Chords for Scales (lesson)

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[[Cetegory:Theory]]
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'''Chords For Scales by Andrew Cockburn'''
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== Introduction ==
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Hi GMCers - in this lesson we're going to take a look at how we match chords to scales, to give you an instant boost when writing songs or solos, and help you pick out musical sounding progressions.
 +
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One question that surfaces a lot is something along the lines of "I am using a scale of D Major, how do I know what chords I can use with that?". Before we delve into that, its worth reading my lesson on degrees of the scale here, as we will be using concepts from that lesson.
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== So, what chords can I use? ==
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If you are after a quick fix, then here you go ... for our example above, D Major, the standard musical theory answer might be:
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D, Em7 F#m7, Gmaj7, A7, Bmin, C#dim
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For the key of C, you would use:
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C, Dm7, Em7, Fmaj7, G7, Am, Bdim
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If you want a general rule based on degrees of the scale, it is as follows:
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I, IIm7, IIIm7, IVmaj7, V7, VIm, VIIdim
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Easy huh? But why is it that way? This is where the interesting stuff starts :)
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== Why Those Chords? ==
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Glad you asked ... what at first might seem an arbitrary and mysterious list of chords that work with a particular key, is in fact very simply understood when you couple an understanding of the notes in a scale with a few basic chord construction rules.
 +
 +
What we are doing, is building a series of chords out of notes taken only from the scale that we are interested in. When you think about it that makes a lot of sense, it means that not only are we selecting all of our melody notes from the scale, but the notes making up the chords are also selected from that same scale. Now, since we need a root note for each chord, we can make one chord for each note in the scale. A standard major scale for instance as we showed above has 7 distinct notes in it, hence we can find 7 chords that match that scale.
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So, our basic rule is that we take each root note in turn and figure out what chords we can make from it. From here on we'll stick with the scale of C for illustration purposes, but nothing I say is specific to that key unless I name notes. If you think about the function of each of the notes in the context of the scale you are using you can use the same rules to construct chords for any scale you can think of.
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== Chords For a C Major Scale ==
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OK, so the scale of C major has the following notes:
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C,D,E,F,G,A,B
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What chords can we make from that? What is a chord anyway? Well lets start simply and talk about triads. You can learn about triads in my lesson [https://www.guitarmasterclass.net/guitar_forum/index.php?showtopic=3342 here]. A triad is composed of 3 notes, most often a root, 3rd and 5th. The relationship of the intervals controls whether the triad is major, minor, augmented or diminished.
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Lets take a moment to review the degrees of the scale that make various different types of chord:
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Major : 1,3,5<br>
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Minor : 1,b3,5<br>
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Diminished : 1,b3,dim5<br>
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Augmented : 1,3,aug5<br>
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Minor 7th : 1,b3,5,b7<br>
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Major 7th : 1,3,5,7<br>
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Dominant 7th : 1,3,5,b7<br>
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Sixth : 1,3,5,6<br>
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Minor 9 : 1,b3,5,b7,9<br>
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Minor 11 : 1,b3,5,b7,9,11<br>
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Minor 13 : 1,b3,5,b7,9,11,13<br>
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== Back to the Scale ==
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To make our triads, we will start at the root note for the chord we are looking at, skip a note, take a note, skip a note, and take a note. That means we will be building a triad based on the root 3rd and 5th, starting from whatever your root note was. The interesting thing here is that as you move up the scale in selecting your root notes, the intervals between the notes shift, according to the formula for the scale (T T S T T T S for a major scale), this has the effect of changing the type of the triads we construct as the relationships between the notes shift slightly. Lets look at the complete list for the key of C:
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Starting with C:
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'''C''' D '''E''' F '''G''' A B C D E F G A B C
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Picking our 3 notes, we get C,E and G. The interval between C and E is a Major 3rd, C to G is a Perfect 5th. Our triad training tells us that a triad with a major 3rd and a perfect 5th is a major triad. Since our root note is C, our first chord is C major.
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Next, D:
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C '''D''' E '''F''' G '''A''' B C D E F G A B C
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Our 3 notes from the scale would be D, F and A. D to F is a minor 3rd, D to A is a major 5th. Minor 3rd + Major 5th = a Minor triad, so D minor is our second chord.
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The story is the same with E - E,G and B - Minor 3rd, Perfect 5th, so the chord is Em.
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C D '''E''' F '''G''' A '''B''' C D E F G A B C
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F and G are both Major 3rd + Perfect 5th, hence are major.
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C D E '''F''' G '''A''' B '''C''' D E F G A B C
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C D E F '''G''' A '''B''' C '''D''' E F G A B C
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A is back to a minor 3rd and perfect 5th, so we get A minor.
