Upper Extensions Chords (formerly: "C6th: Major 11th pos.")

[J D Sauser]

Physics give us the 12 semitones.

Respectfully, no it doesn't. Physics gives us octaves, fifths, fourths, thirds etc.

Mathematics gives us twelve semitones - the twelfth root of two does not occur in nature.

Yes, physics give us Over-Tones, predominantly in Octaves and 4ths/5ths.
IF you take a tone and generate a new one based on the previous one's 4th/5th over-tone and repeat that on and on, you will get all 12 semi-tones. That's what ol' Pythagoras did on something which oddly enough looks like possibly the first S12-weight-actuated (instead of pedals) "steel guitar" .



You may say, aligning tones based on their 4th/5th overtones (CREATING the circle of 5ths) is "Not Physics", it would then be Applied Physics as a result of a physics experiment and demonstration (proof of law of physics). The mathematical aspects (frequencies etc) historically came later.
The fact that over-tones exist and in 4ths/5ths, provides us with the 12 tone system.
See Pythagoras' research using strings of various tensions and how he came to create the first "circle of 5ths" and thus discover the 12 semitones.
If Pythagoras had NOT found that in his time, today we wouldn't find out something else.


However, selecting a group out of these 12 semi-tones and declaring them "The" Holy Grail of musical foundation, is a purely man-made selection.






Btw, nature (physics) does give us M3rd overtones too. (AND they ARE just over 11 cents flat, by the way... but let's not go there here and now).

Overtones happen by fractional vibrations in ANY vibrating object, like strings, reeds & tines, our vocal cords or even speaker cones and so forth. (as they don't just move back and forth, but rather "snake like" in wave forms which are fractions and sub-fractions of different orders).
SOME (predominantly non-consonant over-tones) of the resulting fractions do NOT line up correctly with our equal increment algorithm we use for fretboards or Equal Temperament.

... J-D.

[b0b]

Btw, nature (physics) does give us M3rd overtones too. (AND they ARE just over 11 cents flat, by the way... but let's not go there here and now).

The natural "major third" is made by multiplying a note's frequency by 5/4. In the man-made musical logarithmic scale, that interval is 386.3 cents, or 13.7 cents "flat"*. You can see that "flatness" by sounding a harmonic on a string. It's a little bit below the 4th fret. That's the actual physics of music.

Back to the subject... An 11th chord is a good example of a chord on top of another chord. C11 can be thought of as Bb major over C major: C E G Bb D F. (see https://b0b.com/wp/2016/02/whats-an-11th-chord/). I play in a band that keeps putting 11th chords in charts because they just play all of their guitar strings at one fret. I can't get them to understand that the order of the notes matters.

*I don't like calling a note flat if it sounds in tune, so I put it in quotes.

[Nick Fryer]

JD: basically it sounds to me that you have discovered the idea of superimposing sounds on top of one another to create new colors. This is a basic underlying concept in modern music and improvisation. Playing over static harmony and implying other harmonies to create melody is also a basic concept in modal improv (which you reference with Kind of Blue) Those guys were definitely doing what you describe. That music then evolved and became ever more chromatic, melodically and harmonically. Learning how to create colors on chords is really cool and you can learn the basic pallet of sounds as static harmony and then learn to hear how they work in functional and non functional ways. Each style of music will dictate which pallet we draw from. I’m not really into math or physics but I do know that if you take a 3:4 rhythm and speed it up, it eventually turns into the interval of a perfect fifth, which tells me intuitively that all of this means nothing unless we have rhythm! The good thing about rules in regards to learning harmony is that you can narrow it all down to triads. And as far as having to think, you can manipulate it all very easily in your brain and on your instrument if you think about it from the lowest common structure, which is the major triad.

