As we saw in past Lesson , 12 musical notes that we use in the West to create music are separated from each other by a semitone.
This is the minimum unit with which we measure the difference in height (frequency) from a sound “X” to a sound “B”. And it is at this distance what we call Musical interval:
Musical Intervals are the distances between two notes, considering the number of semitones (and / or tones) that are in the «Journey» between one and the other.However, and as we will see in this lesson, intervals are not always expressed in tones and semitones. But there is a most common way of naming them.
But we go step by step.
Origin of musical intervals
The Origin of Intervals musical dates back to Hellenistic period of Greek culture, with the musical investigations and experiments of the Pythagorean school.
The Pythagoreans, through the monochord and the study of the vibration and movement of the strings, determined in a rational and quantitative way what was the harmonic relationship between two sounds. And they did it from the calculation of the distances between their frequencies.
That is, they began to speculate with numbers about the proportions of musicality, determining certain exact distances between two frequencies (intervals).
As a result, they determined distances (Intervals) that could be calculated through a small fraction or integer ratio. Some intervals that for their simplicity, mathematical accuracy and sense of harmony, are called Fair Intervals:
For example, if you shortened the length of a string just in half (1: 2), it would vibrate at twice its original frequency (2: 1) producing the same sound but higher.
These intervals of Eighth, Fifth Y Fair fourth, are considered as Perfect consonant intervals (they produce a pleasant sound for the ear), and constitute a fundamental basis in the construction of musical scales in practice most times and cultures.
But we insist, we will get to the scales in the next lesson. For now, it will be enough to study the Intervals in the Bass thoroughly, since they are the basis of everything else.
As we have just seen, musical intervals allow us classify sounds in binary form. Which means that the structure of an Interval It’s formed by 2 notes:
In the image we see that an interval is composed of one:
- Keynote: also know as First grade, is the first sound from which an interval is measured.
- Target note: any sound or note following the tonic, up to which an interval is measured.
What are Intervals for?
Although the main purpose of the intervals is indicate the distance between two notesKnowing them gives us much more in terms of musical compression.
And, thanks to them we can understand how the harmony and melody of a song. That is, among other things, musical intervals allow us to:
- Build scales.
- Know and identify the triads
- Form chords and combine them.
- Build or transport hues.
And, trust us, this is a must for any bass player who wants to learn how to create backing tracks, improvise, or compose songs knowing what they want to convey.
But before looking at them, it is interesting to consider how Intervals are measured. Because although they are all made up of semitones and / or tones, there are two ways of understanding and expressing them.
Yes, musical Intervals are measured in Semitones and Tones. And that’s it, that’s all. So, why did we say that there are two ways of expressing them?
Basically, because there are two ways to measure and understand the distance between two sounds
Chromatically, the 12 sounds are considered equally important, and they are separated by half tones, that is, we take as a reference what we call Chromatic Scale, where the distances are measured by the number of semitones between one note and another, so we would say that an Interval from one note to another is equal to “X” semitones.Diatonic
In diatonic form, priority is given to the 7 natural sounds regardless (to some extent) of whether a fret is sharp or flat. An F is an F, and an F is also an F.
That is, we take as a reference what we call Major Scale (diatonic), where the distances are measured in Degrees according to the number of notes from one to another with a different lexical Root. So we would say that an Interval is a 2nd, 3rd… or 8th of the first.Let’s put an example of this to see it more clearly.
Example to understand the Intervals in the Bass Guitar
To do this, take as a reference the following image, in which we represent the fingerboard of an electric Bass with the 12 musical notes (in exact terms, this is a Chromatic Scale), plus the double sound of the first one. In the image we see that C (C) is the tonic note (the first one played), and it is played on the 3rd fret of the 3rd string.
If we remember that the distance between fret and fret is a semitone (minimum unit of measurement of an interval), and we ask you what is the distance from C (C) to B (B), you have two ways to measure it and answer:
Count the semitones from one note to another: 11 semitones.Count the different notes from the first to the last: 7 notes.Why?
Measuring intervals in chromatic mode
In a chromatic mode, to calculate the distance from C (C) to B (B) you count all the semitones from one to the other.And no, it doesn’t matter if they are chromatic semitones (same root name), or diatonic (different root name). So, as each fret is half a tone, in this case you would say that from C to B there are 11 semitones (or that there are 5 tones and 1 semitone).
