Common Parameters and Properties for Modal Objects

Many Modalys objects share common parameters. Some objects may have parameters that others do not (for example, plates have a thickness parameter, whereas membranes do not), and some objects have parameters that are specific to the type of object that is being modeled (for example air-elasticity is specific to air columns in tubes, and will not be found in strings, membranes and other objects).

The values of all physical parameters are controllers (either dynamic or constant). In the Lisp interface numerical values may be given as parameter values; these will be automatically converted into constant controllers by Modalys. If a given parameter is not supplied when using the Lisp syntax, the default parameter value will be used.

For the purposes of discussion, we are grouping the parameters into three general categories: Modal Properties and Material Properties and Physical Measurements. Although all the physical parameters of an object are used together to calculate a model which operates on a modal basis, we are separating the parameters into these groups because, with very few exceptions, the modal properties are common to all Modalys objects, whereas the physical properties and measurements will vary greatly depending on the type and size of object being modeled.

This value determines the number of modes of vibration calculated in the simulation of the object. As the number of modes is increased, higher partials are added to the resultant sound. Thus if ten modes are used, the lowest ten frequencies produced by the vibration of the object are computed. Maximum detail is obtained when the number of modes is high enough so that all frequencies below the Nyquist frequency are accounted for. Most objects will have have a user-definable number of modes, but some objects (such as the bi-two-mass) have a fixed number of modes, in which case this option is not settable.

These are coefficients which describe how the object loses energy. Freq-loss describes the decay of the sound proportionally to the square of the frequencies, whereas const-loss describes the overall decay of all the object’s frequencies.

More specifically, each mode of the object loses energy in proportion to the following equation, where ƒ is the frequency of the mode:

• const-loss + freq-loss (ƒ/1000)^2

If the two values are both zero, the object will resonate forever. If const-loss is non-zero and freq-loss is zero, all modes will lose energy at the same rate. If freq-loss is non-zero, higher frequency modes will lose energy more rapidly than lower ones. When saving modal data to a file (and when reading it again), these two coefficients are combined as above to compute a specific loss value for each mode. These two loss parameters are also part of the definition of the material being modeled, as different materials lose energy at different rates. (Think of the difference between a marimba, a vibraphone, and a lithophone - wood, metal and stone will have different freq-loss and const-loss parameters to model how these different materials lose energy.)

Some objects (such as the bi-two-mass object) have separate freq-loss and const-loss parameters for each of the object's vibrational directions.

In the simplest terms, const-loss affects overall decay/damping of the sound (whether it is sustained or staccato), whereas freq-loss affects the perceived brightness of the resonating sound as it decays.

The density of a material is measured in kg/m^3, and corresponds to mass per unit volume.

See chart of material properties for appropriate values.

The Young's modulus of a material (also sometimes referred to as tensile modulus or elastic modulus) is measured in Pascals (N/m^2). It is a measure of the elasticity of a given material.

Higher values imply more stiffness (less elasticity) in the material, resulting in objects whose mode frequencies have a more inharmonic relationship to one another. Some materials, such as wood, will have a different Young's modulus on different axes (i.e. along the grain, radially to the grain, and tangentially to the grain). Often, Young's modulus is measured in gigapascals (GPa), where 1 GPa = 1.0e9 N/m^2. See the tables of material properties for appropriate values.

Poisson coefficient (or Poisson's ratio) represents the ratio of the change in physical volume between two vibrating directions, in other words the degree to which a material bulges as it shortens.

The coefficient is a value in the range of 0 to 0.5 for most common materials. Metals generally have a Poisson's Ratio of around 0.3, and rocks and minerals around 0.25, wood in the range of 0.35 to 0.4, and fibers generally around 0.4. Incompressible materials (liquids, for example) are considered to have a poisson's ratio of 0.5. Rubber generally has a high poisson's ratio, approaching 0.5, and Cork is at the other end of the spectrum - around zero. See the tables of material properties for appropriate values. Not all Modalys objects take this parameter into consideration.

Density of the air in kg/m^3. On the planet earth at room temperature at sea level this is normally 1.2 See table of air properties at different temperatures (at sea level).

This is another term for density or air-density that is used by some objects, and consequently also given in kg/m^3. In Modalys it usually refers to the density of air or another sound propagation medium, as opposed to the density parameter that describes the physical properties of material.

Elasticity of the air in m^2/kg. On the planet earth at room temperature at sea level this is normally around 7.14e-6 to 7.21e-6. Modalys actually uses the very finely detailed measurement 7.2087658592848905e-6 as a default value, although this is simply given as 7.21e-6 in the object reference pages.

This is another term for air-speed or the speed of sound in air that is used by some objects, given in m/s. The speed of sound in air on earth at room temperature at sea level is usually around 340 m/s.

The use of these parameters will vary from object to object. They are fairly self-explanitory and are used to describe the physical dimensions and other measurements of the objects. Tension usually will refer to strings and membranes, and stiffness to springs.

Length, width, thickness and radius are measured in meters, tension is measured in Newtons, and stiffness (for springs) is measured in N/m.