A new interpretation is proposed of the crucial expression «ἑνὶ ὀνόματι» (‘in one name’) as applied to ratios of the musical concords in the preface of the Sectio canonis ascribed to Euclid. A link is also established with the name of one of the irrational lines introduced by Euclid in Elements 10. Past interpretations of the expression are discussed and shown to be inadequate.