Lesson #5: Intervals, Scale Degrees, Roman Numeral Analysis & Figured Bass

Check out Lesson #4 here: http://paulfredericksmusic.com/lesson-4-minor-scales-minor-keys-relative-minor-inversions/

Welcome to lesson #5 Today we will be looking at intervals, scale degrees, roman numeral analysis and figured bass.

So over the past few lessons we have looked at the major, and minor scale. The major, minor, and diminished triads/chords. Inversions, how to read treble and bass clef, as well as key signatures, and how chords fit within the key.

All of this information will be important in this lesson.

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Let us begin where we usually do, the C Major Scale.

The C Major scale has no sharps or flats within it’s key, it is only the 7 natural lettered note major scale and is also all the white keys on a piano so it’s a great visual representation of these ideas.

C-D- E-F- G-A-B-C1-2- 3-4- 5-6- 7- 8

I’ve used these numbers before in previous lessons, I’m basically numbering the notes of the scale, this idea is called scale degree. It represents what note is in what position within the scale you’re talking about, in this case the major scale, and more specifically the C Major Scale.

So if I say the 6th note of C Major that means the letter A. But the 6th note in G Major would be E.

We also figured out that since we have 7 unique notes within one major scale, we can have 7 triads built upon the notes within the scale/key.

As such:

1-3-5 = C-E-G = C Major

2-4-6 = D-F-A = D Minor

3-5-7 = E-G-B = E Minor

4-6-8 = F-A-C = F Major

5-7-9 = G-B-D = G Major

6-8-10 = A-C-E =A Minor

7-9-11 = B-D-F = B Diminished

Well now we will push this step one step further.

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So I can talk about the scale degree of a scale, but I can also talk about a scale degree and it’s triad built upon it, using roman numerals. Our Roman numerals for this scenario only use 7 numbers, 1-7. This is because this scale only has 7 unique notes.So in a past lesson we figured out the Major Scale’s chords from root-7 will always go in this order:1=C Major Triad2=D Minor Triad

3=E Minor Triad

4=F Major Triad

5=G Major Triad

6=A Minor Triad

7=B Diminished Triad

So we can use Roman Numerals to talk about each triad and it’s quality type:

I-II-III-IV-V-VI-VII – Major Roman Numerals = Capitol “I” = Major Chord

I-ii-iii-iv-v-vi-vii – Minor Roman Numerals = lowercase “i” = Minor Chord

So our Major Scale Chord Progression is:I-ii-iii-IV-V-vi-vii

Now our Minor Scale Chord Progression is:i-ii-III-iv-v-VI-VII

So I can create a chord progression, using the Roman Numerals, and you can figure out that progression in multiple keys

Example: I-vi-ii-V-I = 1-6-2-5-1 in Maj

C Major = I=CM, vi=Am, ii=Dm, V=GM, I=CM: ( C – Am – Dm – G – C )

G Major = I=GM, vi=B=Em, ii=Am, V=DM, I=GM: ( G – Em – Am – D – G )

F Major = I=FM, vi=Dm, ii=Gm, V=CM, I=FM: ( F – Dm – Gm – C – F )

I can create the same progression but in a minor key:

Example: i-VI-ii-v-i = 1-6-2-5-1 in Min

C Minor = i=Cm, VI=AbM, ii=D dim, v=Gm, i=Cm: ( Cm – AbM – Ddim – Gm – Cm )

G Minor = i=Gm, VI=EbM, ii=A dim, v=Dm, i=Gm: ( Gm – EbM – Adim – Dm – Gm )

F Minor = i=Fm, VI=DbM, ii=G dim, v=Cm, i=Fm: ( Fm – DbM – Gm – Cm – Fm )

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So now we can talk about intervals. Intervals are very similar to scale degree. Scale degree tells you what position within a scale.

Intervals tell you the exact distance between two notes, so an interval can tell you the exact distance to any quality note. (Sharp, natural, or flat).

Example and explanation:

Let’s paste that C Major scale here again.

C- D-E-F- G- A-B-C1- 2- 3-4- 5- 6-7- 8

So this is how we can look at intervals.

