The intelligibility of the speech received over a communication system is usually expressed in terms of one or another measure such as the vowel or the consonant articulation, the average speech sound articulation, the syllable articulation, the word articulation, or the sentence intelligibility. The present paper establishes relationships among several of these measures and the articulation index. Relationships based upon statistical considerations are compared with the results of observations. Functions are developed which permit the calculation of articulation index and hence of articulation for communication systems which include a wide variety of responseversusfrequency characteristics and of noise conditions, as well as several special types of distortion. Although the treatment is predominantly empirical, the functions and processes are closely related to various fundamental properties of speech and hearing. Four principal series of articulation tests are cited in detail, some of which have been described in published articles by various persons. The response and the noise, if any, are given for each of these cases and the observed articulations are compared with values calculated by the method here presented. The application of the computational method to the perception of speech by deafened persons is reserved for a subsequent paper. A “Foreword” to the present paper describes the historical importance of articulation tests in the Bell Telephone System.