©Lin Yangchen & Jerry Ng




This case study documents the sound of the Auferstehungsorgel using ultra-high-fidelity recordings of individual pipes and explores the instrument’s tonal characteristics through computational spectral analysis. This is the first and, at press time, the only such study of an organ in Singapore.



Click to sections:

Audio sampling
Attack transients
Stationary spectra
Experimental bamboo pipe
Voicing
Tuning
Low pressure setting
Tibetan Contrabombarde
References

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Audio sampling

Recording in progress: using a Steinberg UR44 audio interface and Logic Pro X software, Jerry Ng checks the signal from the AKG C414 XLII condenser microphones configured in a cardioid polar pattern, which cuts out noise from the rear and is wide enough in front to span the organ case. The balanced pair were made and tuned in Vienna prior to the Samsung acquisition of AKG. They are rated with a fairly flat frequency response from 20 Hz to 20 kHz and a dynamic range of 134 dB. No bass-cut filters or attenuation pads were used.

A pair of beyerdynamic M 160 hypercardioid ribbon microphones captures the magnificent acoustics of the Gustav-Mahler-Philharmonie from the circle. The feed from these were not used in the pipe emission analysis but were part of the complete tonal documentation of the instrument and venue.

We placed the AKG microphones 179 cm above the floor, 49 cm from the front of the case and 25 cm apart. That was close enough to hear the softest pipes and capture most of the rapidly attenuated high-pitched harmonics but far enough from the instrument and close enough to the centre of the façade to sufficiently even out the distance to each pipe, and high enough to give the microphones better “line of sight” to the rear pipes.

Instead of isolating each pipe in an anechoic chamber and positioning the microphone a constant horizontal distance from the flue to dissect the precise effects of pipe design on tone, whose closest real-world manifestation is in what the pipe voicer hears, we wanted to document the sound that the organ as a whole projects to the player or listener in the acoustical space. Štěpánek & Otčenášek (1994) used such an approach to statistically characterize and compare the plena of Czech baroque organs. See Syrový et al. (2003) for a comparison of pipe sound inside and outside an instrument.

Each pipe was played thrice (in case of interjections such as drilling or birdsong) for 8 s with 4 s intervals in between to allow the 2.5 s reverberation to dissipate followed by 1.5 s of silence. The key was pressed and released quickly but gently to minimize keyboard and tracker sounds. The player kept time using a digital metronome through earphones. The sound was sampled at 96 kHz, which gives a Nyquist frequency of 48 kHz leaving a comfortable margin above the microphone’s upper limit. The high sampling rate also helps resolve attack transients. The bit depth of 24 gave a dynamic range of 144 dB, a good match with the microphones and more than enough for the task at hand.

Some pipes were also recorded separately with a Røde Stereo VideoMic Pro held right in front of the pipe mouth to maximize the signal-to-noise ratio. The microphone has a pair of matched condensers of sensitivity 40–20000 Hz in a cardioid pattern. It was connected to a Zoom H1 audio interface recording in 24 bits at 96 kHz.

The recordings were played back for inspection using a Universal Audio Apollo sound card and pair of Yamaha NS-10 studio monitors, which were first released in 1978 and were sought after by rock and pop audio engineers for their ability to reveal less-than-perfect quality in recordings. Audio data were exported in uncompressed wav for analysis using a specially written program in the R Language for Statistical Computing, which can bulk-process any number of pipes (download source code).



