Music: Practice & Theory Stack Exchange is a question and answer site for musicians, students, and enthusiasts. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm working on coming up with prime forms. I've been using this calculator online to check my work.

My problem is that the prime form I compute for a certain PCS doesn't agree with the calculator, but I can't find my error. I need help figuring out where I'm going off the tracks, or if the online calculator is wrong (which seems unlikely).

I'm starting with the PCS: [8, 11, 10, 1, 0]

Showing my work, I enumerate these rotations:

[0, 1, 8, 10, 11]
[1, 8, 10, 11, 12]
[8, 10, 11, 12, 13]
[10, 11, 12, 13, 20]
[11, 12, 13, 20, 22]

I then choose as the normal form [8, 10, 11, 12, 13], because the distance between the first and last items (13 - 8 = 5) is the least of all of the other rotations.

I then transpose the normal form to [0, 2, 3, 4, 5] (through the interval of 4)

So I get to a prime form of [0, 2, 3, 4, 5].

The online calculator (when I click on the buttons for [0 1 8 10 11]) yields a different prime form of (0,1,2,3,5).

So to recap, my prime form is [0, 2, 3, 4, 5] and the calculator says the correct prime form is [0, 1, 2, 3, 5].

What's going wrong here?

share|improve this question
You might find this more detailed pc-set calculator useful to know about. – LiberalArtist Sep 1 '14 at 4:14
up vote 3 down vote accepted

As the PC Set Calculator you link to shows, [0, 1, 2, 3, 5] is the Prime Inversion of [0, 2, 3, 4, 5]. However, as [0, 1, 2, 3, 5] has a lower interval at the bottom, it is considered the correct prime form of these two equivalent PC Sets.

Another page on the website you link to gives a rigorous method for determining the Prime Form of any PC Set. The last of 8 steps asks you to find:

Which form, the original or the inverted, is most packed to the left (has the smallest numbers)? That will be the Prime Form.

share|improve this answer
This seems to be the missing part - the prime form is the most packed to the left, whether that's the way I did it, or in inverted form. In several other online sources of information, it steps you through the algorithm I did, and doesn't explain the inversion part of this. Thanks!. – FrobberOfBits Aug 28 '14 at 17:27

I think you forgot to test inversions -- you should measure the distance between the first two and last two classes, and find the form that packs the smaller intervals to the left.

If you invert [0 2 3 4 5], you get [0 1 2 3 5], which succeeds in packing the shorter distance to the left of the form (starts with a distance of 1 instead of 2).

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.