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.
Whenever I have played with other musicians, I've always experienced difficulty playing in tune from the first note. As an ocarina's pitch is sensitive to blowing pressure this is somewhat a given, as the player must get used to the instrument's breath curve. However, I've been playing this ocarina for over a year, and it feels like I've needed to re-learn the breath curve in every new situation.
Due to this, I have come to suspect that ocarinas have a non-linear response to ambient temperature across their playing range. I initially rejected this idea as the general attitude in the ocarina community has been that ambient temperature does not matter, as the instrument is warmed by the players breath. But after embarrassing myself by playing out of tune in front of a large audience, I decided to study the issue scientifically.
To research the underlying behaviour, I came up with two questions that are testable by experiment:
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.
To test how an ocarina's pitch responds to pressure across its range, I have measured the pressure required to sound every fingering at multiple pitches by varying blowing preassure. These measurements were taken at A440, and offset above/below this in 20 cent intervals using an electronic tuner. The tested tunings were:
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 room was heated to a constant temperature of 20C +/- approximately 1 C, and 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:
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.
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.
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 can swing greatly depending on the temperature outside. I took a measurement playing the high F, at different times of day, adjusting my breath pressure until the note sounded best to my ear. Then I 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. When graphed, this appears to be a linear plot. I have added a line of best fit:
|Temperature||Cents from A440|