Harmony

Harmony is a huge topic. There is no way, and fortunately no need, for me to explain anything other than basic concepts. Tango uses harmony in a simple way. Until Piazzolla…

A basic knowledge of scales is helpful in understanding harmony.  Scales, Keys, and Key Signatures explains them.

I begin with some general remarks about harmony. Then show how harmonies are derived from major and minor scales and explain why the different types of chords sound the way they do.

Some Aspects of Harmony
The word harmony has several aspects and definitions. My working definition of harmony is simple: harmony is three or more different s sounded together. A harmony in this sense is a noun, popularly called a chord. Harmonies are built on top of the notes in a scale. More about that in the next section. Harmony also has a functional aspect, how harmonies are related to one another and how they are used in a harmonic progression. That is, a sequence of chord changes, identified by name and type.

Music is created by combining three very broad categories: melody and harmony, and rhythm. Think of melody and scales being horizontal. On the page they are written sideways, left to right. They are single notes, thought of and heard moving though time, one at a time. Harmonies are thought of vertically, several notes stacked one above the other, heard simultaneously. They move left to right and through time like melody, of course, but their musical effect comes from the specific vertical combination of notes in the chords and the harmonic progression.

There is an important connection between melody and harmony. The choice of notes used in the melody is largely determined by the harmonies. The melody primarily uses the same notes as those in the underlying chord. Those notes are called harmonic tones or chord tones. Often the melody is an arpeggio, sounding only chord tones, ascending or descending. Melodies may contain many nonharmonic, or non-chord tones too, and there are many names for them and the functions they serve. (I don’t need to name or describe them here.) However, a melody that isn’t built mostly on, or at least prominently uses chord tones will sound “off”. It will be very dissonant, sounding in conflict with the harmony.

Harmonic rhythm is the rate harmonies change. When the harmonic rhythm is slow the harmonies do not change often. The music does not change character that much. When the harmonic rhythm is fast we feel action and movement.

Certain harmonies and harmonic progressions are used frequently because they have specific musical qualities and are used to create specific effects. Some progressions sound more pleasing than others and some are used to create tension and resolution or dissonance. (There are specific rules about how each note in the chord should move from the current chord to next, called voice leading. We can ignore them!) Some chords are more important than others and there are some strong relationships between specific chords. The tonic (I), based on the first note in the scale has the most important role and in general is heard the most. The subdominant (IV), based on the fourth note of the scale is also frequently used. The dominant (V), built on the fifth note of the scale, has great significance. It is used to create a bit of tension, some dissonance, and almost always leads back, resolving to the stability and consonance of the tonic (I) chord. Sections always end with a I-V(7)-I cadence or I-IV-V(7)-I cadence. A cadence is a resting or pausing or concluding effect in the music. There are several standard ones. The Perfect Cadence (I-V(7)-I) being the most used.

It is almost impossible to truly understand harmony from a verbal description alone. So, a musical example is in order. The first section of El adiós is an excellent example of the above concepts in actual use.

Edgardo Donato’s 1938 recording:

Some observations on the use of harmony:

  • Not strictly a harmonic aspect, but worth pointing out, the melody is an arpeggio. Meaning it uses only notes from the underlying harmonies. It ascends and descends using harmonic tones. (The melody is the second line. The top line is for the vocals to come. There is a violin counter melody that is not in the score. Ignore it.) There are some nonharmonic tones towards the ends of the 4 bar phrases and they contribute to the cadence effect at those point in time (bars 4 and 8).
  • Only chords i (c minor), iv (f minor), and V (G major) are used and there are three perfect cadences (i-V7-i): at the end of the first 4 bar phrase and two at the end of the section.
  • The harmonic rhythm is one chord per bar until the final perfect cadence at the end. The consistency in timing creates a feeling of constant, gentle, movement until the section’s end. 
  • The two perfect cadences as the section ends use harmonic rhythm to great effect. The first begins on the tonic chord (i, c minor) in bar 6 and moves to the dominant 7th (V7, G major with a fourth note added) in bar 7, which resolves back to the tonic (i) on the first half of beat 1 in bar 8. The harmonic rhythm has been one chord per bar the entire time. Now it gets much faster. After the tonic chord on the first half of beat 1 in bar 8 is played, another dominant 7th chord is quickly played on the second half of beat 1. Which is just as quickly followed by the tonic on beat 2. The perfect cadence played in such a fast harmonic rhythm definitively provides a feeling of conclusion and resolution.

