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What are these chords
#3026231 09/18/20 02:39 AM
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Hi,

I have been away from the forum for a long time now, but in the meanwhile started taking lessons. My teacher is currently covering chords in different major scales. But I do not understand the pattern of the chords. I asked him, but he did not give any clear answer, other than that these chords have last note as the note in the scale. For example, C major chords are EGC, GBD, GCF, ACF, CEG, CFA, DGB and EGC. D major is having F#AD, AC#E, ADF#, BDG, DF#A, DGB, EAC# and F#AD.

But my problem is that I am not able to understand the pattern of these chords. I do not know how to form chords in different scales. Can anyone help me in understanding how these chords are formed?

Thanks,
Manish


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Re: What are these chords
ManishP #3026236 09/18/20 02:55 AM
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Let's go through them:

EGC: C maj 1st inversion
GBD: G maj root position
GCF: C maj + suspended 4th
ACF: F maj 1st inversion
CEG: C maj root position
CFA: F maj 2nd inversion
DGB: G maj 2nd inversion
EGC: C maj 1st inversion

So, you're going through a chord progression: I-V-Isus4-IV-I-IV-V-I.

I think it's better to start by learning the chords in all inversions then it's going to make more sense.

Re: What are these chords
ManishP #3026248 09/18/20 03:34 AM
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A chord is formed from the tonic, the dominant and the mediant. This is the order of the notes in the harmonic series. (I'm sticking only with triads for this.)

The primary chords of a key are the tonic, the dominant (a fifth above) and the subdominant (a fifth below). (These are the adjacent keys in the circle of fifths; the dominant is one chord clockwise and the subdominant is one chord anticlockwise.)

In C Major, the primary chords are C Major, G Major and F Major. The notes, in root positions, are C-E-G, G-B-D and F-A-C. If we arrange the notes in a step-wise pattern we generate the C Major scale, C-D-E-F-G-A-B-C.

Note that the scale comes from the chords, not the other way around, and the chords come from the Harmonic Series though you can, of course, use the scale to generate the chords.
________________________

Chords with the fundamental note in the bass are in root position. When the mediant is the bass note the chord is in first inversion and when the fifth is in the bass the chord is in second inversion.
________________________

Ascending the scale with the scale notes in the bass we can use the primary chords:
C-E-G, D-B-G, E-G-C, F-A-C, G-B-D, A-C-F, B-D-G and back to C-E-G.

With the scale note as the top of the chord we get:
E-G-C, B-G-D, G-C-E, A-C-F, B-D-G, F-C-A, D-G-B and back to E-G-C
but this is an unusual exercise, musically, unless the root note is added below, usually in the left hand. I don't see the purpose of this exercise without first having covered more chord theory.

C and G appear in two of the primary chords so we have a choice of harmonisation. All the other notes appear in only one primary chord.

Qazsedcft: The GCF is a typo since the OP comments that the top notes form the scale.


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Re: What are these chords
ManishP #3026255 09/18/20 04:18 AM
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Originally Posted by ManishP
I do not know how to form chords in different scales. Can anyone help me in understanding how these chords are formed?

It's hard to know how much you know, so apologies if I'm insulting your intelligence. But are you aware of the concept of scale degree and transposition?

Each note in a scale has a "degree". 1 is the root note scale degree and it and increases up from there. So;

In the key of C, C=1, D=2, E=3, F=4, G=5 and so on
In the key of F, F=1, G=2, A=3, Bb=4, C=5 and so on.

The musical system we use means that you can move any sequence of notes from one scale / key to another (transpose) and as long as they have the same scale degrees they will sound the same relative to each other.

So your EGC in the key of C uses notes of scale degree 3, 5 and 1 in that order. If you want to form them in the key of F, you just use scale degree 3, 5 and 1 of F. That gives you A, C and F. That's it. As simple as that. All you need to know is the destination scale and its order. You must use any sharps or flats that occur in the scales.

You don't even need to understand anything about inversions or chord harmonic functions although obviously it is desirable to learn this eventually.


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Re: What are these chords
ManishP #3026308 09/18/20 08:30 AM
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I recommend taking one of the courses in music theory in Coursera.
It’s free (you pay if you want a certificate). You can learn the basics of music theory in your own pace.

