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.
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:
- Major becomes minor and vice versa.
- Diminished becomes augmented and vice versa.
- Perfect intervals remain perfect.
- A tritone remains a tritone.
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:
- Perfect consonance: I, VIII, IV, V
- Imperfect consonance: bIII, III, #V, VI
- Mild dissonance: II, bVII
- Harsh dissonance: bII, bV, VII
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:
- Major triad (1-3-5): Combining major 3rd and minor 3rd.
- Minor triad (1-b3-5): Combining minor 3rd and major 3rd.
- Augmented triad (1-3-#5): Combining two major 3rds.
- Diminished triad (1-b3-b5): Combining two minor 3rds.
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.
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:
|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
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.
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:
|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
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
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
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 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:
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
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:
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, 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
C D# F# A and could also be called
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
Cdim can resolve to
A# and these can be
min7 or even dominant
would also be fine to resolve to a
root or half step above). There are only 3 groups of diminished chords:
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
W W h W W W h. In a piano, the
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|
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 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.
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:
- Tonic chords (T) are stable chords.
- Dominant chords (D) are weak chords and want to resolve to the tonic.
- Subdominant chords (SD) are weak chords and want to resolve to either the dominant or tonic chords.
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.
|IV||maj7||9th, 11th, 13th||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
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.
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:
- Common tone: No movement, the note stays the same.
- Common embellishments:
- Neighbour-tones: Leave the voice note by a whole step and returns back.
- Double neighbour-tones: Same as before but moves in both directions before returning.
- Common embellishments:
- Stepwise movement: Moving by a bII or II interval.
- Common embellishments:
- Escape tones: Move in opposite direction of step and resolve by leap.
- Suspensions/retardations: Held the note from the previous chord and resolve down/up respectively.
- Anticipations: Play the note from the next chord early.
- Chromatic passing tones: We can bridge the gap between the root and the II adding a bII in between.
- Common embellishments:
- Leapwise movement: Moving by a bIII interval or larger.
- Common embellishments:
- Appoggiaturas: Leaps to the note either a whole step up or down the target note and then resolves to the target. These can happen anticipatorily (on the chord performing the leap) or on the leaped chord.
- Common embellishments:
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, 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.
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.
- +4Q (1-#4-7): Combining augmented 4th and perfect 4th.
- Q+4 (1-4-#7): Combining perfect 4th and augmented 4th.
- Q (1-4-7): Combining two perfect 4ths.
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:
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 phrygian or
C dorian. We could also use
D - Gmin7 - C
Gmin7 from the
C mixolydian. In the
following table you can see the equivalent 7th chords for the different
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,
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.
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.
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.
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|
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
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:
- Dorian (Im): Focus on note 6 and intervals II-III and VI-VII
- Phrygian (Im): Focus on note b2 and intervals I-II and V-VI
- Lydian (I): Focus on note b5 and intervals IV-V and VII-I
- Mixolydian (I): Focus on note b7 and intervals III-IV and VI-VII
- Locrian (Im): Focus on notes b2 and b5 and intervals I-II and IV-V
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
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
A#/D we call this the Neapolitan 6.
The cadence is thus
Dmb5 - E7 - Am
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 (
IVm) which either goes back to the
VII or moves to the dominant (
VIIdim) that finally resolves into the
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.
- Add 7th and extensions.
- Diatonic/functional harmonization: Exchanging chords with the same functional harmony (tonic, subdominant, dominant).
- Vary the harmonic rhythm. In other words, change where the chords fell within the beat (e.g. going from one chord per bar to two).
- Tritone substitution: Replace a V7 chord by one a V interval below or bV above it (tritone).
- Secondary dominant substitution: A non dominant chord can be
substituted by its secondary dominant a
Vinterval above it. The secondary dominant can also be inserted before the chord instead of replacing it to also change the harmonic rhythm. In other times the secondary dominant can be preceded by its relative
IIto create a
- Add chromaticism: When going from one chord to another found 1 whole tone away, a chord could be inserted between the two to smooth the voice leading.
- Borrow chords from other modes from the major scale (or melodic minor).
- Change the key to their relative minor/major. For example if the
initial scale was in
C majorwe swap our chords to the
- Replace some dominant chords with the altered chords.
- Add a suspended chord before a dominant:
7 -> 7sus - 7. You can also replace the II or the V in a
II - V - Iwith a suspended chord.
