The Hispanic neumes
The Hispanic chant has reached us in dozens of manuscripts, some dating from as early as ca. 700 and many of them with notated music. This vast corpus of sources, containing over 7,000 chants, gives us substantial knowledge of the Hispanic rite’s ceremonies and texts, but not of its melodies because the Hispanic rite was suppressed before the widespread use of notations indicating precise intervallic relationships.
Thus, unlike the Franco-Roman chant, the Hispanic melodies are only conserved in manuscripts using adiastematic neumes, i.e. notational signs which, according to current consensus, do not specify pitch or intervals between notes but only the qualitative profile of the sounds. Let's exemplify this with the initial neumes of the antiphon Educ domine appearing in the 11th-century Silos 4 source (Figure 1).
In this syllabic beginning a single-sound neume (punctum) is followed by two different instances of pes. A pes is a neume encoding two ascending sounds, from which there exits several variants in terms of shape. The musical implications of the existence of morphological variants within a neume class (in different degree of abundance depending on the class) are largely unknown, so such variants are mainly designated (by modern musicologists) in terms of their visual aspect. In particular, in Figure 1 a short pes is followed by a cursive pes, each encoding two ascending sounds and, finally by two (also different) instances of clivis, each involving two descending sounds. In principle, we do not know the quantities for the ascending or descending intervals of the two-sound neumes (2nd? 3rd? mayor or minor? ...) but only that in a pes the second sound has a higher pitch than the first (the contrary in the case of a clivis). Moreover, we do not have even this qualitative information for the relationship between the last sound of a given neume and the first of the following one.
The tempting possibility that the different shapes for a same class of neumes correspond to different quantitative intervals was already ruled out by musicologists who have studied Hispanic neumes since the beginning of the 20th century (see below). Instead, such alternative forms are traditionally associated with differential (and in many cases unknown) performance details of rhythmic or dynamical nature.
To avoid the old and in many cases cumbersome nomenclature for the neume clases (scandicus subbipunctis resupinus and so on), the sound profiles will be encoded in SONHIS using the single-letter vocabulary  in which the first note of each neume is always identified as N (neutral, i.e. unknown), while the subsequent sounds are identified as having a L (lower), H (higher) or S (same, i.e. unisonic) pitch than the sound which precedes. More ambiguous possibilities are also considered for U (upward tendency, i.e. same or higher but not lower) and D (downward tendency, i.e. same or lower but not higher). For instance, the scandicus subbipunctis resupinus could be easily encoded now as a NHHLLH profile -of course, this coding is especially suitable for any subsequent computational analysis.
Coming back now to beginning of the Educ domine, the 5 neumes in Figure 1 would correspond to the the following profile: N NH NH NL NL. Using the beatiful neume shapes developed for the CEAP software (shapes which has been generously shared with SONHIS by the authors) we can illustrate in the "neume score" engraved in Figure 2 the very ambiguous melodic knowledge that to the date traditional musicology has been able to extract from the Hispanic neumes.
The knowledge achieved so far by traditional musicology states that the vast majority of the pool of Hispanic melodies can only be reconstructed up to the very degraded status of profiles such as that shown in Figure 2, profiles which only indicate at most the melodic direction of the sounds because the neumes constituted originally a mere mnemonic tool that demanded a previous memorization of the repertoire by the chanters. In other words, such cumulated knowledge led to a general consensus that could be enuciated as follows: the information conveyed by the Hispanic neumes is so ambiguous and incomplete that the Hispanic melodies are unrecoverable. It is enough for the reader to explore the hundreds of thousands of neumes that we have optically recognized from the León Antiphonary (the most complete Hispanic source) to realize the cultural loss that such declared irretrievability of the sounds of the Hispanic chants entails.
Before revising the fact that the impossibility-of-recovery consensus assumes that there is no source of pitch definition other than that rendered by the small-scale studies focused on individual neumes, it happens that from the very early times of Hispanic musicology  we do have a close idea of the sounds under the neumes of the Educ domine antiphon, one of the bunch of Hispanic chants which were able to jump over the notational gap to be copied in later intervalic-defining musical notations. This is discussed in the section dedicated to these so-called "Aquitanian" chants found in a Hispanic Liber Ordinum.