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Music Theory


The following are a collection of notes on music theory. Bear in mind that music “theory” should be seen as more of a guideline, where patterns and observations about sounds we find pleasant are collected and categorized. Music theory is typically studied in the context of western music, built around the chromatic 12-note chromatic scale. Other styles of music have different separation of notes and systems of understanding, but my knowledge of these is limited. Even so, the study of music theory can be useful for analysis, composition, improvisation and communication of musical concepts. Some of these notes are built from experience, past writings or by doing active reading/listening, and as such they may be very similar from the original sources. The resources at the end of the page should contain a reference from which some these notes were extracted.

Intervals

In Western tonal music, we divide the different instrument ranges in a 12 note scale separated by the minimum unit of a half step. These notes are arranged sequentially to form the chromatic scale.

By selecting a subset of notes from the chromatic scale we can derive any number of major, minor or exotic scales, as well as the chords therein. First, we are going to take a look at intervals. You can think of an “iterval” in this context as the difference between two pitches or the distance that exists between two of the notes of the chromatic scale. The notes of an interval could be played in unison, in ascending form, or descending form. In the following figure you can see all possible intervals within an octave, starting at a half step and moving half step at a time.

You can also encounter a different nomenclature to refer to these intervals. In the same order:

1 - b2 - 2 - b3 - 3 - 4 - b5 - 5 - #5 - 6 - b7 - 7

or

I - bII - II - bIII - III - IV - bV - V - #V - VI - bVII - VII

Larger intervals, like the 9th, the 11th or the 13th, are also possible but it is nothing more than a 2nd, 4th or 6th interval one octave above. Intervals can also be inverted. To do this, put the lowest note one octave higher or the other way around. By doing so:

It will be really good if we could identify by ear the different intervals. This is a skill that can be learned, allowing us to rapidly transcribe a passage or improvise over it. One of the most effective ways to train this skill is to try to associate different intervals to well known songs that are already stuck in our heads, for example the Jaws main theme starts with a minor 2nd, while Happy Birthday starts with a major second.

We can also classify intervals by their perceived tensions or dissonances:

Triads

Different intervals can be grouped to obtain different textures and provoke an emotional response on the listener. The most common way of grouping intervals is by creating triads stacking a major and minor 3rd together. A triad is a chord formed by the root, the 3rd and the 5th intervals. Triads can be inverted twice, as we would do with two-note intervals. The 4 ways of stacking triads are:

For example, a C major triad can be created by stacking a C to E major 3rd interval, and an E to G minor 3rd interval.

A lot of modern music is created with these simple triads, or sometimes even simpler intervals. For example, a power chord only contains the 1-5-8 chords, without the 3rd.

Seventh chords

The two most important pieces to determine the character of a chord, are the third and the seventh. To find the seventh of a chord we can use the same method we used before, but this time we will be stacking three triads instead of two. With this process the following chords can be created:

Chord name Notation Composition
Major 7th maj7, Δ Major triad + major 3rd / M + m + M
Minor 7th min7, m7, -7 Minor triad + minor 3rd / m + M + m
Dominant 7 Major triad + minor 3rd / M + m + m
Half diminished m7b5, ø Diminished triad + major 3rd / m + m + M
Diminished dim, o Diminished triad + minor 3rd / m + m + m
Minor-major min-maj, min(maj7), -Δ Minor triad + major 3rd / m + M + M

These chords are widely used in Jazz music, but can and do find its way in other styles. Unfortunately the notation is not standardized, and different charts could present chords in different ways. I’ve included some of these in the previous table, for example a “G sharp minor seventh” could be written as G#m7 or G#-7.

If reading a chord sheet from a “Real Book” or similar, when the seventh is not specified it could mean that we must use a triad or that we can use a seventh chord, depending of the context and if the 7th would clash with the melody of the song.

Upper extensions

As we have seen so far, the process of building complex and colorful chords is as simple as just keep stacking thirds together. Upper extensions are obtained in the same way, but because intervals like the tritone can sound dissonant, there are some extensions that tend to work better for a given context:

Chord family Extensions
Major 9, #11, 13
Minor 9, 11, 13
Dominant 9, 11, 13
Half diminished 9, 11, b13

It’s not necessary to include all upper extensions when we are spicing up a chord. For example, for the Cmaj13 chord we can choose to play Cmin7 and add the 13th of C and we can also include the 9th but not the 11th, or any combination that we find pleasing.

Upper extensions should be added tastefully, as they can create a train-wreck with other instruments or even with the melody of a song, but they can also turn a boring chord progression into something unique.

Note that sometimes we see the notation add9 or add11, which refers to a minor/major chord plus the extension but without the 7th.

Suspended and 6th chords

Suspended chords are chords that are missing the third, giving them an ambiguous quality (not major, not minor). In their place the IV (sus4 or sus) or the II (sus2) are used instead. They can be formed from regular triads, chords with 7ths or extensions. For example a C9sus4 (C dominant suspended with a 9th extension) can be formed with the C A# D F notes. Depending on the voicing, the 5th can also be omitted to lessen the dissonance with suspended chords. Suspended dominants can be used as an extra chord before resolving to a regular or altered dominant: A#7 -> A#9sus - A#7b9. Suspended chords don’t necessarily need to be resolved, giving a section an air of ambiguity.

On the other hand, 6th chords are either major or minor chords in which the 7th is changed to a 6th. Sometimes the 5th is elided to avoid the whole tone dissonance. It is a fairly neutral sounding chord and it is often played with an added 9th for some extra flavour. A good rule of thumb about when to use a major/minor 6th chord instead of a major/minor 7th is if the melody is playing the root of the chord. This melody note would clash with the 7th, so this substitution makes it sound smoother.

Augmented chords

Augmented chords have a very strong sense of tension and really want to resolve. We can use Vaug in place of V7 chords adding a non-diatonic note. We can add the b7th or 7th to our V7+ preserving the same function (V+7 or V+maj7/Vmaj7#5).

These chords are also very useful for voice leading purposes. For exaple A (A C# E) A+ (A C# E#) D (A D F#). Notice the voice leading on the upper note. Example progressions: I-Iaug-VIm, I-Iaug-IV, I-Iaug-IIm.

If we treat our augmented chord as a Iaug we could think on this tonality as being in the key of Lydian augmented (one of the modes of the melodic scale).

Their symmetric nature makes it so there are only four augmented chords, each of them having three potential roots:

We can use this property to modulate to a different key center around any of them. For example Caug/Eaug/G#aug are enharmonic, so we can go from C major to E major and/or G# major (or their relative minors) for example: C - Caug - Emaj (E major key) - Eaug - Gmaj (G major key). In other words, from Caug we can smoothly transition to any of these chords: C, C#, C#m, E, F, Fm, Ab, A, Am.

With proper voice leading, we can use augmented chords to connect different chords together from different keys:

     B               F#    G#               B     C#               E      D               A
      \             /        \             /        \             /        \             /
       \           /          \           /          \           /          \           /
A# ---- A#+/D+/F#+ ---- G ----  G+/B+/D#+ ---- C ----  C+/E+/G#+  ---- F ---- F+/A+/C#+ ---- F#
       /           \          /           \          /           \          /           \
      /             \        /             \        /             \        /             \
     D#              D      E               D#     A               G#    A#               C#

Example of augmented chord progression:

Diminished chords

Diminished chords, specially in their 7th form are very interesting. They have an ambiguous sound, as any of the notes of the chord could be considered the root. For example Cdim has C D# F# A and could also be called D#dim, F#dim or Adim. Despite having an ambiguous sound they want to strongly resolve to any minor or major chord that is half step above, half step below or at any of their roots. From the previous example, Cdim can resolve to C#, E, G or A# and these can be maj7, min7 or even dominant 7. It would also be fine to resolve to a C or C# (A root or half step above). There are only 3 groups of diminished chords: C-A-F#-D#, G-E-C#-A#, D-B-G#-F.

