Help: What is a Chord?

Subject: RE: Help: What is a Chord?
From: GUEST,Bruce O.
Date: 01 Feb 01 - 03:25 AM

Lets look at a diatonic scale, [C-->B = 264, 297, 330, 352, 396, 440, 495] so major (triad) chords have notes with frequencies in the classic ratios of 4:5:6 and minors in the ratios 10:12:15. Lets look at the scale of C major/ionian | A minor/aeolian. All the chords from letter notes (no sharps or flats is in the sequence:

F A C E G B D

Note that 3 successive notes is a chord, major if you start on an odd numbered letter and minor if you start on an even numbered letter. We can reverse this ordering by using:

F Ab C Eb G Bb D or F# A C# E G# B D#

From that we can easily go back to the original ordering with:

F# A# C# E# G# B# D# and Fb Ab Cb Eb Gb Bb Db

One discovers with these that to keep the major and minor chord ratios all flats must be 24/25 times the note frequency, and all sharps are 25/24 times the note frequency. A just intonation scale is these 21 notes (based on A=440). This scale includes E#, Fb, Cb, and B#, all rather rarely found. A 12 tone equal temperament scale (commonly abreviated 12TET) only approximates the classical ratios.

Note that the number of chords possible is quite large and depends on the scale used. An experimental consonance distribution is given in Juan G. Roderer's 'The Physics and Psychophysics of Sound', 3rd edition, p. 167, 1995, and note pairs judged consonant by 60% or more untrained ears ranged from a minor 3rd (6/5 ratio) to a major 5th (3/2) ratio, and peaking at just over 80% of ear-pairs for a ratio just barely over a major 3rd (5/4 ratio). Throw in another note or two (using the same ratio range again) and, depending on how many notes are in your scale, you can make a big pile of chords. [Untrained ears were used since a professional singer or musician would listen for what they were trained to listen for.]

Subject: RE: Help: What is a Chord?
From: English Jon
Date: 01 Feb 01 - 04:17 AM

Without going back to Pythagoras, it's probably sufficient to say that Don's implication that A+A octave is a perfect interval is subjective to the context of the system of intonation, as Bruce has described.

There is a piece by Michael Harrison called "from different worlds" or something, that uses a piano cleverly engineered to play just intonation in all keys (by means of a very complex pedal board). It includes a Chorale section (Bach pastiche) that is quite astonishing, simply because of the intonation systems employed at each recapitulation. Listen to that, and it should tell you everything you need to know about pitch systems.

I'm currently working on a Scherzo for harpsichord in Kirnberger tuning. (starts getting wild about E),and I know people who play in Scholar's Lute etc etc. Most people seem to like Equal Temperament though. Blame Bach, blame the Accordion, I don't care. Sure it wiped out a lot of local pitch systems, but it did mean that more people were playing within the same pitch systems.

God, I'm boring. I still maintain that it doesn't matter whether E,B,E is a chord or not. Nobody says you have to play chords.

Best wishes, Jon

Subject: RE: Help: What is a Chord?
From: late 'n short
Date: 01 Feb 01 - 11:00 AM

What is a chord?

...it's one of the first 7 letters of the alphabet in upper case form sometimes joined by lower case letters such as "m" "sus" etc. and an occasional number or symbol that, when associated with a diagram shows me what strings to hold down at which fret of the fingerboard (I love using all of these technical musical terms)of my guitar with which fingers so that when I strum the strings it sounds like it should sound according to the melody of the song I'm attempting to sing (which I do better than most) and play (which I'm getting better at) because I'm already familiar with it.

...it's the thing I desparately search for so that I can expand my limited repertoire and therefore provide some variety as I entertain myself and the limited audiences for which I perform.

...it's something that the Forum in general as I browse through it, and some of you in response to my specific requests, have been great in helping me locate and I thank all of you for that. And I really do wish I understood what you've been talking about!

