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Scales in Harmony

Scales can be practiced in harmony - in thirds, sixths, octaves, and tenths. These intervals also happen to be the most common intervals found in tonal music. Many pieces and studies focus on these intervals (see examples below).

In fact, if you labelled the intervals in your pieces, then you will find the majority to be thirds, sixths, octaves, and tenths! So if you familiarize yourself with these scales, you will be able to quickly learn pieces, improve your sight-reading, and have great material for technique.

Sor: Etude Op. 31, 15

Sor: Etude Op. 6, 9

Sor: Etude Op. 6, 10

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Study in Tenths by Tedesco

Tedesco: Appunti, 11

Thirds

Sixths

Octaves

Tenths

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Intervals and their characteristics

Before looking at scales in harmony, I’d like to begin with a basic outline of intervals. Intervals have both a quality and a distance. There are five qualities of intervals:

While these are not all intervals possible in music, they are the ones that occur with the most frequency. Another level of hierarchy, based on consonance and dissonance, can be created out of these selected intervals and will be discussed soon.

Enharmonic tones:You might have noticed that certain intervals sound the same although use different notes. These are called enharmonic tones. Enharmonic intervals sound the same but are notated with different notes, for example C - Gb (diminished 5th) and C - F# (augmented 4th) sound the same but are notated differently. Why does such a thing exist?

Before equal temperament became established, many different tuning system were used. Some of these systems allowed for a different resulting sound between what are now enharmonic intervals (such as an augmented 4th and diminished 5th). This was reflected in instrument construction; both keyboards and lutes had split keys and frets to allow for playing notes “in-between” what equal temperament allows.

PerfectMajorMinor

DiminishedAugmented

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Compound Intervals:Now I would like to outline these common intervals when sounded greater than an octave. In this form they are called compound intervals.

All of the above intervals have been placed into two categories, indicated by colour. They are simply grouped into either a consonance, marked with yellow, or a dissonance, marked with purple.

Consonance and Dissonance:Consonant intervals are harmonious and pure intervals that have a restful quality; consonant sounds vibrate at ratios of low numbers, therefore their sound-waves contain few beats or few clashes (2:1 = an Octave, 2:3 = a 5th for example).  

Dissonant intervals contain tension and restlessness; their sound-waves literally contain more beats than consonances, as a result of sounds physically clashing at high ratios (approx. 15:8 = a Major 7th for example). Their tendency is to resolve to consonant intervals.

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There are five main types of dissonant-consonant paradigms that can be found in much of tonal music. They are:

a) 2 - 3b) 4 - 3c) 7 - 6d) 7 - 8e) 9 - 8

Typically, dissonances are played with force, weight and length and their consonant resolutions are soft and lifted in articulation and duration. The dissonance - consonance paradigms should be performed something like as follows:

Harmonizing:Notice the prevalence of 3rds and 6ths as resolutions? These are the most harmonious of intervals. Harmonize a melody with another kind of interval and you will end up with something either too dissonant (2nds and 7ths for example) or too hollow (4ths and 5ths for example).

Lagrima harmonized in 3rds: harmonious

Lagrima harmonized in 6ths: harmonious

Lagrima harmonized in 2nds: dissonant

Lagrima harmonized in 7ths: dissonant

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Octaves are somewhat exceptional and occur very frequently, but often with a neutral effect.

Tenths are the compound version of a third (pg. 3), and thus occur very frequently in music. This is in fact how Lagrima is harmonized. You can find many more examples in guitar music!

Lagrima harmonized in 4ths: hollow

Lagrima harmonized in 5ths: hollow

Lagrima harmonized in 8ves: neutral

Lagrima harmonized in 10ths: harmonious

Hopefully the examples have demonstrated why it’s important to practice the common intervals: 3rds, 6ths, 8ves, and tenths. By having these ingrained into your fingers, you will quickly see the abundance of these intervals in music. By also understanding the dissonant-consonant relationship (pg. 4), you will understand how these intervals function.

Lagrima: original harmonization

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Fingerings of Intervals

In his ‘Guitar Taught by a Simple Method’, Aguado provides the fingerings for each basic interval. This provides us with a great reference for playing all of the basic intervals on the guitar.

Common Intervals: 3rds, 6ths, 8ves, and 10ths

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Other Intervals: 4ths, 5ths, 2nds, and 7ths