# Intonation number

The intonation number in combination with the cutup height determines the character of a pipe. Additionally it determines the efficiency of the pipe. At maximum efficiency, the pipe responds the fastest and produces the loudest possible tone. It also produces the least overtones. For most pipes this is not that important or even bad, but it can be a factor for very large, slow pipes which require a lot of air. This peak of efficiency is reached if the intonation number is set to 2.

A principal stop for example would have an intonation number of about 2.5-3.

Near an intonation number of 3 a pipe will start to overblow easier. This is why thin, long pipes like the violins usually have a frein attached to them.

# Pitch notation

This tool uses the scientific pitch notation (International Pitch Notation):

Scientific notation Apostrophe notation Index notation
$\text{C}_{-3}$ ,,,,,$\text{C}$ or $\text{CCCCCC}$ $\text{C}_5$
$\text{C}_{-2}$ ,,,,$\text{C}$ or $\text{CCCCC}$ $\text{C}_4$
$\text{C}_{-1}$ ,,,$\text{C}$ or $\text{CCCC}$ $\text{C}_3$
$\text{C}_0$ ,,$\text{C}$ or $\text{CCC}$ $\text{C}_2$
$\text{C}_1$ ,$\text{C}$ or $\text{C}$ $\text{C}_1$
$\text{C}_2$ $\text{C}$ $\text{C}$
$\text{C}_{3}$ $\text{c}$ $\text{c}$ or $\text{c}^0$
$\text{C}_{4}$ $\text{c}'$ $\text{c}^1$
$\text{C}_{5}$ $\text{c}''$ $\text{c}^2$
$\text{C}_{6}$ $\text{c}'''$ $\text{c}^3$
... ... ...
$\text{C}_1 = \text{MIDI Note }24 \approx 32.7\text{ Hz}$
$\text{C}_5 = \text{MIDI Note }72 \approx 523.25\text{ Hz}$

## Description

This tool is based on formulas by Dr. Ing. H. Ising, published in the German Publication "Walcker Hausmitteilung Nr. 42" from June 1971. I cannot guarantee the correctness of the calculations performed by this tool. However, I can say that I have built a few pipes with the dimensions generated by this tool and they turned out really well.

## Usage

### Input

This tool tries to take all relevant factors for labial pipes into account. The default values provided are about the average, but you might want to adjust the wind pressure and the temperature at which the pipes will operate. In some cases you might also want to adjust the standard pitch. Please note that this tool will perform the calculations of the other tone pitches according to the equal scale only at this moment.

### Output

The tool will output a table of all pipes containing a lot of information.

Column Description
Frequency The frequency of the fundamental note played by that pipe.
Resonator length (theoretical / actual) The theoretical length is the uncorrected length of the pipe's resonator. In reality the resonator has to be shorter, because thicker pipes generally need to be shorter than thinner pipes. The actual length of the pipe's resonator is usually very close to the actual length calculated by this tool.
Diameter The diameter if the pipe is round.
Cross section The cross section of the pipe.
Cutup height The height of the pipe's mouth. Low tolerance! Try to be within ±0.5mm. Otherwise the pipe will sound too quiet or overblow.
Mouth width The width of the pipe's mouth. Not that critical, it basically determines the volume of the tone generated by the pipe.
Pipe depth The depth of the pipe if it is rectangular. Also not that critical as long as the total cross section of the pipe doesn't change too much.
Jet thickness The width of the pipe's jet. Extremely critical! Very low tolerance! Try to be within at least ±0.1mm as this dramatically determines the sound produced by the pipe.
Air consumption rate The amount of cubic meters of air the pipe will use per second. Might be interesting if you need to calculate the volume of your bellows.
Sound power The power of sound the pipe will generate. The formula for this value was just taken from Isings formulas and appears to be somewhat off. It's still given as it might be used to compare the sound powers of similar pipes.

### Notes

• Please don't just take the values the tool gives you and construct your pipes. You should take tolerances into account, especially with the resonator length. Make it longer than the Actual resonator length to allow tuning the pipe!
• Printing the values works best in Chromium-based web browsers.
• If you get a message box about an error and/or can not find the blue Calculate pipe dimensions button please try a different web browser.

The CAD template can be used to generate a representation of the pipes calculated by this tool. You can open it in OpenSCAD, a free CAD software. You can edit the values at the top of the file and change them to the values the tool gives you. You have to specify some parameters which are not calculated by this tool, like foot length and tuning slot dimensions. All the parameters are commented and should be relatively easy to understand.

You can even use the template to 3D print pipes, a few experiments of mine worked pretty well. In that case, set print_model to true, as printing the pipes upright is not that great.

# WebPipeCalc

A tool for calculating the dimensions of labial organ pipes.

Environment
$^{\circ}\text{C}$
$\frac{\text{kg}}{\text{m}^3}$
$\text{Hz}$
Organ properties
Pipe rank options

Stopped pipes?