Calculator pitch change by temperature variation flute clarinet pipe organ calculate frequency tone pitch temperature woodwinds speed of sound speed amplitude level

Pitch change by temperature change (variation)
for wind instruments (clarinet, flute, trumpet, organ)

Because the speed of sound c increases with 0.6 m/s per degree Celsius,
the pitch of wind instruments increases also by about three cents (3/100
of a semitone). The effect of material expansion on the change of pitch is
rather meaningless.

Change in pitch J depending on the ambient temperatureϑ
of vibrating air columns, such as flutes, whistles and other wind instruments

Spannung und Spannungspegel - Sengpielaudio

Get clear, that in a tone of a pipe organ or of another wind instrument − when the
temperature increases from 15°C to 25°C − the speed of sound c and thus the
product of λ × f will be changed. Since the length of the organ pipe and with it
the wavelength λ remains constant, only the frequency f (pitch) will change.

c = λ × f

λ = c / f

f = c / λ

c ~ f

The influence of temperature is independent of the pitch always the same.
This means that the determined deviation in cents is true for each tone.
The specification of cent is independent of frequency.

Conversion of frequency ratio y = f₂ / f₁ to interval ratio J in cents:
J in cents = 1200 × (log y / log 2)
Conversion of interval ratio J in cents to frequency ratio y:
y = f₂ / f₁= 10^{J log 2/1200}

With the following formula you get the with the temperature changing exact speed
of sound:
Speed of sound Schall

in m/s
Temperature ϑ in °C

Frequency ratio
(frequency change)
change with temperature

The influence of temperature on the pitch: The speed of sound in air and thus the pitch (frequency)
of a note as a column of air of a certain length, is directly proportional to the square root of the
absolute temperature. The absolute temperature is the absolute zero temperature, which is
minus 273.15°C. The unit is Kelvin (K); 1 K has the same size as 1°C.
Example:
The frequency change by the increase in temperature of ϑ 1 = 20°C to ϑ 2 = 24°C is the square
root of [(273 + 24 = 297 K) / (273 + 20 = 293 K)] = 1.0069028 ...
Therefore, an increased frequency of 440 Hz at 20 C (440 Hz x 1.0069028) = 443 Hz at 24° C.
It should be noted that the temperature of the air inside the wind instrument is rather complex.
It is between the temperature of the room and the body of the player and by the instrument
heating the tone pitch rises.

A trained hearing takes about 5 cent deviation of the true pitch. A normal hearing person needs
10 cents for recognition. This refers to notes played in succession. If you hear a pitch of 10 cents
from different sounds simultaneously, the beating sounds quite strongly.

Conversion of frequencies and intervals to cents
Temperature Dependence of Physical Entities
Sound pressure and Sound power – Effect of temperature

Conversion frequency to wavelength and reverse

Enter simply the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

The Speed of sound in air

Enter simply the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

Conversion: Fahrenheit to Celsius and Celsius to Fahrenheit

Enter simply the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

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Sound frequency f: Hz	↔	Wavelength λ: m
f = c / λ		λ = c / f
Speed of sound c = 343 m/s at 20°C


Temperature ϑ (theta): °C	↔	Speed of sound v: m/s
Frequency f: Hz	↔	Wavelength λ: m
Frequency and wavelength at given speed of sound


Temperature Fahrenheit scale: °F	↔	Temperature Celsius scale: °C
°F = °C × 1.8 + 32		°C = (°F − 32) / 1.8