# Theory and analysis corner



## danae (Jan 7, 2009)

I don't know if anyone else is interested in starting this new thing, but I have to say I started it out of neccesity. I'll explain: all this time that I've been studying classical music I have accumulated a lot of knowledge, as well as many unanswered questions concerning theory, harmony, analysis etc etc...
So I think it would be useful to use this thread to post whatever questions we have on certain aspects of music theory.
I'll start with this one. It's about harmony. I have 5 harmony textbooks at home. 3 are from greek theorists and 2 are Schoenberg (Structural functions...) and Maler (Beitrag zur Durmolltonalen....). Anyway, the Schoenberg and Maler books are really good and advanced. But I don't need advanced right now because I'm dealing with a student who hasto learn everything form scratch. 
So my question is this: in the 3 greek books that I have, the issue of hidden octaves and fifths is treated in a variety of ways. What specific rules do you know concerning hidden octaves and fifths? Please quote your source if possible. 
And if anyone has the Kostka textbook, please tell what he says in the corresponding chapter. 

Thanks.


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## Dim7 (Apr 24, 2009)

Actually, I would say that having actual subforum for this would be a good idea.


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## danae (Jan 7, 2009)

Dim7 said:


> Actually, I would say that having actual subforum for this would be a good idea.


That would be great, but that's up to the moderator... Krummhorn I think.


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## Dim7 (Apr 24, 2009)

I think "Today's composers" should be simply changed to "Composition, theory & analysis" or something like that. Would make sense to lump these together.

edit. I should really just post this on the "Site feedback & technical support" forum and not here. Which I'm going to do now....


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## Guest (Jul 10, 2009)

Well I have just posted on a similar thread are you two in competition


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## danae (Jan 7, 2009)

Andante said:


> Well I have just posted on a similar thread are you two in competition


No. I started this thread yesterday and the first response was a suggestion to create a subforum on the subject. When and if it's ready, I'll post there.


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## Kuntster (Jun 8, 2009)

This would be a great topic.

Concerning your true question about hidden octaves and fifths. . . Hmmm....my best guess is that the author is talking about the harmonic series. I believe the Kostka books references this (as well as many other books). It really has to do with the physics of sound. 
Example)
f1=220 Hz=A3
f2=440 Hz=A4
f3=660 Hz=E5
f4=880 Hz=A5
f5=1100 Hz=C#6
f6=1320 Hz=E6
etc, etc, etc...

These harmonics (overtones, octave series, whatever you want to call it) are only put to use in an exact world of tuning that sounds nothing like a piano today. When you hit a 220 Hz tone on the piano (which is right around A3) all the other tones are present but just attenuated more and more in succesion. 
If you need to know more let me know,


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## danae (Jan 7, 2009)

Kuntster said:


> This would be a great topic.
> 
> Concerning your true question about hidden octaves and fifths. . . Hmmm....my best guess is that the author is talking about the harmonic series. I believe the Kostka books references this (as well as many other books). It really has to do with the physics of sound.
> Example)
> ...


Thanks for your reply, but no, the term "hidden octaves and fifths" doesn't refer to the harmonic series. It has to do with the rules of 4-part writing in Harmony. It's about the movement of 2 voices in the same direction, starting from any interval (except octave or fifth) and resulting in an octave or a fifth (perfect fifth). There are certain rules that apply to this specific harmonic movement.


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## Kuntster (Jun 8, 2009)

Oh, I've never heard it put into hidden octaves and fifths. 
However what your topic refers to is just just rules of counterpoint. 

Modal and tonal counterpoint are very useful subjects to study. 
Kenan has a good book called 'counterpoint', but focuses really on fugue. 
Koska is probably again a better resource for four voice choral writing where you will learn these basics rules much better. 

I first learned the "Real" basics in modal counterpoint from my professor, but she published only a manuscript that I think is only available to her and her students. 

Ultimately the goal is there should never be parallel octaves and fifths and they can never be approached by two voices from similar direction.


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## danae (Jan 7, 2009)

Kuntster said:


> Oh, I've never heard it put into hidden octaves and fifths.
> However what your topic refers to is just just rules of counterpoint.
> 
> Modal and tonal counterpoint are very useful subjects to study.
> ...


Again I explain: I know all these things. I'm teaching Harmony to a student right now and I would really like to know what certain theorists (for instance Kostka) say about certain rules, in this case, the hidden fifths and octaves. Of course, the fact that parallel fifths and octaves are not allowed is something very basic. I'm looking for more detail.

And the other thing you said "they can never be approached by 2 voices from similar direction", what do you mean? An octave or fifth can't be approached be 2 voices from similar direction? If you mean that, then you're talking about the subject of my inquiry, the hidden octave and fifth. And there are many cases in which hidden octaves and fifths are allowed. I just want to know when they are allowed.


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## Kuntster (Jun 8, 2009)

You have to know the rules before you can break them. Bach broke the rules all the time. 

Read this:
Gradus Ad Parnassum by Johann Joseph Fux
-If you can master this, that's all you need to know. 

These are the rules completely spelled out. You SHOULD not have parallel octaves and fifths, and they (octaves and fifths) SHOULD never be approached by similar motion. 
(In counterpoint I take this statement extremely seriously!)

Of course, there are instances that it is completely unavoidable. Usually done so in the middle voices and sometimes Bach does this by changing the rhythm slightly. 

Get the Bach chorales and analyze all of them, I did it, find out where he does break the rules and find out why there is no other solution. The thing is Fugue writing, the greatest use of counterpoint, comes directly and is derived from 4-part choral writing. Bach's chorales are full to the max of rule bending and breaking! Good Luck!


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## Kuntster (Jun 8, 2009)

Oh yeah, all the Music Theorist say the same thing as the statement above. 
You just have to exhaust all other options before you break this rule.


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## danae (Jan 7, 2009)

I know the Bach chorals and I'm definately not using them to derive rules from, or else my student's exams are gowing down the drain! 

As for the parallels, as I said, knowing that they are not allowed is basic knowledge. Concerning hidden fifths and octaves, this is not the case. I'll state one of many examples: 2 voices moving in the same direction can reach an interval of an octave or a fifth, coming from another interval, as long as the upper voice moves in a step and not a jump. This is allowed. 2nd example: 2 voices moving in the same direction, both jumping, can reach an interval of an octave or a fifth, as long as this happens during a change of position of the same chord.


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## Kuntster (Jun 8, 2009)

I think you already have your answer. There are exceptions to the rule. If you can get to the octave or fifth by any other means then you should avoid breaking it, if not the rule can be broken. 

I believe that there is no right or wrong way in counterpoint, just sometimes a Better option.


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