Tonality
Material from Wikipedia the free encyclopedia
Go to: navigation, Search
This term has other meanings, see tonality (values).
Tonality (fr. tonalité, from the Greek. τννος — tension, tension; from Lat. tonus tone) in the doctrine of harmony: The fret principle, the central category of which is the tonic.
The other categories and functions of tonality (first of all, dominant and subdominant) are directly or indirectly related to tonics.
"The system of functional relations is hierarchically centralized, and the tonic permeates the entire harmonic structure"[1].
The altitude position of a major or minor fret.
The key designation indicates the tonic (it is also the main tone of the tonic triad) and the fret (in this case, major or minor), for example: C dur (C major), Fis dur (F sharp major), a moll (a minor), es moll (E flat minor), etc.
There are other definitions of tonality.
Some of them are described below (see).
Content
1 General characteristics 2 Ratio of tonalities 3 Kinship of tonalities 4 Table of letter designations of tonalities 5 To the History of the Term 6 States of (major minor) tonality 7 Other forms of tonality 8 Tonality in Western musicology 9 Notes 10 See also 11 Literature 12 References
General characteristics[edit / edit wiki text]
For harmonic tonality, regular changes of local harmonic centers are typical, which do not cancel the central gravity, but on the contrary intensify it.
In the development of tonality, the musical meter (which sets the location of consonance and dissonance) and metric extrapolation (the expectation of a regular continuation based on a given beginning) in the form are of great importance.
Tonality is uncorrelative to modality, since the main features of modal and tonal frets are uncorrelative.
The center necessarily dominates in the key, and the sound order basis is observed to varying degrees (for example, the scale of the harmonic minor, melodic major deviates from the main form of the scale of these frets, etc.).
In the modality, the sound order basis is indispensable, and there may be gravitations (for example, in the polyphonic music of Masho and Lasso), or they may be absent altogether (for example, in the great znamenny chant of the Orthodox).
The focus of the theory of major minor tonality is the theory of functions, which considers the values of individual chords within the same key and the relations of tonalities as functions of the highest order.
The main elements of this kind of tonality are the functions of the tonic (T), dominant (D) and subdominant (S), collectively referred to as "main tonal functions".
The ratio of keys[edit / edit wiki text]
In major minor music, the keys (in the 2nd meaning) interact in a variety of ways and in a complex way.
The following relations of tonalities are fixed terminologically: Parallel keys are the major and minor keys, the external sign of" parallelism " is the same key signs.
The essence of" parallelism " is a common set of sound accesses (height positions) for both keys with a mismatch of the tonal functions attributed to these sound accesses.
The sound orders of parallel keys are separated from each other by a small third: major from above, minor from below (for example, C major — a minor, F sharp major and D sharp minor, B flat major and G minor, etc.).
Eponymous keys are keys with the same tonics that belong to opposite fret moods (for example, g major and g minor).
The major and minor keys of the same name are separated from each other by a quarto — fifth circle by three signs (major — in the direction of sharps, minor in the direction of flats).
Single tert keys — two keys, in which tonic triads the tert tone is common (for example: c major — C sharp minor; the general terz tone is E), and the tonics are separated from each other by a semitone (the major is located a semitone below the minor).
The same tone keys belong to different fret moods.
In the English terminology system, parallel keys are called "related" (relative keys, relative literally "correlated"), and the same named ones are called" parallel " (parallel keys), which often creates confusion in translations of English musical theoretical literature into Russian.
Kinship of keys[edit / edit wiki text]
The "kinship" of keys is understood as the ratio of two keys, determined by the number and value of common chords (that is, chords consisting of sounds that occur in both keys).
The kinship of keys is determined by the number of common sounds.
The more common sounds there are, the closer the keys are to each other.
According to the Soviet "brigade" textbook (1937-38), there are four degrees of kinship of tonalities[2] .
In the first degree of kinship there are tonalities, the tonic triads of which belong to the number of common chords.