First we can look at from 1-1, then 1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 1-8. Within a major scale.

1-1 = C-C = Perfect Unison (Same note)1-2 = C-D = Major 2nd (1 whole step)1-3 = C-E = Major 3rd (2 whole steps)1-4 = C-F = Perfect 4th (2 whole steps + 1 half step)1-5 = C-G = Perfect 5th (3 whole steps + 1 half step)1-6 = C-A = Major 6th (4 whole steps + 1 half step)1-7 = C-B = Major 7th (5 whole steps + 1 half step)1-8 = C-C = Perfect Octave (6 whole steps)

So as you can see certain types of whole steps and half steps = a specific interval. These specific intervals are within all Major scales. Just like the chord progression and scale degrees stay consistent within all major scales.

So now let us look at a minor scale:

1-1 = C-C = Perfect Unison (Same note)1-2 = C-D = Major 2nd (1 whole step)1-b3 = C-Eb = Minor 3rd (1 whole step + 1 half step)1-4 = C-F = Perfect 4th (2 whole steps + 1 half step)1-5 = C-G = Perfect 5th (3 whole steps + 1 half step)1-b6 = C-Ab = Minor 6th (4 whole steps)1-b7 = C-Bb = Minor 7th (5 whole steps)1-8 = C-C = Perfect Octave (6 whole steps)

So this is where the names of the major and minor scale come from, from the intervals used within its scales formula.

Quality Types:

At the moment we only see Major, Minor, and Perfect Intervals. These are called Interval Qualities. These are the most common of intervals.

We also have another 2. Diminished & Augmented.

So we have Major and Minor.

When we go from Major to Minor we go from bigger to smaller. So we go down by a half step.

Vice Versa if we go from Minor to Major we go from smaller to bigger, so we go up by a half step.

Augment also means to raise, make wider, make even bigger. So we would take a major interval and go up by a half step.

Diminished means to make it even smaller. So we would take a minor interval and go down by a half step.

Perfect intervals are unique and interesting. The Unison and Octave are a bit of an obvious Perfect Interval. Root-Root/Root-Octave. It’s the same note, doesn’t get any smaller of an interval then itself.

Now the Perfect 5th and Perfect 4th are interesting because they invert into themselves.

A Perfect 5th is 3 whole steps + 1 half step. C-G

A Perfect 4th is 2 whole steps + 1 half step. C-F

Let’s flip them.

G-C & F-C

G-C = 2 whole steps + 1 half step = a Perfect 4th.

F-C = 3 whole steps + 1 half step = a Perfect 5th.

Plus if you count DOWNWARDS they invert again.

C-G

C-B-A-G

8- 7-6-5

C-B = 1 half stepB-A = 1 whole stepA-G = 1 whole step1 + 1 . 5 = 2 whole steps + 1 half step = Perfect 4th

C-F

C-B-A-G-F

8- 7-6-5- 4

C-B = 1 half stepB-A = 1 whole stepA-G = 1 whole stepG-F = 1 whole step

1+1+1+.5 = 3 whole steps + 1 half step = Perfect 5th.

Plus the perfect 4th and Perfect 5th appear in 6/7 modes.All major and minor modes, but the diminished mode has a diminished 5th. Which is where the name comes from. This will be explained in a future lesson more.

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So 1 can be a perfect interval with itself. A Perfect Unison. (C-C)But it can interestingly also be diminished and augmented, like so:C-Cb, C-C#1-b2 = half step down, -h/-1?1-#1 = half step upOnce again very rare and will probably never be seen but good to know if you plan on studying theory.—————————————–

2 can be major, minor, augmented, or diminished.

1-2 = major 2nd, 1-b2 = minor 2nd, 1-#2 = augmented 2nd, 1-bb2 = diminished 2nd.C-D, C-Db, C-D#, C-Dbb

1-2 = Whole step = major 2nd1-b2 = half step = minor 2n1-#2 = whole step + half step = augmented 2nd1-bb2 – ?? This is actually the same as the unison. Since a minor 2nd lowers it by 1 half step, a diminished 2nd would lower the note by 2 half steps which would just go back to itself.

