Inharmonicity

CAST Transforms: Inharmonicity

revised 2/3/98

Introduction

The frequencies of all partials are modified in order to perturb the harmonic relationship that may exist between them.

Parameters

Message Argument(s) Type(s) Description

stretch Partial frequency stretch factor Float This parameter implements a power law rule. It should be a value around 1.0. The frequency of the n'th partial (0 based) is multiplied by stretch to the power n.

add Partial frequency offset (Hertz) Float After the stretch computation is done, the value of add is added to all partials. This causes a frequency shift as well is a change in the partial frequencies when viewed as ratios one with the other.

For example, suppose you're synthesizing a tone with 10 partials with frequencies 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000.

If you set the stretch factor to 1.01, the resulting frequencies would be 100, 202, 306.03, 412.12, 520.30, 630.61, 743.06, 857.71, 974.57, and 1093.69.
If you set the stretch factor to 0.8, the resulting frequencies would be 100.0, 160.0, 192.0, 204.8, 204.8, 196.608, 183.5008, 167.77216, 150.994944, and 134.217728. Note that the higher-numbered partials have lower frequecies than the middle ones!
If you set the stretch factor to 1.0 and the add parameter to 26, the resulting frequencies would be 126, 226, 326, 426, 526, 626, 726, 826, 926, and 1026.
If you set stretch to 1.01 and to 10, the resulting frequencies would be 110, 212, 316.03, 422.12, 530.30, 640.61, 753.06, 867.71, 984.57, and 1103.69.

Examples

For the following examples execute: demosoftcast /usr/local/cast/lib/data/coleman/lick1.fmt.

The identity :

/voices/0/inharm/stretch 1.0
/voices/0/inharm/add 0.0
/voices/0/tm/goto 0.0

Expansion:

/voices/0/inharm/stretch 1.05
/voices/0/inharm/add 0.0
/voices/0/tm/goto 0.0

Contraction:

/voices/0/inharm/stretch 0.95
/voices/0/inharm/add 0.0
/voices/0/tm/goto 0.0

Add:

/voices/0/inharm/stretch 1.0
/voices/0/inharm/add 50.0
/voices/0/tm/goto 0.0

Subtract:

/voices/0/inharm/stretch 1.0
/voices/0/inharm/add -50.0
/voices/0/tm/goto 0.0

Message	Argument(s)	Type(s)	Description
`stretch`	Partial frequency stretch factor	Float	This parameter implements a power law rule. It should be a value around 1.0. The frequency of the n'th partial (0 based) is multiplied by `stretch` to the power n.
`add`	Partial frequency offset (Hertz)	Float	After the stretch computation is done, the value of `add` is added to all partials. This causes a frequency shift as well is a change in the partial frequencies when viewed as ratios one with the other.