Each key has six keys of the first degree of kinship: (1) parallel to this, (2) natural dominant, (3) parallel to it (the last), (4) natural subdominant, (5) parallel to it, (6) minor subdominant in the case of a major and a major dominant for a minor.
Any pair of these 6 keys has many chords in common with each other.
Each major key has two major and four minor keys of the first degree of kinship, the tonic chords of which are triads of the II, III, IV, IV harmonic, V and VI stages (to C major — d minor, e minor, f major, f minor, g major, a minor).
Each minor key has two minor and four major keys of the first degree of kinship, the tonic chords of which are triads of the III, IV, V natural, V harmonic, VI and VII natural stages in it.
(in A minor — C major, D minor, E minor, E major, F major, G major).
In the second degree of kinship, there are four keys that have two common chords (not a tonic function) with two signs of difference in the key designation.
For example, C major and D major have a common triad mi sol si, which is a triad of the third stage in C major and II in D major In the third degree of kinship there are eight keys that have one common triad.
In the fourth degree of kinship (distant kinship) there are tonalities that do not have any common triad (for example, C major and F sharp major).
Each key has five keys of the fourth degree of kinship (one of the same fret and four of the opposite), not counting enharmonic substitutions.
The degree of kinship of the keys determines the possibility and nature of modulation.
Table of letter symbols of tonalities[edit / edit wiki text]
In the Russian tradition, the keys are indicated in two ways — Cyrillic (C major, D minor, E flat major, etc.) or Latin (C dur, d moll, Es dur).
In the letter system of notation, uppercase letters indicate major, lowercase letters indicate minor; therefore, often (for brevity) the second part of the tonality designation is omitted, for example, Es stands for E flat major.
The following table shows the key designations.
The major and minor keys are arranged in the order of the quarto fifth circle, after each major there is a minor parallel to it.
The keys go from flat to sharp, so in the last column, the number of flats is indicated for the upper part of the table, and the number of sharps for the lower part.
The first six keys in the table are respectively enharmonic to the last six.
Russian Russian syllabic name (= German) alphabetic English Number of key characters Table of tonality designations Russian syllabic name Russian (=German) Alphabetic English Number of key characters
(sharps or flats) to dur dur Ces flat major C 7 ♭ a flat minor as moll A flat minor 7 ♭ Sol dur dur Ges G flat major 6 ♭ e flat minor es moll E flat minor 6 ♭ d dur Des dur D flat major 5 ♭ b flat minor b minor B flat minor 5 ♭ La dur As dur A flat major 4 ♭ f minor f minor F minor 4 ♭ e flat major Es dur E flat major 3 ♭ C minor c minor C minor 3 ♭ si e flat major B flat major B flat major 2 ♭ g minor g minor G minor 2 ♭ f major F major F major 1 ♭ d minor d minor D minor 1 ♭ C major C major C 0 major a minor a minor A minor 0 g major G major G major 1 # e minor e minor E minor, 1 # d major D major D major 2 # in b minor h moll B minor 2 # a major A major A major 3 # f sharp minor fis moll F
sharp minor 3 # e major E major E major 4 # C sharp minor cis moll C sharp minor 4 # si dur H dur B major 5 # g sharp minor gis moll G sharp minor 5 # f dur Fis dur F sharp major 6 # d sharp minor dis moll D sharp minor 6 # C sharp major Cis dur C sharp major 7 # sharp minor ais moll A sharp minor 7 #
The French names of the keys do not cause any special difficulties: ré mineur, mi bémol majeur, fa dièse mineur, etc.
The peculiarity here is that the syllable C is denoted as ut: ut mineur - C minor, ut dièse majeur - C sharp major (see Solmization).
To the history of the term[edit / edit wiki text]
The term "tonality" in the modern sense originated in France.
It was first used by Alexandre Etienne Shoron in the preface "A brief overview of the History of Music" to the "Historical Dictionary of Musicians", published in 1810[3].