Measuring intervals in a diatonic mode
In a diatonic mode, to calculate the distance from C (C) to B (B) you count all the notes of different lexical Root.And yes, you ignore the chromatic semitones, or frets, between a note, its flats or sharps.What matters is the number of diatonic Tones and Semitones from one note to another. That is why you would not say that there are 11 semitones, but “there are 7 notes, there is a seventh” (which, in this case would be C, D, E, F, G, A and B, that is, the Major Scale). This is the explanation why if you ask different bassists what is the distance from C to D, you are very likely to receive two different answers (although in essence they are exactly the same):
Some will tell you that there is 1 semitone (or 12 tones) of distance, while others will say that there is a Minor Second (because from one note to the other you pass through 2 different sounds, which are “only” 1 semitone apart, but now we look at this “minor” thing in more detail).
And also, that’s why when we were learning the bass notes in lesson 3 we said that an octave is the same tonic note, but 12 semitones lower or higher, but for the moment it is important that you know how to visualize well these two ways of understanding the intervals, so, if we tell you what is the distance from C (C) to A (A), you know how to relate both answers.
Because you like one more, or you like the other more, you need to know them equally.are you clear? great, let’s see the Classification of the intervals to know how they are grouped, and what is “minor”, “major”, “just”, etc. among other aspects.Let’s go!
Classification of Musical Intervals
Knowing that an Interval can be expressed in semitones or tones, or number of notes of different lexical root, next we are going to see how both forms are combined to classify the intervals.that is to say, you must bear in mind that the musical Intervals are going to be Classified according to 2 aspects linked to each other:
Depending on the Quantity of notes.Depending on the Quality of their distances.Depending on the Quantity of notes in the distance from one sound to another, the Interval will take its own Name according to its numbering.While, depending on the quality of the distance between one sound and another, it will take a qualifier according to the tones and semitones between them.
How Intervals are classified.
First we number the Interval, and then we classify it:
- Interval Numbering
- Qualification of the Interval
- Interval Numbering
To classify musical Intervals according to quantity, we count the notes that are between one sound and another, including the ones that form that interval.But to define the name of the intervals we do not say there are 2 notes, or 5, but we use degrees through the feminine ordinal. That is to say, there is a second, or a fifth.Types of Interval Numerations
According to what we have just explained, we can define 8 possible numberings of Intervals:
- Unison (U)
- Second (2nd)
- Third (3rd)
- Fourth (4th)
- Fifth (5th)
- Sixth (6th)
- Seventh (7th)
- Eighth (8th)
In the case of the electric bass, and going back to the example we gave before (C major scale in the Bass), we would have the following Intervals:
2nd: there is a Second from C (C) to D (D) because two notes are numbered
3rd: there is a Third from C (C) to E (E) because three notes are numbered
4th: there is a Fourth from C (C) to F (F) because four notes are numbered
5th: there is a Fifth from C (C) to G (G) because five notes are numbered
6th: there is a Sixth from C (C) to A (A) because six notes are numbered.7th: there is a Seventh from C (C) to A (A) because six notes are numbered.
7th: there is a Seventh from C (C) to G (G) because five notes are numbered.7th 7th: there is a Seventh from C (C) to B (B) because seven notes are numbered.
8th: there is an Octave from C (C) to C (C) because eight notes are numbered.And you may ask, what about the unison?
This refers to two notes with the same frequency, that is, the same note. And you can execute it either by playing that note twice, or by playing it at the same time on two different strings. For example:
You can get the Unison (U) of D (D) by pressing the 5th fret of the third string twice, or by pressing at the same time the 5th fret of the third string, and the second string in the air.Qualification of Intervals.
But it is not enough to say whether an interval is a Second or a Seventh, it is necessary to specify the quality of that distance.Because from C (C) to E (E) there is a third, but in another key (starting from another tonic note), we also find intervals of third, but they do not have the same distance in semitones. For example:
C = E: there is a Third with 4 semitones (2 tones).E = G: there is a Third with 3 semitones (1 tone and 12 tone).C = Eb: there is a Third with 2 semitones (1 tone).Therefore, the expression of the Interval is incomplete if it is not attributed a Quality, which is defined according to the number of semitones between one sound and another. That is to say, we have to measure the Interval in chromatic mode to understand it.Types of Interval Ratings
Based on what we have just explained, we can define 5 ratings for the Intervals:
- Major (M)
- Minor (m)
- Just (J)
- Decreased (d)
- Augmented (A)
Again, visualizing the intervals on the bass fretboard, and following the example of the C major scale, we would have the following Qualified Intervals:
2nd Major: from C (C) to D (D) there is 1 Tone.