- Add a diminished chord where any of their notes is half step below, below or at an existing chord.
- Change some chords to be augmented to act as a dominant
- Use different types of harmony (chromatic mediants or quartal/quintal).
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.
- Perfect/Authentic cadence:
- Feels like a full-stop.
- Reduces momentum/energy.
- Saved for the ending of a whole piece, section or phrase.
- The strong pull is due to the functional tritone.
- Plagal cadence:
- Feels like a full-stop, but less so than the authentic cadence.
- Reduces momentum/energy.
- Saved for the ending of a whole piece, section or phrase but could be used in the
- Imperfect cadence:
- Can be seen as musical commas.
- Going from a
- Deceptive cadence:
V7 - VIor
- Resolves to a chord other than the root.
- Typically in a major key:
- Typically in a minor key:
V-VIis sometimes called interrupted cadence.
- Ends the progression without reducing momentum/energy.
- Can be used anywhere in the middle of the piece.
- Half cadence:
- Ends a progression with the
- Can be used to connect two chord progressions (For example an A and B section).
- The next chord progression resolves the cadence with either a
- Creates movement/momentum.
- Ends a progression with the
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
Im and both
containing the characteristic notes. We can use
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
- Andalusian cadence:
Im-bVII-bVI-V7. For variety the V7 chord could become a diatonic Vm instead or we could come back to the bVII.
- Jazz bread and butter (minor/major 2-5-1s):
IIm7b5-V7-Im7. Already mentioned thoroughly on these notes, just remember that sometimes we can also chain II-Vs without resolving to the I. Very useful for changing keys.
- Jazz legos: Small building blocks of many a Jazz standard.
- Walking in 4ths:
V7-I7-IV7-bVII7...We don’t always have to use dominant chords, but the dominant cadence is a useful way of moving between keys.
- Key modulation a whole step via minor relative:
IIm. For example:
- Turnaround progression: Coming back to the tonic by walking the
circle of fifths
- Pop music cliché:
- Major flavour:
- Mixolydian flavour:
- Plagal cascade (moving down by perfect 4ths or up by 5ths):
- Basic 12bar blues:
|I7 |I7 |I7 |I7 |IV7|IV7|I7 |I7 |V7 |IV7|I7 |I7 |
- Rhythm changes:
|I-VI7 |IIm-V7 |I-VI7 |IIm-V7 |I-I/III|IV-Idim|I/V-VI7|IIm-V |
|III7 |III7 |VI7 |VI7 |II7 |II7 |V7 |V7 |
- Harmony for Composers Series
- How to write a modal chord progression (that sounds modal)
- Sakamoto, Hisaishi, et. al. - Common Japanese Chord Progressions
- Cadences - The 4 types explained - Perfect, Plagal, Imperfect, Interrupted
- The perfect cadence - Music theory
- The plagal cadence - Music theory
- The interrupted cadence - Music theory
- The imperfect cadence - Music theory
- Quick theory: Cadences (Tabletop composer)
- Quick theory: Cadences in modal music (Tabletop composer)
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:
- Present: The motif is introduced.
- Repeat: The motif repeats with little to no variation.
- Variation: The motif repeats with larger variation.
- Deconstruct: The motif is changed to end the 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.
- Rhythmic variation:
- Augmentation & Diminution: Slows/speeds the tempo or increase/decrease the note values by the same ratio (e.g. double the duration, half the duration)
- Rhythmic transformation (Additive/subtractive): Where only specific notes are lengthened/shortened.
- Metric displacement: Move a motif to start on a different beat. For example if it started on the 1st beat of a bar, it could be moved to the 2nd instead.
- Time signature change: With our without rhythmic transformation.
- Accentuation: Inserting accents at either regular intervals or irregular intervals.
- Melodic variation:
- Sequencing: Moving a motif up or down chromatically or diatonically (Changing some intervals of the motif to ensure we are still in key).
- Melodic inversion: Interval remain the same but the direction they move in swaps (ascending to descending and viceversa). This could also be done exactly or diatonically.
- Retrograde: Playing the motif backwards. This can happen in three
- Complete retrograde: The motif is played backwards exactly.
- Rhythmic retrograde: The pitch is the same but the rhythm is inverted.
- Melodic retrograde: The rhythm is the same but the pitch is inverted.
- Fragmentation: Break a motif into smaller parts that can be moved, replaced or changed.
