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Woodshedding - Learning to Play!
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This is mostly a theoretical question I suppose - but maybe an ear training question also:
How do inversions of chords function identically to their root-form counterparts even though their interval sequences are different ?
I ask for this reason:
1. in most theory books, you will find exactly that statement - that chord inversions function identically to their root counterparts
2. statement 1 is made after they clearly explain that the characteristic sounds of chords are with respect to the root notes and the sequential intervals built upon them (e.g. a C major chord is a major 3rd interval (C-->E) followed by a minor interval (E-->G)
They ask you to accept statement 1, but never explain how the function could possibly be identical given the different interval structures and lack of a root - to 'root' the sound as a starting point for your ear.
My guess is that it has something to do with the overtone series, but I don't know enough about it to articulate it in that way.
Can anyone shed additional light on this ?
Thanks in advance,
Joe V.
Last edited by Joe V; 11/15/13 04:20 AM.
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Woodshedding - Learning to Play!
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Hi Joe, Here is a stab at an answer, its all about context. Firstly remember that chords can have MORE than one function. A C major 7 chord in first inversion can function of course as an E minor b6th . This property of chords, ie. to have more than one function, is often used when modulating. So don't think a chord has only one function. They can have functions (almost) 'identical to their root counterparts' (to quote you), but they also have other functions. Therefore one of your statements above does not exclude the other. Secondly, when playing in a band the root is said to be supplied by the bass player - so, you get those 'Bill Evans' voicings that omit the root - he was playing in a trio. In these cases the full chord sound includes these bass notes supplied by the third party - the bass player. Thirdly, If you play a whole song solo, without accompaniment and you exclusively play inversions in the left hand, its going to sound peculiar - by which I mean it might sound exotic and in it's way OK (sometimes), but it's not going to sound like the original song. If though, on the other hand, you substitute a left hand inversion here and there, that seems, (to my ears) to be fine. I would say that where the chord is in a prominant position such as the end of a song, an inversion would sound incomplete. "Normally" if there is such a musical term  when playing solo, you would try to get the root of the chord in the left hand. This limits where your other left hand fingers can go of course, which is one reason why you might substitute an inversion here and there. Chords and inversions are only a beginning of course, voicings and voice leading is where its at, a much richer canvas. However, personally I first spent a lot of time ensuring I could get to any inversion of any basic chord swiftly, then I started adding tensions to the voicings and of course missing out notes. This is just the way I approached this. Anyway this is my attempt at an answer Zero
Last edited by ZeroZero; 11/15/13 06:06 AM.
Win 11 64, Asus Rog Strix z390 mobo, 64 gig RAM, 8700k
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Woodshedding - Learning to Play!
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In my opinion, right hand inversions are fine anywhere in a song and in fact many times more appropriate than root form. Root is almost always covered elsewhere. Gospel and rock forms, particularly in organ playing depend on moving fluidly between inversions and sometimes the root form doesn't sound right.
Look up concept of 'Phantom Pitch' in psychoacoustics references - not an entire explanation - but some of the reason inversions work.
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Woodshedding - Learning to Play!
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Joe, remember that stuff taught back in EE school in the frosh or soph year where you learned about heterodyning?
Simply put, if we have to waveforms of differing frequency and we mix them, there will be created two other waveforms at about half the amplitude or so of the two original waveforms, one would be the SUM of the two frequencies and the other would be the DIFFERENCE value.
This is physics and applies "across the board" not just at RF frequencies.
Therefore, if we have two audio sinewaves of equal amplitude, one at 1,000Hz and the other at 500Hz, when the two mix, either in the electronics or "in the air" - we will also find that there is an additional 1500Hz tone in there (the sum) and also a 500Hz tone as well (the difference).
Now let's put that first tone at exactly one octave higher, which is simply doubling the frequecy.
2,000Hz and 500Hz now yield those two other frequencies when mixed, but they are now 2500Hz sum and 1500Hz difference.
Notice that the 1500Hz is present in both examples.
Now let's move over to Music Terminology.
The 1, 3, and 5 of the simple Major Triad (KISS) does exactly the same thing as the above.
Therefore, no matter which octave any of the three notes (frequencies) is placed in, we will find the same harmonic relationships going on in there somewhere.
Therefore the three notes perform the same basic harmonic function regardless of where on the keyboard or guitar, octave-wise or inversion-wise that you play them.
However, musically speaking, if the three simple triad inversions are played "standalone" without a Bass note, the lowest note chosen actually defines the chordname and therefore the actual key of the chord at the moment.
C, E, G - The root position C triad. When played standalone as I typed it, this would identify itself as a C Major Triad because the C is the lowest frequency played and the E, being 4 half steps above the C, defines the Major Scale that the Triad is derived from.
1st Inversion, E, G, C, standalone, would have to be identified as an Eminor7#5 chord. (But if the Bass is in there playing a C root, it would become the C Triad again.)
2nd Inversion, G, C, E, standalone would be the G6sus4 chord, but again, if the Bass is playing in C Major, it would be the C chord no matter the stacking, due to the frequency relationship math.
It is also important to realize that my example of the math is intentionally oversimplified for the sake of clarity of concept.
In reality, the interaction of the various frequencies and waveforms we have to use in making what we call Music can get pretty deep pretty quickly. That is why Audio Engineers will often use Fourier Transform software analysis to get to the bottom of what's really going on with the frequencies of music.
The most important thing I can tell you about all of his sort of thing is not to get all involved with trying to figure out these kind of things if your goal is to play music. That can become the proverbial kiss of death, a kill to your primary goal, which is to play the instrument with the ability to turn in the Strong Performance.
