mi fa sol la si), la gamme relative mineure de la pentatonique majeure se construit en jouant toutes les notes formant la pentatonique majeure, en partant une tierce mineure en dessous de la fondamentale de celle-ci : la do ré mi sol.

[5] Les intervalles formés par les notes de cette nouvelle gamme par rapport à sa fondamentale (la) sont :

  • une tierce mineure entre la et do ;
  • une quarte juste entre la et rĂ© ;
  • une quinte juste entre la et mi ;
  • une septième mineure entre la et sol.

Comme tous les intervalles de cette gamme sont mineurs (sauf la quarte et la quinte), elle est souvent appelĂ©e pentatonique mineure. Sa “formule” est : 1 b3 4 5 b7.

En rĂ©sumĂ©, voici les formules Ă  savoir (accompagnĂ©es d’exemples ayant la note do pour tonique dans les deux cas pour faciliter la comparaison) :

Pentatonique majeure1 2 3 5 6do ré mi sol la
Pentatonique mineure1 b3 4 5 b7do mib fa sol sib

Notes

¹ Cette terminologie est utilisée par Michael Hewitt dans son livre Musical Scales of the World (voir Hewitt 2013).

² Plus exactement, il s’agit des chiffres communĂ©ment utilisĂ©s en Europe qui nous viennent du système de numĂ©rotation indo-arabe.

Références

Hewitt, Michael. “Section 5: Pentatonic Scales.” Dans Musical Scales of the World, 125-134. The Note Tree, 2013.

pentatonics: the basics

🇫🇷 → pentatoniques : les bases


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 pentatonic1 2 3 5 6C D E G A
Minor pentatonic1 b3 4 5 b7C 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” – part 1: major and melodic minor

A multifaceted structure

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.”

II-V-I progression in the key of F major. The II chord, Gmi9, is in position A (b3 5 b7 9). The formula for the V chord, C13, is b7 9 3 13.
II-V-I progression in the key of C major. The II chord, Dmi9 is in position B (b7 9 b3 5). The formula for the V chord, G13, is 3 13 b7 9.

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 chord is listed here in prime position, since it is, naturally, the one from which the thought of using the dominant shape to play other chords initially came from. As you will see in the first example below, the lydian dominant or 7(#11) chord, from melodic minor, can be voiced in the exact same way as the mixolydian chord (even though the colourful #11 won’t appear in this specific voicing). 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/locrian natural 2 and dorian/jazz minor 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/lydian augmented and phrygian/phrygian natural 6 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) in order to obtain an ionian sound, 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!

arpeggiating altered chords

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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the six building blocks of jazz piano playing (areas of study)

The foundational level

‘Feel, form, rhythm’, ‘arranging’, and ‘technique’ are what I call the three foundational blocks of jazz piano playing. Without them, you won’t be able to build anything musically solid because your playing will always lack rootedness, depth, and precision. To improve in the area of ‘feel, form, and rhythm’, I recommend immersing yourself in some kind of West African musical traditionÂą (Ewe drumming and dance, djembe and dundun rhythms, etc.).

‘Arranging’ is about mastering different textures and telling an engaging story. The piano has an inherent orchestral quality due to its wide range and polyphonic nature, so there is a lot to cover here, from bass lines, to chord voicings, all the way up to how to interpret and embellish a melody.

As far as ‘technique’ is concerned, some sub-areas are specific to jazz (such as practicing a snippet of music in a variety of keys) and others more peculiar to classical performance (using gravity and proper posture to get a great sound out of the instrument for example). This is why I often encourage my students to work on Hanon’s Virtuoso Pianist in Sixty Exercises, and the Bach Chorales² and Two-Part Inventions at the very least (taking separate classical piano lessons altogether, in addition to the jazz piano lessons, being the ideal scenario).

The heartbeat of jazz

These first three foundational blocks support those that make up the second level in the diagram. ‘Improvisation’, in my opinion, is the heartbeat of jazz. It’s at the very core of the music, which itself is all about individuation (or finding your own voice). At its left, you’ll notice that I represented ‘listening/transcribing’ as an arrow pointing towards ‘improvisation’. That is because the jazz language you will be exposed to, and eventually internalize, will unavoidably feed into your personal style as an improviser (Wernick 2010). The elements of tradition and innovation constantly and dynamically coexist in jazz, very much like the yin and yang components of Taoist philosophy.

Culmination

Finally, all five aforementioned blocks support the final block at the top of the diagram: ‘building a repertoire’. Now the good news is: this task should be relatively effortless if you’ve studied all the other areas conscientiously… This culminating block is all about having fun learning the tunes you like, or even writing, practicing, and performing your own!


Notes

Âą I recall from my time at Berklee that such was also Meshell Ndegeocello’s advice.

² Jazz pianist Fred Hersch (2012) also recommends working on the Chorales, and offers a step by step approach to studying them involving pairs of two voices, then groups of three, and finally all four.

References

Bach, Jean-Sébastien. n.d. 101 Chorals à 4 parties réduction pour orgue ou piano. Paris: Editions Durand.

Bach, Johan Sebastian. 1970. Keyboard Music. New York: Dover Publications, Inc.

Dahn, Luke. 2021. “The Four-Part Chorales of J.S. Bach.” Accessed June 22, 2022. https://www.bach-chorales.com/.

Hanon, Charles-Louis. 1929. Le Pianiste Virtuose en 60 Exercices. Bruxelles / Paris: Schott Frères.

Hersch, Fred. 2012. “Back to Bach: Keys to Jazz Piano Prowess.” Downbeat, September 2012 (pp. 76-77).

Wernick, Forrest. 2010. “The Importance of Language.” Jazzadvice. Posted June 30, 2010. https://www.jazzadvice.com/the-importance-of-language/.


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