According to Shoron, tonality is a combination of tonic, dominant and subdominant chords known to musicians since the time of J. F. Rameau.
Castil Blas (1821) described tonality as "a property of the musical system, expressed in the use of its essential steps"[4][5].
The term tonalité also appears in the" Course of Harmony " by F. Geslen (1826) [6] and in the book by D. Jelensperger "Harmony at the beginning of the XIX century" (1830) [7].
The term came into wide use thanks to the efforts of F.-Zh.
Feti (Fetis), who defined tonality as "a set of obligatory relations between the tones of a scale taken sequentially and in simultaneity"[8].
Although Fetis insisted that the idea of tonalité came to him as a revelation under a tree in the Bois de Boulogne on a warm spring day in 1831, in fact, he borrowed the lion's share of his theory of tonality and the term tonalité itself from (French) works on music of the previous three decades.
Over time, the phenomenon and the concept of tonality have evolved and changed.
In Soviet textbooks of elementary music theory, the terms "fret" and "tonality" (in the 1st meaning) were usually understood as synonyms[9].
For this reason, the tonality (in the 2nd value) was defined as the "high altitude position of the fret"[10] - without specifying what kind of fret (it was believed that all readers already mean "major or minor").
To this understanding of tonality (= major minor tonality), Yu.
N. Tyulin added a reference to a certain "reference basic tone" — a term that he used instead of the (usual) "tonic" [11].
States of the (major minor) key[edit / edit wiki text]
It is generally recognized that the tonality has not remained unchanged for centuries.
It underwent particularly significant changes in the music of the second half of the XIX early XX centuries.
Denoting the forms of such a tonality generically, they say " late romantic "or" extended", or" chromatic " tonality.
Different researchers offer different terms to denote the characteristic particular manifestations of extended tonality[12].
In the doctrine of harmony by Yu.
N. Kholopov, it is proposed to classify these particular forms according to four criteria (called "tonal indices")[13]:
The center (abbreviated in the following schemes — C), its presence or (occasionally) absence.
Tonic (T), its presence or absence.
Sonance (C), the level of consonant and dissonant tension.
Functional gravity (F).
Depending on the combination of the tonality criteria indicated by the indexes, certain states of the extended tonality are marked.
Some of them (due to their specificity) have been assigned special names:
1. Loose tonality (C+ T+ C+ F -), that is, the center is unambiguous, the tonic is represented, the dissonance is subordinate, the functions do not uniquely indicate the tonic center.
Examples: (1) N. A. Rimsky Korsakov.
The legend of the invisible city of Kitezh: Prince Yuri's aria; (2) M. P. Mussorgsky.
The song "Vision"; (3) S. V. Rachmaninov.
All night vigil, part III, 1st line; (4) D. D. Shostakovich.
The 7th symphony, part III, etc.
2. Dissonant tonality (C+ T+ C F+), that is, the center is unambiguous, the tonic is represented, the dissonance is independent (not subordinate to the consonance), the functions are centripetal (definitely indicate the center).
Examples: (1) A. N. Scriabin.
7th sonata, 9th sonata, "Prometheus"; (2) S. S. Prokofiev.
Sarcasm, No. 5, the main topic; (3) A. Berg.
Vozzek, interlude d moll and the dialogue between the 4 and 5 paintings of Act III; (4) N. Ya.
Myaskovsky.
The 7th symphony, part I, the main theme, etc.
3. Floating tonality[14] (C+ T C± F+), that is, the center is unambiguous, the tonic chord does not appear, dissonance can be subordinate, but it can also be free, functions indicate the center.
In relation to this form of tonality, the term "atonicity"is also used.
Examples: (1) R. Schumann.
Kreisleriana, No. 4, main theme; (2) M. P. Mussorgsky.
Children's song (A dur); (3) F. List.
Bagatelle without tonality; (4) A. Schoenberg.