- Expansion/contraction: Increase/decrease the interval between two notes in the motif.
- Embellishment: Adding decorative tones, which may make necessary to change the value of some of the other notes or remove them to accomodate for the addition.
- Reduction: Notes are removed from the original motif.
- Reconstruction: A motif that has previously being reduced is presented again with new decorations.
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.).
- Melodic punctuation:
- Smooth the ending, using smaller intervals.
- Moves down in pitch.
- Ends in a familiar register (don’t move to new octaves).
- Harmonic punctuation:
- Resolve to the tonic.
- Reinforce a cluster chord with an octave or V interval in the lower two voices.
- Only use consonant intervals between harmonic voices.
- End a stepwise baseline with a leap.
- Highest and lowest voices in the harmony move towards each other.
- Slow down the harmonic rhythm near the end of the phrase.
- Rhythmic punctuation:
- Slows down the rhythm.
- Ends on a strong beat.
- Pause momentarily.
- Dynamic punctuation:
- Decrease in volume.
- Texture punctuation:
- Reduce the number of instruments playing.
- Reduce the number of registers being used.
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 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.
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:
- Parallel motion: The voices move the same number of intervals (a major 3rd). For example, if the “cantus firmus” (CF) or initial melody goes from G to E (minor third), the notes from another voice has to move the same amount. If we can’t move the exact same interval lest we go out of key, but we are close enough, we call this “similar motion”. Both of these are considered “direct motion”.
- Oblique motion: The fixed melody changes in pitch but the counterpoint remains stationary.
- Contrary motion: Two voices move in opposite directions, that is, one voice moves down and another one moves up.
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.
- The CF always start and end on the root note.
- The I, III and V scale degrees are considered stable/consonant. II, IV and VI have a tendency to resolve down. The VII tries to resolve down.
- We can have three types of intervals:
- Perfect consonance (I, V, VIII). Try to avoid using these more than once in a row, since they put a stop to the melodic rhythm.
- Imperfect consonances (III, VI, X). The most useful, voices sound in agreement but they create a smooth melodic rhythm.
- Perfect consonances (II, IV, VII). Unstable, they are very good for creating voice leading independance. Not used in 1:1 counterpoint.
- Leaps wider than a 3rd tends to turn to resolve in the opposite direction.
- If the counterpoint melody starts above the CF, it can start on the 1st, 3rd, or 5th of the scale. If it starts below the melody, serving as a baseline, it must start on the I.
- Try to use contrary motion, oblique motion, similar motion, and parallel motion in that order of priority.
- We want an unpredictable type of motion to create interest.
- Level 1 (1:1 counterpoint):
- For every note in the CF, only one note is added to go with it.
- No dissonant harmonic intervals.
- Don’t use direct motion to a perfect consonance.
- A suggested approach is to start with the ending, since the final cadence is already known, then pick a starting point that allows both melodies to develop, and make sure both melodies “peak” (reach their highest note) at different times.
- Level 2 (2:1 counterpoint):
- Add two notes for every note of the CF.
- We can start thinking on accentuation as well. A 2/2 typically follows a D-U-D-U…, where the downbeat (D) is accentuated and the upbeat (U) is not, which is what we dind in 2:1 counterpoint (Duple meter).
- Consonance intervals may happen on either the D or the U.
- We can use dissonant intervals as passing tones (must occur on the upbeat and approached and left by step motion in the same direction).
- Avoid parallel perfect intervals (V, VIII) in consecutive downbeats, but can be used in consecutive upbeats.
- No tone repetitions in 2:1 counterpoint, as this could be considered 1:1.
- Perfect unisons are allowed on the upbeat.
- Can begin as in 1:1 but also with a silence.
- Level 3.1 (3:1 counterpoint):
- Composed in 3/4 meter (D-U-U-D-U-U…) with 3 notes per CF note.
- As before, the dissonances can go on the upbeats (U).
- In addition to the dissonant passing tone, here we can have a dissonant neighbor tone. These are dissonant tones approached by a step by left by a step in the opposite direction, instead of the same one.
- In summary: consonance on any beat, dissonant passing tones on beats 3 or 3 and dissonant neighbor tones only on beat 2, and we can use embellishing tones that form a 5-3-5 or 6-3-6 pattern. It should end on a 6-5-6-1 or 3-5-6-1 cadence if the counterpoint is above or a 5-4-3-1 or 3-4-3-1 if below.
