Major 11th chords

[rbarata]

I think I now understood what you mean.
Let explain:

I've made chart a few months ago for major scales chords. For the CMaj scale I got this:

C Major chords.JPG

I think this "reflects what you are explaining but in the reverse way, i.e., instead of going from the formula to the scales, this table shows the path from scales to formulas.

Now, thinking in the same way as you, going from the formula to the scale:

The chord formula is 1-3-5-7-(9)-(11)-13 which assumes that the 11th degree is a perf 11 / perf 4.

IV Maj7th.JPG

As we can see, the 13th degree corresponds to an interval that is not perfect, therefore the resulting formula is 1-3-5-7-(9)-(#11)-13, which is not the same. Therefore, we say that in the key of C, the IVmaj7 chord doesn't have an 11 degree.

So, as far as I understood, in this particular example, we must use the C major scale notes but they must be compared with the FMaj scale (the root scale).

[Jed]

As we can see, the 11th degree corresponds to an interval that is not perfect, therefore the resulting formula is 1-3-5-7-9-#11-13, which is not the same. Therefore, we say that in the key of C, the IVmaj7 chord doesn't have a (natural) 11th but rather a #11th degree.

So, as far as I understood, in this particular example, we must use the C major scale notes but they must be compared with the FMaj scale (the root scale).

Corrected for you. The typo's are killing you here. These details are critical.

Now go back to your first attachment that shows the IV (F maj) chord scale as 1 2 3 4 5 6 7 1 - when it should be 1 2 3 #4 5 6 7 1.
Each of your other chord scales / intervalic notations (in the original attachment) have similar errors.

[Jed]

Now, thinking in the same way as you, going from the formula to the scale:

I'm not thinking strictly "formula to scale"

The idea is to be able to think in terms of notes and formulas with equal fluency - moving from one to the other without hesitation or error - so that we can see the notes and know what they mean / how they function - or think of a function (number) and be able to determine the proper notes in any particular key without delay.

The function is most easily understood in terms of the numeric notation - because it is the same for every key. But of course the music is played in some tonality which requires we be able to translate the numbers / functions to specific notes of some key without hesitation.

[rbarata]

Corrected for you. The typo's are killing you here. These details are critical.

I'm sorry for that. Although I understand what I want to say, it is difficult for others to understand me if I keep doing this.

Now go back to your first attachment that shows the IV (F maj) chord scale as 1 2 3 4 5 6 7 1 - when it should be 1 2 3 #4 5 6 7 1. Each of your other chord scales (in the original attachment) have similar errors.

That will be my job tonight.

So, basically my mistake was to fail to compare the resultinf notes of the Cmajor scale with the chord root major scale (in this case, F major scale).
Music theory needs a consistency in practice that, sometimes, I can't accomplish. That's why these "confusions" are happening.

[Jed]

So, basically my mistake was to fail to compare the resulting notes of the Cmajor scale with the chord root major scale (in this case, F major scale).
Music theory needs a consistency in practice that, sometimes, I can't accomplish. That's why these "confusions" are happening.

Voila !! This is exactly the the issue.

The details are critical. Any typo's or poor wordings are extremely problematic. This stuff isn't hard - but it's impossible to try and communicate when people cannot use the correct terminology accurately. Once you learn to use the correct terminology all the time / every time - then we can show you how simple this stuff is.

[rbarata]

Voila !! This is exactly the the issue.

Finally! I was expecting a lot of headaches from this thread.

I guess it would be a very good exercise to do the same exercise (from formulas to the scale) for all Major scales. Obviously I will find a pattern as for the triads in all major scales. Something tells me that's what you want me to find.

BTW, how is this chord named? The 1-3-5-7-9-#11-13?

If it was 1-3-5-7-9-#11 it would be a Fmaj7#11 but that 13 is messing things up...or not.

[Jed]

Finally! I was expecting a lot of headaches from this thread.

I don't know about you but I've certainly got a headache.

I guess it would be a very good exercise to do the same exercise (from formulas to the scale) for all Major scales. Obviously I will find a pattern as for the triads in all major scales. Something tells me that's what you want me to find.

It's surprising that no one ever advised that you learn your major scales . . hmmm.
In retrospect, that would have been a good idea - I wish I had thought of that.

BTW, how is this chord named? The 1-3-5-7-9-#11-13?

It could simply be called a "Xmaj13" chord - but some people don't know that the #11 would be required so most people notate that chord as "Xmaj13 (#11)"

If it was 1-3-5-7-9-#11 it would be a Fmaj7#11 but that 13 is messing things up...or not.