The major scale and its modes

The major scale is composed of 7 notes at different intervals. As mentioned before the chromatic scale is separated by 12 notes, each separated from the previous one by a half-step (h/minor 2nd/b2). A whole-step (W/major 2nd/2) is composed of two half-steps. When we refer to scales, we typically notate the scale formula as a number of whole and half steps. The formula for the major scale is: W W h W W W h. In a piano, the C major scale correspond to the white notes. If using the notation previously introduced for intervals, from any root note, a major scale contains the following intervals:

I - II - III - IV - V - VI - VII

People tend to be confused when talking about scale “modes”, but it is actually very simple. A scale mode contain the same notes as the equivalent major scale, but it starts at a different location.

Mode name Root interval Tonality
Ionian I Major
Dorian II Minor
Phrygian III Minor
Lydian IV Major
Mixolydian V Major
Aeonian VI Minor
Locrian VII Half-diminished

For example the C major scale contain the notes C D E F G A B, the D dorian instead uses D E F G A B C and so on. Modes are often more emphasized when playing melodic lines over a static chord, and by emphasizing the chord tones of the desired modal flavor (more on this on the harmony section). While a song in a given key can be analyzed by thinking of different modes playing at different locations, it normally makes more sense to think of the major equivalent instead.

Harmony

Harmony is one of the basic blocks of music, alongside melody and rhythm. When we talk about harmony, we normally refer to multiple notes that play simultaneously, but this is not always true. For example, an “arpeggio” (playing the notes of a chord in succession or following different patterns) can give us the perception of a chord or a melody may suggest being on a given key. Harmony is about managing “tension” or “dissonance” and the corresponding release. Some intervals are more dissonant than others, after all, but in my eyes this is a learned and/or cultural phenomenon. For example, if you are not used to listen to Jazz music with tons of dissonance, it may feel unpleasant. As a rule of thumb however, we tend to avoid intervals or chords with lots of dissonance (such as the tritone) in general music.

Major harmony

We have already covered the major scale and mentioned that different modes have different “tonalities”. The chords of the major scale (also called diatonic) follow the scale notes and avoid too dissonant intervals.

We can classify chords as weak or strong. Weak chords (chords with more tension) want to resolve to more strong chords, which are more stable. In order of increasing tension we have three functional families:

The following table shows the diatonic 7th chords of a major scale, their functional family and possible extensions we can use to avoid excessive dissonance.

Degree Chord Possible extensions Function
I maj7 9th, 13th Tonic
II min7 9th, 11th Subdominant
III min7 9th Tonic
IV maj7 9th, 11th, 13th Subdominant
V 7 9th, 13th Dominant
VI min7 9th, 11th Tonic
VII m7b5 9th, 13th Dominant/Subdominant

For example in the C major scale a II-V-I progression can be Dm7 G7 Cmaj7 and could have any or all the extensions corresponding to them.

Functional harmony and voice leading

To create interesting chord progressions, we can use the technique of functional harmony in which we alternate between strong and weak chords. To end a song or segment we can either end it on a tonic note or follow the classic T SD D T pattern. Normally the bass will play the root note of the chord, allowing the harmonic part to play the chords at different inversions. However, just playing the chords of a given progression can still sound boring or unpleasant, which is why we typically want to use voice leading.

Voice leading can help harmonies to sound more smooth or interesting. This concept focuses on minimizing the amount of movement leading from one chord to another. We achieve this by making use of different chord inversions, but we may want to avoid tritonal movements within the same voice. Typically you want the high and low notes to move in different directions or if this is not possible, to keep one of them moving while the other is stable.

When dealing with big chords, we may want to reduce the number of notes being played, keeping the same number of voices for voice leading purposes. Normally this is done by using 3 or 4 voices. For example, if all our chords are 7th chords, we can either remove the root note (since it’s being played by the bass) and rearrange the remaining three voices or use all four of the notes. If we have non 7th chords mixed in, however, the first approach is preferable.

When we have extensions, we can make use of substitutions to keep the number of voices the same, replacing the 1st or 5th of a chord with one of these extensions. The root note can be provided by the bass and the 5th doesn’t really change the character of a chord unless is altered. If we remove the root and 3rd, we obtain a “hybrid chord”, which can create some pleasant instability when used tastefully.

Part writing

Once we have a chord progression with voice leading, we can add different embellishments to each voice lines. To do so, first we identify what kind of movement the voice performs:

When adding embellishments we want to pay attention to the level of dissonance that these intervals create with the rest of the voices. An embellishments that creates a perfect consonance with the rest of the voices will be more pleasant than if it was a harsh one.

Chromatic mediants

Chromatic mediants, consist on moving chords up or down by thirds. It is highly used in film music as it can create dramatic progressions. We can choose to use minor or major chords and both will have different qualities. For example, if we have a C major chord, we could move down to A (minor 3rd motion) or G# (major 3rd motion). We then repeat the process in the same direction as needed: C major - G# major - F major - D major - etc.

Note that at each point we have four options, we are not bound to the same motion distance that we got on the first one or the same chord tonality. Voice leading works the same as with functional harmony, but since the tonality is not as well resolved or depending on the motion the tonal root may not be present in the progression, sometimes having a “drone” note playing in the higher or lower register may help us center the tonality.

Quartal/quintal harmony

The chords and harmony we have discussed so far is built in the idea of stacking III and bIII intervals to create the different notes (Tertial harmony). We could use the same concept but with 4th or 5th intervals instead. We can stack IV (perfect 4th) or bV (augmented 4th) intervals together.

The chords can also be inverted, where 4ths become 5ths, which is why quartal and quintal harmony are equivalent.

A regular major or melodic scales could also be harmonized in quartal harmony by making use of chord inversions or quartal voicings. Here is an table of quartal harmony for different major modes:

Mode I II III IV V VI VII
Ionian Q+4 Q Q +4Q Q Q Q
Dorian Q Q +4Q Q Q Q Q+4
Phrygian Q +4Q Q Q Q Q+4 Q
Lydian +4Q Q Q Q Q+4 Q Q
Mixolydian Q Q Q Q+4 Q Q +4Q
Aeonian Q Q Q+4 Q Q +4Q Q
Locrian Q Q+4 Q Q +4Q Q Q

An example in C (Note that we can keep stacking 4ths as “extensions”):

      CHORD   EXTENSIONS
CQ+4: C F B | A E G
DQ:   D G C | F B E
EQ:   E A D | G C F
F+4Q: F B E | A D G
GQ:   G C F | B E A
AQ:   A D G | C F B
BQ:   B E A | D G C

We can play quartal chords over regular tertial harmony, but we need to be careful not to play certain “avoid notes” on the top or bottom voice, least we create too much dissonance. These avoid notes are as usual intervals of bII or tritone between the tertial chord and quartal voicing.

It is highly used in modal Jazz and classical composers like Debussy. Quartal harmony has a certain ambiguous quality to it, almost atonal which is why we don’t necessarily have to work in a functional harmony context.