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C D E F G '''A''' B '''C''' D '''E''' F G A B C
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Finally B. Our notes are B, D and F. B to D is a minor 3rd, and B to F is a a diminished 5th - that relationship of notes makes our triad D diminished.
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C D E F G A '''B''' C '''D''' E '''F''' G A B C
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So, in triad terms, our chords for the scale of C are:
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C,Dm,Em,F,G,Am,Bdim
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Easy huh?
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== But That's Not Right! ==
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You said that the 2nd chord was Dm7 not Dm, and all of the other chords are wrong too what's going on? ... well spotted! This is where it gets really interesting. What we have described above is the simplest view of chords we can use to match a particular major scale. A triad is a simple as chords generally get (ignoring power chords), and from the basis above, we can add notes to the basic triads to get more complex chords. The only rule is that we must pick notes from the scale we are using, and when we realize this, the possibilities are literally endless!
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Lets revisit that first list I gave you:
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C, Dm7, Em7, Fmaj7, G7, Am, Bdim
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This selection of chords is quite commonly given as the list of chords for the C major scale - but its not the list, its just a list, we've already seen another slightly different list above. One important thing to note is that although the chords are different, their basic triad families will always remain the same - the 2nd will always be minor, the 7th will always be diminished, the 4th will always be major and so on - that comes out of our basic triad construction, but the flavour of the chords can be altered by adding notes.
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Now, what we have done in the list above is add notes to a few of the chords, to get more complex and flavorful chords. In the examples above, we have added a 7th to D, E, F and G. To add a 7th, we just skip an extra note above the 5th and add the next note.
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So for D:
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C '''D''' E '''F''' G '''A''' B '''C''' D E F G A B C
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We add a minor 7th, to get the chord Dm7.
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For E:
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C D '''E''' F '''G''' A '''B''' C '''D''' E F G A B C
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Again we add a minor 7th to get the chord Em7
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For F:
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C D E '''F''' G '''A''' B '''C''' D '''E''' F G A B C
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We are adding a major 7th, to get the chord FMaj7
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Finally for G:
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C D E F '''G''' A '''B''' C '''D''' E '''F''' G A B C
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We are adding a minor 7th, which when combined with our major 3rd gives us a a dominant 7th chord.
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Now we're just getting started - how about instead of a C major we use a C major 7th? Or a C6? Instead of a D Minor we can use a Dmin9, or even a Dmin11 or Dmin13 - they all fit our scale and stick to our rules! Using this technique we can fit hundreds of different chords to our scale - but equally we can keep it simple and stick with the basic triads.
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== Minor Scales ==
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Ok, how about minor scales? Well not surprisingly, the rules are exactly the same - stick to the notes in the scale, and move through the scale to generate your root notes.
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Lets look at a scale of A minor - I picked that for a reason, we'll see why in a minute.
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Our notes for the scale of A natural minor are:
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A,B,C,D,E,F,G
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Lets kick off with A:
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'''A''' B '''C''' D '''E''' F G A B C
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A minor ...
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Now B:
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A '''B''' C '''D''' E '''F''' G A B C
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B diminished ...
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This is starting to look a little familiar ... well yes, I picked Am because it is the relative minor of C, meaning it shares the same notes. This means that among other things, we will end up with exactly the same list of chords, just offset in order. If you work it through, you will find that the order of chords would be:
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Im, IIdim, III, IVm7, Vm7, VImaj7, VII7
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The order of chord types is the same, we just start at the 6th in the list and work through - why is this?
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== Scales Chords and Modes ==
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(You can skip this if you are unsure about modes)
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The answer lies in modes! The relative minor of a major key is actually the Aeolian mode - which is mode 6. So although we are using exactly the same notes, we offset the root note by 6 degrees, going from C to A. This also has the effect of offsetting the characteristic chords for each degree by 6 steps as we have seen. Modes also relate to the concept of chords for a scale in that the characteristic chords we have seen for each degree of the scale can also be regarded as characteristic chords for the modes for that degree.
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For example, you may have read that the characteristic chord of Dorian mode is the Minor 7th. Using the scale of C, we move up 1 degree to get D Dorian. Also, using the scale of C and stepping up to the chord we identified as being the chord of the second degree, we see it is Dm7 - it matches the chord type for Dorian! This of course is no coincidence, it just reflects the fact that when we are constructing chords for a scale in the way we described, since we have offset the root note we are actually in each case constructing a chord for the specific mode that is the degree of the scale we are working with. Another couple of examples:
