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I've always been fascinated by the shape of SCORE's slurs/ties and I'd like to achieve this look in Lilypond.

My reasons aren't purely aesthetic.

Somebody created this code for me years ago but it has some major limitations. Maybe it can be useful as a starting point though. http://lilybin.com/67h327/1

As you can see, SCORE's slurs/ties aren't completely flat in the middle (the outer side isn't flat at all in many cases expect when the slur/tie is very long) and in fact you can specify how curved or flattened the shape is.

Here are some references to get an idea about the shape:
https://bmt-systems.com/score/Carter--PartSamples.PDF
https://bmt-systems.com/score/Carter--ChamberEnsembleSample.PDF
https://bmt-systems.com/score/Carter--OrchestralScoreSamples.PDF
https://bmt-systems.com/score/Carter--PianoReductionSamples.PDF
https://www.jeffreygrossman.com/images/GrossmanEngraving.pdf
https://wiki.ccarh.org/images/c/c8/Score-Reference-Manual.pdf (printed pg. 51-63)

As requested by a comment I added a few images showing variations of the bezier curve.

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    You should add images, of what you want to achieve, as many people, including me, don't want to click on many links for different reasons. May 8 at 12:31
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    OK, I added a few images May 8 at 13:07

2 Answers 2

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Have a look at the \shape attribute.

https://lilypond.org/doc/v2.22/Documentation/notation/modifying-shapes

To quote that page:

Ties, Slurs, PhrasingSlurs, LaissezVibrerTies and RepeatTies are all drawn as third-order Bézier curves. If the shape of the tie or slur which is calculated automatically is not optimum, the shape may be modified manually in two ways:

  1. by specifying the displacements to be made to the control points of the automatically calculated Bézier curve, or
  2. by explicitly specifying the positions of the four control points required to define the wanted curve.

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Have you tried modifying the tie height limit (\override Tie.height-limit = ...), as seen in this page (Flat Ties) of the documentation?

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