Fingerings for high notes

[Beyond16]

Recently I looked for a trumpet high note fingering chart and couldn't find one. Some say just use fingerings from the octave below. Others say fingering doesn’t much matter for high notes. Neither of these seem ideal, so I wrote a program to generate the needed chart using tube length calculations. The calculation is simple enough: speed of sound divided by tube length equals frequency. But choosing among multiple high note fingerings makes the problem challenging.

Due to equal tempered tuning, the only perfectly in-tune fingerings for a brass instrument are those of the C open valve harmonic series, along with a few 1st valve C's. At least that is true for 3 valve instruments when the main tuning slide is used to tune the instrument to an open valve note. This utility assumes that the main tuning slide will be used to tune the open valve notes for no error.

The challenge to choosing fingerings arises when a note has more than one possible fingering. One rule of thumb is to choose the shortest tube length, which corresponds to the lowest harmonic. Avoiding unnecessary harmonic shifts when playing a scale is probably a good idea too. For low notes, there are no alternative fingerings. For example the first octave for trumpet. The higher the note, the more alternate fingerings.

Traditional fingering charts don't show why a particular fingering is chosen when alternative fingerings are available. If the alternative fingering has both longer tube length and greater error than the preferred fingering, then the choice is easy. But for higher notes, the choice isn't always so clear. For higher notes, the most accurate fingering is often one or more harmonics higher (longer tube length) than the surrounding notes.

This utility generates a diagram that makes the trade-offs easy to see. The diagram is a plot of frequency verses harmonic for each fingering. A gray background grid shows the valid semitones (equal tempering is used). The note name and frequency scale refer to the target note and frequency, not the fingered ones. Every fingering, useful or not, is plotted as a small blue dot. The selected fingering has a red box around it, and a red line leading to the left where the button combination is shown.

For each fingering, a line connects the points at each harmonic. The lines for all fingerings are the same blue coloring. This is because there are not enough colors with good contrast, especially when more than 3 valves are used. The scale at the bottom right helps identify the lines even though they are not color coded. The line for all valves open is always at the top because it has shortest length, resulting in highest pitch. All valves closed is the lowest line by the same reasoning.

To find the best fingering for a particular note, look at the horizontal gray line that corresponds to the note. The blue dot nearest that line has the best pitch match. The left most blue dot has the shortest tubing length. For some notes, shortest tube length and best pitch match occur with the same fingering. For others, a choice has to be made between best pitch match and shortest tube. The utility currently has only a simple method of choosing which fingering to mark as preferred. A maximum pitch error is passed on the command line. The shortest tube length that does not exceed the maximum error limit is chosen. If all fingerings exceed the maximum pitch error, then the fingering with the closest pitch match is used without consideration for tube length.

Running the utility
Some sample fingering chart output can be found on the sourceforge page. These don’t display well because modern HTML insists on resizing images. While resizing images sometimes works OK for photographs, it does not work well for line drawings or function plots. If the utility is run on your local machine, it will size the output to 95% of your maximum display size. The batch files then use the default app to display the output PNG file. If the default PNG handler is Windows photo viewer, the Actual Size button at the bottom must be clicked to see the unmodified output.

The output resolution can be set manually by editing the batch file for the chart of interest. See bFlatTrumpet_Cmajor1octaveForThumbnail.bat for an example. Manually selecting the resolution could be useful for printing.

The utility uses gnuplot for creating the output. Before running the utility, download gnuplot and unzip it to the directory of this utility (or one level up). The raw data for the plots is written to a text file with the same name as the batch file. Running the executable with no command line will cause it to show the command line options. The tuba fingerings examples are an initial guess and may be refined in the future. To customize a chart or make one for a new instrument, use one of the existing batch files as a template.

This utility really needs a refined algorithm for selecting fingerings. For now, the plot could be re-run with some favorite hand selected fingering adjustments. That would be done by editing the text file and modifying the batch files to not rebuild the text file.

[JayKosta]

[mdarnton]

I think your chromatic chart is very interesting, but you have no figures at all for valve 3, alone. I wonder if there aren't a few combinations where the 3 by itself might have an advantage, and the chart should show that, right? (I'm not going to play with the software, so it's nice to see the screen shots!)

[John Mohan]

[Bill Ortiz]

With my present horn (Schilke Handcraft) I find playing G about high C with the 3rd valve slots way better than open, and better than 1 and 3. It's playable open, but it takes a bit more work.
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'56 Martin Committee Deluxe #2 trumpet
14B Schilke mouthpiece
Couesnon Paris flugelhorn
Bob Reeves Sleeves and PVA