Re: What are these chords
ManishP #3026390 09/18/20 12:08 PM
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I think the starting point is knowing the pattern of at least the major and minor scales. Then triads, major, minor, then inversions.

Re: What are these chords
ManishP #3026435 09/18/20 02:17 PM
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Chords are formed from a note, the note 2 higher and a note 4 higher. For instance C+E+G or A+C+E or G+B+D

Try this on your piano, it gives you nice sounds and you can pick any lowest note.

The notes are always taken from the key you are in. So if they key is E major, you have the notes E,F#,G#,A,B,C#,D#. So E major chords do not use F, G, Bflat, C and D.

and then an example chord in this key could be G#+B+D#

Chords are numbered I,II,III,IV,V,VI and VII according to the lowest note of the chord

So if you have the E major again as above, the I chord is E+G#+B and V=B+D#+F#

The I, IV and V are very often used and have special names tonic, subdominant and dominant.

You can alter these chords, these are called "inversions", "7th chords", "9th chords" etc. I can explain that also if you like this approach.


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Re: What are these chords
ZigZagStory #3026536 09/18/20 06:43 PM
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Originally Posted by ZigZagStory
I recommend taking one of the courses in music theory in Coursera.
It’s free (you pay if you want a certificate). You can learn the basics of music theory in your own pace.

+1.

What we're doing in these posts is like developing music theory as a collage:

. . . Every post has a little piece of it.

It might be better to learn it as a coherent whole. This is a question to discuss with your teacher:

. . . He/she probably gave you material that you weren't equipped to absorb, yet.


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Re: What are these chords
zrtf90 #3026578 09/18/20 11:09 PM
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Hello All,

Many thanks for the answers.

I would like to clarify certain points:

1. My question was specific to the chord pattern that I had posted in my original post. The reason was, when my teacher gave me those patterns to practice, he also mentioned that I should be able to form the pattern on my own for other scales. But I could not - and when I asked him to explain to me, he could not explain very clearly.

2. I checked on the Internet and saw the standard major chords and progressions for scales, but could not find anywhere chords formed in such a way that the last note was the note of the scale (teacher mentioned that this is the first inversion of chord and I understand inversions, but keeping aside inversions for the moment, I did not come across any site where chords were explained in such a manner that all the first notes were scale notes).

Originally Posted by wouter79
Chords are numbered I,II,III,IV,V,VI and VII according to the lowest note of the chord

So if you have the E major again as above, the I chord is E+G#+B and V=B+D#+F#

The I, IV and V are very often used and have special names tonic, subdominant and dominant.

You can alter these chords, these are called "inversions", "7th chords", "9th chords" etc. I can explain that also if you like this approach.


Exactly - I came across this and have understanding of inversions (first, second).


Originally Posted by zrtf90
Note that the scale comes from the chords, not the other way around, and the chords come from the Harmonic Series though you can, of course, use the scale to generate the chords.

This is a new line of thinking for me - I have always thought that chords come from scales.

Originally Posted by zrtf90
Ascending the scale with the scale notes in the bass we can use the primary chords:
C-E-G, D-B-G, E-G-C, F-A-C, G-B-D, A-C-F, B-D-G and back to C-E-G.

Shouldn't the second chord be D-G-B and not D-B-G? And also, why not D-F-A? Isn't that also leaving one note of each scale? And each note (D, F, A) is part of the scale. Probably, this is a very basic question and the question that I had asked my teacher - but no answer as yet.


Originally Posted by zrtf90
C and G appear in two of the primary chords so we have a choice of harmonisation. All the other notes appear in only one primary chord.

Thank you - and I guess this concept applies to all scales?

And while writing this particular reply, I tried to understand Circle of Fifths as well as came across other sites like http://www.piano-keyboard-guide.com/ - I guess I will get better understanding after reading this.


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Re: What are these chords
ManishP #3026587 09/19/20 12:51 AM
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Originally Posted by ManishP
I checked on the Internet and saw the standard major chords and progressions for scales, but could not find anywhere chords formed in such a way that the last note was the note of the scale (teacher mentioned that this is the first inversion of chord and I understand inversions, but keeping aside inversions for the moment, I did not come across any site where chords were explained in such a manner that all the first notes were scale notes.

I don't know if this was what you really meant to write, but I think you are quite confused about the whole thing.