Dan

Subject: RE: Help: What is a Chord?
From: Don Firth
Date: 01 Feb 01 - 04:19 PM

I wrote a lot of four-part harmony exercises in freshman music theory classes at the U. of W. School of Music. If I got myself into a voice-leading bind and tried to get out of it by cobbling together a chord with the 3rd missing, the paper invariably came back with a big red circle around the chord and a note, also in red, saying "Missing 3rd!" or "Incomplete chord!" or some other indication that I wasn't going to get an "A" on that paper. Double the root, leave out the 5th if it's absolutely necessary, never double the 3rd, but never leave the 3rd out. It was drilled into my head that a chord requires a root, a 3rd, and a 5th. If the 5th was missing but the tripled root and 3rd sufficiently maintain the identity of the implied chord within the context of what went before and came after, that -- on occasion -- was permissible.

This was freshman theory, and as Prof. John Verrall said, "Here, we are learning the strict rules of harmony and voice leading. Later, when you know the rules thoroughly, we'll learn some ways of breaking them to good effect."

Hand goes up in the back row: "If these rules can be broken, what's the point of spending all this time learning them in the first place?"

Prof. Verrall responds: "If you start breaking the rules now, without knowing them thoroughly, the results will be haphazard and unpredictable. Following the rules helps guarantee that what you write is correct and will sound harmonious. But -- if you always follow the rules strictly, what you write may not be very interesting and certainly not innovative. Once you know the rules, when you break them, you will know exactly what you are doing and why you are doing it!"

There are three songs I sing, Bonnie Dundee, The Earl of Moray, and MacPherson's Lament, in which the accompaniments I play "break the rules" in exactly the manner that started this discussion. To try to evoke the drone sound of a bagpipe, I play open 5ths in the bass -- with no 3rd in sight (but I don't call them "chords," I call them "open 5ths"). I don't do it all the way through; I move into standard chords in the verses and I play a chunk of the melody as a intro and between verses, but the "vamp 'til ready" is open 5ths, to keep the effect going. I'm a bass, not a tenor, and I can't sing the songs in the same keys that he does, so the arrangements are my own, but I snitched the idea from Richard Dyer-Bennet.

It may sound kind of hokey the way I described it here, but it creates the effect I am after and I works for me. I met an old Scotsman once who hadn't been to the old country in years. He liked the Pacific Northwest, but he was, as he told me, "homesick for the heather." He asked me if I knew any Scottish songs, so I played and sang The Earl of Moray for him. At the end of the song, he brushed away a tear and asked me to sing it again.

As I say, it works for me.

Don Firth

P. S. Try going to google.com and type in chord. It's cuh-RAZY out there! Here are a couple of good ones:
here (you can back-track on this into a wealth of information that I sure a lot of Mudcatters have already found. I've spent a lot of time milling around this website.) and here for a lifetime supply of chords.

Subject: RE: Help: What is a Chord?
From: McGrath of Harlow
Date: 01 Feb 01 - 04:43 PM

Sounds like an arsey-versy way of structuring teaching to me, but I know there are lots of people who really do work on the theory-is-the-basis-of-practice approach, rather than theory-grows-out-of-practice.

I think it's like being left-handed or right-handed, largely down to the way our brains are wired. Buty I think people often seem to assume that the way their own brain is wired is the way everyone else's brains are wired, and it's just sheer cussedness when people don't seem to match up to that. (And that can happen just as much the other way round, with theory-grows-out-of-practice types.)

