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 Dominant-diminished 7th theory
Author: DrH2O (---.prvdri.fios.verizon.net - ISP in United States)
Date:   2008-08-11 18:54

My teacher tries to infuse some music theory into my lessons as I progress, but as a total musical neophyte I must admit be being totally bamboozled more often than not.

Our most recent theory discussion was about 7th chords. Figuring that I could learn dominant and diminished 7ths better if I made sure I really understood how they're constructed, I went hunting for more information and being forced to confront my total ignorance of all things theoretical I've decided that music theory was created by a someone with a twisted mind and Klose was a co-conspirator determined to make it as obscure as possible.

For example -
Giving words meanings that run contrary to their usage in lay English:
LEADING - dictionary def. 1. chief; principal; most important; foremost;
2. coming in advance of others; first. It therefore follows that a leading tone should be the first tone of a scale not the LAST!

INVERSION - dictionary def. the act of reversing the order. It therefore follows that a chord inversion should go in reverse order instead of moving the root up an octave.

DOMINANT - dictionary definition. ruling, governing, or controlling. So the dominant tone will be the leading tone, wait, no, that's the last tone, so then it should be the first tone of the scale, no, that would make too much sense, let's make it the fifth tone, that should throw everyone off!

So, no matter how eloquently my teacher might have explained things to me, it was totally hopeless from the start because what I though I understood, I clearly didn't!

But now that I have the vocabulary sorted out, I figure I'm halfway there. Hardly! What really is a dominant 7th chord? One def says it's a major triad and a flatted 7th - so what's dominant about that? Another def says you start with the dominant tone in the major scale and then renumber the tones taking the new 1, 3, 5 and 7 tones without flatting the 7th tone. Gives you the same set of results I guess, but isn't it helpful to keep track of what scale each dominant 7th is really associated with? So a Cmaj7 would be CEGB. Using the first definition a dominant 7th based on a C major triad would be CEGBb, but using the second definition the dominant 7th should be GBDF with no C in sight. CEGBb should be the dominant 7th based on the F scale shouldn't it? Does it matter how you think of it? Or is it really more of a tonal thing? Klose puts his in order according to the root of the dominant 7th not the root of the corrseponding major scale - is that the most useful way to think of it?

Then diminished 7ths. Leading tone, 2nd, 4th, flatted 6th was the simplest definition I found. So a diminished 7th based on Fmajor would be E-G-Bb-Db. But Klose doesn't "spell" it that way. He writes it as E-G-Bb-C# and makes enharmonic substitutions like that throughout his diminished 7th exercises, like writing Bb-Db-E-G instead of A#-C#-E-G for the diminished 7th based on Bmajor. I have to admit that at my level, I appreciate having Bbb written as A, but when I'm trying to go through the inversions I end up mentally double-clutching when the note name doesn't go up by a third. Why not write it to be consistent with the key signature as much as possible or is there some other reason to change the "spelling"?

Can anyone clarify the how and why (in fairly simple terms)?

Thanks,

Anne
Clarinet addict


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 Re: Dominant-diminished 7th theory
Author: liam_hockley (---.bchsia.telus.net - ISP in Vancouver, ON Canada)
Date:   2008-08-11 19:10

The fifth degree of the major scale is called the "dominant" (in C Major that would be G). A "dominant 7th" is a major chord constructed from the 5th degree of the scale, with a flatted 7th added on top (G-B-D-F). Generally speaking, the dominant chord (G-B-D-F) resolves to the tonic chord (C-E-G). The reason it sounds "dominant" is because of the way it resolves: the "B" resolves up a half step to "C", which is the tonic note. The flat 7th ("F") resolves down a half step to "E", which is the third of the tonic chord. Try the "B-F" to "C-E" resolution on a piano... it will be really clear then.

As far as the diminished 7th enharmonic spelling goes, I am not sure why Klose changes the spelling. My guess would be that he was looking for an easier enharmonic spelling for students to learn, but I really don't know.