Some intervals you will never see but it’s still good to understand them.

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3 can be major, minor, augmented, or diminished.

1-3 = major 3rd, 1-b3 = minor 3rd, 1-#3 = augmented third, 1-bb3 = diminished 3rdC-E, C-Eb, C-E#, C-Ebb

1-3 = 2 whole steps = major 3rd1-b3 = 1 whole + 1 half step = minor 3rd

1-#3 = 2 whole + 1 half step = augmented 3rd

1-bb3 = 1 whole step = diminished 3rd

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4 can be Perfect, Diminished or Augmented.1-4 = perfect 4th, 1-b4 = diminished 4th, 1-#4 = augmented 4thC-F, C-Fb, C-F#

1-4 = 2 whole steps + 1 half step1-b4 = 2 whole steps1-#4 = 3 whole steps

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5 can be Perfect, Diminished, or Augmented.

1-5= perfect 5th, 1-b5 = diminished 5th, 1-#5 = augmented 5thC-G, C-Gb, C-G#

1-5 = 3 whole steps + 1 half step1-b5 = 3 whole steps1-#5 = 4 whole steps—————————————–

6 can be Major, Minor, Augmented, or Diminished.1-6 = major 6th, 1-b6 = minor 6th, 1-#6 = augmented 6th, 1-bb6 = diminished 6thC-A, C-Ab, C-A#, C-Abb

1-6 = 4 whole steps + 1 half step1-b6 = 4 whole steps1-#6 = 5 whole steps1-bb6 = 3 whole steps + 1 half step—————————————–

7 can be Major, Minor, Augmented, or Diminished.1-7 = major 7th, 1-b7 = minor 7th, 1-#7 = augmented 7th, 1-bb7 = diminished 7thC-B, C-Bb, C-B#, C-Bbb

1-7 = 5 whole steps + 1 half step1-b7 = 5 whole steps1-#7 = 6 whole steps1-bb7 = 4 whole steps + 1 half step

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8 can be Perfect, Diminished, or Augmented.

1-8= perfect 8th, 1-b5 = diminished 8th, 1-#5 = augmented 8th *8th or octave*C-C, C-Cb, C-C#

1-8 = 6 whole steps1-b8 = 5 whole steps + 1 half step1-#8 = 6 whole steps + 1 half step

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In simple terms:

Perfect Intervals = 1,4,5,8Major/Minor Intervals = 2,3,6,7

Augmented/Diminished Intervals = ALL = 1,2,3,4,5,6,7,8

If you raise a perfect interval by a half step it becomes Augmented.If you lower a perfect interval by a half step it becomes diminished.If you raise a major interval by a half step it becomes Augmented.If you lower a major interval by a half step it becomes minor.

If you lower a minor interval by a half step it becomes diminished.(If you raise a minor interval by a half step it becomes major)

Augmented>Perfect>Diminished

Augmented>Major>Minor>Diminished

This is a big overview but I mostly talked about ascending intervals, next week we will do more descending intervals. All the info is the same, if we go down by a whole step that is a major 2nd downward.

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Let’s now talk a bit about figured bass which ties in a lot of this information. We will not be talking about 7th chords this lesson but we will be next lesson!

Finally we get to figured bass which puts intervals and roman numerals together. There’s also a bit of “lead sheet” theory within this, and a bit of roman numeral/figured bass within “lead sheet” info so there’s a lot of overlap in this section.

First figured bass is a way of analyzing music by not only using roman numerals, but also inversion numbers, as well as extension numbers added onto the roman numerals.

So for today’s lesson we will be talking about only triads, their inversions, major/minor/diminished/& augmented triads, symbols used to notate different types of chords.

Let’s start with a quick review of our types of triads:Major, Minor, Diminished, and Augmented.

Here are some versions/variations of ways you might see these chord/symbols.

Remember major triads will usually be a capitol Roman Numeral.I, II, III, IV, V, VI, VII

Minor triads will be lowercase Roman Numerals.

i, ii, iii, iv, v, vi, vii

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Now Augmented and diminished don’t change from capital or lowercase roman numerals.

