Calculating Room Modes with ModeCalc
Overview
Click here to download ModeCalc  the Graphical Room Mode Calculator (only 56 KB). ModeCalc runs on all DOS and Windows computers, and graphically displays the first ten axial modes for any rectangular room using dimensions you enter as either feet or meters.
ModeCalc can help you design a new room that sounds as good as possible, or predict the low frequency behavior of an existing room. This tutorial explains the basics of room modes, and tells how to use ModeCalc and interpret its results. This text is also available as online Help when you run the program, so there's no need to print this page separately.
Room Modes
Room modes are natural resonances that occur in every enclosed space, and the frequency of each resonance is directly related to the room's dimensions. For example, a room 16 feet long has a mode at 35 Hz because walls that far apart provide a natural resonance at 35 Hz. Additional modes occur at multiples of 35 Hz because those frequencies also resonate in the same space. Wall spacing that accommodates one cycle of a 35 Hz wave also fits two cycles of 70 Hz, three cycles of 105 Hz, and so forth.
When you play a musical note having the same pitch as the natural resonance of the room, that note will sound louder and have a longer reverb time than other notes. Of course, this is undesirable because some notes are emphasized more than others, and the longer reverb time reduces clarity. Therefore, room modes are important because they directly affect the character of a room. Although room resonances can be reduced by adding bass traps, they cannot be eliminated entirely.
For this reason, rooms for recording and playing music are designed to have many resonances that are distributed evenly, rather than just a few resonances at the same or nearby frequencies. Playing music in a room with poor mode distribution is like listening through a 5band graphic equalizer with one or two bands turned up all the way. A room with good modes is more like having a 31band equalizer with all the bands turned up. The frequency response still isn't perfect, but all the small peaks combine to yield an overall response that's reasonably flat. Therefore, the frequency response of a room with many modes close together is flatter overall than a room that has only a few theses far apart.
Small rooms have modes that are spaced farther apart than large rooms because the first mode in a small room is at a higher frequency. For example, when the longest dimension of a room is only 10 feet, the modes for that dimension are 56.5 Hz apart. In larger rooms the first mode is at a lower frequency so the subsequent modes are closer together. Therefore, a large room has a better low frequency response because it has more modes that are spaced more closely.
The formula used by ModeCalc is extremely simple. For dimensions given in feet the first mode occurs at 1130 (the speed of sound in feet per second) divided by twice the dimension. Subsequent modes are multiples of that result. When using meters the formula is 344 divided by twice the dimension. Twice the dimension is used because a room 10 feet long really has a total distance of 20 feet  the wave travels from one end to the other and back to complete one cycle. So for a room 10 feet long, the first mode occurs at 56.5 Hz:
1130 

 
= 56.5 
10 x 2 

The second mode for that dimension is twice 56.5 or 113 Hz, the third is three times 56.5 or 169.5 Hz, and so forth to the tenth mode at 565 Hz.
Room Ratios
The worst type of room shape is a perfect cube  say, ten feet long, ten feet wide, and ten feet high  because all three dimensions are the same and all three dimensions resonate at the same frequency. A 10 foot cube shaped room will have a strong inherent resonance near 55 Hz, which is the open A string on a bass. So when that low A is played it will sound much louder than other notes. This room also has a longer reverb time at that pitch, so low A notes will sustain longer and conflict with other bass notes that follow.
A room whose dimensions are multiples of each other  for example, 10 feet by 20 feet  is nearly as bad as a cube because many of the same frequencies are emphasized. Therefore, the goal is to have a room shape that spreads the modes evenly throughout the low frequency range. This is done by designing the room with dimensions whose ratios of length, width, and height are as unrelated as possible. And here is where ModeCalc is useful because it tells you at what frequencies the modes occur and how close together they are. ModeCalc also shows you the ratios of the dimensions you entered, and lets you compare them to ratios commonly recommended by acoustic engineers and studio designers.
Using ModeCalc
Instructions at the top of the screen explain how to use the program. Simply enter the Length, Width, and Height using the Tab and ShiftTab keys to go between fields, then hit Enter to see the result. The first ten modes for each room dimension are displayed graphically so you can see where they occur and how they relate to one another. Each set of modes is shown in a different color, and when two or more modes occur near the same frequency the duplicates are shown on a separate line so one does not hide the other. Note that the graphic display portion of ModeCalc uses logarithmic spacing. This is how octaves and musical intervals are arranged, and also how mode spacing should be viewed.
You can enter the room dimensions as meters instead of feet by starting the program with /M on the command line. If you use Windows you can rightclick MODECALC.EXE in Windows Explorer, then select Properties, and specify the /M option so it will be used every time you run the program.
Many rooms are not rectangular, and in fact having angled walls or a vaulted ceiling is desirable. Unfortunately, with angles there is no direct way to determine the room modes exactly. Modes still exist  they're just more difficult to predict. If the angles are not too severe you can average the dimensions. For example, if the ceiling varies from 8 feet to 10 feet high, you can use 9 feet when entering the height.
When viewing the results look for an even spacing of the modes regardless of their color (good), and for multiple modes that occur at or near the same frequencies (bad). Also compare the ratios of the dimensions you entered with the recommended ratios, and compare your room's volume with the recommended minimum of approximately 2500 cubic feet or 70 cubic meters.
Finally, if you are using ModeCalc to check an existing room, please don't be discouraged by poor results. All rooms need bass trapping anyway, and poor modes can be improved quite a bit by adding a few more traps. You can also enter dimensions for a large room having one of the recommended ratios, such as 23.3 by 16 by 10 feet. Then you'll see how even with the recommended ratios the modes are still somewhat uneven, and two modes still sometimes occur at the same frequency. So unless you are willing to move the walls, just accept what you have, and maybe install a few more bass traps than you had planned for originally. Then relax and enjoy the music!
Ethan Winer is head of RealTraps, where he designs and manufactures acoustic treatment and bass traps. Visit Ethan any time at http://www.realtraps.com .
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