- Level 3.2 (4:1 counterpoint):
- Composed in 4/4 meter (D-U-U-U,D-U-U-U…) with 4 notes per CF note. The downbeat is the same as before, containing consonant intervals only, beats 2 and 4 are the weakest and can have dissonances or consonancesi. Beat 3 is typically accented and usually form consonances but is capable of having dissonances under certain circumstances.
- Dissonant neighbours are still not allowed on the final beat of a measure (Beat 4 in this case).
- We can have accented dissonances (beat 3) as passing tones or neighbour tones when beats 2 and 4 are perfect consonances.
- We can have two dissonances on beats 2 and 3 (double neighbour).
- Level 4 (Suspensions):
- A silence in the first beat where each counterpoint tone is hold by the same amount as the CF, creating syncopation.
- The counterpoint note must be prepared as a consonance on the previous upbeat.
- Resolves down by step to consonance on subsequent upbeat. Typically 7-6-1 (above) or 2-3-1 (below).
- Level 5 (Florid counterpoint):
- The combination of all previous techniques in 4/4 time, as with 4:1, with free rhythm.
- Suspension elaborations: When we change the ending note of a suspension with two quarter notes. We can have repetition or anticipate the tone of resolution. We can also leap to an innervoice chord member as embelihsing tone. We can also use 8th note elaborations.
- Eight-note fills: Fill the span of a 4th ascending/descending and occurring on a weak beat (2 or 4).
- We can also use dotted half-notes.
- Try to have a rhythmic arc, blending different durations instead of having clusters of rhythms. Rhythm arcs heighten or slows the intensity of a melody.
A contemporary approach
As with the classical approach, we need:
- Cantus firmus (CF): The original melody
- Counterpoint line (CP): A new melodies written to compliment the CF
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.
- Consonant: bIII, III, IV, V, #V, VI, VIII
- Dissonant: bII, II, IV, bV, bVII, VII
With regards to motion:
- Contrary motion: Voices move in opposite direction. Add energy and highlight independence.
- Parallel: Voices move in the same direction by the same interval. Use with care, since it removes independence.
- Similar: Voices move in the same direction by different intervals. Creates unity without the issues of parallel movement.
- Oblique: One voice moves another doesn’t. Adds energy but not as much as contrary motion.
- Start with CF on 4/4 with strong beats on 1 and 3.
- Add half notes starting on each strong beat to create a CP line draft, focusing on maintaining consonant intervals on notes that start at the same time. Keep an eye out for possible motifs.
- Embellish the draft by adding notes without worring about consonance or dissonance so long as the starting point of consonant intervals don’t change and any time we add a note starting at the same time as another in the CF make sure they form a consonant interval.
- Focus on “sounding good” instead of the academic approach (e.g. forbiding P5 parallel movements).
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
- (R)epetition at the beginning or the end. Repetition at the end almost always work, specially when creating decepting cadences. Repetition at the start works, but we must be careful not to make things dull, for example we can echo other voices in a call-response way.
- (E)xtend motives and ideas. Works well in all sections, but specially on the middle section.
- (P)ause. Wait on a silence for longer, for example an extra bar or so. At the beginning could be done by false starts also, where the melody takes a couple of tries before getting started. At the ending, but could be done before we start a final cadence. We can also do it at the end by extending the final bar into multiple ones, building suspense on the cadence. At the middle, pausing can be detrimental, as it stops the development momentum.
- (S)tudy other pieces or music and see how are they doing things and try to use these ideas in your own composition.
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.
- 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.
- Choose a melodic cadence (last two notes). Typically 2-1 or 7-8. In C major, D to C or B to C.
- Draw the contour of your melody, i.e. the peaks and valleys or high/low notes in our melody. Nothing specific, just vibes.
- 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.
- Melody for Composers Series
- How To Use NEGATIVE MELODY To Write Beautiful Music [Negative Harmony]
- A counterpoint crash course in 17 minutes
- How to Compose 1:1 Counterpoint || Tonal Voice Leading 1
- How to write longer music with the REPS method
- How to write a melody 1: Period
- Sentence form in music composition
- Counterpoint made simple
- This Skeleton Can Write a Better Melody Than You
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| |
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| | | | | |
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| |
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| |
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| | | |
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|
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| | | |
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|
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| |
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| | |
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|
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.
