Mystery Resonances
Among things I’ve been tracking are resonances from the air in the chamber caused by blowing over the ff holes.
Consistently, on ff hole mandolins, this yields 3 main peaks/clusters. One at main air mode (A0), one usually at the main top mode (MT1 as I call it) and a third one, usually between 1040-1090hz.
Here’s an example from a recent mandolin I measured (#100 in my goal of 100 ff hole mandolins!).
The tallest peak is at 282 Hz, the A0. The next tallest peak is the main top at 445 Hz (I’m going with the taller of those twin peaks, I am not sure what is going on there). The resonance in question today is the 4th tallest peak at 1072 hz. This lines up with frets 7-9 on the E-course of a mandolin. Anecdotally, some mandolins exhibit stronger notes in this range, and I’ve experienced this magic as low as fret 6 and high as fret 12. When I say stronger notes, I mean they are full, and noticeably louder and sweet and pleasant and commanding compared to their neighboring notes… all good qualities. These are probably considered wolf notes, but frankly, I’d love for the whole instrument to respond the way some mandolins do here. They would probably be problematic if bowed, but with the limited energy input of a pick, the extra juice on these notes is welcome in my mind! Anyway, I decided to investigate… onward!
I used masking tape to block the bass side ff hole. This is not a perfect way to eliminate the hole (the tape can act as a vibrating membrane, like a little tweeter) but it closes the hole off enough to behave like it’s not there. Here’s what that graph looks like…
The tallest peak (A0) is now 206 Hz (dropped by 26%— an interesting ratio with 50% loss of area), and there are still peaks around 445 Hz, but they are less defined. There’s no prominent peak at 1072 Hz anymore, but now there is one at 977 Hz. It appears that high resonance at 1072Hz in question has something to do with the ff holes.
To note: the tone with one hole taped sounds much like an oval hole. Tubbier in the bass, more clarity/airiness through the mids, and ,relating to this topic, the magic at fret 7-9 on the E-course is completely gone! They are just normal sounding notes.
Quick Background: If you ever learned about sound in a physics class you probably learned about resonances in tubes. I don’t have the credentials to give that lecture right now, but the take-away is that a tube with open ends can support a lowest frequency whose wavelength is twice as long as the tube. Or, in other words, the tube is 1/2 as long as the wavelength of its lowest resonance. This is the basis of resonator tubes under marimbas/zylophones, pan pipes, woodwinds etc. though their science is a bit more developed and instrument-specific.
Now, if you were to go and measure a handful of distances between ff holes on a handful of mandolins, and/or mandolin plans you’d find the skinniest distance between the holes is ~ 4.5” (the upper circles), max distance is ~8” (the lower circles) and at the bridge the center of the holes generally spans about 6.25”.
The crux of this blog is this, which I have been mulling over for some time now: Those higher air frequencies at 1040-1090Hz have wavelengths around 12.2-12.9”. Half of which is is 6.1”-6.45”, which happens to be the distance between the ff holes at the bridge! In other words, it appears the ff holes are creating an open-tube air resonance at the bridge controlled by the distance between them!
So… if this is true, how much variation exists in this ff hole distance across different makers? Is this a property that can be exploited? Does the resonance have to exist across the bridge or can it exist elsewhere? The minimum spacing,4.5” corresponds to around F#6 (which I have seen ring out similarly) and the max spacing corresponds to around G5 (which is typically in a weak part of most ff hole mandolins). If the ff holes were made closer together and wider near the bridge would it increase this phenomenon? Also, with the one hole taped, what’s going on with the 977 Hz peak? Did taping it cause that resonance to drop or is that a different showing up? So many questions I hope to sort out over time!
Bonus content… If you were to play all the notes in either of these configurations, then graph them you’d get the following. I call these gaphs AllNotes graphs and sometimes refer to them that way.
The graph on the left is the normal instrument and the graph on the right is with the bass-side hole taped. In both cases they graph each note from the open G course (196 Hz) to the 15th fret on the E-course (1567 Hz). The span of the resonance is from the red line (B5, 988 Hz) plus the next two peaks (C6 and C#6, 1046.5Hz and 1108.73 Hz. respectively). The graph on the left has a taller, more solid base in this area than the graph on the right..
Aside… You will also note how the left shoulder on these graphs differs greatly. The left shoulder on the normal graph rounds down from a peak (A0, at 282Hz) whereas the taped hole graph remains high all the way to the lowest notes, supported by the A0 at 206Hz, close to the second lowest note, G#3. In person, the difference in tone with these is punchy bass on the normal graph and tubby bass on the taped hole graph, which is a helpful little nugget of info.
That’s it for now, I will try to keep these coming more regularly!