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The characteristic chord for Mixolydian is a dominant 7th. Mixolydian is the 5th mode. Checking our list we find that the 5th chord is indeed a dominant 7th.
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The characteristic chord for Locrian is diminished. Locrian is the 7th mode, and checking the list we find that the 7th chord is diminished, so we can now say that we understand why each mode has its own characteristic chord type!
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== Other Scales ==
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We can apply the same rules to any scale - depending on the scale it can become harder to figure out valid chords but it is possible. Lets look at the harmonic minor as another example. The harmonic minor scale is characterized by the following intervals:
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1,2,b3,4,5,b6,7
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Or in formula terms:
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T S T T S T+1/2 S
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We'll work in A, so the notes would be:
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A,B,C,D,E,F,G#
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Now that tone and a half step between the 6th and 7th degrees is going to change the chords we are able to use against this scale - lets see how it works out. The first 2 chords will be identical to the natural minor scale, Am and Bdim. When we hit the 3rd root note, C, we are faced with these notes:
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A B '''C''' D '''E''' F '''G#''' A B C D E F G# A
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A major 3rd and an augmented 5th is an augmented chord.
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Looking at D:
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A B C '''D''' E '''F''' G# '''A''' B C D E F G# A
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A minor 3rd and a perfect 5th gives is a regular minor chord.
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Moving to E:
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A B C D '''E''' F '''G#''' A '''B''' C D E F G# A
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A major 3rd and a perfect 5th making a major chord.
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Next, F:
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A B C D E '''F''' G# '''A''' B '''C''' D E F G# A
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Another major 3rd and perfect 5th making a major.
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And finally G#:
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A B C D E F '''G#''' A '''B''' C '''D''' E F G# A
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A minor 3rd and a diminished 5th making, as we know, a diminished chord.
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So our sequence for A harmonic minor is:
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Am, Bdim, Caug, Dmin, E, F,G#dim
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Or in generic terms for the harmonic minor scale:
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Im, IIdim, IIIaug, IVmin, V, VI, VIIdim
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By now I hope you see where we are going with this, and the next time you encounter a strange scale, with a little work you should be able to come up with a list of chords to fit it!
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== Progressions ==
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Now that we have the chords for the scale, what shall we do with them? Lets build some progressions! Progressions are the building blocks of western music. There are very many combinations, but a few are so effective that they crop up time and again. I'll list a few here for you to try out, it is also possible to buy books that list endless chord progressions as an aid to songwriting.
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A lot of progressions start on the root or I, and involve the 5th or often the 4th, as in:
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I,IV,I
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I,V,I
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The 12 bar blues puts this together in a standard combination to get:
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I,I,IV,I,IV,IV,I,I,V,IV,I,V
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A lot of "doo wop" groups in the 50s added the 6th to get the standard sequence:
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I, VIm, IIm, V
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or
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I, VIm, IV, V
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Various pop songs use a I, IIIm, IV, V progression such as "True Love Ways" to mention Buddy Holly again, and "Take my Breath Away" by Berlin.
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Im, III, IV is used to good effect by Dire Straits in "Money for Nothing"
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A few notable songs like "Peggy Sue" by Buddy Holly and "It won't be long" by the Beatles use a flattened 6th as in:
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bVI, I, bVI, I.
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But the flat 6th isn't in the major scale, so what is going on here? I'm glad you asked, because we've just uncovered a very important point related to song writing.
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== Scales for Chords - An Alternative View ==
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Although the techniques we have discussed above are a very powerful way of picking chords to match a scale, a word of caution ... I tend to think that the initial question "what chords can I use for a scale?" actually misses the point slightly. If everyone who ever wrote a song asked the same question, some of the greatest songs in history would never have been written. The reason for this is that many songs don't stick to a specific scale, even between subsequent chords. Imagine a chord sequence that goes C, Ab, C, Ab - (using the flattened 6th as mentioned above) - a very powerful sounding riff, but those chords do not fit well into any usual scale. If you play the first chord, C, then say, "OK, I'm in the key of C major, what can I use next?" - Ab definitely wouldn't figure. So I am a fan of picking the chords first, then figuring out scales that work over them. In the case I gave, you would probably change scales from C major to Ab major and back, using the appropriate scale for each chord. With a little thought, you might be able to find a couple of scales and modes that would minimize the changes, but the point is that whilst fitting chords to a scale is a useful thing to know how to do, I would suggest that you think more in terms of what chords sound good together when writing riffs and solos.
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OK, that's it for this lesson - see you all on the forum!