Hope this helps,
-Liam



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 Re: Dominant-diminished 7th theory
Author: sfalexi (---.dyn.optonline.net - ISP in Staten Island, NY United States)
Date:   2008-08-11 20:20

As far as Klose spelling, I'd like to believe that he is simply getting you USED to seeing it in different forms. So no matter HOW you see it written, it'll flow naturally through your fingers. So when I'm playing a piece and see it written, I'm used to seeing it written with ALL sorts of different enharmonics, and it's much easier to recognize as a dim 7th, regardless of the spelling. So if I had only seen it spelled one particular way, and then it was spelled a different way, it'd be harder to sight-read it and move on because I'd have to take a second to realize what it was.

Alexi - Who also practices the C# scale in ADDITION to the Db scale . . . for the same reason.

Clarinetist with the 282nd Army Band - Fort Jackson's Own

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 Re: Dominant-diminished 7th theory
Author: mrn (---.dsl.hstntx.sbcglobal.net - ISP in Houston, TX United States)
Date:   2008-08-12 00:41

A "diminished" chord is what you get when you stack minor 3rds on top of one another. If you stack two of them, you get a diminished triad. If you stack three (thus yielding 4 notes), you get a "diminshed 7th."

Since there are 12 semitones in the octave, if you keep stacking minor 3rds, you still have a diminshed 7th chord--the extra notes simply double the notes you already have. If you call each note name in the chromatic scale (C, C#, D, D#, etc.) a "pitch class," there are only three distinct set of pitch classes corresponding to diminished 7th chords. Yet there are 12 keys. Consequently, any time a dim7 chord is written down, you can't readily tell what the spelling is. C, Eb, F#, A might be Cdim7, or it might be Adim7 in first inversion, F#dim7 in second inversion, etc. The augmented 5th chord (C E G# in C major) is similarly ambiguous.

Because of this ambiguity, even music theorists don't agree on what the "root" of a dim7 chord is when played in a particular key. Some people say the root is the leading tone of the key. Others--including Walter Piston, who wrote my harmony textbook--analyze the diminished 7th as being an incomplete dominant 9th chord (a dominant 9th without the root).

The upshot of this is that in actual music you will see many different enharmonic spellings of the same set of pitch classes, regardless of key. The concept of key is thus less meaningful when applied to diminished chords. This is especially true of Klose's exercises, which are all written 20th-century style with no indication of key whatsoever.

Incidentally, Klose's scale pattern a few pages back is full of notational inconsistencies. Sometimes an accidental carries through from octave to octave and sometimes it doesn't--I don't know if this is intentional or not. I think what you have to keep in mind is that Klose was a performing clarinettist, not a composer or theorist, and his main concern was getting students to get the fingering patterns down, not theoretical purity. Note that in the instructions, he recommends that the scale pattern be memorized--so the sheet music is only intended to be a temporary crutch.

The trick in the dim7 exercise is learn to recognize the stacked minor 3rd pattern by sight and have it comfortably under your fingers. If you're trying to associate the notes on the page with particular keys, you're probably thinking too hard. :)

By the way, one thing that might be confusing you is that chords are named for their root notes, and NOT for the key they are in.

C7 (read C dominant 7) is C E G Bb and starts on C. C happens to be the dominant tone in the F major scale, but we don't care about that as far as chord naming goes. If you stack a major 3rd and two minor 3rds together, you get a dominant 7th chord. If the major 3rd starts on C (that is, the "root" is C), it's a C7 chord. If you have E G Bb C (same notes, but different order), it's still a C7 chord, but in first inversion. You can tell it's a C7, because you can figure out how to "un-invert" the chord to find the major 3rd interval there, which still starts on C. Notice that with a diminished 7th you can't do this, because no matter how you invert it, it's always a stack of three minor 3rds.