It depends how much you know . . . .
If you know the simple rules (interval naming, the major scales) then it's easy
If you don't know the simple rules then it's complicated and mysterious

[xyzzy]

If you know the simple rules (interval naming, the major scales) then it's easy
If you don't know the simple rules then it's complicated and mysterious

By my calculations, here's a representation of where we are so far. I've blotted out my answers for the remaining 20 cells... 'til later


This is cool beans. The whole extensions - avoid notes thing has been too much of a mystery. Looking forward to further elaborations....

[Jed]

This is cool beans. The whole extensions - avoid notes thing has been too much of a mystery. Looking forward to further elaborations....

Once rbarata gets back with his corrections - we can pull back the curtain. I promise there won't be too much suspense involved - although I do expect to hear some forehead slapping from afar.

Meanwhile try singing some :
b9ths, 4ths and b13ths over major triads and
b9ths and b13ths over minor triads
. . . . just to remind yourself why these extensions are never found "in the wild".

cheers,

[xyzzy]

Once rbarata gets back with his corrections - we can pull back the curtain. I promise there won't be too much suspense involved - although I do expect to hear some forehead slapping from afar.

Yeah, the end result did look quite very familiar on hindsight, but deriving it took me a lot of time and iterations; more than I'd have thought. Being able to rattle off the A, E, B etc scales while eyeballing their corresponding columns, afterward was quite enlightening and reinforcing. And I'm glad I got comfy early on, using the Roman Numeral notation in the mode-independent manner as you recommended to me a couple of years ago.

I found it quite valuable early on to get a feel for how many flats or sharps in a key and their order (by building scales in order around the Circle of Fifths, both directions) -- so when conjuring up a scale in the mind from scratch, one can do it not only by doing the 2-2-1-2-2-2-1 trick, but by alternately seeing that, .... say, I know Eb has 3 flats, and since the order of flats is B,E,A, then I can just name the 7 letters in order starting from E which are (E F G A B C D) and say "flat" after those three notes, so: (Eb F G Ab Bb C D) voila! ... without need to resort to building from tones and semitones. Not quite automatic yet, but I'm getting there and having a variety of methods to synthesize from helps me develop speed.

Meanwhile try singing some :
b9ths, 4ths and b13ths over major triads and
b9ths and b13ths over minor triads
. . . . just to remind yourself why these extensions are never found "in the wild".

You haven't heard me play at the open mics! Oh, you mean on purpose?!

[Jed]

Yeah, the end result did look quite very familiar on hindsight, but deriving it took me a lot of time and iterations; more than I'd have thought. Being able to rattle off the A, E, B etc scales while eyeballing their corresponding columns, afterward was quite enlightening and reinforcing. And I'm glad I got comfy early on, using the Roman Numeral notation in the mode-independent manner as you recommended to me a couple of years ago.

I find the way all these things work together in complimentary ways to be a validation of the logic behind these various systems. The symmetry between the intervallic notation for scale degrees & chord scales and roman numeral notation for chords is too much of a coincidence to ignore.

I found it quite valuable early on to get a feel for how many flats or sharps in a key and their order (by building scales in order around the Circle of Fifths, both directions) -- so when conjuring up a scale in the mind from scratch, one can do it not only by doing the 2-2-1-2-2-2-1 trick, but by alternately seeing that, .... say, I know Eb has 3 flats, and since the order of flats is B,E,A, then I can just name the 7 letters in order starting from E which are (E F G A B C D) and say "flat" after those three notes, so: (Eb F G Ab Bb C D) voila! ... without need to resort to building from tones and semitones. Not quite automatic yet, but I'm getting there and having a variety of methods to synthesize from helps me develop speed.

It's all good and the more ways you have to perceive these things the better. Each new way to think and see scales and other musical structures reinforces other knowledge. One thing builds on another. In the end everything distills down to just a few simple rules - and it's only the permutations that are numerous. It's kind of like chess, the rules are quite simple but the complexity borne of the possible permutations of various moves seems nearly infinite.

[rbarata]

Ok, so I made a table comparing 4 things:

1 - the chord scale degrees relatively to the chord tonic scale

2 - The chord tonic scales

3 - The chord scales with chord tones in pink, the extensions in blue and the avoid notes in red.

4 - the chord scale degrees relatively to the chord tonic scale with the 9, 11 and 13 degrees replaced by 2, 4 and 6 (according the compound intervals harmonic treatment).


Chords & scales tables.jpg

Conclusions:

1 - In the chord tonic major scale, all flats become sharp in the chord scale. And all sharps become flat.

