CrossTune - Tool for Tuning a Native American flute for a Different Environment
This page provides a tool for the CrossTune situation:
You are tuning a flute in one environment
(temperature and humidity) and
it will be played in another environment.
The code for these calculations is taken directly from
Thanks goes to all the
authors of and contributors to Native American flutomat.
This page provides some background on the issues of temperature and humidity on the tuning of flutes. If you wish to skip the description, you can go directly down to the CrossTune Calculator. If you find any problems or suggestions regarding this page,
please contact me.
The vibrations produced by a Native American flute are generated by a air pressure wave travelling up and down the sound chamber of the flute. The frequency of the sound, which determines the pitch of the sound that our ear's perceive, is determined by how many times per second that the air pressure wave makes a round-trip up and down the sound chamber of the flute.
For a single, held tone, the length of the sound chamber does not change, but the speed that the air pressure wave moves up and down the sound chamber depends of the speed of sound inside the sound chamber. The faster the sound moves, the higher the frequency of the generated sound, and the higher the perceived pitch of the tone. See [Hopkin 1999] for an excellent description of this process.
So, pitch is determined by the length of the sound chamber and the speed of sound inside the sound chamber. Since the length of the sound chamber is fixed (if you don't change your finger position), it is only the speed of sound inside the sound chamber that determines the pitch.
For the typical conditions of flute playing, the speed of sound changes with the:
- Temperature of the air inside the sound chamber, and
- Humidity of the air inside the sound chamber (to a minor degree)
Two other factors are the ambient air pressure and ambient air density. However, in a gas, pressure and density are tied together in an direct relationship (compress the gas and it becomes more dense). Conveniently, the effects of pressure and density on the speed of sound are exactly the opposite. So, the effect of the change in ambient air pressure exactly cancels out the effect of the associated change in ambient air density, and so ambient air pressure can be ignored calculating the speed of sound. The theoretical basis for this has matched observed experimental results ([Dean 1979], page 50).
Notice that I've used used the word "ambient" in the above paragraph. Sound is itself the local variation in air pressure, so air pressure is constantly changing in the presence of sound. However, "ambient air pressure" is used when talking about the general air pressure in the absence of the local pressure variations caused by sound.
Where Do We Measure Temperature?
Since the pitch of a held tone on a flute is dependent primarily on temperature, the question is: where do we measure the temperature? There are three choices:
1. In the room where the flute is being played. This is the easiest to measure with a thermometer. However it is not the speed of sound as it travels from the sound source (the flute) to the ear that determines pitch, but the speed that the air pressure wave moves up and down the sound chamber of the flute.
2. Inside the air pressure wave of the generated sound. This is an interesting one. If you reduce the pressure of a gas, it immediately cools. You experience this when you let the gas out of an aerosol can — both the released gas and the aerosol can become cooler, because the pressure of the gas is reduced in both places.
In the same way, there are local areas of high pressure and low pressure inside a sound wave:
These local, very rapid changes in air pressure produce local, very rapid changes in temperature. And while we usually represent a sound wave as a nice idealized sine curve, like this:
the reality is more complex since these local changes in temperature affect the speed of sound and cause a skew in this idealized sound wave.
However, these differences balance out, since the changes in temperature are so rapid and inverse and there is no change in the ambient air pressure and temperature.
3. Inside the sound chamber of the flute. The temperature inside the sound chamber and, to a lesser extent, the humidity are the primary factors that affect the speed of sound, and hence the pitch.
However, these factors change as the flute is played. As flute “warms up”, the air inside the sound chamber heats up and becomes more moist (unless you're playing in the Amazon, where it could potentially cool down as you play it).
A Small Experiment
To measure how quickly and how much the temperature changes inside the sound chamber, I placed a temperature probe with a remote readout inside the slow air chamber and at two places inside a sound chamber of my Colyn Peterson F# made of Alaskan Yellow Cedar. Here is a graph of the results:
Increase in air temperature at three places inside a flute as it warms up.
I played “normally” (as normally as you can play with a thermometer stuck in your flute).
Some issues are that the head of the thermometer was probably touching the inside bore of the flute, which probably lowered the teperature readout a bit.
All tests started between 70.9°F and 71.8°F, in very high humidity (we were looking at possible tornados in Connecticut). The temperatures stabilized at about 90-91°F in the slow air chamber, 79°F at the uppermost finger hole, and 78°F at the lowest finger hole.
This seems to pretty much agree with the general experience of flute players as to how long it takes to warm up a flute.