Post Edited (2008-08-12 14:36)

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 Re: Dominant-diminished 7th theory
Author: John O'Janpa (---.dhcp.hlrg.nc.charter.com - ISP in Richlands, NC United States)
Date:   2008-08-12 14:32

As a person who has played music on guitar and clarinet for decades without any music theory training, but with a good enough ear to play professionally at times, I have recently decided that I needed to better understand music theory.

I bought a book called The Complete Idiot's Guide to Music Theory and it has helped me understand music structures better.

It's sort of amazing to me that so many things, that are so complicated, are just done as a matter of course by people who play by ear, as I have done on guitar.

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 Re: Dominant-diminished 7th theory
Author: DrH2O (---.prvdri.fios.verizon.net - ISP in United States)
Date:   2008-08-13 02:06

Thanks all for your help. I see how learning the chords in all their various spellings makes you better prepared to recognize the note patterns for what they are. I will persevere.

It's interesting how sometimes my fingers know where they should go and as long as my brain doesn't interrupt they do the right thing. Other times I stumble all over myself and make a total mess of it.

Little by little I'll get there.

Anne
Clarinet addict


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 Re: Dominant-diminished 7th theory
Author: Mark G Simon (---.washdc.east.verizon.net - ISP in Washington, DC United States)
Date:   2008-08-13 15:10

The leading tone gets its name from its tendency to lead the ear to the tonic.

Inversion, in terms of triadic harmony, is a misnomer. It's not really about turning chords upside down, it's about which note of the chord is in the bass, or which note of the chord is on the bottom. Inversion makes a critical difference in the meaning of the chord. Only root position chords are stable. The 6/4 chord is actually a dissonance, which requires resolution to a 5/3 or root position dominant chord.

If you want inversion that really is inversion (i.e. turning things upside down) you'll have to explore 12-tone music.

Clarinetist, composer, arranger of music for clarinet ensemble

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 Re: Dominant-diminished 7th theory
Author: GeorgeL (---.hsd1.az.comcast.net - ISP in Tucson, AZ United States)
Date:   2008-08-13 16:51

As a recreational musician who has played in some pretty good community bands over the last 28 years, I have a question: how did you learn 'chords'? Was piano or guitar (instruments which play chords) part of your early training? Did it take a semester of music education? Were you able to improvise before you learned chords?

If you wonder why I ask the question, read through the answers from people who responded to Anne. Do you think anything that was written will make any sense to someone who does not already know the answer? It certainly did not to me.

I also wonder if musically trained people believe knowledge of chords will help a clarinetist play better. I have no doubt that this subject is a requirement for composing, useful for understanding music, and very helpful for improvising, but I rarely see 'Dim7' written by a series of notes - I see notes that I have to read, and whether or not I can play those notes depends on whether I have practiced them, not whether I can identify them.

I'm done; fire away. I was a lawyer, I can take it.

George



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 Re: Dominant-diminished 7th theory
Author: Dick (---.boeing.com - ISP in Seattle, WA United States)
Date:   2008-08-13 18:27

And (a little off topic), speaking of spelling - why does the simplest scale start on "C" instead of "A"? Asked previously, but no anwer offered.

Dick

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 Re: Dominant-diminished 7th theory
Author: allencole (---.hsd1.va.comcast.net - ISP in United States)
Date:   2008-08-13 19:32

Just a couple of thoughts:

Dominant - This probably isn't the best name for your V (5, that is) chord, but its origins and mechanics were well-explained above. The Musicians' Institute book "Harmony and Theory" beautifully defines it as one type of chord that "creates anticipation" for the chord which follows.

Diminished - One correction. The diminished is not a dominant 9th with the root removed. The HALF-diminished (dizzy yet, DrH20?) chord is the one that answers that description. Guitarists regularly substitute half-diminished chord forms when they want a dominant 9th with the third on the bottom. (bet you're dizzy now...) They also frequently make the substitution described in the next paragraph.

