# Why is a harmonious canon so hard for most intervals?



## caters

Okay, so I have been working on my canons of the second to canons of the seventh in 3 voices and I notice that unlike a canon at the unison or at the octave which is almost guaranteed to have beautiful harmony, it is so hard to get that same degree of harmoniousness with other intervals. Undoubtedly, with a canon at the second between the bass and the alto and intervalic freedom in the soprano, almost every single one has a tritone and even the ones without tritones, still have diminished triads but because there is no tritone, it sounds like a minor chord instead of a diminished chord. 

This is less of an issue with canons at the third or fourth. But that is not what I am directly against when I say that I want the least dissonance in my canon. Neither are incomplete 7th chords. What I'm against the most are suspended chords and 9th chords. Here's why I am against those.

This canon is for a symphony and I was told that because it is a strict canon I have to go through the tedious process of writing canons at all the intervals. Because I was going for mostly major and minor chords, I could right away eliminate the canons which had 2 or more lines at the unison or the octave. That is 16+6 or 22 canons. Subtracting that from 64 total 3 voice canons leaves me with 42 canons to write. That is a lot left.

And while I could get richer harmonies with a fourth voice, this would also increase the possible number of canons from 64 to 512. There was no way I was going to do that. If I want an extra line, I can just have it x octaves above the bass and at a whole number of measures instead of the 1.5 measure delay between the first and second voice and between the second and third voice.

But anyway, back to what I was talking about. I find that the harmony is hard to get to sound decent. Besides 7th chords and diminished chords, the most common dissonant chord I get is the sus4 chord which adds a sort of jazz vibe to otherwise not so jazzy music. After that are the rare 9th chords which give even more of a jazz vibe to the canon and groups of notes that I might consider to be like a non-chordal triad(such as 3 notes, each a second apart from the previous, I know it is an inversion of the ninth chord but it sounds so unlike a ninth chord with just those 3 notes and sounds more like a cluster than a chord without the fifth or the seventh). 

I often will end up with something like this:

Interval -> Major chord -> sus4 -> Minor chord -> sus4 -> Minor chord -> Diminished chord -> Major chord -> Non-chordal triad etc. or something similar to it where the consonant chords have 1 or more dissonant chords between each of them.

As I have said previously, this gives a jazzy vibe which is not really what I'm going for in a symphonic canon. Of course, the lack of syncopation diminishes the jazzy vibe but I still feel it. What I am going for is to have as many major and minor chords as possible. So I have been making a sort of dissonance index by keeping track of each form of dissonance and how often it occurs. Highest number of major and minor chords I have gotten so far is 7 with the canons at the second, a bit less than half of the number of chords which appear. I don't know if this will increase or not with the canons at the third, fourth, fifth, and sixth. I do know though that with the 7th interval, I will probably get fewer than 7 consonant chords as the maximum because then I am basically writing a string of 7th chords and other extended chords.


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## EdwardBast

What you have written above has no discernible connection to the writing of canons. From what you have posted it doesn't sound like you know how to go about writing one.


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## caters

It's not that I don't know how to write a canon, a canon is the simplest form of counterpoint there is, just 1 melodic line being repeated at a delay of x measures. Nothing is implied about it having to be harmonious at every beat, it's really just a single melody in multiple lines delayed by some number of measures(which could be a fraction as in my case) or modified in a way(retrograde, inversion, or retrograde inversion). It's just that with a strict canon where you can't modify the note durations at all, just timing, pitch, and intervals, it is hard to acheive beautiful harmony outside of octave and unison intervals and this is not what I'm going for but rather something that sounds like major and minor chords in 3 voices while still being a strict canon.


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## EdwardBast

caters said:


> *It's not that I don't know how to write a canon, a canon is the simplest form of counterpoint there is,* just 1 melodic line being repeated at a delay of x measures. *Nothing is implied about it having to be harmonious at every beat,* it's really just a single melody in multiple lines delayed by some number of measures(which could be a fraction as in my case) or modified in a way(retrograde, inversion, or retrograde inversion). It's just that with a strict canon where you can't modify the note durations at all, just timing, pitch, and intervals, *it is hard to achieve beautiful harmony outside of octave and unison intervals and this is not what I'm going for but rather something that sounds like major and minor chords in 3 voices while still being a strict canon*.


Taking the bold portions above in order:

No one who has composed canons would ever say it's the simplest form of counterpoint. It is extremely difficult, because …

Canons in a tonal style must follow the same laws of voice-leading and dissonance treatment as any other counterpoint, with the additional constraint of exact imitation.

This is a fantasy. See ^ ^ ^. Three voice canons of any kind that are worth hearing are tremendously difficult.


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## Torkelburger

caters said:


> It's not that I don't know how to write a canon, a canon is the simplest form of counterpoint there is, just 1 melodic line being repeated at a delay of x measures. Nothing is implied about it having to be harmonious at every beat, it's really just a single melody in multiple lines delayed by some number of measures(which could be a fraction as in my case) or modified in a way(retrograde, inversion, or retrograde inversion). It's just that with a strict canon where you can't modify the note durations at all, just timing, pitch, and intervals, it is hard to acheive beautiful harmony outside of octave and unison intervals and this is not what I'm going for but rather something that sounds like major and minor chords in 3 voices while still being a strict canon.


You do not understand how to write a canon. You are confused by the final result, which is "1 melodic line being repeated at a delay of x measures". But that is not how a canon is written. If you were writing an 8-bar canon, you would not write 1 eight-bar melody in its entirety and then see which delay of x measures sounds best with it. That's not how you do it.

You decide on how long the canon is, say 8 bars. Then you decide at what number of measures it will be delayed, say 1 bar. Then you decide at what interval the imitating voice will be transposed at, say a sixth.

Say the lead voice is voice A, and the imitating voice is voice B.

1.	Write voice A bar 1 only.
2.	Copy bar 1 voice A into voice B bar 2 but transposed down a sixth diatonically.
3.	Write counterpoint in voice A bar 2 only. Follow all rules of good voice-leading, dissonance treatment, and counterpoint.
4.	Copy bar 2 voice A into voice B bar 3 (but transposed).
5.	Write counterpoint in voice A bar 3 only.
6.	Copy bar 3 voice A into voice B bar 4.
Continue this pattern until you are done. You should have no problem with the whole thing being harmonious and "achieving beautiful harmony" while being in strict canon.


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