Researching the ocarina's breath curve and how tempriture effects it

The pitch of the ocarina is affected by temperature, though how is not well understood. Being a mouth blown instrument, the air will be warmed by the body. However, this warmed air is constantly mixed with ambient-temperature air from the environment.

Over the past years, I have had the opportunity to play ocarinas in a very wide range of situations. This has meant dealing with freezing temperatures in the middle of winter, to barely tolerable highs in the summer. As their pitch is so sensitive to changes in blowing pressure, ocarinas are tuned by the player raising or lowering their breath. This is done while listening to the pitch and the accompaniment.

Whenever I have played with other musicians, I've always experienced difficulty playing in tune from the first note. As the ocarina is tuned by ear, this is somewhat a given. However, the needed change does not feel like I'm applying an equal breath change to every note. I always need to listen to my pitch relative to the other musicians, making deliberate compensations for every note until my muscle memory takes over. It's like there is a need to re-learn the instrument's breath curve with every playing session.

Due to this, I have come to suspect that ocarinas have a non-linear response across their playing range. To research the underlying behaviour, I came up with two questions that are testable by experiment:

  1. How does the ocarina's pitch respond to changes in pressure across its sounding range, where ambient temperature is constant?
  2. How does the ocarina respond to changes in ambient air temperature?

This article describes my results of testing these two questions. The intention was to obtain a 'high level' or 'ballpark' overview and, as such, my methodology and test equipment is not as rigorous as it could be. Throughout the article, I make note of methods which could be improved, as well as results which appear abnormal. To eliminate variation in instrument tuning, all measurements were taken using the same ocarina.

How does the ocarinas pitch respond to changes in pressure?

To test how an ocarina's pitch responds to pressure across its range, I have measured the pressure required to sound every note. These measurements were taken at A440, and offset above/below this in 20 cent intervals using an electronic tuner. The tested tunings were:

  • A440 minus 40 cents
  • A440 minus 20 cents
  • A440 (zero cents)
  • A440 plus 20 cents

The pressure needed to sound every note at these offsets was measured using an electronic pressure transducer from a tube alongside the instrument's windway. Because I do not have anything to use as a reference, I have made no effort to calibrate to a standard. Thus, my results are given in arbitrary 'units'. While these cannot be compared with 3rd party measurements, they can be compared with other values from the same measurement device. See 'How I made these measurements' for further details.

In order to avoid introducing errors from varying ambient temperature, the ocarina was pre-warmed by playing it for several minutes. After this, all measurements were taken quickly over about 15 minutes, leaving little time for the ocarina to cool.

My tuner was first set to A440 minus 40 cents and the pressure measured for each note one after the other. This was repeated for -20, 0, and +20 cents. Every time the tuner was adjusted, the instrument was re-warmed by blowing 5 full breath long tones immediately before making measurements for that tuner setting. The ambient air temperature was 15 degrees centigrade.

Following are the results of this experiment:

Cents C D E F G A B C D E F
-40 30 31 33 32 33 33 35 37 41 50 56
-20 34 35 39 42 43 43 46 49 55 63 68
0 36 39 44 46 48 51 54 61 69 75 83
20 39 43 48 51 57 61 69 78 85 103 121

And graphed:

The first thing I noticed from the graph is that the curves diverge. As the pitch increases at the low end, a greater amount of pressure is required to maintain the same pitch raise at the high end. Raising the pitch from -40 cents to -20 at the low end required a raise of 4 units (30 to 34), while the same change on the high end required a raise of 12 units (56 to 68).

This divergence between the low and high end also appears to increase the further the pitch is raised. Raising from zero cents to plus 20 required a change of 3 units on the low end (36 to 39), but 38 units on the high end (83 to 121). That is 26 units (38 - 12) more than raising the high F from -40 cents to -20.

These values increase as the pitch is pushed further. For instance, consider high F: minus 40 to minus 20 takes a 12 unit increase, minus 20 to zero takes a 15 unit increase, and zero to plus 20 takes a 38 unit increase. The difference steadily gets larger.

The results at the low end appear to contradict, -40 to 20 changing by 4, -20 to 0 changing by 2 and 0 to 20 changing 3. Based on the shape of the other 3 curves, the -20 cent curve between low C and G appears to be reading high. I would expect it to lie closer to the middle between the minus 40 and zero curves.

I believe this is a quantisation error caused by the limited resolution of my measurement set-up. It is also probable that I contributed to the error. The ocarina is very sensitive to changes in pressure on these low notes, and holding it stable is not easy. The first could be addressed with a more sensitive measurement device, and the second by taking multiple measurements and making an average. However this does increase the chance of error from environmental temperature change, as it would take longer to take more measurements.

Eliminating temperature changes as a factor could be attained by measuring the internal temperature simultaneously with pressure and looking for any correlation between the measurements.

Another abnormality I observed is the sharp angles present in the plus 20 cent curve which do not correlate with any of the other curves. I do not know what caused this, and repeating the measurements would be required to determine if they are a one-off error or not.