The microphones were near enough to the organ that the recorded loudness (RMS, top row; fundamental, middle row) and harmonic spectrum (represented crudely here by the spectral centroid, bottom row) of a given pipe were quite sensitive to microphone position, due to differences in the relative position and orientation of the pipe being recorded as well as in the topographies of obstructions, reflecting surfaces (such as the side of the case) and resonances caused by other pipes and the room and its contents. Voicer Reiner Janke observed that the sound quality of a pipe changed when he moved his head left and right by as little as 50 cm while holding down a note at the console. In the scatter plots above, each point was calculated as the value from the left microphone minus that from the right microphone for a given pipe. A positive point means the left microphone recorded a larger value than the right microphone, and vice versa. The distributions appear essentially random except for a subtle negative slope in the differences in recorded brightness (spectral centroid) in the Flute 4′ (bottom left): the lower pipes sounded brighter to the left microphone and the higher pipes sounded brighter to the right microphone. This could be explained by the more rapid attenuation of higher harmonics over distance. The balanced scatter on both sides of zero over the pitch range of the pipes, with perhaps only a very slight bias towards the left microphone, is also an assurance that the microphones were positioned optimally.

To account for the differences between left and right we ran a replicate analysis on the data from each microphone and took the average values of the metrics above. For attack transients and stationary states we evaluated the pipes using the results from both channels, which turned out to be qualitatively similar.

Correction for non-flat microphone frequency response was not done as the manufacturer was unable to provide raw data. For the part of the analysis dealing with steady states, four seconds were extracted from the stationary phase of each pipe for processing. Detailed information on pipe morphometry and materials is available in the Auferstehungsorgel pipe database.

Ultrasound microphones meant for studying echolocating birds and bats could be used in the future to capture higher frequencies. Although beyond human hearing, these frequencies are scientifically interesting and could reveal things like how bats navigate through a church when the organist practises late into the night.



Attack transients

  The pipes express some individual character in their attack transients. One interesting example is the bottom B flat (pipe 11 sound) of the Flute 4′, a wood pipe that chiffs on the fifth harmonic (left); most of the wood pipes chiff on the third harmonic if at all. Meanwhile the second C (pipe 74 sound) of the Piccolo 2′ chiffs on non-harmonic frequencies that appear to correspond to eigenmodes (see explanation below) and give it a metallic clang. Chiffing is a delightful phenomenon popular in the neo-baroque school, but if too many pipes do that it may disrupt the flow of musical lines.

The spectrograms above also show the characteristic odd harmonic development of a stopped pipe (left) versus both odd and even harmonics in an open pipe (right). The third harmonic of the wood pipes can be heard an octave plus a fifth above the fundamental and gives the stationary tone a subtle “glow” that isn’t muddied by an intervening second harmonic.

The most sluggish attack in the instrument comes from the bottom D (pipe 64 sound) in the Piccolo 2′, nicknamed Slow Loris after the endangered Southeast Asian primate, which initializes with the second harmonic and takes half a second to reach equilibrium.

Decay was not studied. The relative strengths of the harmonics in the decay are generally similar to those in the steady state, with the higher frequencies decaying faster (Rucz 2015).



Stationary spectra

  As expected, the straight-sided pipes (e.g. left, pipe 17 E4 sound) produce more prominent harmonics than tapered ones (e.g. right, pipe 66 E4 sound). The difference is magnified by the tuning slots (see morphometric analysis) in the former, which radiate higher harmonics more efficiently (Colin Pykett comm.). Compared with the wood pipes whose harmonics fizzle out rapidly above the third (see earlier), the metal pipes spew up to at least around the fifth harmonic or a few more above that. However, two or three low pipes, including open metal ones such as the first note of the Piccolo 2′ (pipe 62 sound), are true-blue flutes with an almost pure fundamental. Occasionally, the second harmonic (octave) is as powerful as the fundamental (e.g. pipe 23 sound).

The Auferstehungsorgel is home to a couple of maverick pipes. The E6 in the Piccolo 2′ (pipe 90 sound) emanates a ghost note a third below the fundamental (above). The C4 in the Flute 4′ has two alternate stationary states depending on how fast the key is pressed. If the key is pressed fast as one would in normal playing, the pipe enters the less stable state of a soft quivering tone (sound) as most of the air is directed over the outer face of the upper lip and dissipated to the surroundings. This sometimes flips to the more stable state on its own if the key is held down long enough. If the key is pressed very slowly, the air is introduced more gently through the flue, gets established on the inside of the upper lip and locks into the more stable state (sound).

