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Thread: Question about Augmented chords

  1. #1
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    Question about Augmented chords

    Ok, I started playing guitar about 5 months ago, but ive also been playing eltric bass for 2 year, so i know a little bit of music theory, but not a whole bunch. My question is about Augmented chords. The basic major triad is a 1-3-5, and for Augmented it is 1-3-#5 which make sense because whehn you sharp a note it becomes augmented, but why does the 3rd remain natural as opposed being sharpened as well?

  2. #2
    bitter old fool Jed's Avatar
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    It's just a name . . .

    You can't apply overly critical logic to many music terms. The sounds came first, then someone applied a name or likely several different people applied several different names, and this one stuck.

    Music terms have evolved into a technical language but it wasn't designed from day one with the kind of logic that you are viewing it now.

    It's just a name . . .

  3. #3
    Registered User JonR's Avatar
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    Quote Originally Posted by SnufdaCrimeDog
    Ok, I started playing guitar about 5 months ago, but ive also been playing eltric bass for 2 year, so i know a little bit of music theory, but not a whole bunch. My question is about Augmented chords. The basic major triad is a 1-3-5, and for Augmented it is 1-3-#5 which make sense because whehn you sharp a note it becomes augmented, but why does the 3rd remain natural as opposed being sharpened as well?
    The way I see it is it comes from interval terminology. An "interval" is a pair of notes, measured from the lower one in notes and half-steps.

    A major triad is composed of two intervals: major 3rd (1-3, four half-steps) and perfect 5th (1-5, seven half-steps). When a perfect interval is enlarged by a half-step, it's known as "augmented". So 1-#5 is an "augmented 5th" interval.
    The 3rd is always major, because that's the only kind that will go with an augmented 5th in any of the scales we use. So calling the chord "augmented" (short for "chord with augmented 5th") makes sense.

    Caug
    -0- = E = 3
    -1- = C = 1
    -1- = G# = #5
    -2- = E = 3
    -3- = C = 1

    So what happens if use the note a half-step above the 3rd (as well as the #5)? That makes a perfect 4th above the root:

    Caug(sus4???)
    -1- = F
    -1- = C
    -1- = G#
    -3- = F
    -3- = C

    ..in fact, we would hear that chord as an Fm chord ("Fm/C"), and the "G#" would effectively be Ab.

    Fm/C ("2nd inversion")
    -1- = F = 1
    -1- = C = 5
    -1- = Ab = b3
    -3- = F = 1
    -3- = C = 5


    Technically, the 3rd could be augmented - raised to E#. (Enlarged major intervals are also called "augmented".) But again, such an interval does not occur in any of our usual scales. (E# does occur in some scales, but not with C.)
    If you invented the chord C-E#-G# (which you could), it would need to be called "C#5#3"(!) - but why bother when it sounds like Fm anyway?

    You might be wondering why the same note gets given two different names (G# = Ab, E# = F)?
    A note with two possible names is "enharmonic", and which name is chosen depends on which scale we are referring to. Every scale has to have 7 different notes (one of each letter).
    An Fm chord can't have G#, because there is already a G in the scale it comes from.
    F-Ab is 3 notes - a "minor 3rd" (3 half-steps) - which is where the chord gets its name.

    (Sorry if this is too much info... If your head is exploding, just refer to Jed's explanation... )

  4. #4
    Registered User Malcolm's Avatar
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    .....but why does the 3rd remain natural as opposed being sharpened as well?
    Joh said; --- Technically, the 3rd could be augmented - raised to E#. (Enlarged major intervals are also called "augmented".) But again, such an interval does not occur in any of our usual scales. (E# does occur in some scales, but not with C.)
    I checked my handy dandy chord formula site and sure enough just like Joh said ---- the 3rd is flatted to make the chord minor and left natural to make it a major chord. And that is all that is normally done with the 3rd. My chord formula site does not have a sharped 3rd anywhere.