Borrowed chords and secondary dominants

When we use chords that are non-diatonic we call these borrowed chords. These can really spice up our chord progressions. We can borrow chords for the parallel modal scales for a given key. For example if our key is C major, we can use chords from C dorian, C lydian, etc. Looking at a major progression of II - V - I we would typically use D - G - C, but we can change any of the chords, for example D - G - Cmin borrows the I from the C aeonian, C phrygian or C dorian. We could also use D - Gmin7 - C borrowing Gmin7 from the C mixolydian. In the following table you can see the equivalent 7th chords for the different modes.

Mode I II III IV V VI VII
Ionian maj7 min7 min7 maj7 7 min7 m7b5
Dorian min7 min7 maj7 7 min7 m7b5 maj7
Phrygian min7 maj7 7 min7 m7b5 maj7 min7
Lydian maj7 7 min7 m7b5 maj7 min7 min7
Mixolydian 7 min7 m7b5 maj7 min7 min7 maj7
Aeonian min7 m7b5 maj7 min7 min7 maj7 7
Locrian m7b5 maj7 min7 min7 maj7 7 min7

Is best to first establish the key of the song before using borrowed chords, and using only one borrowed chord before returning to the main tonality, otherwise we may risk having an ambiguous tonality or look like we are suddenly changing keys.

Note that when using borrowed chords while using functional harmony, the borrow retains the same function as the equivalent major chord. For example in the D - Gmin7 - C example, Gmin7 has the dominant (weak) function.

Sometimes we can also bridge the gap between chords by using the equivalent dominant for a particular chord, that is, a dominant chord located a perfect fifth (V interval) from it. We call these secondary dominants. For example, a II - V - I in C major is Dm - G7 - C can use a secondary dominant for the II, transforming it into a A7 - Dm - G7 - C. Sometimes this is denoted as V7/II - II - V - I.

Harmonizing melodies

If we start with a melody and want to create a chord progression around it, we first need to decide what kind of chords do we want to use. For example, what key or mode are we in? Do we want simple chords, 7th chords, extensions? Can we mix in tertiary harmony? Are we using borrowed or hybrid chords? We can always change our palette, but it is useful to start with some building blocks.

On each bar we want to identify the notes on the strong beats (1 and 3 in 4/4) and notes that play for a longer time, either because they are held or due to repetition. This gives us an idea of the chords we want to target.

If using functional harmony, we can restrict our chord choices even more by using the strong-weak-strong-weak or tonic-subdominant-dominant-tonic patterns.

After selecting the chords we can perform voice leading and add embellishments as desired.

Altered and melodic minor harmony

The melodic minor scale can be seen as a major (ionian) scale with a bIII. It thus follows the following formula W h W W W W h. In classical music the melodic minor is only played in ascending form, when descending, the aeolian is used instead. It is highly used in Jazz, where it is played both in ascending and descending form. Very often the seventh degree of the melodic minor is played over dominant chords. This is known as the altered scale.

Mode name I II III IV V VI VII
Melodic minor min(maj7) min7 maj7#5 7 7 m7b5 m7b5
Dorian b2 min7 maj7#5 7 7 m7b5 m7b5 min(maj7)
Lydian augmented maj7#5 7 7 m7b5 m7b5 min(maj7) min7
Lydian dominant 7 7 m7b5 m7b5 min(maj7) min7 maj7#5
Mixolidian b6 7 m7b5 m7b5 min(maj7) min7 maj7#5 7
Half-diminished m7b5 m7b5 min(maj7) min7 maj7#5 7 7
Altered scale m7b5 min(maj7) min7 maj7#5 7 7 m7b5

Sometimes we may find the notation of 7alt to refer to a dominant chord that can contain any alteration (bII, bIII, bV, #V or b9, #9, #11, b13). In Jazz is common to substitute regular V7 chords with V7alt to access a palette of “outside” songs.

The harmonic scale and the minor II-V-I

When trying to center a piece around a minor tonality, it is sometimes desirable to use the harmonic minor scale and modes.

Mode name I II III IV V VI VII
Harmonic minor min(maj7) m7b5 maj7#5 min7 7 maj7 dim7
Locrian nat6 m7b5 maj7#5 min7 7 maj7 dim7 min(maj7)
Ionian #5 maj7#5 min7 7 maj7 dim7 min(maj7) m7b5
Ukranian dorian min7 7 maj7 dim7 min(maj7) m7b5 maj7#5
Phrygian dominant 7 maj7 dim7 min(maj7) m7b5 maj7#5 min7
Lydian #2 maj7 dim7 min(maj7) m7b5 maj7#5 min7 7
Superlocrian bb7 dim7 min(maj7) m7b5 maj7#5 min7 7 maj7

It can be commonly seen in minor II-V-I progressions, at least partly. For example a Dm7b5 - G7b9 - Cm7. The first two chords imply the harmonic minor, but the last one resolves to Cm7, which could be a C aeolian, dorian, or phrygian. We could fully resolve a II-V-I cadence as Dm7b5 - G7b9 - Cmin(maj7), which is quite dissonant but can work beautifully to convey the harmonic minor flavour. A Cm6 would also be a suitable candidate for the I chord, which sounds somewhat in between regular minor and harmonic minor.

When we want to emphasize the sound of the different modes of the major or minor scales, we probably want to stay away from functional harmony. Tonic, subdominant, dominant are not important, and we want to avoid using dominant or (half)diminished chords, since they strongly want to resolve. Instead we want to focus on the tonic chord of the mode and try to emphasize the notes characteristic to that modal sound. It is also possible to use ambiguous chords to add variety (such as sus chords or add9 chords).

In this type of harmony we have modal tonic chords (I III VI), built on the root note and modal cadence chords (II IV V VII) which want to return to the tonic. One thing we can do is to use “lateral chords”, which are chords that are next to the modal tonic. An example in the key of C is presented below.

Mode name VII I II Focus notes
Ionian Bdim C Dm
Dorian C Dm Em B
Phrygian Dm Em F F
Lydian Em F G B
Mixolydian F G Am F
Aeonian G Am Bdim
Locrian Am Bdim C C#,F#

We don’t have to stick exclusively with lateral chords. We previously presented a table with 7th chords for the different modes, which we can still use, we just have to be careful not to use dominant 7 and half diminished m7b5 chords, opting instead for minor/major triads or suspended chords. The same idea would apply to upper extension notes, avoid using extensions that may create tritonal sounds or tensions.

Avoid using too many chords in modal harmony and make sure to repeat the tonic of the mode thoroughly for best results. Using pedal tones and suspended/add9 chords may help keep the modal flavour

When writing a modal melody, we want to emphasize the distinct intervals and focus notes for the mode:

Neapolitan chord

There is a special type of chord and not to be confused with the previously discussed 6th chords. The 6th in this case refers to a classical chord inversion. The name is not too important however, but rather is best to know how to use it. It was used quite a bit in European classical music in the minor IV - V - I cadence (though the concept could still be applied in major tonality). In the case of A minor, we can borrow the dominant from the harmonic scale, resulting in Dm - E7 - Am. This cadence doesn’t really have such a strong subdominant to dominant flavour, but if instead we flatten the fifth of the D minor chord resulting in Dmb5 or A#/D we call this the Neapolitan 6. The cadence is thus N6-V7-Im or Dmb5 - E7 - Am or A#/D - E7 - Am. The notation can get confusing, but the concept is not so complicated. This cadence have a lot of classical flavour and could be something to consider in compositions, even when is not very used in popular music today. I’ve seen some diagrams that describe the use of N6 cadence by Chopin by following a VII-II-VI to an subdominant option (IIdim, N6 or IVm) which either goes back to the VII or moves to the dominant (V or VIIdim) that finally resolves into the I.