The sound chamber seems to heat up about 7.5°F. In terms the change in tuning that this will produce, you can use the calculator below to do your own experimentation.
So the temperature in the sound chamber is a mix of breath temperature and room temperature. Here are some factors that also affect how quickly and to what temperature the sound chamber heats up:
- The amount of air that the flue allows into the sound chamber
- The volume of the sound chamber
- The amount of breath volume put out by the player
- The size and number of finger holes and direction holes that are open
- The effect that the player's hands have on heating up (or cooling down) the flute.
- The material of the flute - how much the body of the flute heats up or cools down the air in the sound chamber.
- The temperature of the breath blown by the player. This relates to how much the room air is heated up to body temperature, which is subject to the amount of breath and the length of time the play holds their breath.
... and probably a number of other factors that I have not thought of.
So, the temperature inside the sound chamber changes over a period of 2-3 minutes to somewhere between the room temperature and body temperature. The change in the air temperature in the sound chamber will be greater if the difference between he room temperature and body temperature are greater.
So the the above experiment needs to be repeated for different room (starting) temperatures and for the variety of other factors mentioned above. However, until that is done, looking at the one experiment that was done, we see that the air temperature in the sound chamber rose from a room temperature of 71-72°F up to 78-79°F. The difference between the room temperature and the body temperature is about 27°F, so the rise in air temperature in the sound chamber of about 7°F gives us the general rule-of-thumb that:
The rise in the temperature of the sound chamber is about 26% of the difference between room temperature and body temperature.
So What Temperature Do I Plug Into The Calculator?
Getting back to practicalities, let's say you have an idea of the room temperature where you are tuning the flute, and the room temperature where it is being played. Let's use an extreme case of tuning a flute in your chilly workshop at 60°F (you're a fresh-air fiend) that will be played by a sun-loving flute player in Arizona (let's say at 85°F). Let's also say that you're in a relatively moist 60% relative humidity and the Arizona climate is dry (10% relative humidity).
You could plug in 60°F and 85°F in the calculator below, but that would produce misleading results (leading to an over-correction of tuning).
Using the rule-of-thumb from above that the temperature rises about 26% of the way from room temperature up to body temperature, we can assume that:
- the temperature inside the sound chamber rises 10°F in your workshop ((98.6°F - 60°F) × 26%), and
- the temperature rises only 3.5°F in the Arizona climate ((98.6°F - 85°F) × 26%).
Adding those numbers to the starting temperatures of 60°F and 85°F gives us a tuning temperature of 70°F and a playing temperature of 88.5°F. Plugging these numbers into the calculator below, together with the 60% and 10% relative humidities in these environment, gives us a pitch adjustment of 27 cents.
by Clint Goss, with core calculation routines by Edward Kort, version 1.03
- Enter the temperature and relative
humidity for the environment you will be tuning the flute.
- Enter the temperature and relative
humidity for the environment the flute will be played.
- Enter the refrence pitch for for the playing environment.
This is typically A=440 for modern concert pitch,
but there are many variations.
Historical instruments are tunes as low as A=415,
and some orchestras tune today as high as A=446.
- Press "Calculate" button.
- The results will tell you two possible ways to compensate for the
difference in tuning and playing environments. You can either:
- adjust your tuner's reference to a pitch other than A=440.
Many, but not all, tuners can be adjusted in this way. … OR
- Leave you tuner's reference pitch at A=440 and tune each note
sharp or flat by a number of cents.
- If the bias exceeds 50 cents,
you will probably need to convert your tuner's readings.
For example, for a bias of +70 cents (70 cents sharp),
you will probably need to tune each note 30 cents flat of the
next higher semitone.
Tuning an A 70 cents sharp is the same as tuning to a Bb 30 cents flat.
- If the bias exceeds 100 cents,
then move the note you are tuning by one semitone for each 100 cents of bias.
For example, for a bias of +210 cents (210 cents sharp),
you would tune each note 10 cents sharp of the
note two semitones higher.
Tuning an A 210 cents sharp is the same as tuning to a B 10 cents sharp.
For more background information on this calculator, including the folks who contributed to the code base, see the Tools and Calculators Overview page.
Version 1.03 - December 10, 2010
- User interface improvements.
- Include information on tuning and bore temperature from the September 28, 2010 experiments.
Version 1.02 - December 8, 2010
- Use common code extracted from NAFlutomat version 1.37.1.
- Eliminate altitude parameter.
Version 1.1 - May 20, 2004
- First version based on an early NAFlutomat version. This version uses altitude as a parameter in determining frequency,
based on the Lew Paxton Price approach.