In a major key, if you are playing the seven basic triads from I to vii dim that belong to that key, ALL the notes in ALL the chords are scale notes that belong to that key. Not just the first note, not just the last, all of them. So obviously you have to know what notes make up the scale you are planning to use or else you won't know what notes you can select from to make up the chords.

This principle applies regardless of what inversions you are using - you are not changing the harmonics or name or function of the chord by changing the order of the notes.

So once you know what notes are in the scale you plan to use, you stick to those. If you want the I chord (tonic) you use notes 1, 3 and 5 of whatever scale you plan to use. You can play them in that order or you can mix them up like your first inversion example and use 3, 5 and 1 (E, G and C in the key of C; A, C and F in the key of F for example).

So you don't need a website, you can do it out of your head, even if you have to sit and figure each one out slowly for a while. Write it down on paper if you need. But you HAVE to know the notes of the particular key.

Anything more than that is overthinking it.


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Re: What are these chords
scirocco #3026590 09/19/20 01:01 AM
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Originally Posted by scirocco
I don't know if this was what you really meant to write, but I think you are quite confused about the whole thing.

That's putting it mildly.

To the OP: If you have a teacher, then why are you asking us? You should keep asking your teacher until you get a satisfactory response. If you can't get a satisfactory response, then you should look elsewhere for instruction. You sound hopelessly confused.


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Re: What are these chords
ManishP #3026598 09/19/20 01:53 AM
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I think what I meant has not come out correctly - I know that the notes in the chord have to belong to the scale. My point was that I have not come across chords in the sequence I have mentioned in my first post (EGC, GBD, GCE, ACF, CEG, CFA, DGB and EGC) where last note is in the sequence of notes in the scale. Anyway, I do plan to continue asking my teacher.


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Re: What are these chords
ManishP #3026621 09/19/20 03:58 AM
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Originally Posted by ManishP
I think what I meant has not come out correctly - I know that the notes in the chord have to belong to the scale. My point was that I have not come across chords in the sequence I have mentioned in my first post (EGC, GBD, GCE, ACF, CEG, CFA, DGB and EGC) where last note is in the sequence of notes in the scale. Anyway, I do plan to continue asking my teacher.

This is just one example of how to harmonize a scale in the top voice. All the chords are either degree I, IV or V. In root position or in one of the inversions. To replicate that pattern, you need to know how to form chords and the inversions. If you know that the first chord is a first inversion of I, the C is is in the top voice, the E must be in the bass and therefore G will be in the middle voice. And so on. Given the top voice note, there is usually only 1 chord that works except when the top note is G, where there are 2 options. For the reason why you would write for example GCE and not CGE, that is because there are additional counterpoint rules which put some constraints as to how the various voices can move. It is too complicated to explain here, but outside of strict counterpoint, there is much more freedom as to what you can do. In which case there are in fact multiple options in the way you can harmonize a top line.

By the way, if abiding to strict counterpoint, it would be much better to write the 7th chord as GDB. There are 2 main reasons which are complicated to explain but essentially it is because written as DGB there is an unprepared 6/4 chord and followed directly by EGC does not sound too good. Also GDB provides a much better resolution of the previous 6/4 (even if not exactly normal resolution but that is the best one can do) and you certainly dont want to have 2 chords 6/4 in sequence. You can pass this on to your teacher. I doubt you can understand what i am explaining, but it is to highlight the relative complexity of classical music theory and counterpoint.

Without some serious knowledge on music theory and counterpoint, you would not be able to understand completely all the rationale of the sequence. So the simpliest for now is to identify the chords and their inversion, and from there it is pretty simple to replicate in any scale. Like others have said, the best is to work with your teacher to do the exercice that he wants you to do. He must give you the knowledge to be able to execute properly, even if i think that to me it seems rather premature, given your relative inexperience in the subject.

Re: What are these chords
ManishP #3026627 09/19/20 04:11 AM
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Originally Posted by ManishP
My point was that I have not come across chords in the sequence I have mentioned in my first post (EGC, GBD, GCE, ACF, CEG, CFA, DGB and EGC) where last note is in the sequence of notes in the scale.

But why does it matter if you can't find them on a website? Why are you trying to do that in the first place?

My guess is that your teacher simply wants you to understand the way each of the chords is made in the origin scale of C and work out for yourself what each one transposes to in a different key, in other words to do it by understanding, not just by copying by what someone else has written down for you.