Subject: RE: Help: What is a Chord?
From: Don Firth
Date: 01 Feb 01 - 06:56 PM

Actually, the bus runs both ways. Music theory is not a rigid set of rules that everybody (except folk musicians) has to follow. It's fluid and ever changing. It is derived from studying what real live musicians do, looking for patterns and principles, and trying to work it into some comprehensive system. For example, the first time a Dominant 7th chord was ever used (that anyone knows about), it was by Monteverdi an a choral arrangement of Summer is a-Comin' In, right at the end. The Dominant 7th chord contains a diminished 5th (in a G7, it's the combination of B and F. In medieval times, a diminished 5th was regarded as "The Devil in Music" and it was considered on the verge of blasphemy to write it or play it. But Monteverdi wanted a "drop the other shoe" effect at the end of the piece, so he went ahead and used it anyway. Critics at the time were outraged. One of them said "The human ear will never grow to tolerate such dissonance!" But . . . there are not very many pieces of music written within the last couple centuries that don't make extensive use of Dominant 7th chords. It's one of the Big Three basic chords in any key. "The Devil in Music" is the famous "flatted fifth" in jazz. Nowadays, it's pretty tame. Music theory adapts to what is actually being done.

I started singing and playing the guitar when I was 22, and I was a real musical ignoramus. I had to rely on other people or on chord diagrams in songbooks to show me what chords to play. Since my interest in folk music was really serious, I decided to study music so I would know what the hell I was doing. A few of my folksinging compatriots had a hissy-fit. "They'll ruin your creativity." "You'll be bound by all kinds of rules." "They'll stifle you." And all kinds of other dire warnings. But far from being stifled, studying music theory showed me what is possible. Within a couple of months I was working out my own accompaniments. Within a few more months, people were asking me what chords to use!

Sure, I could take a folk song and arrange it like a Beethoven string quartet. But that didn't mean I had to. My guitar accompaniment for The Three Ravens is a dead-ringer for a Renaissance lute accompaniment. But I accompany Down in the Valley with two first position chords and a thumb-strum-strum, thumb-strum-strum right hand.

I've always been curious. . . a very good folksinger-guitarist friend of mine was one of the most vociferous in trying to persuade me not to study music formally. He told me that he couldn't even read music, he didn't know how chords were constructed or what notes made them up, and he didn't know how the chord families related to each other. He had learned everything he needed to know from a copy of Guckert's Chords for Guitar without Notes or Teacher, and he was getting along just fine. I learned much later that before he took up the guitar, he had studied classical violin for nine years. What was he playing at, I wonder. . . ?

Don Firth

Subject: RE: Help: What is a Chord?
From: McGrath of Harlow
Date: 01 Feb 01 - 07:21 PM

I'm not knocking the musical theory, I'd love to understand more about it. It's just that I get into theory by trying to make sense out of stuff that has interested me in practice (in all kinds of fields), and I've observed that some people seem to work the other way round.

And I've also seen how the two sorts of people often do in fact tend to take it for granted that the people they are teaching, or dealing with in other ways, think the same way as they do.

I think that this misunderstanding lies at the root of a lot of problems that arise, both in teaching and in other settings.

Subject: RE: Help: What is a Chord?
From: Lucius
Date: 01 Feb 01 - 08:01 PM

In my younger days I loved to play jazz guitar. Tunes like "So What!" and "Maiden Voyage" were my delight. I loved to stack fourths (E-A-D-G) in what I thought was quartal harmony, but apparently I wasn't playing chords?? No wonder my mates were always wondering who had the solo.

These days I spend my time teaching fourth graders how to play "Smoke on the Water" I don't tell them that the open fifths that they are playing are diads. They probably hear enough of diads in Greek mythology.

I really don't remember much about the grades that I got in freshman theory, but I remember more about what I learned in my 16th century counterpoint class. Funny how Joseph Fuch's made no mention of chords in "Gradus an Parnassus". Then again words like polyphony and homophony are no longer bandied about in polite company.

So I'm obviously being too generic, but I'll continue to solo on my fiddle (even if I toss in an occasional double stop) and bang out chords on my guitar. If it looks like a duck and quacks like a duck.......

Subject: RE: Help: What is a Chord?
From: McGrath of Harlow
Date: 01 Feb 01 - 08:15 PM

If it looks like a duck and quacks like a duck....... it might well be a decoy.