Acoustic eigenmodes or standing waves are also present (e.g. red circles above, pipe 88 sound) in the form of lower spectral peaks whose frequencies and periodicity depend on the physical length of the pipe and are often slightly different from those of the harmonics (Angster et al. 2017). The further the eigenmodes are from the harmonic frequencies, the greater the inharmonicity or proportion of sound of indefinite pitch in the pipe’s tone (Sakamoto et al. 2005, Rucz 2015).

  Many of the pipes (e.g. pipe 18 sound) generate irregular harmonic envelopes, successive spectral peaks getting louder or softer in a seemingly haphazard order (left, red line) instead of getting progressively softer. This is partly due to interference between the harmonics and eigenmodes: if an eigenmode coincides with a harmonic, the harmonic is amplified (Angster et al. 2017). The emergent shape of the envelope is also influenced by the loss of sound energy due to air volume, viscosity and friction with the pipe wall, radiation from pipe openings and vibration coupling with the wall (Angster et al. 2017). The historical 1912 Bevington pipe (sound) has a remarkably smooth and regular envelope (right) among the pipes of the Auferstehungsorgel. This might have something to do with its high lead content, as lead suppresses higher harmonics and dulls the tone. Despite this, the pipe's principal scaling gives it a brilliance matched only by some of the high Zimbeln.

The broadband baseline noise of the power spectra is generally constituted by turbulent air flow in the vicinity of the pipe mouth and from structural irregularities in the pipes. Noise may also arise at very high frequencies from transverse resonances and pipe wall vibrations. See Angster et al. (2017). Our baseline noise is relatively pronounced across the board compared with other studies. This is partly because the blowers are relatively loud from the player's position and the microphones were positioned a fair distance from the pipes rather than right in front of the mouths.

  We have so far discussed the spectral components of stationary phases mostly on the assumption of a perfectly constant tone over time, but in reality some of the pipes can be heard “fluttering” during the stationary phase due to fluctuations in wind pressure (Taylor 2016) or to pipe structure. The flutter can be investigated by examining the pressure time series and the humps or peaks in the immediate vicinity of the fundamental frequency peak in the power spectrum. For example, the A5 pipe (pipe 34 sound) in the Flute 4′ flutters in both loudness (left) and pitch through a frequency band of about 25 Hz (right) centered on the fundamental frequency of 905.68 Hz.



Experimental bamboo pipe

Specially made by Jerry Ng for the Auferstehungsorgel.
 
  Power spectra (left) show louder baseline noise and considerable non-alignment of the harmonic and eigenmode frequencies in the bamboo pipe (top), compared with essentially perfect alignment and more prominent harmonic peaks in the previous pipe in the rank (bottom), a nicked and slightly tapered open metal (recording). The greater inharmonicity in the bamboo sound is also apparent as graininess in the corresponding spectrogram (upper right). The especially thin flue of the bamboo pipe may be partly responsible (see Colin Pykett comm.). Nevertheless the bamboo pipe has a more uniformly sloped harmonic envelope.

The first 15 mel-frequency cepstral coefficients (mfcc) of the bamboo pipe (red line) and its neighbour are highly “synchronized”, but those beyond start getting “out of sync”. The coefficients indicate a quantifiable difference in timbre that could be used to train machine-learning algorithms to infer pipe materials and morphology from just the sound, with potential scientific or forensic applications. See later for background explanation of mfcc.

Photomicrograph of the transverse section of a cured bamboo culm from Ng's pipemaking stock (microscopical analysis). The tonal characteristics of cured bamboo could be due to its extensive vascular cavities and low density, which make the pipe wall more prone to vibrations and resonances at random high frequencies. The high silica content of bamboo increases its rigidity (Ito et al. 2015) and probably reduces elastic dampening of the vibrations. The pipe sings in a slightly more airy tone (recording) reminiscent of the tropical mountain breezes of the Malay Archipelago.