[J D Sauser]

JD: basically it sounds to me that you have discovered the idea of superimposing sounds on top of one another to create new colors. This is a basic underlying concept in modern music and improvisation. Playing over static harmony and implying other harmonies to create melody is also a basic concept in modal improv (which you reference with Kind of Blue) Those guys were definitely doing what you describe. That music then evolved and became ever more chromatic, melodically and harmonically. Learning how to create colors on chords is really cool and you can learn the basic pallet of sounds as static harmony and then learn to hear how they work in functional and non functional ways. Each style of music will dictate which pallet we draw from. I’m not really into math or physics but I do know that if you take a 3:4 rhythm and speed it up, it eventually turns into the interval of a perfect fifth, which tells me intuitively that all of this means nothing unless we have rhythm! The good thing about rules in regards to learning harmony is that you can narrow it all down to triads. And as far as having to think, you can manipulate it all very easily in your brain and on your instrument if you think about it from the lowest common structure, which is the major triad.

Thanks Nick.
It has EXPLAINED to me the origins or the concept of "superimposing" triads over a different bass or other triad.
What really was an eyeopener or surprise to me, was the fact that ALL these Major and minor and Dominant as well as the HalfDiminished "7th/9th/11th,13th chords with their respective Major and flat 7ths, Natural and b9ths, Natural and the #11ths, and Natural and b13ths the Diatonic approach generates are the SAME... just shifting the respective root/starting at different degrees of that scale.
In retrospect, once one realizes that one is looking at a Diatonic concept, it's logical.
To us, steel guitar players, this is more relevant than to key-players, as when we learn a chord formula, have it really easy to play it in any of the 12 keys.

I am integrating this in my playing and find positions I had Triad-over-Bass "chords" now located and thus "certified" as "right", which I wondered a long time about.

So, while this thread can read as a personal rant or largely a monologue, it was part of documenting my experiment. Your suggestion really helped a great deal because it got me to experiment further which led to the resolution described on the previous "page".


It's a funny coincidence, that I had just last week "bought" into an online course geared to wind players (Sax, Horns etc) which concept it is to solo over different triads "left and right" a minor's main arpeggio. I bought it, because I found the concept pitched on a youtube "trailer"... interesting, although I don't believe much in soloing following a system (like a mode, scale, etc), but as I found the sound or "colors" they generated in the demonstration pleasantly "unusual", I was hoping for an explanation to "WHY?" or "HOW SO?". Yet, all I got is 13 sets of concepts of different triads to bounce to and back from to the main minor chord's arpeggio.

However, NOW seeing how 7/9/11/13 chords are a such a tightly repeating pattern of triads stacked above and thus also below each others, I see where all that comes from too. It's based on the exact same phenomenon.

When you find a way (and there are many ways) to explain to yourself "What's going on", you have a better way to INCORPORATE it into your musical explorations and gradually make some of it part of one's playing or musical articulation.

I hope this thread will not only serve myself but others.

Thanks!... J-D.

[J D Sauser]

....

Back to the subject... An 11th chord is a good example of a chord on top of another chord. C11 can be thought of as Bb major over C major: C E G Bb D F. (see https://b0b.com/wp/2016/02/whats-an-11th-chord/). I play in a band that keeps putting 11th chords in charts because they just play all of their guitar strings at one fret. I can't get them to understand that the order of the notes matters.

*I don't like calling a note flat if it sounds in tune, so I put it in quotes.

Four-Over-Five comes to mind, and evidently the elusive sound of the ol' B11th tuning, which is a great tuning as it has a II dominant over the Major chord.


I seem to see mostly piano (keys) players hoping for more chords being written as Triad-over-Bass. To them, it's easier information to quickly "grap" what is asked for.
I think however us "steelies" are better served looking at the interval formula to find ways to play them.

It's similar with Tritone substitutions too often written as the Dominant chord used to substitute instead of writing what chord is being substituted. It is sadly not unusual to see a C#7th (sus4) written (in lieu of the G7th (V7th)) instead of C#7th/G before resolving to CM (I M) after a Dm iim). Imagine the BASS player get's that chord sheet starts waltzing off C# instead of G

However, I think that too many of the Triad-over-Bass chords are being mistaken as universally a "IV/V" (which often they can).
Their interval structure can invert into a many other chords with often the root even missing and thus the count or ID'ing of the chord further blurred... and then, thats when the theories hit the fan.

Thanks!... J-D.