I explained how to do this in my earlier post. And other posters have explained the names and functions of each of the chords in the progression if that is what you are interested in - that doesn't change when you transpose to a different key.


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Re: What are these chords
ManishP #3026662 09/19/20 06:47 AM
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Originally Posted by ManishP
Hello All,

Many thanks for the answers.

I would like to clarify certain points:

1. My question was specific to the chord pattern that I had posted in my original post. The reason was, when my teacher gave me those patterns to practice, he also mentioned that I should be able to form the pattern on my own for other scales. But I could not - and when I asked him to explain to me, he could not explain very clearly.

2. I checked on the Internet and saw the standard major chords and progressions for scales, but could not find anywhere chords formed in such a way that the last note was the note of the scale (teacher mentioned that this is the first inversion of chord and I understand inversions, but keeping aside inversions for the moment, I did not come across any site where chords were explained in such a manner that all the first notes were scale notes).

Originally Posted by wouter79
Chords are numbered I,II,III,IV,V,VI and VII according to the lowest note of the chord

So if you have the E major again as above, the I chord is E+G#+B and V=B+D#+F#

The I, IV and V are very often used and have special names tonic, subdominant and dominant.

You can alter these chords, these are called "inversions", "7th chords", "9th chords" etc. I can explain that also if you like this approach.


Exactly - I came across this and have understanding of inversions (first, second).

But you asked
Quote
For example, C major chords are EGC, GBD, GCF, ACF, CEG, CFA, DGB and EGC. D major is having F#AD, AC#E, ADF#, BDG, DF#A, DGB, EAC# and F#AD.

But my problem is that I am not able to understand the pattern of these chords. I do not know how to form chords in different scales. Can anyone help me in understanding how these chords are formed?

These are just inversions of C major and D major. And you just said that you have understanding of what I said and inversions.

So either you understand inversions and then the answer should be clear, or you don't understand inversions although you say you do, or you did not explain your problem properly


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Re: What are these chords
ManishP #3026706 09/19/20 09:17 AM
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Originally Posted by ManishP
Shouldn't the second chord be D-G-B and not D-B-G? And also, why not D-F-A?
Yes it should be D-B-G (fingers too fast and eyes too slow) but not D-F-A because D Minor is not one of the primary chords. Your OP suggests you are only using the three primary chords.

Originally Posted by ManishP
...I guess this concept applies to all scales?
To all keys, yes.


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Re: What are these chords
ManishP #3026718 09/19/20 09:55 AM
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Originally Posted by ManishP
I have been away from the forum for a long time now, but in the meanwhile started taking lessons. My teacher is currently covering chords in different major scales. But I do not understand the pattern of the chords. I asked him, but he did not give any clear answer, other than that these chords have last note as the note in the scale. For example, C major chords are EGC, GBD, GCF, ACF, CEG, CFA, DGB and EGC. D major is having F#AD, AC#E, ADF#, BDG, DF#A, DGB, EAC# and F#AD.
I am going to make some guesses. When I look back at your earlier posts, you were teaching yourself and for quite some time. Now you have a teacher, to whom you went with that background. This teacher will have had to guess what you know. He may think you know things that you don't know. What you don't know is creating your present problem. This is my guess.

We can help you with the present problem. The larger problem is if your teacher assumes you know things you don't. You may need to get together to hammer this out so you can work together successfully. Or if you can't do it for the big picture, tell him you don't understand the patterns for repeating this in other keys. If he's a decent teacher, he'll figure out where the holes are, and teach you the prerequisite.

You already have some good answers. One problem for us as well, is not knowing what you do and don't know.
Quote
For example, C major chords are EGC, GBD, GCF, ACF, CEG, CFA, DGB and EGC. D major is having F#AD, AC#E, ADF#, BDG, DF#A, DGB, EAC# and F#AD.

Some different ways of seeing this (since we don't know what your knowledge base is).

A rewrite:
C/E, G, Csus, F/A, C, F/C, G/D, C/E ..... The same pattern exists in the D major version.

1. The first thing we see is that he is using only three chords: C, F, G. These chords are built on degree 1 (I), 4 (IV), 5 (V). You're right that they cover all the notes of the scale, but that is not the main point. The I, IV, V chords are often taught first in traditional music, because they build the skeleton of harmony. I is your "Tonic" or home base, V is the "Dominant" which "wants to go back to" the Tonic, and IV is the chord that leads to V. This is not the only possible combo - ii (Dm) is also often used to led to V - but the IV is what is usually taught.