Reharmonization

Jazz musicians have a lot of fun taking popular songs in the form of “Jazz Standards” and making complicated arrangements. This technique can be used in any style of music if we are adventurous. To reharmonize a song is to change the chords and/or their harmonic rhythm. Sometimes this also involve changing the melody to fit with the new set of chords. Even though one can go “all in” to change absolutely everything about a song, sometimes is more effective to modify some bars or sections sparingly or after the original chord progression has been heard. The techniques described here can be used for the purpose of reharmonization but also to spice up chord progressions during composition.

Cadences

Cadences are a form of music punctuation that marks the end of a chord progression. Just like we need commas and periods when writing English, so do we need cadences when writing music. Cadences create a tension that want to resolve to a more stable sound, creating a sense of pull. There are different types of cadences which create different effects.

When working with modal music, we don’t often see the same types of cadences or movement. In general V7 is not used often in modal cadences. We want to make emphasis on the “characteristic notes” of a mode. So for modal cadences, we use any chord that contain these notes as a substitute for the V7. For example, when working with a Dorian mode (Im-IIm-III-IV7-Vm-VI7b5-VII) our tonic being Im and both IV and IIm containing the characteristic notes. We can use IV-Im or IIm-I as a pseudo-authentic cadence. All types of cadences are possible but in general, working with modal music, try to use authentic or half-cadences.

Common chord progressions

Resources

Melody

Melody is another cornerstone of music, together with harmony and rhythm. Writing melody is sometimes intuitive, but there are some guidelines that can help us make more memorable pieces. First of all, we need to focus on motifs. Motifs are small units of music that can be repeated and develop to create phrases and progressions. Melodies are not made only of motifs, but they are a powerful tool in our melodic toolbox. Motifs can be achieved by taking a sequence of notes and creating variation in one or two of the following types:

Note that we can have variation of more than two types, but commonly is best to focus on one or two of these options.

Once a motif is established, it is typically developed throughout the song. One of these strategies for development is the PReVaDe method. Here a motif repeats four times, creating a single phrase:

The general, we add variation to a motif via rhythmic or melodic changes. That is, changing tempo, rhythm or the notes in the motif.

A melody consists on a series of musical phrases. Phrases are typically longer and express a complete melodic idea with a beginning, development and end. Phrases can be categorized as 1) mono-motivic vs poly-motivic phrases or 2) question vs answer phrases.

The beginning section of a phrase establishes the motivic material (it can be a variation of the primary motif of the piece). During the development of the phrase is where we encounter the main differences between categories.

In mono-motivic phrases, a single motif is developed as previously described with the goal of getting closer or reaching a “local peak”, the purpose of the phrase. The “local peak” is the moment of high/low intensity that culminates the different musical parameters (rhythm, pitch, harmony, etc.). The ending of mono-motivic phrases happens after the peak, ending the phrase with some musical punctuation (more on that later).

Poly-motivic phrases contain more than one motif (typically two, but can have more). These phrases typically don’t focus on a local peak, but instead walks towards the additional motifs from the one introduced on the beginning. Each of the motifs can be further developed in later phrases. The ending happens at after or during the final motif and is also established using musical punctuation.

Question vs answer is a typical construction in music, where a musical phrase (question) presents an idea but it doesn’t feel complete when it ends. A later phrase (answer) can use the same ideas presented on the question but making a statement much more final. This concept is a bit abstract when described like this, but musical punctuation help us identify or write question or answer phrases. Every ending section must contain at least two “answer” or two “question” parameters. The following are some “answer phrase” parameter traits, and in general “question phrase” traits are opposite to them (down vs up, etc.).

As each phrase have a “local peak”, phrases can be grouped together into a paragraph/section. These sections have their own “section peaks” and when all put together in a song, the sections form a peak of their own (the climax of the song). In a paragraph, the phrases must use similar motivic and thematic material. The thematic material of the next section must build on different material. Paragraphs tell different parts of the same story. It is generally a good idea of starting compositions with the climax of the song in mind, since the different phrases and sections must build to it.

Chromatic inversion

Chromatic inversion is the process of turning a melody into another by inverting the direction of the intervals of an existing motif. For example in a melody with A C B A we move up a bIII, down a bII and down II. If we instead move down bIII, up bII and up II we get A F# G A. This technique could be used to generate new ideas from existing songs or to create motif variations for development within a single piece.

Counterpoint

Music is composed in counterpoint when multiple melodic voices have lines that are independently of one another, sound good independently and when paired together. Widely used in the Baroque period by Bach, Hayden et al. To maintain independence, we want to avoid lines that when played together form consecutive 5ths or octaves. Sometimes, however this unification effect can be used, specially when finishing on a V-I cadence. This means we can have:

Once of the techniques that we can use is to stagger the voice movement. For example, if a voice is moving then another one awaits. Let’s explore some guidelines for classical counterpoint. First of all, it is normally classified in several “levels” (1-5) in order of increasing complexity. Counterpoint is typically studied in exercises.

A contemporary approach

As with the classical approach, we need:

The CF and CP lines must be rhythmically independent while being rhythmically and harmonically complementary. A CP line should try to offer rhythmic contrast to the CF keeping the 1:2, 1:3 and 1:4 ratios in mid.

We need to try to keep “consonant” intervals between melodic lines on strong beats and where all notes start at the same time.

With regards to motion:

Suggested process

The period form

The “period form” is typically an 8-bar form. The first two bars have a basic idea, the next two bars have a contrasting idea, the next two restate the basic idea and it closes with a 2 bar cadence.

Typically the basic idea is harmonically stable, preferring the “tonic”. The contrasting idea could be a response to the basic idea, or a variation of it. The contrasting idea should feel unresolved (the first 4 bars really) and feel like a question, which will be answered by the final half of the piece. When repeating the basic idea, we can add some variation, but ideally the beginning should stay the same or be similar. The cadence should feel like a strong sign of punctuation and the form should feel like we are ready for a repetition or something new. The cadence should generally do the opposite as the contrasting idea, for example if the contrast ended on a V we want to have a I chord, or the other way around.

The sentence form

The “sentence form” is an 8-bar form. Starts with a 2 bar basic idea, which is repeated in the next 2, with or without variation. Bars 5-6 are called the “continuation” and the last 2 bars is a cadence. The continuation have more movement, more notes, more pitch height, more harmonic rhythm, etc. Very similar to the period form, but where the period form feels more stable, the sentence form can help add movement and momentum to a piece.

The REPS method

A melodic skeleton

A melodic skeleton can be used as a cantus firmus or a base to build a melody by adding rhythm, variations and adornments.

  1. Choose an opening pitch from the I chord. Furthermore we can choose the root, third or fifth of the I chord. For example C major, we can start with C, E or G.
  2. Choose a melodic cadence (last two notes). Typically 2-1 or 7-8. In C major, D to C or B to C.
  3. Draw the contour of your melody, i.e. the peaks and valleys or high/low notes in our melody. Nothing specific, just vibes.
  4. Write following the contour.
    • Aim for a line length of 9-14 notes adding 4-5 notes at a time. This is to avoid the melody to feel disjointed.
    • Balance steps and leaps.
    • Prepare your wide leaps by either leaping up and resolving down (B A E) or steping down and then leaping up (A E D).
    • Avoid tritone jumps or line of straight notes that end in the tritone (F# G A B C).
    • Make sure you don’t use the same tone more than 3 times in the whole line.
    • The line shouldn’t reach the highest (apogee) and lowest (perigee) point more than once.
    • Try not to approach the apogee by a leap, but it is ok for perigee.