3rd Major: from C (C) to E (E) there are 2 Tones.
4th Just: from C (C) to F (F) there are 2 Tones and 1 Semitone.
5th Just: from C (C) to G (G) there are 3 Tones and 1 Semitone.
6th Major: from C (C) to A (A) there are 4 Tones and 1 Semitone.
7th Major C: from C (C) to B (B) there are 5 Tones and 1 Semitone.
8th Just: from C (C) to C (C) there are 6 Tones.
We recommend that you learn this equivalence well, because it will always be this way, independently of the note that marks the tonality:
It does not matter which tonic Note you choose to calculate an interval.
Whenever between two notes of different root there are two semitones, it will be an Interval of major 2nd; when between three notes of different root there are 4 semitones, it will be a major 3rd; between seven notes at eleven semitones of distance, there will be a major 7th; etc. So when is an interval given a minor, diminished or augmented qualifier? you can already sense it, right?
Table of Musical Intervals
Bassist, attentive, attentive. Because we are going to see one of the most important points of this Lesson, of the music theory in general, and of our Bass Course: the Table with all the musical Intervals.but having arrived here, and before seeing and explaining this table, it is important to make a series of clarifications to understand how the different Intervals are calculated and expressed.it is necessary to relate everything we have seen in previous points.calculation scheme of the musical Intervals.
The first thing we want to clarify is that, the qualifiers do not apply to all numbering equally:
“Major and Minor” apply to Seconds, Thirds, Sixths and Sevenths. “Just” only says to the Unison, Fourths, Fifths and Octaves. “Diminished and Augmented” applies to any, except the unison which has no diminished. Although in 2nd, 3rd, 6th and 7th, we consider them exceptional cases (the most normal is that they are major or minor, and you are rarely going to see them diminished or augmented. Although they exist, they do exist).
Thus, and before looking at the Table of Musical Intervals, it is interesting to observe how the qualifiers are related to each other, taking into account their distance in semitones:
Major (M): all Major Intervals have 1 semitone more than their Minor (m), and 1 tone more than their Diminished (d).Minor (M): all Minor Intervals have 1 semitone less than their Major (M), and 1 tone less than their Augmented (A).Just (J): they are the Unison, 4th, 5th and 8th Intervals, also called perfect.
Diminished (d): all diminished Intervals have 1 semitone less than their Just (J) or their Minor (m), 2 less than their Major (M), and 3 less than their Augmented (A).Augmented (a): all augmented Intervals have 1 semitone more than their Just (J) or their Major (M). 2 more than its Minor (r), and 3 more than its Diminished (d).our suggestion is that you review this classification and calculation scheme before looking at the different intervals.because understanding the relationship between their numbering and their rating is FUN-DA-MEN-TAL to understand the different intervals in the bass individually.Table of Musical Intervals.
If with the above scheme in hand, we measure and order the Intervals according to the different combinations of numberings and possible qualifiers, we obtain the following Table of Musical Intervals:
Interval Diminished Minor Minor Just Major Augmented Major Augmented
Second – 1sT – 2sT 3sT
Third 2sT 3sT – 4sT 5sT
Fourth 4sT – 5sT – 6sT
Fifth 6sT – 7sT – 8sT
Sixth 7sT 8sT – 9sT 10sT
Seventh 9sT 10sT – 11sT 12sT
Octave 11sT – 12sT – 13sT
sT = Semitone of distance starting from the Tonic Note.As you can see in the Table of Musical Intervals, within the scope of an Octave (12 semitones) we have a total of 24 Musical Intervals. And they are the following:
List of Musical Intervals
Major (M): 1 tone away.
Minor (m): 1 semitone away
Augmented (A): 1 tone and 1 semitone away
Major (M): 2 tones away
Minor (m): 1 tone and 1 semitone distance (the same as a 2A, but with three notes of different root). Augmented (A): 2 tones and 1 semitone distance.
Diminished (d): 1 tone distance (same as a 2ªM, but with three notes of different root).4ths (4ª):
Just (J): 2 tones and 1 semitone away (same as a 3rdA, but with four notes of different root).Augmented (A): 3 tones away.
Diminished (d): 2 tones away (same as a 3ªM, but with four notes of different root).5ths (5ª):
Just (J): 3 tones and 1 semitone distance.