So here's the first part of the pattern, and reason for it. We're using only the I IV V chords. In D major, those chords are I (D), IV (G), V (A). Your 2nd set holds only those chords. So yup, we've got the pattern.

2. I'm going to use an old fashioned symbol system, where Ia = root position (CEG, called C as a jazz chord), Ib = 1st inversion, EGC, called C/E), c = 2nd inversion (GCE, C/G). We get the pattern

Ib, Va, I"sus", IVb, Ia, IVc, Vc, Ib.

I think there's an error in the 3rd chord, and that it should be C/G = Ic. See **

-----------
If you know your scales and chords, you should be able to duplicate this in any major key - which is what you are asked to do. In jazz chord notation we have

C/E, G, Csus**, F/A, C, F/C, G/D, C/E

In the D major, with I = D, IV = G, V = A, we have

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

** I'm noticing that in what you wrote, the 3rd chord in D major is not Dsus. I'm wondering if you transcribed one of the two wrong for the 3rd chord, because they should match up. I'm guessing that your teacher did NOT give you a sus chord (GCF) If the 3rd chord in the D one is correct (ADF#) that is D/A = Ic. Then the third chord in the C major should be C/G

I think the C major is supposed to be

C/E, G, C/G, F/A, C, F/C, G/D, C/E


which gives us
Ib, Va, Ic, IVb, Ia, IVc, Vc, Ib.

If that is the pattern, then you'd do the same thing for, say, F major: I = F, IV = Bb, V = C. Do you have the the required knowledge to do this in other keys? (Do you know the chords vis-a-vis keys to do this?) If you are missing needed knowledge, you should tell your teacher, so that he can backtrack to the simpler levels you need first.

Sorry that this turned out so long.

(If I messed up letters anywhere, someone please let me know. Since I lived Do Re Mi for 50 years, I'm still weak in that part, and probably will always be.)

Re: What are these chords
ManishP #3026719 09/19/20 09:58 AM
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I'm surmising that your teacher is thinking of some specific patterns by choosing those inversions. He may be able to point these out after you do the exercise, if you are now able to do it.

Always tell your teacher if you don't understand something, or if there is some knowledge you still lack. Your job is not to "produce correct answers" for your teacher, but to learn. The activity is there for your learning, and if you don't know something, a good teacher is delighted to discover this, so he can teach it.

Re: What are these chords
ManishP #3026856 09/19/20 04:13 PM
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Originally Posted by keystring
. . .We can help you with the present problem. The larger problem is if your teacher assumes you know things you don't. You may need to get together to hammer this out so you can work together successfully. Or if you can't do it for the big picture, tell him you don't understand the patterns for repeating this in other keys. If he's a decent teacher, he'll figure out where the holes are, and teach you the prerequisite.

+1 !!!!


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Re: What are these chords
Sidokar #3026970 09/19/20 10:30 PM
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Originally Posted by scirocco
Originally Posted by ManishP
In a major key, if you are playing the seven basic triads from I to vii dim that belong to that key, ALL the notes in ALL the chords are scale notes that belong to that key. Not just the first note, not just the last, all of them. So obviously you have to know what notes make up the scale you are planning to use or else you won't know what notes you can select from to make up the chords.

This principle applies regardless of what inversions you are using - you are not changing the harmonics or name or function of the chord by changing the order of the notes.

You are right - I followed the above logic and was able to understand how the chords were formed. It was for exactly understanding this that I posted the question here. I was able to form chords in other scales too!


Originally Posted by zrtf90
Originally Posted by ManishP
Shouldn't the second chord be D-G-B and not D-B-G? And also, why not D-F-A?
... but not D-F-A because D Minor is not one of the primary chords.

Yes - I understood this after working out the chords for C and other scales.




Originally Posted by keystring
1. The first thing we see is that he is using only three chords: C, F, G. These chords are built on degree 1 (I), 4 (IV), 5 (V). You're right that they cover all the notes of the scale, but that is not the main point. The I, IV, V chords are often taught first in traditional music, because they build the skeleton of harmony. I is your "Tonic" or home base, V is the "Dominant" which "wants to go back to" the Tonic, and IV is the chord that leads to V. This is not the only possible combo - ii (Dm) is also often used to led to V - but the IV is what is usually taught.