The song "Temptation" (Lockung) Op. 6 No. 7; (5) the same, the orchestral song "Voll jener Süße" op.
8 No. 5, etc.
4. Inversion tonality (C12 T+ C+ F+), that is, everything is as in the usual harmonic tonality, but due to the action of functional inversion[15] — either the ending is not on the tonic, or there is no feeling of the tonic at the beginning, or both the beginning and the end are not on the tonic.
Examples: (1) N. A. Rimsky Korsakov.
Sadko: Picture 2, chorus of Red girls; (2) F. Chopin.
Scherzo No. 2 Des dur; (3) M. P. Mussorgsky.
The song "Orphan"; (4) P. I. Tchaikovsky.
Iolanthe: Aria of Iolanthe et al.
5. Variable tonality (C1-2+ T+ C+ F+), that is, the beginning in one key (fully expressed and defined), and the end go to another one.
The tonalities are either equal or subordinate[16].
Examples: (1) M. P. Mussorgsky.
Khovanshchina: the dance of Persians; (2) Tchaikovsky.
Romance "We were sitting with you"; (3) A. N. Scriabin.
5th sonata; (4) D. D. Shostakovich.
5th symphony, part III, 2nd side theme, etc.
6. Fluctuating tonality (C1-2-3 T+ C+ F -), that is, the center is unstable (although in each case the tonic is quite unambiguous), dissonance is subordinate, functionality does not indicate a common tonic.
It differs from the loose one in that the tonic at the end and at the beginning is the same, there is no one here.
It differs from a variable in that it has a through tonal gravity (despite the fact that there are two or more centers), there is no such thing here.
Examples: (1) N. A. Rimsky Korsakov.
Sadko: Picture 4, the song of the Vedenetsky Guest (part 1); (2) R. Wagner.
The Ring of the Nibelung: the motif of fate; (3) D. D. Shostakovich.
5th symphony, part III, 1st side theme, etc.
7. Multi valued tonality (C1-2 T S± F -), that is, harmony is defined in one key, but approximately the same in another at the same time.
It differs from the oscillating one in that both keys are heard at once, and not alternately.
An example of a multi valued tonality is the dominant fret of a minor, or (the currently accepted abbreviated name) the dominant fret.
Examples: (1) S. V. Rachmaninov.
From the Gospel of John; (2) A. P. Borodin.
Prince Igor: act I, chorus of girls "We are coming to you, Princess"; (3) S. S. Prokofiev.
Love for three oranges: introduction to the march and the march, etc.
8. The removed tonality[17] (Cneopred. T S F -), that is, each of the chords taken by itself is easily guessed in some key, while no tonics and functional gravitations are heard.
Examples: (1) F. List.
Preludes (the first section of the development); (2) F. List.
Faust, introduction; (3) N. A. Rimsky Korsakov.
The Golden Cockerel: intermission to Act III, etc.
9. Polytonality (C1+/C2+ T+ C+ F+), that is, two music are combined, each in its own (functionally defined) key.
Examples: (1) M. P. Mussorgsky.
Pictures from the exhibition: "Two Jews" (reprise); (2) I. F. Stravinsky.
Parsley: c. 73; (3) R. Strauss.
The Cavalier of the Rose: the conclusion of the opera; (4) A. Berg.
Vozzek: Act II, picture 4, tt.
425-429, etc.
Other forms of tonality[edit / edit wiki text]
Relying on the functional triad T S D is not the only possible way to implement tonality as a fret principle, there are other types of tonal structure.
A special form of "loose" tonality ("prototonality" according to S. N. Lebedev) can be observed in the harmony of polyphonic compositions of the late Middle Ages and the Renaissance[18].
Yu.
N. Kholopov called this form of ancient tonality "modal tonality" [19].
In Europe, back in the early 1960s, he described the loose tonality (with the metaphorical term kurzatmige, lit. "suffering from shortness of breath", "asthmatic") Ernst Apfel[20].