Euclidean rhythms come from the idea of distributing K beats into a
measure of N beats as evenly as possible. The terminology is typically
E(K,N,R) where R is the rotation of the pattern.
For example a four-in-the-floor beat could be noted as E(4,16,0):
E(4,16,0) = [x...x...x...x...] E(4,16,1) = [...x...x...x...x] E(4,16,2) = [..x...x...x...x.] ...
Depending on the length of the note that we use for each beat, common divisors are equivalent. If instead of 1/8 notes per beat we use 1/4:
E(4,8,0) = [x.x.x.x.]
To generate interesting patterns, it is often preferable to use patterns in which K doesn’t divide by N, such as E(5,8) or E(9,16). The fun of these types of patterns it to combine multiple combinations of rhythms for different instruments, creating groovy polyrhythms. They are not limited to percussive elements and can be used in tonal leads and bass elements. They are very fun to use in generative music or as a compositional tool.
A lot of world music’s rhythms can be described in terms of Euclidean rhythms patterns. Below you can see a reference of different patterns and how they relate to music from different cultures. Not including rotations for simplicity.
|0|1|2|3|4|5|6|7|8|9|A|B|C|D|E|F| E(2,5,0) |x| |x| | | Khafif-e-ramal, Thaikovsky (Symphony No. 6), Brubeck (Take Five) E(3,5,0) |x| |x| |x| Rumanian folk-dance E(5,6,0) |x| |x|x|x|x| York-Samai E(3,7,0) |x| |x| |x| | | Ruchenitza, Pink Floyd (Money) E(4,7,0) |x| |x| |x| |x| Ruchenitza E(5,7,0) |x| |x|x| |x|x| Nawakhat E(3,8,0) |x| | |x| | |x| | Cuban tresillo E(5,8,0) |x| | |x|x| |x|x| Cuban cinquillo, Spanish tango, Al-saghilal-sani E(7,8,0) |x| |x|x|x|x|x|x| Tuareg rhythm in Libya E(4,9,0) |x| |x| |x| |x| | | Aksak, Brubeck (Rondo a la Turk) E(5,9,0) |x| |x| |x| |x| |x| Agsag-Samai E(4,11,0) |x| | |x| | |x| | |x| | Zappa (Outside Now) E(5,11,0) |x| |x| |x| |x| |x| | | Mussorgsky (Pictures at an Exhibition) E(4,12,0) |x| | |x| | |x| | |x| | | Flamenco clapping (Fandango) E(5,12,0) |x| | |x| |x| | |x| |x| | Venda clapping E(7,12,0) |x| |x|x| |x| |x|x| |x| | West African bells E(4,16,0) |x| | | |x| | | |x| | | |x| | | | Four in the floor E(5,16,0) |x| | |x| | |x| | |x| | |x| | | | Bossa Nova E(7,16,0) |x| | |x| |x| |x| | |x| |x| |x| | Samba, Clapping from Ghana E(9,16,0) |x| |x|x| |x| |x| |x|x| |x| |x| | Samba, bells from Central African Republic
- How to write drum parts (for non drummers)
- 10 Popular Drum Patterns Every Producer Should Know
- Polyrhythms vs polymeters
- Euclidean Rhythms paper (Godfried Toussaint)
- Digging in to Euclidean Rhythms (Sound + Voltage)
In a modern orchestral setting, we have 4 main sections of instruments:
- Strings: Violin, viola, chello, bass, etc.
- Brass: French horn, trumpet, trombone, tuba, etc.
- Woodwinds: Flutes, single reeds, double reeds.
- Percussion: Idiophones, membranophones, aerophones, chordophones.
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:
- Melody: The general tune/shape of the music. Typically belongs to the foreground material, which is content that is the most important for the listener to pay attention to.
- Harmony: Typically is background material that creates the sonic texture of our piece. Includes the harmonic bed (chord progression), harmonic foundation (bass line), harmonic voicing (melody-like harmony) and comping (Provides harmony as well as rhythm).
- Countermelody: Floats between background and foreground whenever is needed. It is sometimes called a “mid ground”.
In general we want to avoid mixing foreground and background material, otherwise the music will sound directionless. We can follow two guidelines for this:
- 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.
- 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.
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:
- Violin (I & II)
- Tuning: G3, D4, A5, E5
- Violin section: G3-E7
- Violin solo: G3-B8
- Pizzicato range: G3-E6
- Great for melodies, but consider:
- E5+ is good for any melodic line.
