Generating inversions

I have no Linux expertise so I can't help you there, but if someone said "folder" instead of "directory", would that help? It's a basic computer concept - a place where related files go. Like, "/users/posercom/".

Anyhow, the plugins are listed in alphabetical order. The "Retrograde" plugin is right where it belongs, with the other R's, toward the end of the list.

As I explained, one way to do the inversion would be to swap the pitches so that the highest becomes the lowest and so on. This would happen all along the diatonic scale of the present key. But would it be more useful, if the swapping would be more interval perfect. Like an upward C - E - G would become a downward C - Ab - F?
Here's an image to show how I'd make it to work. Bars 1&2 is the original melody. Bars 3&4 are same inverted (I did it by hand). The notes follow the diatonic scale of D major. Bars 5&6 are bars 3&4 transposed diatonically a 4th down (I did that with my plugin).

A smaller problem is to decide what to do with accidentals. I've met the same problems when I did the diatonic transposing plugin. So far I've just ignored them and set them back to the corresponding unaltered diatonic tone.

Hi underquark,
I got your Invert.js plugin installed. It is just what I was looking for and will save loads of time for the project I'm working on currently.
Wow and thanks!

Yes, now that we have cleared up the misunderstanding about the clef, thongs are making more sense. Your pitch axis opis middle C only if you changw the clef like they did in the example. That's fine, but it does mean your initial descriptions were incorrect. The inversion of E-FG is not F-E-D - that would be the case only if you didn't change clefs and therefore weren't using middle C as your pitch axis but are instead using, as I said, B half-flat. Using middle C as the pitch axis, E-F-G maps to A-G-F or Ab-G-F, depending on if you want diatonic or real onversion

If I take you literally, I think you might want A-G-D - surely a mirror would not add flats to notes. So notes with no accidentals would remain notes with no accidentals, would they not?

Hiwever, if that's what you mean, again, your example actually shows something else. If you look more closely, you'll see physical accidentals are not preserved. Motes with sharps in the prime may turn into notes with flats, or notes with no accidental, in the inversion. That's why it is important for you to be more clear about how you want things handled *musically* if you wish anyone to be able to answer your questions or build a plugin that would serve your needs.

BTW, regarsing the misunderstanding about axis of symmetry: you referred to horiztonal symmetry, which is a somewhat ambiguous term, especially when applied to music, I see now that you meant a horizontal *axis* of symmetry, which in musical terms reaults on *vertical* symmetry.

Anyhow, feel free to drop out of the discussion. But you did originate the thread asking abiut inversion, which is a common musical device and worthy of a plugin. If you would like any such plugin developed to meet your needs, it will behoove you to explain your needs better.

Well, I might start a new thread for this or I might continue in this thread, because lots of interestting aspects have come up in this thread. I guess you will get the best result by doing the inversion by hand. I know that when my plugin is ready and I start to use it, I'll still be correcting accidentals here and there, because no logic can fully achieve what I want in all possible cases.

It seems that there's one point, where you could place the symmetry axis so that the intervals would be perfect: At the tone D.
A mixolydian ascending scale G A B C D E F G turns beautifully into a natural A minor descending scale A G F E D C B A, where all whole steps and half steps are in order. This way you get both a diatonic and a perfect inversion. You still need a cleff, which puts D on the third staff line: the bass cleff! So this is the ultimate case, where every requirement is met. Every sharp turns into a flat and vice versa in the inversion. Looking at a keyboard helps to understand. You see the beautiful symmetry of the black keys, when you put D as the symmetry point. Ab works as well, it just throws the inverted notes into another octave.

The bass cleff is a great thing here! I happen to be very fond of instruments playing in the bass cleff range, like the cello, the bassoon and the baryton horn.

Who ever said you should bow out? We want you to explain yourself better, not bow out. But it's not about "posh technical terms". If your explanations were clear and consistent, we would be able to understand what you mean even with incorrect terminology. But unfortunately, the fact that your posted example is showing something *entirely different* from what you say you want means there is no way for us to be sure what you want. You say one thing, but show an example of something entirely different. So this is what we are trying to resolve - what you actually mean here. Using appropriate terminology makes the job easier, but the terminology is *not* the problem here - it's the contradiction between what you say you want and what you are actually using as examples.

So, as mentioned, the change in clef in your initial example means it is not inverting around mid-line B, but rather, around middle C. So, you now say you want to invert around mid-line B so the inversion will appear to be a visual reflection when staying in treble clef. Fine. But look more closely at your posted example. It is most definitely *not* a simple visual reflection. The third note of the prime is D - written in the space just below the staff. The third note of the inversion is Bb - written in in the space just above the staff (so far so good) *but with an added flat sign*. Where did that come from? Surely not from visual reflection. No, it came from the fact that your example is showing "real" inversion. D is two half steps *above* the axis of inversion (middle C), so it maps to the note two half steps *below* - Bb. That's where the flat came - *musical* considerations (number of half steps), not *visual* ones (position on the staff). So it's not about "posh technical terms". It's about realizing that the musical concept of inversion requires use of musical terms, not just visual ones, because it is *not* a purely visual phenomenon.

If you were to do a simple visual reflection of the prime, you wouldn't have any flat signs at all, since the prime didn't have any either. The first few notes C-C#-D-D# would map to A-A#-G-G#. Meaning a line that strictly ascending has now turned into one that alternates between ascending and descending. That turns out to be not an inversion at all. So if this is what you want to see - C-C#-D-D# becoming A-A#-G-G# (the result of a purely visual reflection), then it is not any kind of inversion at all, and you can forget you ever thought it would work out that way, because it won't.

However, if you actually mean to do something different with the accidentals, so that C-C#-D-D# maps to something other than A-#-G-G#, then it may indeed still turn out to be a type of inversion. Until you explain - using whatever terminology you like, as long as it is not self-contradictory - how you actually see this working, we cannot tell if what you want is a form of inversion or not.

It's a simple question with a simple yes/no answer: either what you are wanting is a form of inversion or not. Right now, you don't know enough about inversions to answer it, and we don't know enough about what you want to answer it. I think you can explain what you want a lot more easily than we can explain what inversion actually is. So, if you want the question answered - "is what you want a form of inversion or not" - then it seems we are going to be the ones who will best be able to answer it. But we won't be able to do so until you successfully explain what you want. Actual examples of what you actually want - not examples grabbed off a web site somewhere that turn out to be rather different from what you thought they were - would help.