In the USA, the hypothesis of the existence of a "Renaissance tonality" of the XVI century, specifically different from the major minor tonality of the XVIII century, was actively promoted by Harold Powers[21].
The American musicologist Peter Bergquist found "Proto A minor" in Lasso music[22].
The American researcher K. K. Judd (the author of a dissertation and many articles devoted to the genesis of tonality) went even further into the centuries, finding "tonalities" in the motets of Josquin Despres[23].
Tonality in Western musicology[edit / edit wiki text]
In Western musicology, the term "tonality" (German Tonalität, English tonality) also describes the fret in a broad sense[24].
In this sense, the term "tonality" is defined as "the system organization of sound pitch phenomena and the relations between them"[25] and is applied to any professional and folk tradition, both European and non — European.
Leading scholars speak, for example, about the" tonality " of the medieval Western chorale[26], Arabic maqam, Indian raga, Indonesian gamelan, etc. [27]
This meaning was inherited from the French musical theory of the XIX century.
(Shoron, Fetis, etc.), which distinguished between " ancient tonality "(fr. tonalité antique) — it included, for example, monodic church tones — and" modern tonality " (fr. tonalité moderne), that is, classical romantic tonal harmony.
Notes[edit / edit wiki text]
Хол Kholopov Yu.
N. Harmony.
Theoretical course.
St. Petersburg, 2003, p. 236 .
И. I. Dubovsky, S. Evseev, I. Mododin, V. Sokolov.
Textbook of harmony.
M.: Music, 2007 (reprint of the 1937-38 edition).
Ch Choron A. E. Sommaire de l'histoire de la musique / / (co author F. J. M. Fayolle) Dictionnaire historique des musiciens.
Paris, 1810, p.XI XCII; Hyer B. Tonality, 2002, p.730.
↑ Castil Blaze F.-H.
-J.
Dictionnaire de musique moderne.
V. 1-2.
Paris, 1821.
Хол Kholopov Yu.
N. Harmony.
Theoretical course.
St. Petersburg, 2003, p. 235.
G Geslin Ph. Cours d'harmonie.
Paris, 1826.
↑ Jelensperger D. L'harmonie au commencement du 19me siècle.
Paris, 1830.
↑ Fétis F.J. Traité complet de la théorie et de la pratique de l'harmonie.
Paris, 1844, p.
22. Тю Tyulin Yu.
N., Privano N. G. Textbook of harmony.
Edition 3.
M., 1986, p.
9. Способ Mododin I. V. Elementary theory of music.
M., 1963, p.
93. ↑ "In the usual name of the tonality of a work, two sides are meant: the absolute height of the fret, determined by its reference main tone, and the fret itself by its most characteristic feature major or minor."
Cit.
according to: Tyulin Yu.
N.
A brief theoretical course of harmony.
L., 1960; edition 4 (reprint of the third edition).
St. Petersburg, 2003, p.
9. For the first time, the idea of special states of tonality was put forward by A. Schoenberg in his doctrine of harmony (Harmonielehre, 3te Aufl. Wien, 1922, S. 459 ss.).
In Russian, the idea of states of tonality was developed in the dissertation of T. G. Mdivani "Problems of late romantic harmony in the works of Austro German composers of the late XIX early XX century (A. Bruckner, G. Wolf, G. Mahler, M. Reger)".
Minsk, 1983.
Хол Kholopov Yu.
N. Practical harmony ... part 1, p. 363-366; he, Harmony.
Theoretical course..., p. 383-399.
↑ Translation from German.
schwebende Tonalität (borrowed from Schoenberg).
↑ Functional inversion of slaves called the complex phenomena of extended tonality, characterized by a desire to highlight in some way the tone of the periphery: the movement from the main function to side, from one non chord sound to another non chord, etc.
On the functional inversion, it is possible to speak only when the focus to the modal unst is consistently maintained as a structural idea, substituting the idea of a functional relationship of chords in traditional classical mode.