- E5- is best for quieter moments.
- Tuning: C3, G3, D4, A5
- Range: C3-A7
- Good for solos, melodies and countermelodies. Best on:
- C3-C4 (lowest octave) is the most ideomatic.
- C5+ has the greatest carry power
- Tuning: C2, G2, D3, A4
- Range: C2-G5
- Versatile, both for lower ranges and higher ones.
- For melodies:
- E4+ ideomatic.
- E4- possible but depends on the rest of the orchestration.
- Double bass
- Tuning: E1, A2, D2, G2
- Range: C1-Bb4
- Used for bass lines and foundational harmonies. Melodies are possible specially when doubled with tuba and contrabassoon (unison) and cello and bassoon (one octave above).
We generally write for strings using 4-part/SATB writing. As follows:
- Soprano: 1st violin.
- Alto: 2nd violin.
- Tenor: Viola.
- Bass: Cello and double bass in octaves.
- Default process
- Asign melody to one of the voices (typically soprano)
- Write bass line in the bass voices.
- Assign remain chord tones to the alto and tenor voices, trying to avoid as much movement as possible.
- Harmonic voicing process
- Asign melody to one of the voices (typically soprano)
- Write bass line for the double bass.
- Treat the cello, viola and violin II their own independent lines.
- Stick to chord tones as much as possible.
- Create variations of the full chord between the three voices and the bass line as much as possible.
- Use as much repetition in each voice as possible.
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 are wind instruments. Traditionally consists of (but is not limited to):
- 4 horns
- 3 trumpets
- 3 trombones
- 1 tuba
Organized in 3 sub-sections that will split their roles between harmony, melody and bass:
- Trumpets & trombones
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:
- Higher pitches will be generally louder.
- Volume can and will change the tone color.
- 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.
- Horn (in F)
- Versatile instrument. Blends well with woodwinds.
- The sound it produces will sound a perfect fifth lower than the note it was written.
- Sounding range: B2-F5
- Written range: F#2-C6
- Melodic range: F3-C5
- Trumpet (in C or Bb)
- The soprano instrument of the brass family
- Sounding range (Bb): E3-Bb6
- Written range (both): F#3-C6
- Trombone (Tenor and Bass)
- The tenor/bass instrument of the brass family.
- The bass tenor often doubles or replaces the tuba.
- Closely related to the trumpet.
- Sounding range: E2-Bb5 (tenor) Bb2-D4 (bass)
- Lowest sounding brass instrument.
- They mainly provide the bass line.
- Range: Bb1-D4
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 that don’t have a wooden reed in the mouth piece. Piccolos and flutes are the most common.
- Most powerful in their higher registers.
- Sounding range: D5-C8
- Written range: D4-C7
- Different tone colors:
- High register is piercing, requires a lot of stamina and can be easily heard. Best in strategic bursts.
- Middle register is strong, bright and clear.
- Low registers are haunting and intimate, best for quiet moments and doubling other instruments for color.
- Range: (B4) C4-D7
- Different tone colors:
- High register is piercing, requires a lot of stamina and can be easily heard. Best in strategic bursts.
- Middle register is sweet, bright and lyrical, best for melodies.
- Low registers are rich and beautiful, best for intimate moments.
- Use a single wooden reed in the mouth piece. In an orchestra, normally only clarinets (but saxophones are in this family too).
- Clarinets (in A or Bb):
- Range: D3-Bb6
- Clarinet in A sounds a minor third lower than written.
- Clarinet in Bb sounds a major second lower than written.
- Breaking point between Bb5-B5, which means we need to avoid repetitive figures between these two.
- Different tone colors:
- High register is powerful and shrill. Easy to hear. Best saved for strategic moments.
- Middle register is expressive and melodic. Most frequent register, very emotional.
- Low registers are rich, deep and full, but have very weak carry power, best for intimate moments.
- Bass Clarinets (in A or Bb):
- Range (an octave and major 2nd lower than written):
- Sounding range: Bb1-B5
- Written range: E3-A7 (major 9th)
- Normally only the lowest registers are used, since higher registers are reserved for the regular clarinets.
- Range (an octave and major 2nd lower than written):
- Use two wooden reeds reed in the mouth piece. Behave opposite to flutes and single-reeds, where they are more powerful in lower registers and thinner in upper ones.
- Soprano of double-reeds.