Resources

Rhythm

Rhythm should vary across sections of a song, but keeping the general groove. Fills are used to bridge sections or phrases and add extra flavor to the percussion. Here are some common rhythmic grooves and ideas in different styles.

Four on the floor

            BEAT
INSTRUMENT |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK       |x| | | | | | | |x| | | | | | | |x| | | | | | | |x| | | | | | | |
SNARE      | | | | |x| | | | | | | |x| | | | | | | |x| | | | | | | |x| | | |
HH-C       | | |x| | | |x| | | |x| | | |x| | | |x| | | |x| | | |x| | | | | |
HH-O       | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |x| |

The trap beat

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | | | | | | |x| | | | | | | | |x| | | | | | | | | | | |x| | | | | | | | | | | | | | | | | |
SNARE       | | | | | | | | | | | | |x| | | | | | | | | | | | | | | | | | | | | | | |x| | | | | | | | | | | |
HH-C        |x| | |x| | |x| | |x|x|x| | | |x| | |x| | |x| | |x| | |x| | |x| | |x| | |x| | |x| | |x| | |x| | |

Bo diddley beat

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | |x| | | |x| | | |x| | | |x| | | |x| | | |x| | | |x| | | |x| | |x| |x| | | |x| | |x| | | |
SNARE       | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |x|x| | |x| | | |x| | | |x| | | |x| |
TOM-M       |x| | |x| | |x| | | |x| |x| | | |x| | |x| | |x| | | |x| |x| | | | | | | | | | | | | | | | | | | |
TOM-L       | |x|x| |x|x| |x|x|x| |x| |x|x|x| |x|x| |x|x| |x|x|x| |x| |x| | | | | | | | | | | | | | | | | | |
HH-C        | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |x| |x| |x| |x| |x| |x| |x| |x| |

Boom bap

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x|x| | | | | | |x|x| |x| | | | |x|x| | | | | | |x|x| |x| | | | |
SNARE       | | | | |x| | |x| | | | |x| | |x| | | | |x| | |x| | | | |x| | |x|
HH-C        |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |

Impeach the president

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | | | | |x|x| |x| | | |x| |
SNARE       | | | | |x| | | | | | | |x| | | |
HH-C        |x| |x| |x| |x|x|x| | | |x| |x| |
HH-O        | | | | | | | | | | |x| | | | | |

Iconic 8ths

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | | | | | | | |x| | | | | |
SNARE       | | | | |x| | | | | | | |x| | | |
HH-C        |x| |x| |x| |x| |x| |x| |x| |x| |

12/8 Feel

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
RIDE        |x| | | | | | | | | | |x|x| | | | | | | | | |x| |x| | | | | | | | |x|x| |x| | | | |x| | | | | |x|
SNARE       | | | | | | |x| | | | | | | | | | | |x| | | | | | | | | | | |x| | | | | | | | | | | |x| | | | | |
RIDE        |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |

Shuffle

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
TOM-L       |x| |x| | | | | |x| |x| | | |x| |
SNARE       | | | | |x| |x| | | | | |x| | | |
HH-C        | | | | |x| | | | | | | |x| | | |

Swing

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
HH-F        | | | | |x| | | | | | | |x| | | |
RIDE        |x| | | |x| | |x|x| | | |x| | |x|

Motown

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | | | | | | | |x| | | |x| |
SNARE       |x| | | |x| | | |x| | | |x| | | |
HH-C        |x| |x| |x| |x| |x| |x| |x| |x| |

Metal (Straight 16th)

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x|x|x|x|x|x|x|x|x|x|x|x|x|x|x|x|
SNARE       | | | | |x| | | | | | | |x| | | |
HH-C        |x| | | |x| | | |x| | | |x| | | |

Bossa

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | | | |x| |x| | | | | |x| |x| | | | | |x| |x| | | | | |x| |
CLAVE       |x| | | | | |x| | | | | |x| | | | | | | |x| | | | | |x| | | | | |
HH-C        |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |x| |
            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | |x|x| | |x|x| | |x|x| | |x|
RIMSHOT     |x| | |x| | |x| | | |x| | |x| | |
RIDE        |x|x|x|x|x|x|x|x|x|x|x|x|x|x|x|x|

Disco

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | |x| | | |x| | | |x| | | |
CLAPS       | | | | |x| | | | | | | |x| | | |
HH-O        | | |x| | | |x| | | |x| | | |x| |

Levee Break

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x|x| | | | | |x| | |x|x| | | | |
SNARE       | | | | |x| | | | | | | |x| | | |
HH-C        |x| |x| |x| |x| |x| |x| |x| |x| |

The funky drummer

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| |x| | | | | | | |x| | |x| | |
SNARE       | | | | |x| | |x| |x| |x|x| | |x|
HH-C        |x| |x| |x| |x| |x| |x| |x| |x| |
HH-O        | | | | | | | |x| | | | | |x| | |

Son clave

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | |x|x| | |x|x| | |x|x| | |x|
RIMSHOT     |x| | |x| | |x| | | |x| |x| | | |
RIDE        |x|x|x|x|x|x|x|x|x|x|x|x|x|x|x|x|

Mardi gras

            BEAT
INSTRUMENT  |0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F|
KICK        |x| | | | | | | | | |x| | |x| | |
SNARE       | | | | |x| | | | |x| | | | | | |
HH-C        |x| |x| |x| |x|x|x| |x| |x| |x|x|
BELL-H      |x| |x| | |x| | | |x| | |x| | | |
BELL-L      | | | | |x| | |x| | |x| | |x| |x|

Polyrhythms vs polymeters

A polymeter is when we have multiple sequences of different lengths playing together at the same pulse. For example a 4 note sequence and a 5 note sequence, all quarter notes. Since they have different lengths, they will eventually sync up after a number of repetitions.

A polyrhythm is when we have two different sequences of different durations (though evenly spaced) but that they both take the same amount of time, thus are synced on the 1st beat. For example a quintuplet and a triplet playing at the same time will both take the same amount of time to complete. Naturally the quintuplet notes will play faster. The most common ones are 3:2 and 4:3 polyrhythms.

Resources

Orchestration

In a modern orchestral setting, we have 4 main sections of instruments:

Of course, we can also make use of modern devices like synths and treat them accordingly. These knowledge transfers regardless of available instruments.

We also divide orchestral music into the following building blocks:

In general we want to avoid mixing foreground and background material, otherwise the music will sound directionless. We can follow two guidelines for this:

  1. Foreground material should be performed in a strong/appropriate register for the instruments performing them.
    • Depends on which instrument we are using. This means the range where the instrument has the most power and can be heard the easiest.
    • We need to be deliberate about our instrument choices.
  2. Pay attention to differentiating the foreground and background material with the PDART method:
    • Pitch: Separate foreground/background by placing them in different pitch registers. Traditionally, melody in higher register than harmony.
    • Dynamics: Foreground should be louder than background on average. We can play around with this but must be deliberate.
    • Articulation: For example, melody can be staccato and background legato. Not so important compared with the previous two, but still worth considering.
    • Rhythm: Foreground and background should make use of different rhythms.
    • Tone color: We want our background/foreground to use different tone colors/sound qualities. Examples:
      • Using strings for foreground and brass for background.
      • Muted strings in background, unmuted in foreground.
      • String section in background, solo player in foreground.
      • Pizzicato strings in background, bowed in foreground.