Cm.
detail: Kholopov Yu.
N. Harmony.
Theoretical course ... ss.
375-383.
This form of tonality has received the name "progressive" in English language literature.
Перевод Translated from the German aufgehobene Tonalität (borrowed from Schoenberg).
Lebedev S. N. Prototonality in the music of the Western European Middle Ages and Renaissance / / Ad musicum.
Moscow, 2008, pp.
33-47.
↑ For the first time — in the article "Tonality" in the Musical Encyclopedia (vol. 5 — Moscow, 1981, stlb. 567-568) ↑ Spätmittelalterliche Klangstruktur und Dur Moll Tonalität // Musikforschung 16 (1963), S. 153.
↑ For the first time in the article "Tonal types and modal categories" 1981, especially marked — in the article "Is mode real?" (1992), see pp.
9-13.
However, neither the concept nor even the definition of such a tonality, Powers did not dare to offer.
In a late article "Anomalous modalities" (1996), he admits: "I am not ready to advance any new hypothesis about Renaissance tonalities or any particular Renaissance tonality" (cit.soc., p.226).
↑ Bergquist P.
The modality of Orlando di Lasso's compositions in 'A minor' // Orlando di Lasso in der Musikgeschichte.
Bericht über das Symposium der Bayerischen Akademie der Wissenschaften 4.
-6.Juli 1994, hrsg.
v. Bernhold Schmid.
München, 1996, S.7-15.
↑ Judd C.C. Modal types and "Ut, Re, Mi" tonalities.
Tonal coherence in sacred vocal polyphony from about 1500 // Journal of the American Musicological Society 45 (1992), pp.428-467.
There is no complete analogue of the Russian term "lad" in the West.
In English speaking languages, the fret is transmitted either by the word tonality or by the word mode (see Modality).
↑ "systematic arrangements of pitch phenomena and relations between them" (Hyer B. Tonality; bibliographic. see the description of the article below).
A 300 page book by the Danish scientist F. E. Hansen is dedicated to the "Gregorian tonality" (that is, the fret system of the Western chorale): Hansen F. E.
The grammar of Gregorian tonality.
Copenhagen, 1979.
In the article "Tonality" (German Tonalitat) in the well known Riemann dictionary, the German K. Dahlhaus: "The fret structure (tonale Struktur) in the melody of the Gregorian chorale is determined by the difference between the backbone and its filling, or [the difference] of the main and side tones, and also expresses itself through functions such as the final, initial, extreme and recitative tone" (Dahlhaus C. Tonalität // Riemann Musik Lexikon. Sachteil. Mainz, 1967, S. 960.).
"Tonality" in gregorianica finds and an English Medievalist, author of a fundamental monograph on the subject, David hilyard: "Easily confused mode and [psalm] tone; therefore, it is necessary to remember that the mode is an abstract quality that belongs to the fret [Gregorian] chant (tonality of chant), while [psalmody] tone is a type of chant as such, the melodic formula, adaptable to the execution of the infinitely varied psalmody poems" (D. Hiley, Western plainchant. A handbook. Oxford, 1993, pp.60-61.).
↑ Hyer B.
In the same place.
See also[edit / edit wiki text]
Pantonality
Literature[edit / edit wiki text]
Fétis F.-J.
Traité complet de la théorie et de la pratique de l'harmonie contenant la doctrine de la science et de l'art.
Bruxelles, 1844; 9th ed. Paris, 1867.
Riemann H. Katechismus der Harmonielehre (theoretisch und praktisch).
Leipzig, 1890; from the 2nd ed. (1900) under the title "Katechismus der Harmonie und Modulationslehre"; from the 5th ed. (1913) under the title "Handbuch der Harmonie und Modulationslehre".
Riemann G. Simplified harmony or the doctrine of the tonal functions of chords.
Translated from German.
Yu.
Engel, M.-Leipzig, 1896.
Mododin I. V. Elementary theory of music.