However, the diminished chord is a very popular substitute for V7b9 chord in minor keys. Listen to Benny doing "Sing, Sing, Sing" or Dizzy doing "Bebop" to hear it in action. I'm not sure if I should offer any further technical explanation of this.

Spelling the diminished chord - Proper spelling of a C diminished is C-Eb-Gb-Bbb. But that could also be A diminished, spelled A-C-Eb-Gb, or Eb diminished, spelled Eb-Gb-Bbb-Dbb. To really blow your mind, a Gb diminished would be Gb-Bbb-Dbb-Fbb. Or D#-F#-A-C, F#-A-C-Eb and the cycle starts again. I agree that proper spelling is pretty much out the window, except when stacking up piano chords. I also agree that Klose was probably exposing you do different spellings, as does the Universal Method for Sax on p. 212 or 214. (I sure hope I spelled these anywhere near right)

Diminished chords are generally used to transition between chord changse that are already pretty smooth. Between a scale's diatonic chords, for example. A very nice piece was done on them by Guitar Player magazine a year or two ago.

Theory Books - They're getting better every year. The "Idiot's Guide" is great. Also "Edly's Music Theory for Practical People" and "Harmony and Theory" from the Musician's Institute. Authors are getting better all the time at verbalizing this extremely abstract subject. If you want a crash course, get "Classical Music for Dummies" and read Ch.11 - "The Dreaded Music Theory Chapter."

Allen Cole

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 Re: Dominant-diminished 7th theory
Author: mrn (---.dsl.hstntx.sbcglobal.net - ISP in Houston, TX United States)
Date:   2008-08-13 20:51

That's right. I should have said dominant 9th with flatted 9th (V7b9) instead. Sorry about that.

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 Re: Dominant-diminished 7th theory
Author: buedsma (---.access.telenet.be - ISP in Leuven, 12 Belgium)
Date:   2008-08-14 19:18

georgeL,


When you know your chords by heart , you start reading the music in patterns
and don't have so much work with analysing every piece. Eg in weber you have descending diminished patterns. When you recognise the chord and did train intervals , starting with the correct note saves you reading the other 8 or 12 notes. When you didn't train this , you always have to read and learn those


Also handy : when making a mistake in a piece , knowing the place , chord etc makes you more agile in repairing your mistake


Why is the simplest scale called C and not apple or banana, is as good a question : maybe a musicologisty can tell us when note names were choosen and became standard.

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 Re: Dominant-diminished 7th theory
Author: Bubalooy (---.dip.t-dialin.net - ISP in Germany)
Date:   2008-08-14 20:07

Ok, I'll go out on a limb. The Klose spellings are wrong. Full diminished chords are stacked minor thirds. d flat to f flat is a minor third c sharp to e is a minor third but d flat to e is not. The sound is the same but the function is not.

GeorgeL Does learning theory make you a better clarinet player? You answered your own question inadvertently. You state that it helps you understand music. If you understand what you are playing, it makes you a better player. Interpretation should be based on understanding the construction of a piece of music. I admit that many players play well using intuition and what their ears tell them, but having a good understanding of how the music is constructed cannot make your playing worse, and is often the core of why a player may choose to phrase something in a particular way. When playing in a pretty darn good community band, and I believe there are many, these decisions are made primarily by the conductor, who hopefully has a good understanding of the construction of the piece.

Finally, to answer Dick's question of why the simplest scale starts on C instead of A. I'm afraid you are assuming that C major is simpler than A minor. A minor also has no sharps or flats. We could go into the history of plain chant and the eventual emergence of tonal music but that would take a great deal of time. Suffice it to say that A minor is just as simple as C major and does , in fact, start on A rather than C.

If any of this sounds in any way patronizing or condescending to anyone unfamiliar with music theory, I apologize. I don't want it to. Music is enjoyed by far more people with no theory background than people with it. I just feel strongly that a good knowledge of music theory is extremely helpful for enhancing a players performing abilities. The best performers no the entire score and how their individual part works in relation to the total.

