Major second

Abstract: This article presents a study of intonation in performances of Schubert’s “Ave Maria,” both a cappella and with accompaniment, by six undergraduate and six professional singers. The analysis focuses on the tuning of melodic semitones and whole tones and explores the impact of training and musical context on intonation, as well as whether intonation is significantly affected by the presence of accompaniment. The data from the recordings was analyzed automatically using a MIDI-audio alignment algorithm to annotate the note onsets and offsets and a fundamental frequency estimation algorithm to extract pitch-related information. Overall the singers tended more toward equal temperament except for the nonprofessional group’s semitones, which were closer to Pythagorean tuning.

Abstract: ion level of the viewpoints should be high enough to capture variability in the melodies as caused both by the process of oral transmission and by variations in choices that were made in the process of transcription into music notation. To achieve a suitable level of abstraction, we measure relative values for all viewpoints derived from pitch or duration. For the current study we define the following viewpoints: phrpos, which records whether the note is the first in a phrase, the last in a phrase, or inside a phrase; intref, which represents the scale degree of the note given the key of the song; c3i(level), which records whether the metric level of a note is higher, lower or equal with respect to the previous note; c3(dur), which records whether the note is shorter, equal, or longer in duration than the previous note; c3(pitch), which records whether the note is higher, equal, or lower in pitch than the previous note; c5(pitch, 3), which records whether the note was approached by a leap (three semitones or larger), a step (smaller than a three semitones), or a unison, with distinction between ascending and descending intervals; and c5(pitch, 7), which records whether the note was approached by a leap (seven semitones or larger), a step (smaller than seven semitones), or a unison, with distinction between ascending and descending intervals. A feature is a tuple τ : v comprised of a viewpoint name τ paired with a value v. A feature set is a set of features, for example the feature set { c3(pitch) : − intref : M2 } contains two features, expressing that the pitch of the corresponding note is lower than that of the previous note, and is the major second (M2) of the scale. An event instantiates a feature set if all features in the set are true for the event. A feature set pattern is a sequence of feature sets, and a song instantiates a pattern (or, stated equivalently, the pattern occurs in the song) if the successive feature sets of the pattern instantiate successive events in the song in at least one place. For example, the patterns shown in Figure 1 have four feature sets, with different features in each of them. Following the method presented by Conklin (2010), a one vs. all strategy (Neubarth & Conklin, 2016) is used for mining patterns that contrast between groups of data. The method is designed to discover maximally general distinctive patterns (MGDPs), meaning that for each reported discovered pattern there is no more general pattern that is also distinctive. Each tune family is mined individually for distinctive sequential patterns, using each tune family F as a positive corpus and the rest of the pieces (¬F ) as the anticorpus. In this work a statistical approach is used to measure the distinctiveness of a pattern: it is the probability p of finding at least the observed number of pieces of family F when taking a single random sample of pieces from the entire corpus F ∪ ¬F . A pattern is then considered distinctive if its p-value falls below some specified significance level α (see Conklin, 2013, for details). The MGDP set may contain overlapping patterns, so for the tune family mining task this set is further reduced by a greedy pruning strategy. Proceeding from the best (lowest p-value) pattern, a pattern is placed in the final set if it does not overlap, in any piece, with any pattern already in the final set. Thus none of the patterns in the final set will overlap in any piece with any other pattern.

Abstract: Until the present time, my study of the music of the Aranda-speaking people of Central Australia has been in greater detail than my study of aboriginal music from other areas. This has been possible as a result of the large collection of sacred and ceremonial songs recorded in Central Australia by Mr. T. G. H. Strehlow. These recordings, supplied together with transcriptions and translations of texts, details of the function of each song, the reason for the performance, the place of performance, etc., has enabled me to consider many aspects of the music which would not otherwise have been possible. It is from this material that the main part of the present study on ornamentation has been taken. There are two types of sacred song which are obviously distinct in the mind of the Central Australian performer. The one, a ceremonial song of a particular totem in the particular locality, is a choral song performed by initiated men; the other is always performed by one person. In this latter group of songs, we find the charms which may be used, for instance, for making rain, or for causing bodily harm or other evil to an enemy. There are many musical features which differ in these two types of song. The melodic outline of the choral song is more extensive than that of the solo song. While both retain the characteristic descending scale pattern, the choral song can be divided into three sections. The first of these is from the upper third (very often a minor third) to the tonic; the next is from the upper tonic down to the third in the lower octave; the final section is a repetition of the first section (with slight alterations) in the lower octave. There are variations of this standard pattern. Sometimes the important interval of a third is anticipated, but never replaced in importance, by higher notes. Sometimes this interval is not the more usual third, but a major second, which, also, may be introduced by higher notes. Yet another variation is to omit the middle descending section altogether, and to proceed directly from the upper tonic to the first note of the final section. The melodic outline of the solo song may be similar to the first section of the choral song, but it is rarely found repeated in the lower octave, and it is probably an error on the part of the singer when this does happen. Decoration around an interval of a second or third is common, but more often the range is slightly extended, and the total distance covered, about a sixth. In this case the emphasis given to the higher notes is noticeably more than that given to the upper extension of the standard interval of a choral song. This differentiation of melodic outline gives rise to distinctive approaches to ornamentation. The main purpose of ornamentation is to embellish the important notes. Ornaments will therefore rarely be found on the fourth, fifth or sixth degrees of a choral song, while these same notes may be highly decorated in the solo song.

Abstract: BEFORE CONSIDERING the problem of expanded pitch resources in contemporary composition of music, I shall contrast two different traditions for the realization of precise pitch relations in performance. The first tradition may be represented by the practice of Gregorian chant.1 In plainchant the melody is unaccompanied, or monophonic. Thus the relations of melodic tones to each other are the only intervals used. The perfect fifth and perfect fourth and the interval of difference between them, the major second, are the basis of pitch choice. The particular distribution of the seconds within the melodic distances of fifths and fourths, and the choice of cadence points, determine the "mode" of the music. All major seconds are always the same size,2 as are all minor seconds, since these are the remainder intervals when the largest possible whole number of major seconds subdivides either a perfect fifth or a perfect fourth. All other intervals are likewise fixed in size, but are much more difficult to sing in tune. A contrasting type of pitch usage is illustrated in East Indian monophonic musical practice.A This monophony "opposes" a line of fluctuating pitch against a fixed pitch, or drone. A specific emotional expression is achieved by means of a particular set of intervals measured against the drone. The "harmonic" relation of melodic pitches to the drone is primary to this expression, whereas the intervallic relations between melodic tones are less important. Possible relations to the drone are classified as consonant,4 dissonant, and out-of-tune; i.e.,