    Again, just one of those things the old guys worked out a long time ago --- just flat it don't sharp it.

    Here is the chord formula site I talked about:
    http://www.smithfowler.org/music/Chord_Formulas.htm
    Last edited by Malcolm; 03-29-2008 at 02:34 PM.

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    Or, without ridiculous enharmonic obsessiveness, and without claiming that it's just a name - there's no such thing as a sharpened third, it's just a perfect fourth.
    There is such a thing as quartal harmony, which sounds like it's from Star Trek, where you build chords as fourths rather than thirds, but it's a bit different - and might not technically exist.....

    Anyway, augmented chords pretty much come from building chords from the harmonic minor scale, rather than the major scale.

    So in A harmonic minor, there are the notes a, b, c, d, e, f, g#, a
    (start it on c to get the augmented scale.)

    If you build chords from that you get:

    A minor
    B diminished
    C augmented <---here it is!
    D minor
    E major
    F major
    G# diminished

    or if you wanna delve further into what you can get out of the scale you can even get more than one chord on some degrees of the scale, and some interesting alterations. I love the Fmin -Amin progression. You also get the diminished chord trick, where there are four diminished chords a minor third apart with exactly the same notes, which leads to some fascinating moves.

    I put some of the cool ones below.

    Amin; A min/maj 7
    Bdim7
    Caug
    Dmin; Ddim7; Dmin7#11
    E7; E7b9; Eaug; Eaug+b9; Eaug+dom7b9
    Fmaj; Fmin; Fdim7; Fmaj7#9
    G#dim7; G#aug;

    Most of them are sweeter than they look too. They're not just crazy dissonant jazz chords, they've got a lovely augmented exotic feel to them.

    Apart from Fmaj7#9. It is to my ears the most creepy, weird and unnatural chord in the whole of music =)
    Last edited by daysinthewake; 03-31-2008 at 01:54 AM.

  6. #6
    bitter old fool Jed's Avatar
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    Quote Originally Posted by daysinthewake
    Or, without ridiculous enharmonic obsessiveness, and without claiming that it's just a name - there's no such thing as a sharpened third, it's just a perfect fourth.
    For any Major interval:
    Converting the interval to Minor reduces it by one 1/2 step
    Converting the interval to Diminished reduces it by two 1/2 steps
    Converting the interval to Augmented enlarges it by one 1/2 step

    For any Minor interval:
    Converting the interval to Diminished reduces it by one 1/2 step
    Converting the interval to Major enlarges it by one 1/2 step
    Converting the interval to Augmented enlarges it by two 1/2 steps

    For any Perfect interval:
    Converting the interval to Diminished reduces it by one 1/2 step
    Converting the interval to Augmented enlarges it by one 1/2 step

    For Triads:
    A Major triad has a Major 3rd and a Perfect 5th
    A Minor triad has a Minor 3rd and a Perfect 5th
    An Augmented triad has a Major 3rd and an Augmented 5th
    A Diminished triad has a Minor 3rd and a Diminished 5th

    These are conventions, that do not stand up to logical analysis. They are what they are. You can try to impose logic on the system (Ex. For triads, the terms major / minor reflect the nature of the major/minor intervals only. Perfect intervals are neither major nor minor and so are unaffected by the change from major to minor). But the same logic cannot be extended to Diminished / Augmented triads. Standard logic is based on symmetry, musical intervals and triads follow an asymmetric logic with asymmetric rules.

    The names / terms used are not important beyond that fact that they are standard conventions. These terms are defined by the rules / definitions listed above. Since the definitions are asymmetric (context dependent) there will be no symmetry to the logic. They are just names. ("Nothing to see here, move along")

    The OP asked why an augmented triad has an augmented 5th but not an augmented 3rd. He could as easily have asked why a diminished triad has a diminished 5th but not a diminished 3rd.