Augmented (A): 4 tones of distance.
Diminished (d): 3 tones of distance (the same as a 4th A, but with five notes of different root).Sixths (6th):
Major (M): 4 tones and 1 semitone distance.
Minor (m): 4 tones away (same as a 5th A, but with six notes of different root).Augmented (A): 5 tones away.
Diminished (d): 3 tones and 1 semitone distance (same as a 5thJ, but with six notes of different root).7ths (7th):
Major (M): 5 tones and 1 semitone distance.
Minor (m): 5 tones away (same as a 6thA, but with seven notes of different root).Augmented (A): 6 tones away.
Diminished (d): 4 tones and 1 semitone distance (same as a 6thM, but with seven notes of different root).Octaves (8th):
Just (J): 6 tones of distance.
Augmented (A): 6 tones and 1 semitone distance.
Diminished (d): 5 tones and 1 semitone of distance (the same as a 7th M, but with eight notes of different root).Fundamental intervals (most common).
Now, from all this classification we have just made, the fundamental intervals you should learn are:
2nd, 3rd, 6th and 7th Major and minor.
4th Just and augmented
5th Righteous, diminished and augmented
Why? Because they are the most common. Cases like augmented seconds, diminished thirds, etc. are particular cases (so to speak), which depend on the initial key.For example: the note B (B) on the 7th fret of the 4th string is repeated on the 2nd fret of the 3rd string.
The Interval is always the same, regardless of where you start.
So be prepared, because the “only” thing you have to do is to know the positions of each interval to know that, no matter which fret you start at, you will always have the same interval.
For example: if you start from a 1st fret, and you move just one string below, and one fret less (to the left), it is always a Major Third (3rdM). That is to say, between those two frets (notes) there are always 2 tones of distance.
NOTE: to show the examples we take as tonic note middle C (C) at the 8th fret of the 4th string, but these intervals are played in the same way starting from any other note.
Second Intervals (2nd) in the Bass Guitar
Second Intervals on the fundamental electric bass can be played in 2 different positions.
Which one you choose depends on whether you are looking for the harmonic or melodic 2nd Interval.
Minor Second on the Bass (2ªm)
1 sT away from C is its 2ndm.
Major Second in the Bass (2ªM)
At 1 T away from C is its 2ndM.
Bass Third (3rd) Intervals
The fundamental Electric Bass Third Intervals can be played in 2 different positions.
Which one you choose will depend on whether you are looking for the harmonic or melodic 3rd Interval.
Minor Third on the Bass (3rdm)
1.5 T away from C is its 3rd m.
Major Second in the Bass (2ªM)
At 2 T away from C is its 3ªM.
Fourth Intervals in the Bass (4th)
Fourth Intervals on the Electric Bass can be played in 1 position, either to play a harmonic or melodic 4th Interval.
Just Fourth on Bass (4thJ)
2.5 T away from C is its 4thJ.
Augmented Fourth in the Bass (4thA)
At 3 T away from C is its 4thA.
Intervals of Fifth (5th) in the Bass
Fifth Intervals on the electric Bass can be played in 1 position or 2, either to play a harmonic or melodic 5th Interval.
Righteous Fifth on the Bass (5thJ)
3.5 T away from C is its 5thJ.
Augmented Fifth in the Bass (5thA)
Intervals of Sixth (6th) in the Bass
Sixth Intervals on the fundamental electric Bass are usually played in 1 position, either to play a harmonic or melodic 6th Interval.
Minor Sixth in the Bass (6th m)
At 4 T away from C is its 6th.
Major Sixth in the Bass (6ªM)
At 4.5 T away from C is its 6thM.
Intervals of Seventh (7th) in the Bass
Seventh Intervals on the fundamental electric Bass are played in 1 position, either to play a harmonic or melodic 7th Interval.
Minor Seventh in the Bass (7thm)
5 T away from C is its 7thm.
Major Seventh in the Bass (7thA)
At 5.5 T away from C is its 7thM.
Intervals of Octave (8th) in the Bass
Octave Intervals on the fundamental electric Bass are played in 1 position, either to play a harmonic or melodic 8th Interval.
Just Octave on Bass (8thJ)
6 T away from C is its 8thJ.
Bass Interval Considerations
If you have followed this lesson carefully, you will have noticed that, among the intervals we have just seen in the bass, two would be missing if we take C (C) as the tonic.