There was a sad story a couple of moths ago about some guy who used to go out hunting, and he could make a wonderful imitation of the mating call of a female duck, and when the hopeful drakes turned up, he'd shoot them.

One day he was doing this and another hunter turned up, thought he was a duck, and shot him dead.Well it was sort of sad, but...

That was unconscionable thread drift, I'm afraid.

Subject: RE: Help: What is a Chord?
From: pict
Date: 01 Feb 01 - 10:53 PM

I think if you want to be the kind of musician who wants to maximise their creative potential and be able to fluently play on their instrument what they hear in their head it is wise to make use of the accumulated musical knowledge of centuries after all many great masters have contributed to that store of knowledge.Having a good knowledge of theory is invaluable when it comes to any serious attempt at composition and orchestration/arranging there comes a point when you know what you need to know and that knowledge opens doors to musical dimensions you might otherwise never have had access to.

I think the best way to come to theory is after playing a few years having learned by ear.I'm amazed at how incapable some classically trained musicians are of improvisation.I don't think becoming a notation slave is very good for a players musicianship but then again complete ignorance of what is actually happening on your fingerboard,keyboard etc isn't the best thing either.

Subject: RE: Help: What is a Chord?
From: finnmacool
Date: 02 Feb 01 - 05:38 PM

I had a chord once but I lost it.

Subject: RE: Help: What is a Chord?
From: mousethief
Date: 02 Feb 01 - 05:45 PM

Finn, I think the Moody Blues did an album about looking for that runaway.

Subject: RE: Help: What is a Chord?
From: GUEST,Bruce O.
Date: 02 Feb 01 - 06:09 PM

I believe that 'music theory' is a generalization of that which has been found to work in practice. It's usefull for analysis, but no predictor of what a composer should do (except to avoid those concepts that didn't prove to be very good). As far as I'm concerned the 7 'greek' modes are just tags that have been accepted through long usage, so it doesn't matter if any Greeks ever heard them. They're still moderately useful as a starting point for a classification scheme (as they would be by any name, except maybe for locrian, as there are several 7 note scales that would be far more useful).

Subject: RE: Help: What is a Chord?
From: Lucius
Date: 02 Feb 01 - 06:47 PM

I'm not trying to keep this thread alive, honestly!!! But Bruce O, theory is no predictor of what a composer should do?? Where does this leave Schoenberg?? Where he belongs; )

Subject: RE: Help: What is a Chord?
From: GUEST,Burke
Date: 02 Feb 01 - 11:36 PM

Instead of reading mudcat yesterday I was at choir practice & in the process looking at the music trying to evaluate the idea of chords in that context. Then tonight there was a musical & I got a chance to briefly quiz the college's resident composer.

My personal conclusion is that context is everything & even the lofty Dr. said as much in 2 different ways. So to the initial question, without fully knowing your context, Ed, we can't answer for you. I seems to be called a power chord by some, I've heard it called an open 5th.

Some of the contexts I was thinking apply are that for a guitar the process of holding down strings in some pattern & strumming would be thought of as playing a chord. If one could pretzel the fingers up (or is it spread them out) and have all 6 strings playing the same note, I think there's a stong sense for the guitarist that they are playing a chord. A unison chord would otherwise certainly an oxymoron, but in the context probably the best that fits. Similarly holding down the strings that in strumming would constitute a chord, but instead of the strumming that plays them all essentially simultaneously, the stings are individually plucked. Does a guitarist still think of it as playing a chord? Or is it something else?

I thought of the finger picking as I looked at an accompaniment that involved a lot of arpeggios in a piano accompaniment. An arpeggio being the production of the tones of a chord in succession and not simultaneously, theorists & composers look at them pretty much the same way as a chord & define them with the same neat numbers. So they are sortof, but not quite chords. We also had a couple of sections where we were singing in 2 parts. Unaccompanied 2 parts are?