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 Re: Dominant-diminished 7th theory
Author: golden.earring (---.lv.lv.cox.net - ISP in Henderson, NV United States)
Date:   2008-08-27 20:05

When I was living in Seoul I was dating a lady who taught singing. As I became interested in music I searched online to try to learn about music. I found lots of stuff, but most presupposed an existing knowledge of music of some sort, or it started you at the very basics and took you not very far. I found nothing to bridge the two...

"Music Theory for Dummies" to the rescue!! I actually found this to be a useful tool. It may not go into depth in all areas, but it did cover necessary items in a way that I was able to cross the bridge from basic to beyond basic.

Buy it from Amazon. If you don't like it, you can always send it back.

I have a question... If the C scale and its companion minor scale A consist of the same notes, and a music composer uses a scale as the primary source of notes for a composition, why have a C Major and an A minor scale? I don't understand why we have both when they consist of the same notes.

Anyone have an answer a neophyte can understand?

Thanks

Michael D

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 Re: Dominant-diminished 7th theory
Author: mrn (---.tx.res.rr.com - ISP in Frisco, TX United States)
Date:   2008-08-27 22:20

mrn wrote:

> I have a question... If the C scale and its companion minor scale A consist
> of the same notes, and a music composer uses a scale as the primary
> source of notes for a composition, why have a C Major and an A minor
> scale? I don't understand why we have both when they consist of the
> same notes.

Actually, they don't necessarily have the same notes. Only the "natural" minor scale has all the same notes (albeit with a different starting pitch).

Most of the tonal music we westerners are used to listening to is built using the "melodic" and "harmonic" minor scales, which are not quite the same as the "natural" minor scale.

See http://en.wikipedia.org/wiki/Minor_scale for more details.

The thing that make a minor scale minor is that the 3rd degree of the scale is a minor third up from the tonic.

Why we have both has to do with the way people in the good old days thought about music theory--building scales by defining intervals from a starting pitch. This makes sense when you think about how people sing--you start on a note and sing intervals based off of the starting note. Unless the singer has perfect (absolute) pitch, thinking of a scale as a collection of notes is kind of meaningless to a singer. Singers think in terms of intervals, not notes. If you tell someone to sing a major scale starting on A they can do it, but if you tell them simply to sing a collection of pitches you will leave them perplexed.

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 Re: Dominant-diminished 7th theory
Author: Bassie (---.perpetuum.co.uk - ISP in Southampton, M4 United Kingdom)
Date:   2008-08-28 12:57

The most important note in a scale is the tonic, the one it's named after, the one that feels like 'home' to our ears, and the one on which pieces usually end, and often start.

The /second/ most important note is the dominant, or fifth. It has the simplest relationship to the tonic in terms of frequency (3:2). It's the same in major and minor scales. And it indicates the nearest related scale, which lies on the cycle of fifths. Sharpen the 'F' in the scale of C major and you get to the scale of G major.

Logically the fourth has a similar role to play (the fourth in G is, of course, C) and so the fourth is termed the 'sub-dominant'.

The chord 'GBDF' might look at first sight like it's built out of G major, but by making the 'F' natural instead of sharp it immediately leads the ear to C major. GBDF forces the mind to anticipate CEG.

Quite often a symphony will be heard to end on alternating chords of '1' (e.g. C) and '5' (G), finally settling on the '1'. Sacred music often ends on an 'Amen' of the chords '4' and '1'.

A very important exception to the rule of 'start on the tonic' is 'Happy Birthday'. For any impromptu performances, it's well worth knowing that this starts on the dominant!

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 Re: Dominant-diminished 7th theory
Author: BobD (---.hsd1.il.comcast.net - ISP in Plainfield, IL United States)
Date:   2008-08-28 15:14

When clarinetists play chords they are called arpeggios. If you can sound all the notes in a chord at the same time you are truly exceptional. Arpeggios are quite important when playing Western music.....not country and western.

Bob Draznik

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