- Range: Bb3-A6
- Melodic range: F4-C5
- English horn (extends range of oboe):
- Sounding range: E3-C6
- MWritten range: B4-G6
- Tenor/bass of double reeds and woodwinds.
- Range: Bb1-F5
- In their middle register they blend well with horns and other instruments.
- Usually used for doubling the bass lines.
- Contrabass bassoon:
- True bass of the orchestra.
- Sounding range: Bb0-C4
- Written range: Bb1-C5
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.
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.
- Timpani: A collection of 4-5 membranophones of different sizes,
where each drum is tuned one pitch at a time. They can be retuned, given
- Range: C2-C4 (Each drum covers a range of approximately a fifth).
- Best for fast rhythmic passages and building tension and energy with rools and swells.
- Xylophone: Collection of small blocks that produce pitch when
- Written: C4-C6
- Sounding: C5-C7 (Or even lower).
- Bright sounding and can easily cut through the mix.
- Fast decay.
- Can only play 2 notes are a time.
- Good choice for fast rhythmic passages and doubling to add tone color or attack to a sound.
- Marimba: Very similar to the xylophone.
- Range: C3-C7
- Can be played with 2 mallets per hand.
- Good choice for fast rhythmic passages and doubling to add tone color or attack to a sound.
- Vibraphone: Very similar to the xylophone.
- Range: F3-F6
- Has a motor that can be used to add vibrato to a sound and help sustain notes longer.
- Glockenspiel: A small Xylophone.
- Written: G3-C6
- Sounding: G5-C8
- Can only play 2 notes are a time.
- Very bright, reminiscent of bells.
- Tubular bells: Collection of large chimes that produce bell like
sounds when struck.
- Range: C4-G6
- Has a sustain pedal.
- Can be used to double slow melodies.
- Careful of cluttering the sound if too many overtones overlap each other.
The traditional roles of the percussion section are:
- Doubling for color.
- Look for opportunities where percussion instruments can be used to add additional color. Often this color is the transient/attack that these instruments provide.
- Using percussion for a repetitive, rhythmic figure.
- Other instruments can build on top of it or can be used to emphasize pre-existing rhythms in the music.
- Extreme dynamics.
- Loud dynamics are useful for adding energy.
- Quiet dynamics are useful for setting mood/texture.
- Solo statements.
- Look for moments where the foreground/midground can benefit from a solo percussion instrument to add a new rhytmic feeling to the music.
- Highlighting accents.
- Look at existing accents in the music or moments where you want more emphasis and consider adding a percussion hit to add to them.
- Builds and climaxes.
- Look for moments where rolls/swells/crash can add or remove energy.
- Harmonic support.
- Once the arrangement is drafted fully, maybe is best to step away from the piece for a bit and when revisited, evaluates if some sections feel flat. If so, adding an arpeggio or some other harmonic voicing with percussion is a way of addressing that.
Piano, celeste and harp
- Range: A1-D8 (One key for each chromatic note, 88-keys)
- Can play 5 notes at a time with one hand.
- Keep in mind hand size.
- The grand piano has 3 pedals.
- Sustain: Removes the damper, so notes can sustain even after releasing the key.
- Una corda: Shift the hammers slightly so that they strike one less string per note. Creates a more delicate tone color and reduces color.
- Sostenuto: Will only sustain the notes being played at the moment they are played. Useful for mixing sustained and staccatto notes.
- Common roles:
- Reinforce accents and staccato chords.
- Doubling instruments for color and/or attack.
- Melodic/harmonic materials as solo.
- Doubling instruments.
- Very similar to a piano, but uses chimes instead of strings. Normally played by the pianist.
- Written: C3-C7
- Sounding: C4-C8
- The harp
- Range: C1-C8
- It doesn’t have dedicated strings for every pitch, only the major scale. Instead it uses pedals to raising/lowering these pitches.
- Pedal changes can happen during performance, but it needs to be given time to do it.
- Good for diatonic passages but not so good for chromatic passages.
- Glissandi and harmonics are common and very characteristic of the instrument.
Some useful techniques for arranging and merging instruments in the orchestra are:
- Woodwind dovetailing: We can blend the flutes and clarinets together by weaving the notes of the chord between them. For example in a Cmaj7 (C-E-G-B) the clarinets play C-G and the flutes E-B (In the same range).
- French horns and trombones: Play closed voicings with french horns and open voicings for trombones.