How does ambient air temperature affect an ocarinas tuning?

To test how ambient air temperature affects the tuning of an ocarina, I have measured the pitch of an ocarina's high F at different temperatures. The high F was used as a reference as this note is the least affected by changes in breath pressure

The ambient temperature of my workshop swings greatly depending on the temperature outside. I took a measurement playing the high F, adjusting my breath pressure until the note sounded best to my ear, then took note of how many cents it differed from F at A440. This was recorded along with the ambient air temperature.

Breath warming was minimised by leaving the ocarina for several hours before taking each measurement, and then taking the measurement during the first breath. A number of measurements were taken over several days.

Results; all temperatures are in degrees Celsius:

Temperature Cents from A440
2.5 -39
10 -25
12 -22
14 -19
17.4 -14
16.7 -15
20 -7
22 -3

When graphed, this appears to be a linear plot. I have added a line of best fit:

Without the effect of breath warming, the pitch of the ocarina appears to shift linearly at a rate approximately 9 cents per 10 degrees. There is some variation in the plotted points, which I assume is due to variation in what I was perceiving as 'best sound' at a given time.

As the ocarina is a blown instrument and the human body warms the air it is breathing, this air will warm the ocarina over the duration of a playing session. However, the air inside the ocarina is continually being mixed with air syphoned in through the voicing from the surrounding environment. Because of this, the internal air temperature will find an equilibrium between the breath and ambient air temperature. Consequently, I would expect the ocarina's pitch to sharpen if played from cold. Exactly how much, and over what time duration would require another experiment to determine.

Conclusions

Ocarinas are affected by ambient air temperature. While this can be compensated for by changing breath pressure, the ocarina responds non-linearly to these changes across its sounding range. Ocarinas will play best at the temperature they where tuned at. When played in a environment colder than it was tuned in, the notes may be blown up to pitch. However, doing so requires a larger change in breath pressure on the instrument's high notes than its low notes.

This non-linearity is likely responsible for the pitch errors I have been experiencing. It makes it difficult to learn an ocarina's breath curve as the curve required to play in concert pitch changes with ambient temperature. Dealing with a non-linear breath curve shift as a player is problematic. This is analogous to having a string instrument whose frets move with temperature. As the 'set points' of the breath change, muscle memory is not reinforced. This non-linearity is likely responsible for the pitch errors I have been experiencing. It makes it difficult to learn an ocarinas breath curve as the curve required to play in concert pitch changes with ambient temperature.

In light of this, I'd recommend blowing the ocarina to stabilise its temperature before a performance. From there, play the ocarina with your usual breath curve and re-tune any accompaniment to you. Doing so will allow your breath curve to remain more consistent, allowing muscle memory to be reinforced. If you absolutely have to play in concert pitch in a cold situation, I would recommend obtaining an ocarina tuned to play in A440 at a lower ambient temperature. Ocarinas tend to have a relatively limited pressure range in which they have their best tone. Blowing harder will raise their pitch, but it also makes the tone increasingly airy. In extreme cases, this causes the high notes to squeak.

Because the needed pressure change appears to grow the higher the note, I suspect ocarinas with fewer holes would experience less divergence between their high and low end. The measurements where taken on an 11 hole ocarina, though I did not measure the low B. On a 10 hole ocarina, I would expect the required pressure change between the low and high end to be smaller.

I think that makers should specify the temperature an ocarina was tuned to play best at. If someone plays an ocarina in concert pitch in a cold environment and the high notes squeak as a result, they may assume they have a badly made instrument.

How were these measurements made?

The pressures involved with blown wind instruments are low. Water in a U-tube may be used to measure these low pressures; the difference between the water level in the two tubes is proportional to the pressure applied. This is commonly given as inches of water or centimetres of water.

While the U-tube works for measuring low pressures, I found it cumbersome to use as the water takes several seconds to stop moving after pressure is applied. All commonly available 'dial' and digital pressure gauges are designed for measuring pressures considerably higher than the range I'm interested in—for example, car tyre pressures and compressed air systems which use tens to hundreds of PSI. I have measured ocarina breath pressures in the past using a U-tube filled with water, and the highest pressure observed was 19 centimetres of water, about 0.27 PSI.

I discovered that pressure transducers do exist for such low pressure ranges. These are electronic components which linearly convert pressure into a voltage. I created a gauge using one of these and an Arduino microcontroller to sample its analogue output, the values from which were streamed to a Linux computer via USB serial.

The values obtained from this are simply the direct output of the Arduino's ADC, minus a zeroing offset as the transducer outputs a voltage higher than zero volts when no pressure is applied. I have made absolutely no attempt to calibrate these units to a universal standard as I do not have a reference standard with with to do so. However, measurements taken may be compared with others made from the same device.

Since buying this transducer, I have become aware of others which are designed to work with lower pressures. Using one of these would increase the resolution in the low pressures being measured. As is always the case, when you do something for the first time, you inevitably find better ways of doing it.