Revision as of 16:45, 20 January 2009

Cetegory:Theory

Chords For Scales by Andrew Cockburn


Contents

Introduction

Hi GMCers - in this lesson we're going to take a look at how we match chords to scales, to give you an instant boost when writing songs or solos, and help you pick out musical sounding progressions.

One question that surfaces a lot is something along the lines of "I am using a scale of D Major, how do I know what chords I can use with that?". Before we delve into that, its worth reading my lesson on degrees of the scale here, as we will be using concepts from that lesson.

So, what chords can I use?

If you are after a quick fix, then here you go ... for our example above, D Major, the standard musical theory answer might be:

D, Em7 F#m7, Gmaj7, A7, Bmin, C#dim

For the key of C, you would use:

C, Dm7, Em7, Fmaj7, G7, Am, Bdim

If you want a general rule based on degrees of the scale, it is as follows:

I, IIm7, IIIm7, IVmaj7, V7, VIm, VIIdim

Easy huh? But why is it that way? This is where the interesting stuff starts :)

Why Those Chords?

Glad you asked ... what at first might seem an arbitrary and mysterious list of chords that work with a particular key, is in fact very simply understood when you couple an understanding of the notes in a scale with a few basic chord construction rules.

What we are doing, is building a series of chords out of notes taken only from the scale that we are interested in. When you think about it that makes a lot of sense, it means that not only are we selecting all of our melody notes from the scale, but the notes making up the chords are also selected from that same scale. Now, since we need a root note for each chord, we can make one chord for each note in the scale. A standard major scale for instance as we showed above has 7 distinct notes in it, hence we can find 7 chords that match that scale.

So, our basic rule is that we take each root note in turn and figure out what chords we can make from it. From here on we'll stick with the scale of C for illustration purposes, but nothing I say is specific to that key unless I name notes. If you think about the function of each of the notes in the context of the scale you are using you can use the same rules to construct chords for any scale you can think of.

Chords For a C Major Scale

OK, so the scale of C major has the following notes:

C,D,E,F,G,A,B

What chords can we make from that? What is a chord anyway? Well lets start simply and talk about triads. You can learn about triads in my lesson here. A triad is composed of 3 notes, most often a root, 3rd and 5th. The relationship of the intervals controls whether the triad is major, minor, augmented or diminished.

Lets take a moment to review the degrees of the scale that make various different types of chord:

Major : 1,3,5
Minor : 1,b3,5
Diminished : 1,b3,dim5
Augmented : 1,3,aug5
Minor 7th : 1,b3,5,b7
Major 7th : 1,3,5,7
Dominant 7th : 1,3,5,b7
Sixth : 1,3,5,6
Minor 9 : 1,b3,5,b7,9
Minor 11 : 1,b3,5,b7,9,11
Minor 13 : 1,b3,5,b7,9,11,13

Back to the Scale

To make our triads, we will start at the root note for the chord we are looking at, skip a note, take a note, skip a note, and take a note. That means we will be building a triad based on the root 3rd and 5th, starting from whatever your root note was. The interesting thing here is that as you move up the scale in selecting your root notes, the intervals between the notes shift, according to the formula for the scale (T T S T T T S for a major scale), this has the effect of changing the type of the triads we construct as the relationships between the notes shift slightly. Lets look at the complete list for the key of C:

Starting with C:

C D E F G A B C D E F G A B C

Picking our 3 notes, we get C,E and G. The interval between C and E is a Major 3rd, C to G is a Perfect 5th. Our triad training tells us that a triad with a major 3rd and a perfect 5th is a major triad. Since our root note is C, our first chord is C major.

Next, D:

C D E F G A B C D E F G A B C

Our 3 notes from the scale would be D, F and A. D to F is a minor 3rd, D to A is a major 5th. Minor 3rd + Major 5th = a Minor triad, so D minor is our second chord.