Voicing



The root-mean-square (rms) sound pressure of each pipe (top row) was calculated from its stationary waveform while its fundamental (frequency and) pressure (middle row) was measured from the power spectrum obtained through a fast Fourier transform. The rms and fundamental pressures vary considerably from pipe to pipe as functions of both the pipes’ intrinsic voicing and their physical locations with respect to the listener or microphone, but are correlated with each other (bottom row).

In the Flute 4′, the metal pipes of unknown provenance are slightly louder than the Klais pipes on average, but the ear, being less sensitive to lower frequencies, hears less of a difference. Some of the pipes in the top octave have a “sore throat” due to their battered condition. No frequency weighting was done to approximate human loudness perception as our purpose was to detect discontinuities in loudness gradation as one progressed along the rank, which if absent or present would be apparent regardless of weighting. The omitted data point in the Piccolo 2′ is the B7. It wasn't speaking properly due to an air leak in the toe board that has since been plugged. The two stops are similar in overall power.

The spectral centroid, or centre of mass of the spectrum, is the mean of spectral frequencies weighted by magnitude. It is a measure of a pipe’s perceived brightness. For comparability across pipes, the relative brightness of each pipe (above) was calculated as its spectral centroid minus its fundamental pitch, which was then normalized to (divided by) the latter. It reveals a few (relatively) superbright pipes in the lower part of each stop. This metric incorporates not only the harmonics but also inharmonic and broadband noise. It is much more sensitive than the ear, which hears less variation than the plot suggests. Negative values in the higher reaches should be interpreted with caution as they incorporate low-frequency noise from external sources such as the blowers. The high pipes were also disadvantaged by the microphones' 20 kHz frequency response ceiling. Nevertheless these negative values reflect real-world constraints on human perception, as the ears can hear the blowers too and can’t hear above 20 kHz.

Voicing consistency was also analyzed using mel-frequency cepstral coefficients (mfcc), which are like “distillates” that capture the essence of a pipe’s timbre. A set of mfcc values is obtained from what is essentially the spectrum of the spectrum of the pipe's sound, using the mel frequency scale to better approximate the response of the human ear. These coefficients are widely used in computer speech recognition.

The second to fiftieth mfcc (rows) of every pipe (columns), coloured by value (colours are not comparable across stops). The first coefficient of each pipe was discarded as is common practice, being affected by the computation process and unstable. Vertical dashed lines demarcate the boundaries separating the main pipe varieties. Cross-boundary discontinuities are apparent in the coefficient patterns, for example in the transitions from wood to metal to Klais in the Flute 4′, but some of the patterns straddle the boundaries. The two varieties of Klais are more akin to each other than what their differences in morphology and alloy composition would suggest. The Bevington pipe, sandwiched between the two Klais varieties (above), can be told apart but blends in well enough. In the Piccolo 2′, pipes 50 to 56 appear remarkably uniform, but that is because their pitches are almost identical; more suitable pipes were unavailable for the organ.



Tuning

Tuning errors (deviations) in semitones by note. The deviations from reference frequencies based on A = 440 Hz were calculated using the equation 1200 × log₂ (actual frequency/reference frequency). The values were then shifted to match the organ’s average pitching.

As it turns out, lower pipes tend to be slightly low while higher pipes tend to be slightly high. This reminds one of the stretch tuning done on pianoforte to compensate for the human ear's natural tendency to overestimate low pitches and underestimate high pitches. However, it is more likely in this case to be a result of the organ having been moved from its place of construction to a new home where the average temperature and humidity are significantly higher. A rise in temperature sharpens small pipes more than large ones, while an increase in humidity would have caused the wood pipes of the bottom octave of the Flute 4′ to swell slightly and go flat.

