Guitar resonance and soundhole geometry – Part 8: HIGH P:A SOUNDSLOT DESIGN PRINCIPLES

PART 8: A FINAL SOUNDSLOT DESIGN FOR A PARLOUR GUITAR

This is the eighth in a series of nine posts summarising the results of an experiment I carried out during 2017 and 2018 to try to increase my understanding of resonance in acoustic guitars, and in particular how the design of soundholes could be improved.

Here is a summary of my findings so far:

  • If using round soundholes, the larger the area of the hole the better it is at radiating sound produced inside the soundbox, which represents about 30% of the total sound generated by a guitar.
  • Helmholtz resonance can be detected in the signal coming from a soundhole, but only very close to it. The significance of Helmholtz resonance in forming the bass response of an instrument is its function as an important coupling between the other main resonators – the soundboard and the back/sides system.
  • There is a strong relationship between the radiative performance of a soundhole of given area and the ratio of its perimeter to its area (P:A ratio). If this ratio is greater than 0.1 there is a very marked increase in radiation from a soundbox. A high P:A ratio can be achieved by longer, narrower apertures called soundslots. The classic f-hole in violin family instruments is an example.
  • The finding is supported by the 2015 Royal Society paper The evolution of air resonance power efficiency in the violin and its ancestors (see Part 1)

A soundslot of equal area to a 50mm soundhole must be quite long to have a reasonably high perimeter : area ratio – for example an 18mm wide slot must be 436mm long. The only practical way to achieve this without badly compromising the strength and resonant characteristics of the soundboard is to make two slots instead of one. We’re back to the violin approach, or looking to the archtop jazz guitar of the twenties and thirties, made to play with big bands before electric pickups became available.

However, placing the f-holes in the lower bout as in the violin or jazz guitar is not the only approach possible, and is not even desirable in a flat top guitar. Putting the slots around the edge of the upper bout has the advantage of leaving the lower bout unpierced so it can resonate in the same way as a standard guitar. In addition, removing the round hole with reinforced edges from the middle of the upper bout should free that area up to vibrate as well.

If true, would that be a good thing? Normally the guitar soundboard vibrates as a plate with fixed edges, producing a defined set of vibrational modes that make a guitar sound like a guitar. The extra live area in the top bout defined by the slots will effectively have free edges, introducing an unknown element into the mix.[1]

So the upper bout two-slot system introduces a new element: half of the soundboard now has free edges. Without building such an instrument, it’s hard to predict what this will mean. If the upper bout becomes live, then the soundboard will become effectively larger and therefore produce more sound – a good thing for several reasons. However, the free edge of the new live area will cause a change in how the whole soundboard responds. Will it still sound like a guitar?

There’s only one way to find out, of course. The question for now is whether changing to slots is worthwhile at all in terms of better efficiency.

DOES A PAIR OF SUITABLY SIZED SLOTS RADIATE EFFECTIVELY?

The graph below shows how two round soundholes compare with the two-slot geometry, one having the same area (R41.1) having the same total area as the slots, and one a “standard 50mm radius soundhole).

Figure 1: Performance of double slot geometry compared to two round soundholes

The double slot DSLOT1 is very clearly superior to the round hole of equal area (in green) and the “standard” size 50mm soundhole (in blue).

The next graph shows how the total radiated power compares:

Figure 2: Comparison of total radiated power from 50 to 1,000Hz

Keep in mind that these are as always in this paper comparative results only, and the actual figures on the y-axis show the differences only, and are not absolute values.

Here is the same result expressed as a percentage, with the “standard” round soundhole with 50mm radius pegged at 100%

Figure 3: Comparative performance of double slot geometry compared to standard round soundhole

The main point is how much more efficient the two-slot geometry is – an 80% improvement over the standard soundhole even with 70% of the area (7885mm2compared to 5542mm2for the double slot). Unfortunately a double slot with equal area is not really achievable.

But are there any differences in how the two geometries select out the frequencies that they radiate? 

The graph below breaks down the response into octave bands. The bands are:

OCTAVEFREQUENCY BAND (Hz)GUITAR FRETBOARD RANGE
282 – 165STRING 6 FRET 0 TO12
3165 – 330STRING 4 FRET 2 TO 14
4330 – 660STRING1 FRET 0 TO 12
5660 – 1319STRING 1 ABOVE FRET 12

Figure 4: Comparison of octave band response between round soundholes and double slot

The main features are:

  • There is little to choose between the three geometries at low frequencies
  • The two-slot geometry performs by far the most strongly in Octave 3 (165 to 330Hz)
  • None of the three perform well in the highest frequency band, although the double slot marginally outperforms the round holes

SOUNDSLOT CONCLUSIONS

  • There is strong evidence that soundslots outperform round soundholes of the same area by a significant margin, and not just at air-cavity resonance frequencies
  • The P:A ratio needs to be above 0.1 for this to be so
  • It is likely that applying this approach to a guitar will result in an overall higher projected volume of sound, possibly by up to 80% of the total 30% soundhole projection
  • The overall effect on a guitar’s timbre is hard to predict because of the different vibrational modes available to the soundboard due to some free edges

FOOTNOTES

[1]Differences in timbre between instruments are largely caused by different top bracing systems and different qualities in the soundwood used for the top plate. These variables result in different weightings between the defined set of vibrational modes. In my opinion, the material used for the sides and back of a soundbox has very little influence on timbre, popular opinion notwithstanding

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