# Looking for a Function to reorder a series of progressing ascending pitches?

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Hello,

Somewhat stupid question but I do not find a function that would allow me to reorder a sequence of pitches.
Let me explain, on a forum where Messiaen's limited transposition modes are discussed, I wanted to show that with Opumodus we could very easily analyze the modes and recreate them. I have no problem with those who are in total symmetry and divisible by two, but if I take the mode 3: (c4 d4 eb4 e4 gb4 g4 ab4 bb4 b4), using the function pitch-transpose-start I get in the end the mode but according to the postponement of the intervallic structure on c4 d4 ab4 is => ((c4 e4 gs4) (d4 fs4 bb4) (eb4 g4 b4)). I tried to reorder with the function pcs-normal-order the mode is reordered but with however the c4 in last position: (d4 eb4 e4 fs4 g4 gs4 bb4 b4 c4). Now, I suppose there is a function that makes it possible to obtain the right disposition. What is it ?

```(setf modmessiaen3 '(c4 d4 eb4 e4 gb4 g4 ab4 bb4 b4))
(setf SIMessiaenMod3 (pitch-to-interval modmessiaen3)) ; =>  (2 1 1 2 1 1 2 1)
(setf mod3divide (gen-divide 3 modmessiaen3))
(setf firstmodmessiaen3 (filter-first 3 modmessiaen3))
(setf report3 '(c4 e4 ab4))
(setf rep3 (gen-repeat 3 (list report3)))
(setf pch3 (modus (flatten (pitch-transpose-start firstmodmessiaen3 rep3))))
(setf MessiaenMod3 (pcs-normal-order pch3 :pitch))
(setf SIMessiaenMod3a (pitch-to-interval MessiaenMod3)) ; => (1 1 2 1 1 2 1 -11)
(setf mod3chordsM (melodize '((c4eb4gb4) (d4gb4bb4) (eb4gb4bb4) (e4g4b4) (gb4bb4db5) (g4b4d5) (ab4b4d5) (bb4gb5) (b4d5gb5))))
(setf analysechords3 (pcs-analysis (integer-to-pitch (modus mod3chordsM))))```

In particular, this distorts the analysis of the interstellar structure of mode 3:
of (2 1 1 2 1 1 2 1) I get (1 1 2 1 1 2 1 -11)
Besides, there is probably a more efficient script than the one I tried?

Best.

Didier

PS : In fact, I realize that the function pcs-normal-order is not adapted at all according to the modes.

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What is the output you are looking for.

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I would like to get the mode in the right order: '(c4 d4 eb4 e4 gb4 g4 ab4 bb4 b4)) and not '(d4 eb4 e4 gb4 g4 ab4 bb4 b4 c4))

Hence this question: is there a function to get an ascending order in a list rather than using pcs-normal-order?

(setf modmessiaen3 '(c4 d4 eb4 e4 gb4 g4 ab4 bb4 b4))

(setf pch3 ( ? (flatten (pitch-transpose-start firstmodmessiaen3 rep3))))

=> ((c4 e4 gs4) (d4 fs4 bb4) (eb4 g4 b4)) =>  (c4 e4 gs4 d4 fs4 bb4 eb4 g4 b4) ?

If I go look for mode 3 in the library OPMO I have this:

`(setf Messiaen3 (pitch-transpose 0 (expand-chord-name (library 'modes 'messiaen 'messiaen-mode3) :type :pitch)))`

=> (c4 d4 eb4 e4 fs4 g4 gs4 bb4 b4)

`(expand-chord-name (library 'modes 'messiaen 'messiaen-mode3) :type :interval)`

=> (2 1 1 2 1 1 2 1)

In the result with pitch-transpose-start : (c4 e4 gs4 d4 fs4 bb4 eb4 g4 b4) and => (4 4 -6 4 4 -7 4 4) => The music notes are correct but permuted.

and with pcs-normal-order : (d4 eb4 e4 fs4 g4 gs4 bb4 b4 c4) => (1 1 2 1 1 2 1 -11) => The music notes are correct but permuted.

I get the intervallic structure is shifted.

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Why you use the PITCH-TRANSPOSE-START function and what is the goal. What about PCS-PRIME-FORM.

Should this be generated or given by hand:

```(setf mod3chordsM
(melodize
'((c4eb4gb4) (d4gb4bb4) (eb4gb4bb4) (e4g4b4) (gb4bb4db5)
(g4b4d5) (ab4b4d5) (bb4gb5) (b4d5gb5))))```

I can't find the thought in your progression.

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Simpler:

```(setf mod3chordsM (melodize '((c4eb4gb4) (d4gb4bb4) (eb4gb4bb4) (e4g4b4)
(gb4bb4db5) (g4b4d5) (ab4b4d5) (bb4gb5) (b4d5gb5))))
(setf analysechords3 (pcs-analysis mod3chordsM))```

In general your code could be much simpler.

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I wish to analyse process of Messiaen's modes of limited transpositions. I choose one of the modes, say the 3, from OPMO's "modes" library, which gives me the mode :  (c4 d4 eb4 e4 f4 g4 gs4 bb4 b4) - and its intervallic structure: (2 1 1 2 1 1 2 1). And I want to replicate the process. it's a starting point. There are 9 notes, I divide them by 3 and I get three trichords ((c4 d4 eb4) (e4 gb4 g4) (ab4 bb4 b4)) and the same 3  (1 2 1). if I select the first trichorde (c4 d4 eb4) and I report it on each of the first notes of the three trichordes c4 - e4 - ab4 from the function Pitch-Transpose-Start I get as result mode 3 but disordered :

```(setf mod3divide (gen-divide 3 modmessiaen3)) ; => ((c4 d4 eb4) (e4 gb4 g4) (ab4 bb4 b4))
(setf firstmodmessiaen3 (filter-first 3 modmessiaen3)) ; => (c4 d4 eb4)
(setf report3 '(c4 e4 ab4))
(setf rep3 (gen-repeat 3 (list report3))) ; => ((c4 e4 ab4) (c4 e4 ab4) (c4 e4 ab4))
(setf pch3 (flatten (pitch-transpose-start firstmodmessiaen3 rep3))) ; => ((c4 e4 gs4) (d4 fs4 bb4) (eb4 g4 b4)) => (c4 e4 gs4 d4 fs4 bb4 eb4 g4 b4)```

This result I wanted to reorder in an upward progression and as I did not find the function, I tested pcs-prime-form but which is not adapted.

But I found the function that I wanted with sort-asc and I reconstruct the mode 3 and its intervallic structure :

```(setf Messiaen3order (sort-asc pch3)) ; => (c4 d4 eb4 e4 fs4 g4 gs4 bb4 b4)
(setf SIMessiaenMod3a (pitch-to-interval Messiaen3order)) ; => (2 1 1 2 1 1 2 1)```

Of course, I can combine the two functions together :

`(setf process3Messiaen (sort-asc (flatten (pitch-transpose-start firstmodmessiaen3 rep3)))) ; => (c4 d4 eb4 e4 fs4 g4 gs4 bb4 b4)`

But thank you Janusz for your questions. concerning the Pitch-transpose-Start function you had indicated to me when I wanted to recreate the multiplication chords of Pierre Boulez.

Best wishes.

Didier

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