The story is the same with E - E,G and B - Minor 3rd, Perfect 5th, so the chord is Em.

C D E F G A B C D E F G A B C

F and G are both Major 3rd + Perfect 5th, hence are major.

C D E F G A B C D E F G A B C

C D E F G A B C D E F G A B C

A is back to a minor 3rd and perfect 5th, so we get A minor.

C D E F G A B C D E F G A B C

Finally B. Our notes are B, D and F. B to D is a minor 3rd, and B to F is a a diminished 5th - that relationship of notes makes our triad D diminished.

C D E F G A B C D E F G A B C

So, in triad terms, our chords for the scale of C are:

C,Dm,Em,F,G,Am,Bdim

Easy huh?

But That's Not Right!

You said that the 2nd chord was Dm7 not Dm, and all of the other chords are wrong too what's going on? ... well spotted! This is where it gets really interesting. What we have described above is the simplest view of chords we can use to match a particular major scale. A triad is a simple as chords generally get (ignoring power chords), and from the basis above, we can add notes to the basic triads to get more complex chords. The only rule is that we must pick notes from the scale we are using, and when we realize this, the possibilities are literally endless!

Lets revisit that first list I gave you:

C, Dm7, Em7, Fmaj7, G7, Am, Bdim

This selection of chords is quite commonly given as the list of chords for the C major scale - but its not the list, its just a list, we've already seen another slightly different list above. One important thing to note is that although the chords are different, their basic triad families will always remain the same - the 2nd will always be minor, the 7th will always be diminished, the 4th will always be major and so on - that comes out of our basic triad construction, but the flavour of the chords can be altered by adding notes.

Now, what we have done in the list above is add notes to a few of the chords, to get more complex and flavorful chords. In the examples above, we have added a 7th to D, E, F and G. To add a 7th, we just skip an extra note above the 5th and add the next note.

So for D:

C D E F G A B C D E F G A B C

We add a minor 7th, to get the chord Dm7.

For E:

C D E F G A B C D E F G A B C

Again we add a minor 7th to get the chord Em7

For F:

C D E F G A B C D E F G A B C

We are adding a major 7th, to get the chord FMaj7

Finally for G:

C D E F G A B C D E F G A B C

We are adding a minor 7th, which when combined with our major 3rd gives us a a dominant 7th chord.

Now we're just getting started - how about instead of a C major we use a C major 7th? Or a C6? Instead of a D Minor we can use a Dmin9, or even a Dmin11 or Dmin13 - they all fit our scale and stick to our rules! Using this technique we can fit hundreds of different chords to our scale - but equally we can keep it simple and stick with the basic triads.

Minor Scales

Ok, how about minor scales? Well not surprisingly, the rules are exactly the same - stick to the notes in the scale, and move through the scale to generate your root notes.

Lets look at a scale of A minor - I picked that for a reason, we'll see why in a minute.

Our notes for the scale of A natural minor are:

A,B,C,D,E,F,G

Lets kick off with A:

A B C D E F G A B C

A minor ...

Now B:

A B C D E F G A B C

B diminished ...

This is starting to look a little familiar ... well yes, I picked Am because it is the relative minor of C, meaning it shares the same notes. This means that among other things, we will end up with exactly the same list of chords, just offset in order. If you work it through, you will find that the order of chords would be:

Im, IIdim, III, IVm7, Vm7, VImaj7, VII7

The order of chord types is the same, we just start at the 6th in the list and work through - why is this?

Scales Chords and Modes

(You can skip this if you are unsure about modes)

The answer lies in modes! The relative minor of a major key is actually the Aeolian mode - which is mode 6. So although we are using exactly the same notes, we offset the root note by 6 degrees, going from C to A. This also has the effect of offsetting the characteristic chords for each degree by 6 steps as we have seen. Modes also relate to the concept of chords for a scale in that the characteristic chords we have seen for each degree of the scale can also be regarded as characteristic chords for the modes for that degree.

For example, you may have read that the characteristic chord of Dorian mode is the Minor 7th. Using the scale of C, we move up 1 degree to get D Dorian. Also, using the scale of C and stepping up to the chord we identified as being the chord of the second degree, we see it is Dm7 - it matches the chord type for Dorian! This of course is no coincidence, it just reflects the fact that when we are constructing chords for a scale in the way we described, since we have offset the root note we are actually in each case constructing a chord for the specific mode that is the degree of the scale we are working with. Another couple of examples:

The characteristic chord for Mixolydian is a dominant 7th. Mixolydian is the 5th mode. Checking our list we find that the 5th chord is indeed a dominant 7th.