M.-L.: Muzgiz, 1951; M.: Muzgiz, 1954; 3rd ed. M.: Muzgiz, 1955; M.: Muzgiz, 1956; M.: Muzgiz, 1958; M.: Muzgiz, 1959; M.: Muzgiz, 1961; M.: Muzgiz, 1963; M.: Music, 1968; 6th ed. Moscow: Music, 1973; 7th ed. Moscow: Music, 1979; 8th ed. Moscow: Music, 1984; Yerevan, 1987 (translated into Armenian. language); Moscow: Kifara, 1994.
Salzer F. Structural hearing: Tonal coherence in music.
2 vls.
N.Y.: Charles Boni, 1952.
(= Strukturelles Hören: der tonale Zusammenhang in der Musik. 2 Bde.
Deutsche Übertragung u.
Bearb. von Hans Wolf.
Mit einem Vorwort von Leopold Mannes.
Wilhelmshaven: Noetzel, 1960).
Apfel E. Die klangliche Struktur der spätmittelalterlichen Musik als Grundlage der Dur Moll Tonalität // Musikforschung 15 (1962), S.212-227.
Apfel E. Spätmittelalterliche Klangstruktur und Dur Moll Tonalität // Musikforschung 16 (1963), S.153-156.
Dahlhaus C. Der Tonalitätsbegriff in der Neuen Musik // Terminologie der Neuen Musik.
Berlin, 1965, SS.83–8.
Dahlhaus C. Untersuchungen über die Entstehung der harmonischen Tonalität.
Kassel — Basel, 1968.
Atcherson W. Key and mode in seventeenth century music theory // Journal of Music Theory 17 (1973), p. 204-232.
Simms B. Choron, Fétis, and the theory of tonality // Journal of Music Theory 19 (1975), pp.
112–38.
Powers H. Tonal types and modal categories in Renaissance polyphony // Journal of the American Musicological Society, XXXIV (1981), pp.
428–70.
Bates, Robert Frederick.
From mode to key: a study of seventeenth century French liturgical organ music and music theory.
PhD.
diss.
Stanford University, 1986.
UMI No. 8700725.
Kholopov Yu.
N. Harmony.
Theoretical course.
M., 1988.
Anderson N.D. Aspects of early major minor tonality: structural characteristics of the music of the sixteenth and seventeenth centuries.
Ph.D. diss.
Ohio State University, 1992.
Powers H.
Is mode real?
Pietro Aron, the octenary system and polyphony // Basler Jahrbuch für historische Musikpraxis 16 (1992), pp.
9–52.
Powers H. Anomalous modalities // Orlando di Lasso in der Musikgeschichte, hrsg.
v. Bernhold Schmid.
München: Verlag der Bayerischen Akademie der Wissenschaften, 1996, S. 221-242.
Powers H.
From psalmody to tonality // Tonal structures in early music.
New York: Garland, 1998, p. 275-340.
Tonal structures in early music: criticism and analysis of early music, ed. by Cristle Collins Judd.
New York: Garland, 1998.
ISBN 0-8153-2388-3 (collection of articles).
Hyer B. Tonality // The Cambridge history of Western music theory.
New York: Cambridge University Press, 2002, pp.
726-752 (slightly edited reprint of the author's article from NGD2001) Kholopov Yu.
N. Categories of fret and tonality in the music of Palestrina / / Russian book about Palestrina.
Scientific works of MGK.
Sat. 32. Moscow: MGK, 2002, pp.
54-70.
Kholopov Yu.
N. Harmony.
Practical course.
In 2 h .
m., 2003.
McAlpine F. Tonal consciousness and the medieval West.
Bern: Peter Lang, 2008.
ISBN 978-3-03911-506-8.
Lebedev S. N. Prototonality in the music of the Western European Middle Ages and Renaissance / / Ad musicum.
Moscow, 2008, pp.
33-47.
Tonality 1900-1950.
Concept and practice