 

The rest of this post is more technical and describes in detail how chords are created and why they sound different from one another. Some of you may want to skip the technical details, which is understandable, but I urge everyone to listen to the audio samples.

The Basis of Harmony: How Chords are Created

Triads in Root Position
The foundation of harmony is the three note chord called a triad. Triads are built by adding two notes above each of the notes in the scale. The interval is a third, meaning each is three notes above the prior one.

The following triad examples are in root position. Root position is when the note naming the chord is the bottom note, the lowest in pitch. In the examples the bottom note is a scale note. The scale degree – the Roman numeral – and the functional/relationship descriptor (tonic/supertonic/mediant, etc) and the tone-semitone intervals between the scale notes are listed below each note. The name and type of triad (chord) is identified above each one.

Triads built on the C major scale:

Triads built on the A natural minor scale:

Triads built on the A harmonic minor scale:

Triads built on the A melodic minor scale:

 
Inversions
As noted, the above examples are in root position. The bottom note in root position is the note name of the triad. Any of the three notes can be the bottom note. A first inversion triad has the second note on the bottom. A second inversion triad has the third note on the bottom. The root is still the note the triad is built on, in all these examples the scale tone, not the note currently on the bottom.

Triads on the C major scale in root position, first and second inversions, finishing in root position an octave higher.

In actual use triads are expanded to four or more notes, seldom four different notes. One or more of them will be repeated in another octave, most often the root – the scale note. And the notes will be spread out into more than one octave to achieve a bigger, fuller sound.

Chord Types
Recall from the Scales, Keys, and Key Signatures page there is a striking musical difference between major and minor scales, that there are three types of minor scale, and all scales have a unique tone-semitone order between successive notes. The harmonies built on the scale tones vary substantially between the scales. The tone-semitone order and the harmonies built on the notes in the scale are largely responsible for the musical character and emotional responses we get from the music.

It is often said major keys are “happy” and minor keys are “sad”. The reason is largely due to the quality of the third note in the scale, how far away it is from the first note, the tonic. In major keys it is a major 3rd; in minor keys a minor 3rd. A major 3rd is 2 tones apart. A minor 3rd is one tone plus one semitone apart. When triads are built on the tonic note, major keys form major triads because the third note is a major 3rd above the tonic. In minor keys it is a minor 3rd, creating a minor chord. Triads/chords are called major or minor to describe and reflect the quality of the type of third occurring between the first two notes, in root position. Major 3rds and chords sound “happy”; minor 3rds and chords sound “sad”.

The triads on the scale degrees – identified by the Roman numerals in the examples above – are always the same type. Major scales have the same type of chords on the scale degrees and the minor keys do on theirs. There are four types of triad: majorminor,  diminished,  augmented.

Chords and triads get their type and specific sound qualities from the intervals, the distance, between the notes. As noted, major triads have a major 3rd interval between the bottom two notes and minor triads have a minor 3rd between those notes. The top note in both is a perfect 5th above the root. Diminished triads have a minor 3rd and another minor 3rd above that. The “diminished” name comes from the distance between the root and the top note. It is a semitone lower than a perfect 5th, therefore it is “diminished”. Augmented triads have a major 3rd and another major 3rd above that. The distance between the root and top note is a perfect 5th plus a semitone. The 5th is “augmented”. We only need to hear the difference between major, minor, and diminished chords. Augmented chords are extremely rare.

Dominant, Dominant 7th Chords and the Perfect Cadence

Chords usually have three different notes. Very often a fourth note, an interval of a minor 7th above the root, is added to the dominant chord, the chord built on the fifth note, V. It is then called a dominant 7th and labelled V7. Dominant chords are always major. The dominant 7th is a major chord with an added minor 7th above the root. Major chords on the fifth scale degree occur in major keys but not in natural minor keys. Recall in the harmonic and melodic minor scales the 7th note, called the leading tone, is raised a semitone. That raised note creates a major 3rd in the dominant harmony. It becomes the required major chord. In minor keys the dominant chord is labelled V# and dominant 7th, V#7, to acknowledge the raised leading tone. To verify, check the A harmonic and melodic minor examples above, specifically the E major chord on scale degree V. 

There is a strong functional relationship between the and notes and the harmonies built on them. The fifth scale degree has a natural, indeed need, to resolve to the tonic. So does the . These two notes, dominant (V) and leading tone (VII) are in the dominant (and dominant 7th) chord, and require resolution back to the stability of the tonic (I).