Voicings and note priority

There are many ways of arranging/voicing chords, but because of the overtone series, it tends to sound better to have open voicings in the lower registers and close voicings in the upper registers. This would improve clarity, but if we want to make our music sound muddy that is also ok! In any case, the open voicings in the lower registers is almost always used, but the closed voicings in the upper registers is more of a suggestion.

We can use the 1537 rule for reinforcing (doubling) different notes of a chord. In other words, doubling the root or fifth of a chord will be more clear than doubling the thirds or 7ths intervals. For 1st inversion chords, we can avoid using the 3rd in upper voices, since it is already in the bassline.

Strings

The largest section of the orchestra. It is not uncommon for half the players in an orchestra to be in the string section. All of these instruments sound very similar and a variety of techniques are available to obtain different sounds. They can do melody, harmony, rhythm and texture and obtain a variety of dynamics from very soft (ppp) to very loud (fff).

They all have 4 strings and are tuned to a different fundamental pitch. Because of the fretless nature of these instruments, when playing solo instruments it is more difficult to perceive the discrepancies in tuning. Conversly, if we have 2 instruments playing exactly the same part it may be a bit jarring, but the more instruments we add this difference gets averaged by the human ear. The string section have 4 different instruments and organized in 5 sections:

We generally write for strings using 4-part/SATB writing. As follows:

Note that string instruments can play chords, typically as double stops (or succession of 2 double stops). We need to account for real instruments for this, so each note in a chord must be performed in its own string and within reach of human hands. You can use a guitar or a grid controller in note mode to check the possibility.

We also can divide the string section in equally sized groups and have more voices by playing “divisi”. This means for example that half of the violas will play a “C” and the other half a “G”. This of course, makes the sound quieter, since there are less players playing the same note.

Brass

Brass are wind instruments. Traditionally consists of (but is not limited to):

Organized in 3 sub-sections that will split their roles between harmony, melody and bass:

These instruments are less homogeneous than the strings. Each instrument have different sonic qualities. Brass instruments are quite strong sounding both in volume and power. They are consturcted with various lengths of metal tubing, a mouthpiece and valves/slides to control the length of the tubing. Because of their construction and usage we need to consider the following guidelines:

  1. Higher pitches will be generally louder.
  2. Volume can and will change the tone color.
  3. Higher/louder pitches are more demanding to produce than lower/quieter ones. We need to account for the stamina of the performers.

In terms of harmony consider that for brass open voicings in upper registers create more ambience and presence, whereas close voicengs have more power. Commonly, tubas where handle bass and trombones/horns the chords. Brass can help provide a sense of growth and climax.

Woodwinds

It is the least powerful section of the orchestra, but it has available a wide variety of tone colors and timbre. In terms of tone colors we encounter the sub-sections of:

Woodwinds are best employed by taking advantage of their variety of tone colors. Commonly perform scale runs and trills once the melody and harmony have already been established. These scales should add color, but remain in the background. They can be used for bass line and chords, but best used like so in intimate and quiet moments. Woodwinds are great for soloing or doubling melodies, but mind the ranges and tone colors we want to achieve.

Percussion

The largest section of the orchestra, capable of the loudest and quietest sounds. They are typically categorized by their construction (idiophones, membranophones, chordophones, aerophones) and whether they are pitched or non-pitched.

The traditional roles of the percussion section are:

Piano, celeste and harp

Merging concepts

Some useful techniques for arranging and merging instruments in the orchestra are:

Resources

Circle of fifths

The circle of fifths is a widely used tool for composition and analysis of musical pieces. One of the first things you can use this diagram is to understand the number of flats or sharps that are in a given major key. When thinking about major keys, they can be unaltered C major or contain up to 6 sharps or flats. You can find the number of sharps by moving clockwise from the top on the outermost circle (e.g. D major has 2 sharps, F# and C#). The same applies for finding the number of flats (Db/C# major has 5 flats, Bb, Eb, Ab, Db, Gb). Note that the position of the diagram is also encoded in the diagram (Sharps start at F and move clockwise and flats at B and move counter clockwise). Furthermore, the order of sharps is F C G D A E B and the order of flats is the same, but backward B E A D G C F. The innermost circle indicates the number of flats (left) or sharps (right) corresponding to the key on the outer ring.

When looking at any note in the circle of fifths, if we move clockwise, we will find the perfect fifth, which can be helpful for finding the diatonic dominant of a key. Moving counter-clockwise we move in 4ths, also useful for the resolution of V-I cadences. This diagram can be very useful to connect different keys in this fashion. For example, G7-C-C7-F-F7-A#... is a progression that can be heard in a lot of music.

In this figure I’ve included three extra inner circles containing the notes a VI apart from the outer one. Each inner circle is the relative minor (aeolian) of the previous major mode (G minor and A# major, F major and D minor, etc.). Thanks to this, the circle of fifths can be used to find relative notes for a given root in order to help us form chords. The legend at the bottom of the circle illustrates this property.

Some ways of finding the notes for a chord from the diagram are that if we go straight down from the top circle, we can find a diminished chord. Going down a circle is a major 6th interval (VI) and going up finds the minor 3rd (bIII). Going down and clockwise we find the major 3rd (III). A major triad is easily formed by the triangular pattern down-right (III) and up (V) (C-E-G). Similarly for a minor triad we go up (mIII) and clockwise (V) (A-C-G). With this diagram is easy to find for example the bVII of G# (F#). Another funny pattern is to go down-right twice, creating a spiral representing an augmented chord (C-E-G#).

We can also easily find tritonal substitutions by moving down two circles. For example if we had the progression Dm7-G7-C6 and we wanted to spice it up, we could do Dm7-C#7-C6. Taking this further we could find the secondary dominant of Dm7 by moving clockwise from D and even for the newly added tritonal substitution C#7, prepending it with G#7, creating a A7-Dm7-G#7-C#7-C6 progression.

Chords closer to each other in the circle of fifths tend to transition more smoothly. Let’s look at a classical example with the following Beethoven chord progression from “Pathetique” in C major, extracted from this video:

|1   |2   |3   |4   |5   |6   |7   |8   |9   |10  |11  |12  |13  |14  |15  |16  |
|I   |I7  |IV  |IV7 |IIm |VI7 |IIm |II7 |V   |II7 |Vm  |V7  |I   |I+  |IV  |V   |
|C   |C7  |F   |F7  |Dm  |A7  |Dm  |D7  |G   |D7  |Gm  |G7  |C   |C+  |F   |G   |

Note the following movements: C-F, F-D, D-A, A-D, D-G, G-C, C-F. See how they follow a smooth path throughout the circle? Obviously part of the smoothness is the voice leading between the chords and the dominant cadences, but regardless, I think it’s a very interesting example!

Composers and artists study

Rachmaninoff

Alexander Scriabin

Ludwig van Beethoven

Frédéric Chopin

Claude Debussy

Resources

Other tools and diagrams

Matrix chord/scale reference

I created a number of diagrams for chords and scales for a matrix 8x8 controller. I intend to use this with my Launchpad Pro but it can also be used with a guitar tuned in all 4ths (E-A-D-G-C-F tuning), which I use from time to time. Here is an example of how the diagrams look like:

I compiled the main chords and scales presented here in a pdf but you can also browse the directory for individual diagrams in png and svg format.