So here's the first part of the pattern, and reason for it. We're using only the I IV V chords. In D major, those chords are I (D), IV (G), V (A). Your 2nd set holds only those chords. So yup, we've got the pattern.



Well, the issue has been that my teacher asked me to practice chords by giving me the chords but not explaining yet how they have been arrived at (no major, minor chords etc) - so the above that you explained has not been discussed in detail till now. But I have seen the above chord progression in various tutorials and I had thought that I would also be taught in a similar manner.

Originally Posted by keystring
2. I'm going to use an old fashioned symbol system, where Ia = root position (CEG, called C as a jazz chord), Ib = 1st inversion, EGC, called C/E), c = 2nd inversion (GCE, C/G). We get the pattern

Ib, Va, I"sus", IVb, Ia, IVc, Vc, Ib.

I think there's an error in the 3rd chord, and that it should be C/G = Ic. See **

-----------
If you know your scales and chords, you should be able to duplicate this in any major key - which is what you are asked to do. In jazz chord notation we have

C/E, G, Csus**, F/A, C, F/C, G/D, C/E

In the D major, with I = D, IV = G, V = A, we have

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

** I'm noticing that in what you wrote, the 3rd chord in D major is not Dsus. I'm wondering if you transcribed one of the two wrong for the 3rd chord, because they should match up. I'm guessing that your teacher did NOT give you a sus chord (GCF) If the 3rd chord in the D one is correct (ADF#) that is D/A = Ic. Then the third chord in the C major should be C/G

I think the C major is supposed to be

C/E, G, C/G, F/A, C, F/C, G/D, C/E


which gives us
Ib, Va, Ic, IVb, Ia, IVc, Vc, Ib.

If that is the pattern, then you'd do the same thing for, say, F major: I = F, IV = Bb, V = C. Do you have the the required knowledge to do this in other keys? (Do you know the chords vis-a-vis keys to do this?) If you are missing needed knowledge, you should tell your teacher, so that he can backtrack to the simpler levels you need first.

Sorry that this turned out so long.

(If I messed up letters anywhere, someone please let me know. Since I lived Do Re Mi for 50 years, I'm still weak in that part, and probably will always be.)
Why have you used slashes in between (C/E), C/G etc?


And yes - I am definitely going to ask him - just practicing chords without understanding how to create them has not worked out well with me.

Originally Posted by Sidokar
This is just one example of how to harmonize a scale in the top voice. All the chords are either degree I, IV or V. In root position or in one of the inversions. To replicate that pattern, you need to know how to form chords and the inversions. If you know that the first chord is a first inversion of I, the C is is in the top voice, the E must be in the bass and therefore G will be in the middle voice. And so on. Given the top voice note, there is usually only 1 chord that works except when the top note is G, where there are 2 options. For the reason why you would write for example GCE and not CGE, that is because there are additional counterpoint rules which put some constraints as to how the various voices can move. It is too complicated to explain here, but outside of strict counterpoint, there is much more freedom as to what you can do. In which case there are in fact multiple options in the way you can harmonize a top line.

By the way, if abiding to strict counterpoint, it would be much better to write the 7th chord as GDB. There are 2 main reasons which are complicated to explain but essentially it is because written as DGB there is an unprepared 6/4 chord and followed directly by EGC does not sound too good. Also GDB provides a much better resolution of the previous 6/4 (even if not exactly normal resolution but that is the best one can do) and you certainly dont want to have 2 chords 6/4 in sequence. You can pass this on to your teacher. I doubt you can understand what i am explaining, but it is to highlight the relative complexity of classical music theory and counterpoint.

Without some serious knowledge on music theory and counterpoint, you would not be able to understand completely all the rationale of the sequence. So the simpliest for now is to identify the chords and their inversion, and from there it is pretty simple to replicate in any scale. Like others have said, the best is to work with your teacher to do the exercice that he wants you to do. He must give you the knowledge to be able to execute properly, even if i think that to me it seems rather premature, given your relative inexperience in the subject.

Yes - at this moment this is far too complicated for me, though this post becomes a source for me to read and try to understand this later. Thanks.


Wish I had started earlier!
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