# Problem with transposable fugal parts



## paulc (Apr 18, 2011)

I've been working through exercises, with a view to writing invertible counterpoint and permutation fugue.

I'm encountering a persistent problem.

According to strict Fux rules, you should avoid outlining the tritone in melodies, eg. F down to C down to B, OR B up to E up to F without following with a "covering" step (B up to E up to F up to G). Of course, in the repetoire, the melodic intervals of a tritone, major sixth and seventh appear all the time. For the sake of study, I'd like to do things the "strict" way.

As far as I can tell, there are three ways to avoid this 'tritone problem' when dealing with transposable fugal parts which re-enter at different entrance intervals:

1) Make sure that none of your melodies contain the interval of a fourth of fifth! Aside from being restrictive, the most likely result is the skip of a sixth instead of fourth:

F C B
A A G
...
F A B
A A G

This results in a dull-sounding unison on the A, at least with two voices only.

2) Sharpen or flatten notes in the answer in order to convert the melodic tritone (F down to C down to B) to a melodic fifth (F down to C down to Bb). This well and truly confirms a 'tonal answer' as opposed to 'real answer'. While possible, this inevitably has harmonic implications and can lead to the same problem only in a new key, depending on the shape of the melody.

3) Keep track of melodies with problematic intervals (fourth and fifth) and make sure to only transpose them to other places that maintain the intended intervallic relations.

E A B
...
G C D
...
(avoid)
B E F

4) Stop worrying about such rules, which have limited value in real-world cases?

Any suggestions or comments are appreciated. This has been taking up a lot of my time and is quite frustrating.

Paul.


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## bagpipers (Jun 29, 2013)

you seem to be right.although such rules have any meaningfull basis in actual composition it never hurts to learn the right way to do things in practice.
rules are there to be broken but one cant break the rules properly unless one understands them first.
i have never heard of any rules concerning the use of the tritone melodicly though.but yes i can see how going to from 1 to diminished 5 and then to 5 or 4 could sound hollow.if thats what your asking although im not quite sure i fully understand your post


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## paulc (Apr 18, 2011)

Hi bagpipers, thanks for the reply.



> "i have never heard of any rules concerning the use of the tritone melodicly though"


Unless I have misinterpreted, this is mentioned in Alfred Mann's The Study of Counterpoint (on page 35 of my W.W Norton paperback). In the footnotes concerning the prohibition of 'mi against fa', Mann also references a book by Jeppesen. As far as I recall, this rule is broken only once in the third part of the book with four voices (eg. rules decrease as voices increase).

Still, my problem remains. If you write a melody which 'starting on any one note, goes up a fourth, then up a second' in a strict (modal) setting, then the moment the melody containing that sequence is transposed such that the sequence begins on F, you have a tritone. Same with 'starting on any one note, goes up a fifth' transposed such that the sequence begins on B, when the melody appears as an answer.

The only ways I can think to get around this are the ones I listed. 2 is the most promising, but starts to mess with the sense of key if that useful sequence is repeated. I'm hoping someone else has noticed this in their study and can share their experiences.


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## bagpipers (Jun 29, 2013)

paulc said:


> Hi bagpipers, thanks for the reply.
> 
> Unless I have misinterpreted, this is mentioned in Alfred Mann's The Study of Counterpoint (on page 35 of my W.W Norton paperback). In the footnotes concerning the prohibition of 'mi against fa', Mann also references a book by Jeppesen. As far as I recall, this rule is broken only once in the third part of the book with four voices (eg. rules decrease as voices increase).
> 
> ...


i have never read those books.the only books i have read are hindimith craft of composition and a few orchestration books.i dont think you miss read.are you talking about a melodic or a harmonic line.

do you mean a melodie that goes (lets use the key of A for practical purposes) A D# E or do you mean a chord or contrapunctal counter subject where D# and E intersect in the hypothetical key of A


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## paulc (Apr 18, 2011)

> "do you mean a melodie that goes (lets use the key of A for practical purposes) A D# E"


Yes, a melodic line like A D# E. In strict writing, you mostly use the modes formed by white keys, with only the occasional flat or sharp, mostly before a cadence.

So, I avoid A D# E ... F B C ... B E F ... unless I can soften that interval with the extra step (see above). I write something without the tritone (A D E ... G C D ... C F G), but when the melody containing that sequence becomes an answer which enters (starts) at a different interval than before, sometimes that sequence (fourth, second) coincides with F or B. Hence, the tritone occurs, unless you do something about it. This concerns imitative counterpoint.


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## bagpipers (Jun 29, 2013)

i would say to use german,italian and especialy french 6th chords.always a good way to deal with the tritone.you may be taking these exersises to literaly,i dont know.
i dont see the notes you wrote above as being melodic,melodies usualy run in rising and falling seconds


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## paulc (Apr 18, 2011)

> i would say to use german,italian and especialy french 6th chords.always a good way to deal with the tritone.


Which seems like a harmonic concern! I think I need to find a teacher. I've made some progress on my own, but now I'm getting overly confused. 



> you may be taking these exersises to literaly,i dont know.


You could be right. I may have too many self-enforced rules.

Thanks for your help


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## bagpipers (Jun 29, 2013)

paulc said:


> Which seems like a harmonic concern! I think I need to find a teacher. I've made some progress on my own, but now I'm getting overly confused.
> 
> You could be right. I may have too many self-enforced rules.
> 
> Thanks for your help


you have to find a teacher.writing classical music is just to hard without large amounts of detailed instruction.if i had known you didnt have a teacher i would have said that first.i was very lucky,my best friend happened to be one of the more important living composers of our time,so i learned from him

augmented 6th chords are a melodic concern because they allow you to develop melody and harmony together.they are of equal melodic and harmonic concern.also get the hindimith guide to the craft of composition and study step progresions and degree progresions


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