The characteristic chord for Locrian is diminished. Locrian is the 7th mode, and checking the list we find that the 7th chord is diminished, so we can now say that we understand why each mode has its own characteristic chord type!

Other Scales

We can apply the same rules to any scale - depending on the scale it can become harder to figure out valid chords but it is possible. Lets look at the harmonic minor as another example. The harmonic minor scale is characterized by the following intervals:

1,2,b3,4,5,b6,7

Or in formula terms:

T S T T S T+1/2 S

We'll work in A, so the notes would be:

A,B,C,D,E,F,G#

Now that tone and a half step between the 6th and 7th degrees is going to change the chords we are able to use against this scale - lets see how it works out. The first 2 chords will be identical to the natural minor scale, Am and Bdim. When we hit the 3rd root note, C, we are faced with these notes:

A B C D E F G# A B C D E F G# A

A major 3rd and an augmented 5th is an augmented chord.

Looking at D:

A B C D E F G# A B C D E F G# A

A minor 3rd and a perfect 5th gives is a regular minor chord.

Moving to E:

A B C D E F G# A B C D E F G# A

A major 3rd and a perfect 5th making a major chord.

Next, F:

A B C D E F G# A B C D E F G# A

Another major 3rd and perfect 5th making a major.

And finally G#:

A B C D E F G# A B C D E F G# A

A minor 3rd and a diminished 5th making, as we know, a diminished chord.

So our sequence for A harmonic minor is:

Am, Bdim, Caug, Dmin, E, F,G#dim

Or in generic terms for the harmonic minor scale:

Im, IIdim, IIIaug, IVmin, V, VI, VIIdim

By now I hope you see where we are going with this, and the next time you encounter a strange scale, with a little work you should be able to come up with a list of chords to fit it!

Progressions

Now that we have the chords for the scale, what shall we do with them? Lets build some progressions! Progressions are the building blocks of western music. There are very many combinations, but a few are so effective that they crop up time and again. I'll list a few here for you to try out, it is also possible to buy books that list endless chord progressions as an aid to songwriting.

A lot of progressions start on the root or I, and involve the 5th or often the 4th, as in:

I,IV,I I,V,I

The 12 bar blues puts this together in a standard combination to get:

I,I,IV,I,IV,IV,I,I,V,IV,I,V

A lot of "doo wop" groups in the 50s added the 6th to get the standard sequence:

I, VIm, IIm, V

or

I, VIm, IV, V


Various pop songs use a I, IIIm, IV, V progression such as "True Love Ways" to mention Buddy Holly again, and "Take my Breath Away" by Berlin.

Im, III, IV is used to good effect by Dire Straits in "Money for Nothing"

A few notable songs like "Peggy Sue" by Buddy Holly and "It won't be long" by the Beatles use a flattened 6th as in:

bVI, I, bVI, I.

But the flat 6th isn't in the major scale, so what is going on here? I'm glad you asked, because we've just uncovered a very important point related to song writing.

Scales for Chords - An Alternative View

Although the techniques we have discussed above are a very powerful way of picking chords to match a scale, a word of caution ... I tend to think that the initial question "what chords can I use for a scale?" actually misses the point slightly. If everyone who ever wrote a song asked the same question, some of the greatest songs in history would never have been written. The reason for this is that many songs don't stick to a specific scale, even between subsequent chords. Imagine a chord sequence that goes C, Ab, C, Ab - (using the flattened 6th as mentioned above) - a very powerful sounding riff, but those chords do not fit well into any usual scale. If you play the first chord, C, then say, "OK, I'm in the key of C major, what can I use next?" - Ab definitely wouldn't figure. So I am a fan of picking the chords first, then figuring out scales that work over them. In the case I gave, you would probably change scales from C major to Ab major and back, using the appropriate scale for each chord. With a little thought, you might be able to find a couple of scales and modes that would minimize the changes, but the point is that whilst fitting chords to a scale is a useful thing to know how to do, I would suggest that you think more in terms of what chords sound good together when writing riffs and solos.

OK, that's it for this lesson - see you all on the forum!

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