All 4ths (EADGCF) reference diagrams

Scales and chords quick reference

Harmonization

Function           T          SD         T          SD         D          T          SD/D
Mode name          I          II         III        IV         V          VI         VII
------------------ ---------- ---------- ---------- ---------- ---------- ---------- ----------
Ionian             maj7       min7       min7       maj7       7          min7       m7b5
Dorian             min7       min7       maj7       7          min7       m7b5       maj7
Phrygian           min7       maj7       7          min7       m7b5       maj7       min7
Lydian             maj7       7          min7       m7b5       maj7       min7       min7
Mixolydian         7          min7       m7b5       maj7       min7       min7       maj7
Aeonian            min7       m7b5       maj7       min7       min7       maj7       7
Locrian            m7b5       maj7       min7       min7       maj7       7          min7
----------------------------------------------------------------------------------------------
Harmonic minor     min(maj7)  m7b5       maj7#5     min7       7          maj7       dim7
Locrian nat6       m7b5       maj7#5     min7       7          maj7       dim7       min(maj7)
Ionian #5          maj7#5     min7       7          maj7       dim7       min(maj7)  m7b5
Ukranian dorian    min7       7          maj7       dim7       min(maj7)  m7b5       maj7#5
Phrygian dominant  7          maj7       dim7       min(maj7)  m7b5       maj7#5     min7
Lydian #2          maj7       dim7       min(maj7)  m7b5       maj7#5     min7       7
Superlocrian bb7   dim7       min(maj7)  m7b5       maj7#5     min7       7          maj7
----------------------------------------------------------------------------------------------
Melodic minor      min(maj7)  min7       maj7#5     7          7          m7b5       m7b5
Dorian b2          min7       maj7#5     7          7          m7b5       m7b5       min(maj7)
Lydian augmented   maj7#5     7          7          m7b5       m7b5       min(maj7)  min7
Lydian dominant    7          7          m7b5       m7b5       min(maj7)  min7       maj7#5
Mixolidian b6      7          m7b5       m7b5       min(maj7)  min7       maj7#5     7
Half-diminished    m7b5       m7b5       min(maj7)  min7       maj7#5     7          7
Altered scale      m7b5       min(maj7)  min7       maj7#5     7          7          m7b5
-----------------------------------------------------------------------------------------------
Quar. Ionian       Q+4        Q          Q          +4Q        Q          Q          Q
Quar. Dorian       Q          Q          +4Q        Q          Q          Q          Q+4
Quar. Phrygian     Q          +4Q        Q          Q          Q          Q+4        Q
Quar. Lydian       +4Q        Q          Q          Q          Q+4        Q          Q
Quar. Mixolydian   Q          Q          Q          Q+4        Q          Q          +4Q
Quar. Aeonian      Q          Q          Q+4        Q          Q          +4Q        Q
Quar. Locrian      Q          Q+4        Q          Q          +4Q        Q          Q
----------------------------------------------------------------------------------------------

Scales

Scale formulas

Ionian              | 1  2  3  4  5  6  7   | W   W   H   W   W   W   H   |
Dorian              | 1  2  b3 4  5  6  b7  | W   H   W   W   W   H   W   |
Phrygian            | 1  b2 b3 4  5  b6 b7  | H   W   W   W   H   W   W   |
Lydian              | 1  2  3  #4 5  6  7   | W   W   W   H   W   W   H   |
Mixolydian          | 1  2  3  4  5  6  b7  | W   W   H   W   W   H   W   |
Aeonian             | 1  2  b3 4  5  b6 b7  | W   H   W   W   H   W   W   |
Locrian             | 1  b2 b3 4  b5 b6 b7  | H   W   W   H   W   W   W   |

Harmonic minor      | 1  2  b3 4  5  b6 7   | W   H   W   W   H   W+H H   |
Locrian nat6        | 1  b2 b3 4  b5 6  b7  | H   W   W   H   W+H H   W   |
Ionian #5           | 1  2  3  4  #5 6  7   | W   W   H   W+H H   W   H   |
Ukranian dorian     | 1  2  b3 #4 5  6  b7  | W   H   W+H H   W   H   W   |
Phrygian dominant   | 1  b2 3  4  5  b6 b7  | H   W+H H   W   H   W   W   |
Lydian #2           | 1  #2 3  #4 5  6  7   | W+H H   W   H   W   W   H   |
Superlocrian bb7    | 1  b2 b3 4  b5 b6 bb7 | H   W   H   W   W   H   W+H |

Melodic minor       | 1  2  b3 4  5  6  7   | W   H   W   W   W   W   H   |
Dorian b2           | 1  b2 b3 4  5  6  b7  | H   W   W   W   W   H   W   |
Lydian augmented    | 1  2  3  #4 #5 6  7   | W   W   W   W   H   W   H   |
Lydian dominant     | 1  2  3  #4 5  6  b7  | W   W   W   H   W   H   W   |
Mixolidian b6       | 1  2  3  4  5  b6 b7  | W   W   H   W   H   W   W   |
Half-diminished     | 1  2  b3 4  b5 b6 b7  | W   H   W   H   W   W   W   |
Altered scale       | 1  b2 b3 b4 b5 b6 b7  | H   W   H   W   W   W   W   |