- Strings in octaves: Playing the same lines by Violins 1 and 2, but in different octaves (Or using divisi).
- Add countermelodies in the spaces where the other instruments are sustaining anote.
- Build emotion by doubling melodic lines in subsequent repetitions. Common doubling pairs are: Flute & strings, flute & oboes, celli & bassoon, celli & base (in octaves but try not to overdo it).
- Add color to staccatto strings by doubling them with tremolo ones.
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
D major has 2 sharps, F# and C#). The same
applies for finding the number of flats (
Db/C# major has 5
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
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
F major and
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
and we wanted to spice it up, we could do
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
G#7, creating a
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. 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
- Uses arpeggios spanning multiple octaves, sometimes making them more
complex with some (implicit?) harmonic variation
Im-IIdim/I-Im, for example
- Use of galloping dotted rhythm (
|x| | |x|or
|x| | | |x|or
|x|x| | |, where each bar is a 16th note).
- Add chromatic neighbour tones for the chords.
- Use of pedal point in harmonic progressions.
- Augmented chords.
- Chords in triplets, as wide as possible.
- The chromatic scale is sometimes nudged between phrases or arpeggios.
- Multiple layers of sound and inner lines.
- Lots of question and answer lines.
- Many chords use extensions except the resolving chords.
- Use of polyrhythms in melodies.
- Very eccentric composer with interest in mysticism and romanticism. He had synesthesia.
- Use of short-short-long phrases.
- Switches moods fluidly, going from intimate phrases to more dramatic ones.
- “Chopin-esque elements”:
- Progressions involving the circle of fifths.
- Borrowed motifs from Chopin.
- Sweeping melodies in the bel canto style.
- Augmented sixth chords and accented non-chord tones in resolutions.
- Similar musical forms (Mazurka, Fantasies, Nocturnes, Preludes).
- Elaborate left hand lines due to chronic pain on right arm.
- Smooth voice leading and use of chromatic chords for transitioning.
- Lots of extensions/“Jazzy chords”.
- Use of chords based on 4ths.
- Floating quality with some descending lines on the left hand instead of playing the root first.
- Heavy use of his “mystic chord” (dominant 7th chord and whole-tone
scale mashup). Formed of
I-b5-bVII-III-VI-IIbut typically used in different transpositions.
Ludwig van Beethoven
- Use of repeated chords, often in groups of 3.
- Wide-broken chords (Right hand plays arpeggio, left hand bass only).
- Use of unison melodies.
- Broken and staggered octaves.
- Lots of contrast.
- Diminished chords for tension and harmonic motion in chord and arpeggio forms.
- Use of long trills at the end of phrases.
- Imitative layers (Right mimics left for example).
- Use of inner lines.
- Warm melodies.
- Raw scales and arpeggios as single notes or in octaves.
- Dotted rhythms accompanied with periods of rest.
- Use of call and response.
- Pedal points and sustained notes.
- Repetition of sequences at different pitches.
- Use of the waltz form.
- Pedal points and upper common tones (like a pedal point but on the higher register).
- Arpeggios and sometimes linked with chromatic runs.
- Very lyrical melodies.
- Use of trill and other embellishments.
- Multiple voices in melodies.
- Use of Neapolitan sixth progressions.
- Diminished chords as transition points.
- Atmospheric, focused on moods and adding a lot of space between notes in a line.
- Use of arpeggiated harp-like cascades with a resonant bass line that accentuates the perfect 5th.
- Avoid using functional cadences, it is more reminiscent of modal harmony. There is plagal movement but not in the form of a typical cadence.
- Ambiguous tonality achieved by using chords with tritones without resolving them.
- Using tremolos to add tension.
- Lots of rhythmic variation in a fluid manner.
- Use of syncopated lines for an ambiguous sense of pulse.
- Move chords and gestures with parallel movement (For example unison octaves).
- Tends to use non-western scales/modes and whole tone scales.
- Bell-like sounds and lines.
- How to sound like Rachmaninoff
- How to sound like Scriabin
- How to sound like Beethoven
- How to sound like Chopin
- How to sound like Debussy
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 (
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
All 4ths (EADGCF) reference diagrams
Scales and chords quick reference
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 ----------------------------------------------------------------------------------------------
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 |
|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|
|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|
|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#|
|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|
|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|
|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#|
|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
|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
|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
|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
|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
|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#|