When the dominant or dominant 7th resolves to the tonic – V(7)-I – the progression is called a Perfect Cadence. This highlights the important functional basis these chords have in creating tension and instability followed by resolution and release. The extra note in the dominant 7th adds a strong feeling of tension and dissonance. The Perfect Cadence occurs often at the end of phrases and almost certainly at the end of sections.

Diminished chords on scale degree VII sometimes act as dominant 7th chords (V7) because they share three common notes, all but the root of the V7 chord. In C major: B diminished is B-D-F and G dominant 7 is G-B-D-F. In A minor: G sharp diminished is G#-B-D and E dominant 7  is E-G#-B-D

Perfect Cadences, in A minor and C major:

Some remarks about notation. When analyzing harmonic progressions musicologists use the Roman numeral scale degree rather than chord names. For example, I-V-I. The chord type is known because the chord type built on each Roman numeral scale degree is the same, determined by the scale type. Popular music is not written or thought of this way. The chord names and types are explicitly named. I use both. I like the Roman numeral basis because chord progressions are represented the same way. For example, I-IV-V-I always has the same character in any major key, and a different character, but the same in every minor key. Saying or writing just the chord names and their type, in C major for example, C major – F major – G major – C major, doesn’t convey the same level of information. The functional relationship is missing. Traditionally, upper case Roman numerals are used to identify major chords and uppercase letters for naming major keys. Lower case numerals for minor chords and minor keys are labeled with lowercase letters.

No doubt there are other things I should say about harmony, which I overlooked. Other cadences and harmony’s contribution to Question and Answer Phrasing come to mind.   Another time. As I said at the top of the post, harmony is a huge topic. 

A note is a sound or tone having two aspects:
1) The primary, auditory one, is pitch. Each note has a unique pitch, with a sound wave frequency measurable in hertz. In many parts of the world instruments are tuned to A at 440Hz.

2) The secondary, temporal one, is duration, called "time value" or "note value". When written or played each note has a specific duration, how long it lasts relative to the beat.

When pitch and duration are combined we get melodic shape and rhythm. Pitch creates melody and gives it direction, the melodic shape; duration provides the melodic rhythm.

The tonic is the first note, or scale degree, in the Western diatonic scale system, and is indicated by the Roman numeral I. It is the primary and foundational note in the scale.

Tango music most often begins on and ends phrases and/or sections on the tonic harmony; the chord built on the first note in the scale, which is a major chord in a major key and a minor chord in a minor key.

See Scales, Keys, and Key Signatures and Harmony for more information about scale degrees and their function.

The dominant is the fifth note, or scale degree, in the Western diatonic scale system, and is indicated by the Roman numeral V. It is next in importance to the tonic (I).

The dominant note creates instability and tension, and the harmony built upon it, a major (or major-minor 7th) chord, most often resolves by moving to the tonic.

Tango music usually ends phrases and/or sections by moving to the dominant harmony then resolving to the tonic.

See Scales, Keys, and Key Signatures and Harmony for more information about scale degrees and their function.

The leading tone is the seventh note, or scale degree in the Western diatonic scale system. It is indicated by the Roman Numeral VII.

The leading tone usually "leads" to the tonic (I) note and the harmony built on it, a diminshed chord, frequently functions as a dominant (V) harmony, creating tension and resolving to the tonic (I)

See Scales, Keys, and Key Signatures and Harmony for more information about scale degrees and their function.

4 Responses to Harmony

  1. Jantango says:

    The incredible richness and simplicity of those eight measures! I’m usually playing those arpeggios on the table at a milonga. How wonderful to read the music for El adios.

    Once again you’re taking me back to my childhood when my mom taught the Saturday morning music theory class at my piano teacher’s house. I didn’t appreciate it then as I do now.

    • tangomonkey says:

      I wrote most of the post before I discovered El adios was a perfect example of what I was saying about tango harmony. I wanted to include an actual tango as an example, and for some reason El adios came to mind. I really enjoy dancing to it and have heard it countless times, but I had never checked out the music before. For some reason I did, the other day, and I was happy to see it is a great match for what I was saying about tango harmony.

      I’ve syncd the music with Donato’s recording – all of it, not just the first 8 bars – and will post it soon.

  2. Matthias Wendel says:

    Tiny typo: g minor in:

    Only chords i (c minor), iv (g minor), and V (G major) are used and there are three perfect cadences (i-V7-i): at the end of the first 4 bar phrase and two at the end of the section.

    must be: f minor

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