Narrow vs wide bore regarding finger spacing for High D

I read through several threads looking for an answer to a specific question but did not find it, so I thought I would ask it.

The question only concerns high-d whistles. I have heard conflicting information and want to understand the difference between a narrower and wider-bore high-d whistle concerning the finger spacing between B1 and B2 holes. In my head, I am trying to think of this as an equation. This question is not intended to be about airflow or intonation, nor does it regard finger placement on the low whistle.

I understand hole sizes are variable and might change, and overall finger hole placement might shift forward and back. With all other factors equal, which size bore (narrower or wider) would increase the space between B1 and B2 on a high-d whistle?

Feel free to point me to a thread I may have missed.

Thank you.

Well I did a quick look over my whistles, and I don’t see much correlation between the spacing between those two holes and bore size. Most of my larger bore whistles have marginally smaller hole spacing overall, since they tend to be a tiny bit shorter than my smaller-bore whistles, but the spacing between those two holes in particular seems to vary enough from whistle to whistle that it’s hard to make a generalization.

For what it’s worth, my largest-bore whistle is my Kerry Busker, and it does seem to have an unusually small space between B1 and B2. But David Furman’s whistles also have large bores, and they have a very large space between those holes. So overall, I’d say there’s probably little to no correlation. But I could be totally wrong.

If you make a flute/whistle with a wider bore, the holes do get closer together if you try to keep all other aspects of the design the same. (This leads me to wonder whether a low whistle could bring the holes closer together by having substantial widening of the bore between holes without wrecking the sound characteristics.)

Indeed, I’ve wondered why people don’t make larger-bore low whistles. The only downsides of widening the bore, I’d think, are (1) the whistle takes more air (which may be a good or bad thing depending on your preferences), and (2) you might run into octave spread issues - which can be corrected by tapering the head.

The spacing between tone holes B1 and B2 is probably influenced most by the choice the maker made in how to tune F#. Those tone holes will be closer together on whistles that have F# tuned to equal temperament (where F# is ~14 cents sharp), and further apart on those with F# tuned closer to just intonation.

The effect of bore aspect ratio on this distance will be smaller than the effect of tuning choices, but it is conceivable that makers who prefer a narrower bore aspect ratio, for its more balanced top end notes, may also be more inclined to tune their whistles such that they have sweeter major thirds (i.e., closer to just intonation). In practice, nearly all whistles and flutes embody some kind of compromise between these choices.

Can you point me to a reading source on this topic?

Thanks for your response.

I don’t think there is a single source that will explain all of the above, nor do I think what I said is really just one topic, so you’ll likely have to research a few different related topics, depending on the level of knowledge you are starting with.

The first part of my statement above is really concerned with how sound waves resonate in tubes. Here you need to read a bit about the physics of flute acoustics. There are some good papers from the University of New South Wales on this, and various books on musical acoustics, such as Benade’s Fundamentals of Musical Acoustics, but they may not get to the level of detail needed to fully understand the above statement.

To understand why narrower bore flutes and whistles are physically longer than wider bore flutes and whistles of the same pitch, you will need to dig down to the level of understanding end correction. When you get there you will see that end correction is a function of bore diameter, and gets larger as the bore diameter gets larger. Most coverage of the topic stops there, but it is also important to understand that end correction is frequency dependent, and that for each harmonic component of a note there is a different end correction. A side effect of this is that as bore diameter grows the contribution of higher harmonics is reduced, resulting in wide bores having a loud fundamental, but weaker harmonics, and narrow bores having notes with richer harmonics.

There is a pretty good discussion of this advanced topic here, in the context of organ pipes, but if you need more introductory information first you should search for articles on resonance in open ended tubes, and end correction:

The last part of my statement is also about harmonics but about how they relate to musical temperaments in tuning. More specifically, it is about the difference between the size of intervals (particularly the major third, which determines the location of tone hole B2) in just intonation vs equal temperament tuning systems.

There are many sources that discuss various aspects of the above, at different levels of detail. If you want to do a deep dive that will cover everything, building from first principles, and giving you an interesting historical perspective, you might enjoy reading a copy of Hermann Helmholtz’s seminal work “On the Sensations of Tone”. In that case set aside a few weeks to absorb it, but then you’ll be well prepared to read all kinds of other material on the topic.

The last part of my statement is really just my own hypothesis that a maker who is more sensitive to harmonics will be more likely to make tuning and voicing design decisions that are influenced by the above harmonic considerations.

Thank you. That is helpful.

Sensations of Tone PDF:

Fundamentals of Musical Acoustics PDF:

End Corrections, Natural Frequencies, Tone Colour and Physical Modelling of Organ Pipes :