In reading Don's composition class & listening to the professor (a cool guy) I can't help focusing in on how immediatly they move from defining a chord into rules of composition. Don's professor allowed that 1-3 was ok but 1-5 was not (some root doubling as well) in a compostion. Don almost, but not quite says that first, because permitted is a chord, while the second is not. My prof. basically said you could get away with 2 notes where the 3rd was implied by the context. I also then was told of pieces he delights to assign for analysis because they don't fit the expected conventions.

When I told him our debate was in regard to folk or popular music his immediate reaction was that, the rules don't necessarily apply. Almost without prompting the 'power chord' came up. It would seem the chord is played in the very low range, which, especially with amplification, ends up creating a whole lot of cool overtones & is exactly the desired effect. It's also flexible because neither major nor minor it can fit into either context.

I am self taught when it comes to theory because what I've cared most about is understanding the Sacred Harp music I sing; & perhaps more, understanding the way other people talk about it. Almost everyone I know who's got the technical musical backgroud gets into relishing how it breaks so many of the rules they learned. This is particularly in the area of open 5ths, parallel 5th, and dissonances that do not properly resolve. (You hear that enough & you have to go learn some theory)

Historically the music of the New England singing masters that is included in the Sacred Harp was utterly disdained by the growing European art music informed music establishment. The music of people like William Billings, Daniel Read, Lewis Edson, etc. did many of the things forbidden by the rules of composition. This music was tremendously popular with the everyday, ordinary singer. I personally am immensely grateful that at least some folks refused to bend to the dictums of taste & kept it alive. If you want more information on that particular period I recommend Music of the highest class : elitism and populism in antebellum Boston / Michael Broyles. New Haven : Yale University Press, c1992. It applies to far more than just Boston. Another interesting book is Lowens, Irving, 1916- Music and musicians in early America. New York, W. W. Norton [1964]

A lot of the later music in the Sacred Harp is of folk origin & was frequently written in just 3 parts. I can't say I pay a lot of attention to what the chords are, but I can assure you that even with added alto parts, there are frequently tunes that begin with no 3rd on the opening note. When the keyer sounds the opening notes we all sure think of it as being the opening "chord" regardless of the 3rd. Yes, if someone doesn't at least sound the 3rd before we start I can get confused on the tonality of the piece, but then I've been known to blow singing straight up a minor scale. The Sacred Harp is not online, but the closely related Southern Harmony is. A couple of tunes (melody on middle line) clearly of folk origin to look at are Indian Convert (Nashville in Sacred Harp with much better words), Sweet Rivers, Green Fields, and New Britain. David's Lamentation, Easter Anthem, Schenectady, & Ocean are all 4 part songs by 18th century northeasterners

I know people who are pretty successful in writing music in this style. Some of these are professional musicians who heard the music, loved it, & used the analysis tools they learned in music theory to understand how the effect they heard is accomplished. Figuring out the 'rules' of Sacred Harp harmonies enabled them the write in the style. There are others who have no formal training, but singing it all their lives have put their hand to it & can write perfectly in the style. I can think of 2 or 3 tunes that were added in the 1991 edition, that I can't belive were not among the first I learned, they are that wonderful & on target.

The library is about to close & I must go. On Wednesday I was mostly bent out of shape because I took the trouble to go 'look it up' & got basically no acknowledgement.

Subject: RE: Help: What is a Chord?
From: Don Firth
Date: 03 Feb 01 - 05:52 PM

Subject: RE: Help: What is a Chord?
From: Don Firth
Date: 03 Feb 01 - 05:56 PM

(Whoops! Clicked on "Submit" before I was ready.)

A lot of good points, Burke. This spirited discussion was good for me in that it got me digging into my old textbooks, which I should have spent more time with the first time around.