Half-whole          | H W H W H W H W |
Whole-half          | W H W H W H W H |

Chords

C
Chord Formula Notes
Cmaj7 1-3-5-7 C E G B
Cmin7 1-b3-5-b7 C D# G A#
C7 1-3-5-b7 C E G A#
Cm7b5 1-b3-b5-b7 C D# F# A#
C6 1-3-5-6 C E G A
Cm6 1-b3-5-6 C D# G A
Cdim 1-b3-b5-6 C D# F# A
Caug 1-3-#5 C E G#
Cmin(maj7) 1-b3-5-7 C D# G B
Cmaj7#5 1-3-#5-7 C E G# B
Csus4 1-4-5 C F G
Csus2 1-2-5 C D G
CQ 1-4-b7 C F A#
CQ+4 1-4-7 C F B
C+4Q 1-#4-7 C F# B
Extensions 9, 11, 13 D F A
D
Chord Formula Notes
Dmaj7 1-3-5-7 D F# A C#
Dmin7 1-b3-5-b7 D F A C
D7 1-3-5-b7 D F# A C
Dm7b5 1-b3-b5-b7 D F G# C
D6 1-3-5-6 D F# A B
Dm6 1-b3-5-6 D F A B
Ddim 1-b3-b5-6 D F G# B
Daug 1-3-#5 D F# A#
Dmin(maj7) 1-b3-5-7 D F A C#
Dmaj7#5 1-3-#5-7 D F# A# C#
Dsus4 1-4-5 D G A
Dsus2 1-2-5 D F# A
DQ 1-4-b7 D G C
DQ+4 1-4-7 D G C#
D+4Q 1-#4-7 D G# C#
Extensions 9, 11, 13 E G B
E
Chord Formula Notes
Emaj7 1-3-5-7 E G# B D#
Emin7 1-b3-5-b7 E G B D
E7 1-3-5-b7 E G# B D
Em7b5 1-b3-b5-b7 E G A# D
E6 1-3-5-6 E G# B C#
Em6 1-b3-5-6 E G B C#
Edim 1-b3-b5-6 E G A# C#
Eaug 1-3-#5 E G# C
Emin(maj7) 1-b3-5-7 E G B D#
Emaj7#5 1-3-#5-7 E G# C D#
Esus4 1-4-5 E A B
Esus2 1-2-5 E F# B
EQ 1-4-b7 E A A#
EQ+4 1-4-7 E A B
E+4Q 1-#4-7 E A# B
Extensions 9, 11, 13 F# A C#
F
Chord Formula Notes
Fmaj7 1-3-5-7 F A C E
Fmin7 1-b3-5-b7 F G# C D#
F7 1-3-5-b7 F A C D#
Fm7b5 1-b3-b5-b7 F G# B D#
F6 1-3-5-6 F A C D
Fm6 1-b3-5-6 F G# C D
Fdim 1-b3-b5-6 F G# B D
Faug 1-3-#5 F A C#
Fmin(maj7) 1-b3-5-7 F G# C E
Fmaj7#5 1-3-#5-7 F A C# E
Fsus4 1-4-5 F A# C
Fsus2 1-2-5 F G C
FQ 1-4-b7 F A# D#
FQ+4 1-4-7 F A# E
F+4Q 1-#4-7 F B E
Extensions 9, 11, 13 G A# D
G
Chord Formula Notes
Gmaj7 1-3-5-7 G B D F#
Gmin7 1-b3-5-b7 G A# D F
G7 1-3-5-b7 G B D F
Gm7b5 1-b3-b5-b7 G A# C# F
G6 1-3-5-6 G B D E
Gm6 1-b3-5-6 G A# D E
Gdim 1-b3-b5-6 G A# C# E
Gaug 1-3-#5 G B D#
Gmin(maj7) 1-b3-5-7 G A# D F#
Gmaj7#5 1-3-#5-7 G B D# F#
Gsus4 1-4-5 G C D
Gsus2 1-2-5 G A D
GQ 1-4-b7 G C F
GQ+4 1-4-7 G C F#
G+4Q 1-#4-7 G C# F#
Extensions 9, 11, 13 A C E
A
Chord Formula Notes
Amaj7 1-3-5-7 A C# E G#
Amin7 1-b3-5-b7 A C E G
A7 1-3-5-b7 A C# E G
Am7b5 1-b3-b5-b7 A C D# G
A6 1-3-5-6 A C# E F#
Am6 1-b3-5-6 A C E F#
Adim 1-b3-b5-6 A C D# F#
Aaug 1-3-#5 A C# F
Amin(maj7) 1-b3-5-7 A C E G#
Amaj7#5 1-3-#5-7 A C# F G#
Asus4 1-4-5 A D E
Asus2 1-2-5 A B E
AQ 1-4-b7 A D G
AQ+4 1-4-7 A D G#
A+4Q 1-#4-7 A D# G#
Extensions 9, 11, 13 B D F#
B
Chord Formula Notes
Bmaj7 1-3-5-7 B D# F# A#
Bmin7 1-b3-5-b7 B D F# A
B7 1-3-5-b7 B D# F# A
Bm7b5 1-b3-b5-b7 B D F A
B6 1-3-5-6 B D# F# G#
Bm6 1-b3-5-6 B D F# G#
Bdim 1-b3-b5-6 B D F G#
Baug 1-3-#5 B D# G
Bmin(maj7) 1-b3-5-7 B D F# A#
Bmaj7#5 1-3-#5-7 B D# G A#
Bsus4 1-4-5 B E F#
Bsus2 1-2-5 B C# F#
BQ 1-4-b7 B E A
BQ+4 1-4-7 B E A#
B+4Q 1-#4-7 B F A#
Extensions 9, 11, 13 C# E G#
G# / Ab
Chord Formula Notes
G#maj7 1-3-5-7 G# C D# G
G#min7 1-b3-5-b7 G# B D# F#
G#7 1-3-5-b7 G# C D# F#
G#m7b5 1-b3-b5-b7 G# B D F#
G#6 1-3-5-6 G# C D# F
G#m6 1-b3-5-6 G# B D# F
G#dim 1-b3-b5-6 G# B D F
G#aug 1-3-#5 G# C E
G#min(maj7) 1-b3-5-7 G# B D# G
G#maj7#5 1-3-#5-7 G# C E G
G#sus4 1-4-5 G# C# D#
G#sus2 1-2-5 G# A# D#
G#Q 1-4-b7 G# C# F#
G#Q+4 1-4-7 G# C# G
G#+4Q 1-#4-7 G# D G
Extensions 9, 11, 13 A# C# F
A# / Bb
Chord Formula Notes
A#maj7 1-3-5-7 A# D F A
A#min7 1-b3-5-b7 A# C# F G#
A#7 1-3-5-b7 A# D F G#
A#m7b5 1-b3-b5-b7 A# C# E G#
A#6 1-3-5-6 A# D F G
A#m6 1-b3-5-6 A# C# F G
A#dim 1-b3-b5-6 A# C# E G
A#aug 1-3-#5 A# D F#
A#min(maj7) 1-b3-5-7 A# C# F A
A#maj7#5 1-3-#5-7 A# D F# A
A#sus4 1-4-5 A# D# F
A#sus2 1-2-5 A# C F
A#Q 1-4-b7 A# D# G#
A#Q+4 1-4-7 A# D# A
A#+4Q 1-#4-7 A# E A
Extensions 9, 11, 13 C D# G
C# / Db
Chord Formula Notes
C#maj7 1-3-5-7 C# F G# C
C#min7 1-b3-5-b7 C# E G# B
C#7 1-3-5-b7 C# F G# B
C#m7b5 1-b3-b5-b7 C# E G B
C#6 1-3-5-6 C# F G# A#
C#m6 1-b3-5-6 C# E G# A#
C#dim 1-b3-b5-6 C# E G A#
C#aug 1-3-#5 C# F A
C#min(maj7) 1-b3-5-7 C# E G# C
C#maj7#5 1-3-#5-7 C# F A C
C#sus4 1-4-5 C# F# G#
C#sus2 1-2-5 C# D# G#
C#Q 1-4-b7 C# F# B
C#Q+4 1-4-7 C# F# C
C#+4Q 1-#4-7 C# G C
Extensions 9, 11, 13 C# D# F# A#
D# / Eb
Chord Formula Notes
D#maj7 1-3-5-7 D# G A# D
D#min7 1-b3-5-b7 D# F# A# C#
D#7 1-3-5-b7 D# G A# C#
D#m7b5 1-b3-b5-b7 D# F# A C#
D#6 1-3-5-6 D# G A# C
D#m6 1-b3-5-6 D# F# A# C
D#dim 1-b3-b5-6 D# F# A C
D#aug 1-3-#5 D# G# A#
D#min(maj7) 1-b3-5-7 D# F# A# D
D#maj7#5 1-3-#5-7 D# G# A# D
D#sus4 1-4-5 D# G# A#
D#sus2 1-2-5 D# F A#
D#Q 1-4-b7 D# G# C#
D#Q+4 1-4-7 D# G# D
D#+4Q 1-#4-7 D# A D
Extensions 9, 11, 13 F G# C
F# / Gb
Chord Formula Notes
F#maj7 1-3-5-7 F# A# C# F
F#min7 1-b3-5-b7 F# A C# E
F#7 1-3-5-b7 F# A# C# E
F#m7b5 1-b3-b5-b7 F# A C E
F#6 1-3-5-6 F# A# C# D#
F#m6 1-b3-5-6 F# A C# D#
F#dim 1-b3-b5-6 F# A C D#
F#aug 1-3-#5 F# A# D
F#min(maj7) 1-b3-5-7 F# A C# F
F#maj7#5 1-3-#5-7 F# A# D F
F#sus4 1-4-5 F# B C#
F#sus2 1-2-5 F# G# C#
F#Q 1-4-b7 F# B E
F#Q+4 1-4-7 F# B F
F#+4Q 1-#4-7 F# C F
Extensions 9, 11, 13 G# B D#