# What can be "two horizontal intervals of equal distance and discordant" on diatonic scale?

I keep reading this set of rules for counterpoint.

The rule number G5 states:

If there are two horizontal intervals of equal distance and discordant, the next interval must differ.

I try to figure out in what situation the rule can be triggered. First, among the allowed intervals (m2, M2, m3, M3, P4, P5 and m6) only m2 and M2 are dissonant (discordant).

In a diatonic scale to m2 in a row are impossible. So, the only what remains is M2. Therefore, I guess, that the rule can be formulated like this:

If you go F - G - A, you are not allowed to go further to B. Similarly, if you go B - A - G, you are not allowed to go to F.

Is my interpretation correct?

There is a clarification of the rule, which made me even more confused:

Rule G5 is another case of IR. Many observations against redundancy, similar sequences and other forms of repetition can be found in all five textbooks we analysed. However, the supporting examples were extremely variable and context-dependant, and the prescriptions imprecise and subject to personal taste. Therefore, our rule vetoes only the most extreme form of repetition, the trill (see Figure 3)

Could it be that "discordant intervals", does not mean "dissonant" and, instead, it mean that intervals are in opposite direction?

• It might help to indicate where these quotes are from. The context of the work might provide clues as to the intended meaning. May 2 '19 at 14:46
• Heck, trills aren't even banned in counterpoint to my knowledge--Bach's Little Fugue has trills in a countersubject. May 2 '19 at 15:30
• @ Roman: you can't go on asking the next day without referring to the sources - especially if it's not the one you were quoting in your earlier question but one that you got in an answer. I had also to look up again as I didn't remember exactly to whom this point was concerning: music.stackexchange.com/questions/84339/… May 2 '19 at 16:33
• -1 down voted. You have been asked twice to provide a source for these quotes. From the last question, it seems you got them from a paper about computer program. May 2 '19 at 18:40
• @MichaelCurtis, here is the source: researchgate.net/profile/Marcella_Mandanici2/publication/… . And it is not a paper about "computer program". May 3 '19 at 12:03

The modes were not only written in C.

Your formulation of this rule would be correct if it were in relative doremi as there have been altered tones like F# or Bb etc. (not all - originally!)

I don't mind if you didn't look up in google as I learn each time a lot if I don't know what means concordant and discordant - or anything else ...

"Every interval is either concordant or discordant. The concordant comprise all perfect intervals and all major and minor 3rds and 6ths; the discordant comprise all augmented and diminished intervals and all 2nds and 7ths. It therefore follows that all concordant intervals when inverted remain concordant and all discordant intervals remain discordant."

https://www.encyclopedia.com/literature-and-arts/performing-arts/music-theory-forms-and-instruments/interval

...G5. If there are two horizontal intervals of equal distance and discordant, the next interval must differ. IR (Implicit Rule)

I think it's important to show the illustrating example from the article...

The see a horizontal interval `C4` to `E4` and it repeats so there are two of them and they are equal distances, both are major thirds. But, these intervals are not discordant!

If the word 'discordant' were removed from the rule, the the rule and example would be perfectly clear. But, the authors add a lot of caveats to the rule. I think their intention is clear from this...

...Many observations against redundancy, similar sequences and other forms of repetition...

I pointed out this principle to you in my answer to your previous question. Notice how the authors call this an implicit rule. They are saying it is so fundamental that it is taken for granted by the authors of many counterpoint treatises. You really want to understand how important that concept of non-repetitive variety is to counterpoint aesthetics, especially at the note to note or per beat level of movement.

While the rule wording is kind of unclear, and the caveats do not really provide much clarity, they thankfully conclude with one simple point for their algorithm...

...Therefore, our rule vetoes only the most extreme form of repetition, the trill (see Figure 3.)

I don't understand why the rule `G5` is worded as it is when the actual rule applied seems so clear, simple, and quite different than `G5`.

If you really want to understand the author's meaning, I think you need to contact them. You may be able to find their email addresses with some online searching. I have contacted authors in this way a few times and I have always received a reply.