Up until the early 1700s composers and musicians thought almost exclusively in "horizontal" terms -- melodic line -- with the interweaving of two or more melodic lines (counterpoint) being subject to all kinds of rules. One of the things that makes J. S. Bach such a biggy is that just about everything he wrote (and some very complex stuff) was super-"correct" in terms of the rules, but in the process he somehow rewrote the rule book for counterpoint. Strange that harmony, i.e., thinking "vertically" didn't really get started much before the early or middle eighteenth century.

Another tidbit I just ran across was that the first extensive use of the modern major scale as we know it (actually the same as the Ionian mode) was by the early troubadours. When, exactly, nobody can say, but the troubadours started their wanderings as early as the eighth or ninth century. Many of the younger monks and scholars had been set to the task of translating early Roman poets from the Latin in an effort to improve the church's rather abysmal knowledge of Latin grammar. In doing so, they encountered Catullus, their eyebrows (among other things) went up, and they began suspecting that the "sins of the flesh" might be worth some further investigation. At the same time, monasteries near the coastlines were increasingly subject to Viking raiding parties (the Vikings, being pagans at the time, were not averse to stomping in, laying about them with sword and ax, and running off with golden crosses, chalices, and other pretty trinkets) so sometimes churches and monasteries were not real safe places to be. Many young monks and scholars defrocked themselves, picked up a portable musical instrument of some kind, and took to the roads to see some of the world. They supported themselves through their knowledge of poetry (Catullus and others) and their musical skills. Helen Waddell's The Wandering Scholars details the fascinating story of the early troubadours and wandering minstrels who, she says, were responsible for writing and spreading many of the older folk ballads!. Taking the news of the day or some interesting story, writing it into a poem, and setting it to music. Anyway, the major scale (Ionian mode) wasn't used that often by the church, because it wasn't mournful-sounding enough for chants. It sounded too bright, happy, and full of lust! Church musicians of the time called it modus lascivus! But the troubadours were undeterred (not unlike modern folksingers) and used it freely. They also made extensive use of the other modes, which may account for so many of the older ballads being modal.

On chords, I just recalled a demonstration in a theory class I took in 1963 at Cornish School of the Arts. Professor John Cowell, stepped up to the piano and carefully arranged his feet and fingers (I don't play piano, so I'm not sure how he did it). He held the appropriate pedals down so that the sound would sustain, then he came down heavy on a combination of notes -- a stack of perfect fifths, as many doublings as his fingers would allow. We could hear a major 3rd, even though he wasn't playing one! He told us that the combination of notes he played, further combined with the piano's sustain, reinforced the overtones so strongly that you could hear notes that -- well -- were they really there, or weren't they? On paper, no. But in the reverberating air, yes!

I think you are right about context. Whether a particular combination of notes should or should not be called a "chord" -- especially as it relates to folk music -- is literally academic.

Whatever works.

Don Firth

Subject: RE: Help: What is a Chord?
From: Murray MacLeod
Date: 04 Feb 01 - 02:17 AM

Don, you are obviously much better versed in the theory of harmony than I am, but I have to take issue with your contention that it only takes three notes to make a diminished chord, no matter what the theory might say.

When B,D, and F are sounded together whether simultaneously or as an arpeggio, the western ear will automatically hear a G7 chord,( subconsciously interpolating a G) and want to hear a resolution to C major. The fact that the three notes together are called a dimiminished triad by theorists is neither here nor there. However , if you add a G# then the listener's expectation is totally changed, and you do in fact have a diminished chord.

Murray

Subject: RE: Help: What is a Chord?
From: Don Firth
Date: 04 Feb 01 - 03:49 PM

Well, it's still a diminished chord. By definition. Believe me, I'm not making any of this up. But that's not the whole story. Again, it's a matter of context. There's no way of explaining this stuff briefly (would that there were), but if you follow me all the way here, I think you'll find the ultimate answer satisfactory.