The distribution of tuning errors in each stop is slightly skewed towards the low side. The unevenness on the high side could be due to smaller pipes being more fiddly.

Aside from deterministic patterns, the pipes are subject to temperature fluctuations owing to the absence of air-conditioning and the gradual warming-up of the blowers during use. These constitute the random “untunability” component of the Auferstehungsorgel’s “stochastic” temperament. The last 14 notes of each stop were excluded from this part of the analysis as those pipes had not been tuned at the time of the recordings.



Low pressure setting

We tried sounding the pipes at half the rated wind pressure by turning off one of the two separately controlled blowers. This is very rarely if ever done, as researchers and organ builders usually go for the correct sound. But it is highly fascinating and could deepen our understanding of organ pipe acoustics by exploring the boundary of the multidimensional parameter space beyond which pipes stop working.

  Low pressure apparently avoids “locking” the pipe to a fundamental frequency and allows more harmonics to develop (left). Sometimes the pipe produces multiple audible pitches (e.g. pipe 70 sound). The densely packed harmonics seem to belong to a fundamental frequency much lower than the loudest frequency or frequencies which the ear hears as the main pitch(es). The tone has a curious “sour” or “bitter” taste and may be nasal or raspy. The “stationary phase” is sometimes so unstable that it spontaneously flips to a different set of harmonics, such as in pipe 37 (sound). This pipe starts speaking somewhat reluctantly, and pitch is unstable within each phase as well (right). The larger pipes are more prone to these behaviours while the smallest pipes stopped speaking altogether when wind pressure was halved.



Tibetan Contrabombarde

The single D2 of the Tibetan Contrabombarde 32′ issues a variety of attack transients depending on the magnitude and acceleration of wind pressure from the player’s lungs.

  Spectrograms showing the “volcanic eruptions” of the first (left) and last (right) notes in this recording. The attack of the first note comprises a rush of wind and a momentary E2 with a prominent second harmonic just after the 1 s mark, while the last note flips from the higher (overblown F2) to lower-energy (D2) stable state at the dashed line. As expected, the higher frequencies decay faster (Rucz 2015).

Power spectrum of the Tibetan Contrabombarde up to the 50th harmonic. The pipe has a rich and irregular harmonic development, with prominent third, eighth and thirteenth harmonics.



References

The authors are grateful to Paul Marzetti-Godman and Peter Jones for insights that improved the interpretation of the data.


Angster, J., Rucz, P. & Miklós, A. 2017. Acoustics of organ pipes and future trends in the research. Acoustics Today 13(1):10–18.

Angster, J., Wik, T., Taesch, C., Sakamoto, Y. & Miklós, A. 2004. The influence of pipe scaling parameters on the sound of flue organ pipes. The Journal of the Acoustical Society of America 116:2513.

Ito, R., Miyafuji, H. & Kasuya, N. 2015. Rhizome and root anatomy of moso bamboo (Phyllostachys pubescens) observed with scanning electron microscopy. Journal of Wood Science 61:431–437.

Rucz, P. 2015. Innovative Methods for the Sound Design of Organ Pipes. PhD dissertation, Budapest University of Technology and Economics.

Sakamoto, Y., Yoshikawa, S. & Angster, J. 2005. Acoustical investigations on the ears of flue organ pipes. Forum Acusticum 2005 Budapest pp. 647–651.

Štěpánek, J. & Otčenášek, Z. 1994. Acoustic documentation of 12 pipe organs and analysis of their plena. Journal de Physique IV Proceedings 4(C5):645–648.

Syrový, V., Otčenášek, Z. & Štěpánek, J. 2003. Subjective evaluation of organ pipe timbre in the standard listener positions. Proceedings of the Stockholm Music Acoustics Conference pp. 333–336.

Taylor, A. J. 2016. Effects of centrifugal blowers and reservoir resonance on organ pipe flutter. EuroRegio2016.