    There are no logical answers to these questions because the very definitions of these terms are not based on standard (symmetric) logic, but rather are rooted in observation relative to the behavior (or apparent behavior) of intervals. The terms do not refer to mathematical operations but intervalic operations. They are naming conventions - in other words, "It's just a name." The sound existed and someone named it. End of story.

    cheers,

  7. #7
    bitter old fool Jed's Avatar
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    So 1-#5 is an "augmented 5th" interval.
    The 3rd is always major, because that's the only kind that will go with an augmented 5th in any of the scales we use. So calling the chord "augmented" (short for "chord with augmented 5th") makes sense.
    The above is as close as we will get to logic in this regard, but it still flawed unless we accept Jon's expanded definition of augmented being <short for "chord with augmented 5th">.

    By the same token, 1-b5 is a diminished interval. The 3rd is always minor, because that's the only kind that will go with an diminished 5th in any of the scales we use. So calling the chord "diminished" (short for "chord with diminished 5th") makes sense.

    Again, all of this makes perfect sense if we are thinking in terms of intervallic logic as defined by the scales common to our musical system. But from a mathematical pov, the logic is a bit "fuzzy".

    cheers,

  8. #8
    Registered User JonR's Avatar
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    Quote Originally Posted by Jed
    The above is as close as we will get to logic in this regard, but it still flawed unless we accept Jon's expanded definition of augmented being <short for "chord with augmented 5th">.

    By the same token, 1-b5 is a diminished interval. The 3rd is always minor, because that's the only kind that will go with an diminished 5th in any of the scales we use. So calling the chord "diminished" (short for "chord with diminished 5th") makes sense.

    Again, all of this makes perfect sense if we are thinking in terms of intervallic logic as defined by the scales common to our musical system. But from a mathematical pov, the logic is a bit "fuzzy".

    cheers,
    "Mathematical" - since when do we expect music to have any logic of the mathematical kind?
    (Many people with a natural mathematical pov have followed that tempting but misleading cul de sac before... )

    You're right I regard the system you neatly spelled out as "logical". It makes perfect sense. Well OK, it's "rational" (maybe a better word), as long as you allow for certain shorthand conventions of a very human kind - and those conventions are also rational in their own practical terms. Plus, of course, a few historical/aural principles dating back to medieval times, if not to Ancient Greece.

    We DO get into awkward areas (in the sense of logic/rationality) when we hit "add9" "sus2" etc. The symbols can still be explained according to the evolution of a few sensible basic principles (which get pretty convoluted as they evolve) but on the face of it - analysing them as they are - there's a fair amount of bafling inconsistency.

    You're probably right a beginner should just accept "that's the way it is" - the more curious can delve into "why" if they want to, but it's not necessary.
    You know me, I always like to provide Too Much Information...
    (Personally, I worked out the "logic" myself. I came up with a "system" which seemed to explain the terminology to my own satisfaction. I guess that's all any of us can do. )

  9. #9
    bitter old fool Jed's Avatar
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    Quote Originally Posted by JonR
    You're probably right a beginner should just accept "that's the way it is" - the more curious can delve into "why" if they want to, but it's not necessary.

    You know me, I always like to provide Too Much Information...
    (Personally, I worked out the "logic" myself. I came up with a "system" which seemed to explain the terminology to my own satisfaction. I guess that's all any of us can do. )
    Jon,

    Like you, many of us that have done this for a while have no problem seeing the rationale as you describe it. You have a nice way of presenting mnemonics that aid with the transition from the mathematic to intervallic logic. But I do remember clearly, needing to suspend my need for strict mathematical logic when I first learned these conventions. (This may be the only thing I remember clearly from the 70's). Once I got over the horror of how inconsistently these terms were defined (as seen through the eyes of a scientist), I was able to get down to the business of learning about music.

    My point to the OP (as you pointed out with your cul-de-sac analogy) is that there is no peace to be found if we insist on resolving these inconsistencies in mathematical terms. The peace and the learning comes after we make these minor accommodations, leaps of faith as it were, into the language of music.

    cheers,

    PS Of course between you and I this is very much "preaching to the choir" but I think it's an important point for those who are internalizing the so-called logic of music.

