Recorder fingering diagrams in lilypond

(OR: Adventures in scheme)

Summary

Given a piece of lilypond music markup, e.g. (*)
```
\relative c'' {\key d \major
	  d-^\ff r cis4.->( b8 | a4-.) fis-. d-. fis-. |
	  a-. a8(b a4-.) a8(b->| g1->)
	  }  }
```
we can wrap it in the command \finger #'<recorder> {...} to include recorder fingering diagrams for our chosen recorder (eg soprano), based on a chart: We can mark up a whole piece, or just a tricky few notes.
Given an individual note, we can place the command \addf <note> #'(<holes>) around it, where <holes> is a list of holes (or half-holes) to cover, to suggest alternate fingering for a specific note.
(NB: here, note is an object with type ly:music; it is the user's responsibility to only place a single note in the argument. Otherwise, the same diagram will be drawn onto all the notes in the argument!)

The functions

recorder-diagram takes as its argument a "size" and a list of holes, and creates a piece of markup representing the recorder diagram, scaled to size, with the specified holes (or half-holes) covered. The holes are named as:

thumb	thumb hole covered
thumbhf	thumb hole half covered (horizontal)
one...five, onehf...fivehf	hole $n covered / half covered (vertical)
sixl, sixr	big sixth hole covered, small sixth hole covered
pinkyl, pinkyr	big seventh hole covered, small seventh hole covered

They can be listed in any order.

myxxFingerings is a chart for the recorder xx. I added charts for the alto F and the descant; macros for tenor and sopranino simply refer to (transpositions of) these. The charts have a little introductory code and a series of lines like:

	    ; C# or Db4
    ((= (ly:pitch-semitones pitch)
            1)
      (recorder-diagram size '(thumbhf one two three four five sixl sixr pinkyl)
	    ))

where the number (here 1) is the lilypond numeric representation for the absolute pitch (middle C is 0), and we provide the list of holes to cover. It calls recorder-diagram and returns the piece of markup with the chart.

finger and addf take an object of type ly:music and print the diagram markup as lilypond NoteNames for the music.

How to use it

Save the auxiliary file recorder-fingerings.ly and include it in your lilypond music file (where you have the music you want to add fingerings to): \include "recorder-fingerings.ly"
If you want the diagrams larger or smaller than the default, specify the scale you want: #(define myFingSize 2)

If you plan to just use one recorder, an auxiliary macro could save a little typing. E.g.:

altoFinger = #(define-scheme-function (mus) (ly:music?)
	    #{
	    \finger #'alto $mus
            #})

Wrap your lilypond music (anything of type ly:music) in e.g. \finger #'alto {...music...} or \altoFinger {...music...} (replace alto with descant, tenor as required) -- whether just for a few bars, single note, or the entire piece
If you want an alternate fingering for a note, interrupt the finger command (if one is open) and specify the fingering with \addf {...music...} #'(list of holes): NB all notes in the {...music...} will then be assigned the same fingering, so there should only be one note! (but it can be marked up with all the usual lilypond music functionality such as articulations etc)
e.g. to finger a longer section, but with an alternate fingering suggested for one note, you might have
```
      \altoFinger { r4 c\>(d ees) | f->\!(d) r2 | r4 }
      \addf bes'\<( #'(thumbhf one four five pinkyl pinkyr) 
      \altoFinger{ aes2) | a4--\! a-. r a-. | 
                           bes-- bes-. r bes-. | a1( | a4) r r2 |}
```
A recorder diagram can also be added manually as markup above or below or a note (or anywhere lilypond accepts markup objects); the size is then specified each time:
```
   a_\recorder-diagram #2  #'(thumb one two)
```

How to modify it

To restyle the markup diagram (e.g. for a thumbhole to the left instead of above, or to treat the six as one circle with half-hole fingering), modify the markup in function recorder-diagram. The diagram is currently a single center-column.
To rename the holes, search and replace in the file...
To correct fingerings, find the entry for the incorrect fingering, e.g. (thumb one two), and change it to the correct fingering e.g. (thumb one three)
To extend the range, adjust the max and min in the fingering chart function, and add lines analogous to the existing ones with the new fingerings
... what other changes would you like to make? Email me!

References / credits

The original inspiration was a snippet offering this functionality for the tin whistle. Although we gutted the fingering chart function to use the new recorder-diagram instead of the built-in lilypond woodwind diagram, the code structure is adapted from https://lsr.di.unimi.it/LSR/Snippet?id=1177.
For the recorder diagram markup, I started from a markup structure designed by reddit user raskalnikow, although the final version has been modified considerably.
Thanks to music.stackexchange user "lazy" for explaining contexts to me:
https://music.stackexchange.com/questions/141098/lilypond-notenames-and-vertical-spacing/141100

Notes

Another "obvious" way to do this (and my initial idea), rather than implementing the recorder diagram markup from scratch, would have been to patch the .scm files display-woodwind-diagram.scm and define-woodwind-diagram.scm, modifying e.g. the tin whistle diagram with the double holes at the bottom and the thumb hole at the top (or at the side, to taste), as done by a user on the lilypond mailing list (2017) for an eight-holed instrument. The fingering charts and \addf function would then have been defined using the lilypond built in syntax for woodwind diagrams, rather than the locally defined recorder-diagram.

However, I couldn't find out how to create a patch in a local file that will then just extend the lilypond built-ins. It seems you have to actually modify the system files. I didn't think this was a suitable solution for our use case...

(*) A bonus point if you can name the piece this comes from (Back)

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The original tex.se question (although this lilypond solution uses no tex at all...)
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Email me: mair@allen-williams.com
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