Any group of three or more notes, composed of a root, 3rd, and 5th is a chord. A chord frequently has more notes than just three (I'm not talking about added-note chords like 6ths, 7ths, 9ths, 11ths, and 13ths here, that would just add needless complication, but suffice it to say that added note chords usually start with the basic triad [root, 3rd, and 5th] then go from there). For example, A first position C chord on the guitar. The notes, beginning with the fifth string and going up, are C E G (the basic triad) C (doubling the root) and E (doubling the 3rd). A full symphony orchestra may be playing hundreds of notes at any given moment, but it you eliminate all of the doublings, you usually wind up with three basic notes -- a triad. With some modern music, e.g. twelve-tone, all bets are off!

Both the major and minor chords contain an interval of a perfect 5th. It's the note between the root and the 5th that make the difference. A major chord has an interval of a major 3rd on the bottom and an minor 3rd on top. A minor chord has a minor 3rd on the bottom and a major 3rd on the top. Now -- a diminished chord has a minor 3rd on the bottom with another minor 3rd on the top. The result of this is that it does not contain a perfect 5th. It contains a diminished 5th. That's where it gets it's name. All it requires to identify it as a diminished chord is the basic triad -- three notes. You can say with certainty that in the key of C, the root of the diminished triad is , the 3rd is D, and the 5th (in this instance, diminished rather than perfect) is F. You form the Dominant 7th chord either by adding an F to the G major triad, or adding a G to the B diminished triad. If you add a G# to the B diminished triad, you are adding a note that does not belong in the key of C.

But -- if you do add a G# to a B diminished triad, no one will smite you hip and thigh and cast you hence. In fact, you have a very useful chord. This is the configuration that is commonly called a "diminished chord."

In a way, a diminished chord (G# B D F) is neither fish nor fowl. It has a very vague identity. Follow me here, because this gets cute:

If you start with a Dominant 7th chord (say a G7), you instantly know what key you are in -- or, least what key you are heading for: C. The 3rd of a Dominant 7th (in this case, a B) is the "leading tone" of the key it's in, so you know it's pointing directly at the C chord. At the same time, the F wants to drop a half-step to an E. The ear wants to hear a C chord. It may not actually go there, but that's the kind of tease that keeps a piece of music going. I'm sure you're familiar with songs, e.g., in the key of C, where you go to a D7 then to a G, then to a G7, and back to a C again. That's a mini-modulation. For a second there, you were in the key of G before you changed it to a G7 and returned to the original key.

With our four note diminished chord, all of the intervals are dead even. It is a pile of minor thirds. If you invert any of the notes (take the bottom note and put it on top) you still have a pile of minor thirds. In addition, all of the 5ths are diminished 5ths. If it suddenly appears out of nowhere, there is no way of identifying which is the root, which is the 3rd, which is the 5th and which is the added note. The result is any one of the four notes can be regarded as the leading tone. Some of the notes want to go up a half-step and some of them want to go down a half step but there is no way of telling which is which. The ear is waiting for some other shoe to drop, and it will accept any resolution of the harmonic tension, just to get it over with.

So -- if you go to a G7, then suddenly slide the root (G) up a half-step to G# to form a four note diminished chord (which you can call by any one of four names -- G#dim, Bdim, Ddim, or Fdim -- your choice), you can then resolve it to A, C, Gb, or Eb. But going back to the C would make the exercise kind of fruitless, because you just came from there.

This is why jazz musicians in particular like diminished chords (the four-note kind). You can toss in a diminished chord, modulate to another key, toss in another one and go to yet another key, and on through the night. . . .

The fact that a B, D, and F are all you need to constitute a diminished chord (as I say, by definition) doesn't change the standard practice of adding a G# to the triad. It just (I hope) clarifies the use of terminology.

Don Firth

Subject: RE: Help: What is a Chord?
From: Don Firth
Date: 04 Feb 01 - 03:58 PM

Blast! Once again, I miss a closing HTML code! Or something! Sorry.

It should read "root of the diminished triad is B, the 3rd is D," etc. . . .

Don Firth