A diminished triad has a minor third, so it will still use the lower case roman numeral.

Then you may see the word diminished, .dim, or a full tiny circle to its upper right.

So here is as an example of how the diminished triad would look.

vii diminished, vii dim, viiO

Just because there is only 1 diminished chord within a major or minor scale, does not mean we can’t change other triads to diminished triads. It’s very common to borrow chords and key change within a song so you can still use roman numerals to make it understandable as a progression.

So I can have a ii dim chord for example. In the key of C that would be D diminished which would be D-F-Ab (Ab is not in the key of C) but Ab is in the key of C minor so we “borrowed” it from our parallel minor.

Now the Augmented triad has a major third, so it will still use the capital roman numeral.

Then we add a plus sign to it, which means to add/to raise which is what augmented also means.

So there are no naturally occurring augmented chords in major or minor scales so they are usually dissonant sounding, but it also depends on what chords come before and after.IV+ could be an example of an augmented triad. IV+ in the key of C Major would be 4= F,F+ = F Augmented = F-A-C# (once again C# is not in the key of C major)

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Finally we would get to inversion numbers. So we learned previously about inversions and how it’s just a different configuration of the same notes within a chord. We can also use specific numbers in a specific visual way that would let the reader/player know what inversion chords are played in.

Let’s take a look at our major and minor triads first.

C-E-G = C Major1- 3-5

C-Eb-G = C Minor1- 3- 5

C-G = perfect 5th (1-5)C-E = major 3rd (1-3)

C-G = perfect 5th (1-5)

C-Eb = minor 3rd (1-b3)

So a 5/3 would be a root position triad. It is telling us how far our bass note is to our other notes in our chord. If C is in the bass then we are 5 away from G and 3 away from E.

I 5/3 for example would just be a C major chord in root position.

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Let us now look at our first inversion.

E-G-C = C Major 1st inversion3- 5-1

Eb-G-C = C Minor 1st inversion3 – 5-1

First inversion is where we put the 3rd of the chord into the bass (lowest voicing).

E-C = minor 6th (3-8)E-G = minor 3rd (3-5)

Eb-C = major 6th (b3-8)Eb-G = major 3rd (b3-5)

So then we would count from the lowest voicing/whatever is in the bass. Almost as if it’s the root, and we count the distance from there outward.

So a 6/3 would be a triad within its first inversion meaning the 3rd of the chord is in the bass.I 6/3 for example would mean a major I chord in it’s key, but also within it’s first inversion.

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Lastly we have our 2nd inversion.

G-C-E = C Major 2nd Inversion5- 1-3G-C-Eb = C Minor 2nd Inversion5- 1 -3

Second inversion is where we put the 5th of the chord into the bass (lowest voicing).

G-E = major 6th (5-10)G-C = major 4th (5-8)

G-Eb = minor 6th (5-b10)G-C = major 4th (5-8)

So a I 6/4 for example would mean a major I chord in it’s key but also within it’s first inversion.

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Quick Review: all 4 chord types, with all 3 inversions. Major, augmented, minor, diminished.

IVIV 6/3IV 6/4IV+IV+ 6/3IV+ 6/4iviv 6/3

iv 6/4iv dim

iv dim 6/3

iv dim 6/4

Here are a few examples of taking one type of roman numeral and putting it into all 4 types of triad types, as well as all 3 positions using it’s inversions.

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Here is an entire chord progression with it’s figured bass written in.https://imgur.com/Fo0UmFa

Here are 2 examples for you to do on your own.One will only have letters on the staffs and you will need to fill in the figured bass.The second will only have figured bass and you will need to fill in the sheet music.

Remember you will need to:Read both bass and treble clef.Understand/read key signatures.Understand how chords in key work/how to build triad types.How to notate/write/read figured bass and roman numerals within music.

Example one: No figured Bass. – https://imgur.com/880jSKF

Example two: No Music. – https://imgur.com/4XYaHiK

Check out this link here to get the .png, .pdf, .midi, and musescore files.

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Next week we will look into 7th chords, 7th chord inversions, suspension chords, reading lead sheets, and more figured bass using 7th chords.