Or, as my late father once told me years and years ago, "Look. Plenty of guys who can barely read and write the spoken language, couldn't pass an admissions test to get into a school, figured this stuff out and became some of the greats you listen to on your phonograph all the time!"
Indeed.
To become good at doing anything, one must first simply do the drills that the teacher tells us to do, whether they are music lessons or martial arts katas, grasshopper, and keep doing them, applying both the repetition of practice and the tutoring of the master and one day you will find that the understanding light suddenly illuminates.
To perform like Bruce Lee did, you first have to know the Katas, completely, in order to be able to throw them away and just BE with it. There is no shortcut to that kind of performance.
"LEARN it, Forget it, then PLAY."
Note well which one of those three comes first, and GET BACK TO PRACTICING. Not Posting. All Posting will do is make you a better internet poster.
--Mac
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Woodshedding - Learning to Play!
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Joined: Feb 2006
Posts: 1,129
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OP
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Thanks for your great responses - now I'll get back to practicing : )
...but I LIKE talking 'theory' and 'philosophy' - even though it doesn't put bread on the table - or make me a better player in and of itself.
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Woodshedding - Learning to Play!
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Joined: Jul 2007
Posts: 1,739
Expert
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Expert
Joined: Jul 2007
Posts: 1,739 |
Joe, remember that stuff taught back in EE school in the frosh or soph year where you learned about heterodyning?
Simply put, if we have to waveforms of differing frequency and we mix them, there will be created two other waveforms at about half the amplitude or so of the two original waveforms, one would be the SUM of the two frequencies and the other would be the DIFFERENCE value.
This is physics and applies "across the board" not just at RF frequencies.
Therefore, if we have two audio sinewaves of equal amplitude, one at 1,000Hz and the other at 500Hz, when the two mix, either in the electronics or "in the air" - we will also find that there is an additional 1500Hz tone in there (the sum) and also a 500Hz tone as well (the difference).
Now let's put that first tone at exactly one octave higher, which is simply doubling the frequecy.
2,000Hz and 500Hz now yield those two other frequencies when mixed, but they are now 2500Hz sum and 1500Hz difference.
Notice that the 1500Hz is present in both examples.
Now let's move over to Music Terminology.
The 1, 3, and 5 of the simple Major Triad (KISS) does exactly the same thing as the above.
Therefore, no matter which octave any of the three notes (frequencies) is placed in, we will find the same harmonic relationships going on in there somewhere.
Therefore the three notes perform the same basic harmonic function regardless of where on the keyboard or guitar, octave-wise or inversion-wise that you play them.
However, musically speaking, if the three simple triad inversions are played "standalone" without a Bass note, the lowest note chosen actually defines the chordname and therefore the actual key of the chord at the moment.
C, E, G - The root position C triad. When played standalone as I typed it, this would identify itself as a C Major Triad because the C is the lowest frequency played and the E, being 4 half steps above the C, defines the Major Scale that the Triad is derived from.
1st Inversion, E, G, C, standalone, would have to be identified as an Eminor7#5 chord. (But if the Bass is in there playing a C root, it would become the C Triad again.)
2nd Inversion, G, C, E, standalone would be the G6sus4 chord, but again, if the Bass is playing in C Major, it would be the C chord no matter the stacking, due to the frequency relationship math.
It is also important to realize that my example of the math is intentionally oversimplified for the sake of clarity of concept.
In reality, the interaction of the various frequencies and waveforms we have to use in making what we call Music can get pretty deep pretty quickly. That is why Audio Engineers will often use Fourier Transform software analysis to get to the bottom of what's really going on with the frequencies of music.
The most important thing I can tell you about all of his sort of thing is not to get all involved with trying to figure out these kind of things if your goal is to play music. That can become the proverbial kiss of death, a kill to your primary goal, which is to play the instrument with the ability to turn in the Strong Performance.
Or, as my late father once told me years and years ago, "Look. Plenty of guys who can barely read and write the spoken language, couldn't pass an admissions test to get into a school, figured this stuff out and became some of the greats you listen to on your phonograph all the time!"
Indeed.
To become good at doing anything, one must first simply do the drills that the teacher tells us to do, whether they are music lessons or martial arts katas, grasshopper, and keep doing them, applying both the repetition of practice and the tutoring of the master and one day you will find that the understanding light suddenly illuminates.
To perform like Bruce Lee did, you first have to know the Katas, completely, in order to be able to throw them away and just BE with it. There is no shortcut to that kind of performance.
"LEARN it, Forget it, then PLAY."
Note well which one of those three comes first, and GET BACK TO PRACTICING. Not Posting. All Posting will do is make you a better internet poster.
--Mac How's that go again? Could you perhaps whistle it? You know, maths and arithmetic were the three things I hated most at achool
Last edited by ZeroZero; 11/15/13 03:37 PM.
Win 11 64, Asus Rog Strix z390 mobo, 64 gig RAM, 8700k
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Woodshedding - Learning to Play!
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Joined: May 2000
Posts: 38,502
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How's that go again? Could you perhaps whistle it? You know, maths and arithmetic were the three things I hated most at achool You and me both, ole buddy. I figured out at some point that the blame should be placed on the teaching methods and the teachers, though. Had to resort to autodidactic study in order to understand. Along the way, the art of reading became my staunchest ally and good friend. My approach to research is simple enough; I'm just always on the lookout for a few clues at the scene o' the crime... --Mac
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