# Canons at the Fifth



## Fagotterdammerung

I don't count myself as a composer in the proper sense, but I love to study music and write music just for the sake of learning about it and understanding it.

A subject that is confusing me: how can you have a canon at the fifth ( in common practice tonal harmony ) without it continually modulating upwards?

Example, the V-I G to C in C Major becomes V-I D to G in G Major, and then if the first voice follows that modulation, then the second voice sends the key up a fifth again, etc

I'm probably missing something incredibly obvious, as canons at the octave etc. are easy, but this is proving impossible unless I just keep modulating endlessly in a circle of fifths.


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## Mahlerian

The voices will (traditionally) alternate between fifth and tonic, as in a fugue. Of course, an endlessly modulating canon is possible, and has been done.


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## Fagotterdammerung

I guess my problem is how to get it heading back to the original key. In a fugue the answer only lasts so long so it's a bit easier. My problem is that any modulation back to the home key in the first voice becomes a modulation to _one key sharper_ in the entry on the fifth, trapping me in this constant modulation.

Perhaps I'm missing something obvious, but if anyone has any canons at the fifth that begin and end in the opening key that would be awesome. Maybe if I see it, I'll get it.


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## Mahlerian

What you'll find is that cadential material is often not treated strictly. This inverted canon at the fifth (between the upper two voices) continues up until the penultimate bar for the lower voice and until the beginning of the last bar for the upper voice, and the continuation from there is similar but not exact.


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## Vasks

Here's a paraphrase from Gauldin's "_A Practical Approach to 18th Century Counterpoint_"

One way to avoid this "bitonal" conflict is to limit the number of scale degrees used by choosing only common tones (in other words avoid the 7th step of the original key)


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## Fagotterdammerung

Vasks said:


> Here's a paraphrase from Gauldin's "_A Practical Approach to 18th Century Counterpoint_"
> 
> One way to avoid this "bitonal" conflict is to limit the number of scale degrees used by choosing only common tones (in other words avoid the 7th step of the original key)


That... makes a lot of sense! Thank you! 

If I avoid the leading tone of the dominant, the chord can be arranged to work as the subdominant of the first key.

I'll be giving this a try tonight.


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## paulc

I've just started noticing this exact problem in my studies! The modulating indefinitely issue.

Would love to see a score illustrating the problem and at least one solution. I have the Gauldin book, but haven't read it yet!


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## Fagotterdammerung

paulc said:


> I've just started noticing this exact problem in my studies! The modulating indefinitely issue.
> 
> Would love to see a score illustrating the problem and at least one solution. I have the Gauldin book, but haven't read it yet!


I'm sure there are other ways of doing it, but after the above comments ( avoid the leading tone in the tonic key ), I've found it works out. Without the leading tone in the home key melody, the dominant of the new key can be interpreted as the supertonic of the tonic key. So: I-IV-V-I "becomes" V-I-II-V if you harmonize it correctly. ( I'm sure there are other solutions as well ... but this is an easy one.  )


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