2 - Their position, comparing both scales, are kept.

3 - All avoid notes are F or C because they are the only ones who are half-step above from another note. This is valid only for C Major scale as chord scale. I haven't confirmed it yet but I'm assuming that if the chord scale changes we must check which notes can be half-step above another (for example in Emajor scale they it can be the A, or in the Dmajor scale they can be the D or the G) to see which can be candidates for avoid notes.

Basically, knowing the major scale of the chord tonic that's all we need to find the chord tones and teir respective extensions and avoid notes.

[rbarata]

I have tried now to apply all this knowledge to the maj7 chords in the key of Dmaj. I concluded that my previous point nº 1 is not correct. It is correct for the CMaj7 chords.
But I also noticed that the chord scale degrees relatively to the chord tonic scale are kept constant. This means that I can find the notes for all chords in all major keys by using only the CMaj scale and their respective chord major scales.

[Jed]

Just to the right of the Chord Number (in roman numeral notation):
is the "chord scale formula presented in ascending 3rds" - to the right of that
is the "chord root's major scale" - to the right of that
is the "chord scale in the key of C major" - to the right of that
is the "chord scale formula"

You don't have anything that illustrates which extensions are available over which chords. (* Actually it looks like you have - but I cannot see the information - Can you fix the colors so that only the avoid notes are called out?* You don't list the extensions and avoid notes as arabic numbers (with avoid notes in red) as was the request from yesterday) I suggest you take the "chord scale formula presented in ascending 3rds" and mark the avoid notes in red. Leave all other chord tones and extensions in black. Mirror that same information in terms of notes in an adjacent panel - use the same color-coding.

Meanwhile let's look at what we can see from the chart you've produced. Since this chart compares one chord scale to another:

1) We can see / say that as we move from the chord scale for the IVmaj chord downward - we are moving into scales that vary more and more from the major scales of their tonics. Also there are seven variations all based on one major scale. (I seem to remember a similar thing happening via another musical construct)

2) Each scale formula moving downward has one more flat (or one less sharp) than the formula above it. (I seem to remember a similar thing happening via another musical construct - search your memory)

3) All major triads have unaltered roots, 3rds, 5ths, 9ths and 13ths. Whether or not these are available as extensions will require you to create another chart. The differences among the major triad's chord scales occur only relative to the 7th and/or 11th degrees. All other chord degrees (as intervals but not as notes) are identical from the IV > I > V maj triads

4) All minor triads have unaltered roots, 5ths and 11ths - further all minor triads share the flatted 3rd and flatted 7th. Whether or not these are available as extensions will require you to create another chart. The differences among the minor triad's chord scales occur only relative to the 9th and/or 13th degrees. All other chord degrees (as intervals but not as notes) are identical from the IIm > VIm > IIIm triads

5) I wonder how we could use this similarity among the major triads and among the minor triads to find some useful structures that relate to the chords within each chord type - but irrespective of the chord number. (I seem to remember a similar thing being available via some musical construct - search your memory)

1 - In the chord tonic major scale, all flats become sharp in the chord scale. And all sharps become flat.

That is true but not very important.

2 - Their position, comparing both scales, are kept.

I have no idea what you mean by this.

3 - All avoid notes are F or C because they are the only ones who are half-step above from another note. This is valid only for C Major scale as chord scale. I haven't confirmed it yet but I'm assuming that if the chord scale changes we must check which notes can be half-step above another (for example in E major scale they it can be the A, or in the D major scale they can be the D or the G) to see which can be candidates for avoid notes.

This is not true and your charts do not show this or any information relative to the available extensions versus avoid notes.
** Correction - this is true but there is a more general and more valuable rule to be drawn from this specific example in C major **

Basically, knowing the major scale of the chord tonic that's all we need to find the chord tones and their respective extensions and avoid notes.

This is not true.

[Jed]

I have tried now to apply all this knowledge to the maj7 chords in the key of Dmaj. I concluded that my previous point nº 1 is not correct. It is correct for the CMaj7 chords.
But I also noticed that the chord scale degrees relatively to the chord tonic scale are kept constant. This means that I can find the notes for all chords in all major keys by using only the CMaj scale and their respective chord major scales.

Correction:
This means that you can use the chord numberings and scale formulae to determine any chord (and it's chord scale) diatonic to any major key. It's not the instance of C major that matters - but rather the formula that we derived from C major (Using C major as a specific example of a more general rule) - it's the chord numbers and their corresponding scale formulae that are the real lesson here.

Look for more general rules rather that getting lost in the specific example of any one key / note set.