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    Quote Originally Posted by SnufdaCrimeDog
    Ok, I started playing guitar about 5 months ago, but ive also been playing eltric bass for 2 year, so i know a little bit of music theory, but not a whole bunch. My question is about Augmented chords. The basic major triad is a 1-3-5, and for Augmented it is 1-3-#5 which make sense because whehn you sharp a note it becomes augmented, but why does the 3rd remain natural as opposed being sharpened as well?
    'Cos the Aug sign '+' means that it refers ONLY to the 5th of the chord, For instance to Augment the 3rd of a chord, then that would be a Perfect 4th or to put it another way, in a 'C' major chord, the 4th could become a suspended note held over from the previous chord which, in this case could have been a 'G7'...Anyways ,the '+' sign always refers only to the 5th degree in a chord.any exception to this rule would mean, that the Augmented degree-say a 9th, - would have that stated in the chord symbol!....For instance.an Augmented 9th would be written- C7+9, meaning that the '+' referred only to the 9th of the chord!

  11. #11
    Registered User JonR's Avatar
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    Quote Originally Posted by leegordo
    For instance.an Augmented 9th would be written- C7+9, meaning that the '+' referred only to the 9th of the chord!
    True, except that takes us into the world of jazz chord shorthand, which has its own ways of confusing the rest of us...

    C7+ = C7#5 (augmented 5th)
    C7+9 = C7#9 (perfect 5th, augmented 9th) *
    C9+ = C9#5 (augmented 5th, major 9th)
    C7-9 = C7b9
    C-9 = Cm9
    C-7-5 = Cm7b5

    * In rock this means the "hendrix chord", but in jazz "C7#9" is commonly used to indicate an altered chord, which has a b5 or #5.

    Sometimes, shorthand can get too short...

  12. #12
    Registered User JonR's Avatar
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    Quote Originally Posted by Jed
    Jon,

    Like you, many of us that have done this for a while have no problem seeing the rationale as you describe it. You have a nice way of presenting mnemonics that aid with the transition from the mathematic to intervallic logic. But I do remember clearly, needing to suspend my need for strict mathematical logic when I first learned these conventions. (This may be the only thing I remember clearly from the 70's). Once I got over the horror of how inconsistently these terms were defined (as seen through the eyes of a scientist), I was able to get down to the business of learning about music.

    My point to the OP (as you pointed out with your cul-de-sac analogy) is that there is no peace to be found if we insist on resolving these inconsistencies in mathematical terms. The peace and the learning comes after we make these minor accommodations, leaps of faith as it were, into the language of music.

    cheers,

    PS Of course between you and I this is very much "preaching to the choir" but I think it's an important point for those who are internalizing the so-called logic of music.
    All agreed, but I don't think most people will be bringing a strict scientific definition of "logic" to their study of music. (My best subjects at school were actually maths and physics, but not to the degree that it inhibited me when I began learning music - which was at the same time. I quite honestly don't remember ever being confused about musical terms. I was ignorant, then learned stuff, then knew it; never came up against a "huh, that doesn't make sense" moment. Maybe I'm just weird... )

    I think music terminology is fully consistent with a layman's understanding of the concepts of "logic" and "rationality". However, you really do need a little experience of music, and knowledge of theoretical concepts, before it does begin to make sense. (I guess I happened to learn things in the right order, by accident...)
    Which is, of course, because chord symbols are a shorthand designed by people who already understand all that stuff, and just want to communicate quickly with each other - it's not designed as a teaching tool. (Mind you, that can be a problem with many other aspects of music theory too... )

  13. #13
    bitter old fool Jed's Avatar
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    Quote Originally Posted by JonR
    All agreed, but I don't think most people will be bringing a strict scientific definition of "logic" to their study of music.
    Fair enough, but it would seem the OP did.

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