It is suggested that it may be possible to transmit speech and music in much narrower wavebands than was hitherto thought necessary, not by clipping the ends of the waveband, but by condensing the information. Two possibilities of more economical transmission are discussed. Both have in common that the original waveband is compressed in transmission and re-expanded to the original width in reception. In the first or "kinematical" method a temporary or permanent record is scanned by moving slits or their equivalents, which replace one another in continuous succession before a "window". Mathematical analysis is simplest if the transmission of the window is graded according to a probability function. A simple harmonic oscillation is reproduced as a group of spectral lines with frequencies which have an approximately constant ratio to the original frequency. The average departure from the law of proportional conversion is in inverse ratio to the time interval in which the record passes before the window. Experiments carried out with simple apparatus indicate that speech can be compressed into a frequency band of 800 or even 500 c/s without losing much of its intelligibility. There are various possibilities for utilizing frequency compression in telephony by means of the "kinematical" method.In a second method the compression and expansion are carried out electrically, without mechanical motion. This method consists essentially in using non-sinusoidal carriers, such as repeated probability pulses, and local oscillators producing waves of the same type. It is shown that one variety of the electrical method is mathematically equivalent to the kinematical method of frequency conversion.