Do Pitagor i napred: novo muzikalno poznanie ; motivacija, idei, tvorčestvo
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| Format: | Book |
| Language: | Bulgarian |
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V.Tărnovo
Izdat. Faber
2010
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| Online Access: | Inhaltsverzeichnis Abstract |
| Item Description: | In kyrill. Schr., bulg. - Zsfassung in engl. Sprache u.d.T.: To Pythagoras and forward |
| Physical Description: | 183 S. graph. Darst., Notenbeisp. |
| ISBN: | 9789544003555 |
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| 245 | 1 | 0 | |a Do Pitagor i napred |b novo muzikalno poznanie ; motivacija, idei, tvorčestvo |c Christo Pitev |
| 264 | 1 | |a V.Tărnovo |b Izdat. Faber |c 2010 | |
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| 500 | |a In kyrill. Schr., bulg. - Zsfassung in engl. Sprache u.d.T.: To Pythagoras and forward | ||
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Record in the Search Index
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| adam_text | СЪДЪРЖАНИЕ
Рецензия от ст.н.с.
II
ст. д-р
Ангелина Петрова
.................11
Предговор
......................................................................................15
Композиция със свободни елементи и форма
....................21
От автора
........................................................................................22
Глава първа. По пътя към композиция със свободни
елементи и форма (КСЕФ)
-
факти, обстоятелства,
основания
.......................................................................................27
1.
Мотивация
.............................................................................27
2.
Поглед към развитието на класическата форма
..........31
2.1.3а сложността по линия на диференциация
на елементите на формата
....*...........................................33
2.2.
За сложността по линия на диференциация
на хармоничните средства
-
акордиката
и тонално-хармоничния език
..........................................35
3.
Формата като език на композиторите
............................37
3.1.
Комуникативни аспекти на музикалната форма
... 37
3.2.
Принципи на формата и езика
.................................39
Глава втора. Основни положения в теорията на КСЕФ
... 44
І.Елемент-образ
(ЕО)
................,............................................44
2.
Елементите-образи като Принадлежност
на определено Множество
.....................................................46
3.
За принципите на класическата форма и на КСЕФ
.....48
4.
Енергичност на връзката
...................................................50
Глава трета. Структура и експозиция на елемента-образ.....
52
1.
ЕО като Разграничение
......................................................52
2.
Свободният избор в КСЕФ
................................................55
3.
Структура на
Елементите
-образи
....................................58
3.1.
Факторите симетрия
-
асиметрия
...........................58
3.2.
Вид на мотивите
...........................................................61
4.
Видове
връзки
.......................................................................64
4.1.
Структурна
връзка
......................................................66
4.2*.
Функционална връзка
................................................67
4.3.
Връзките в структурата на ЕО
.................................68
5.
Граничността в образуванието ЕО
..................................69
Глава четвърта. Формообразуването в КСЕФ
.................73
1.
Затрите
функции на формообразуване
.........................73
1.1.
Функция на Извикването
.........................................73
1.2.
Функция на Комбинирането
...................................74
1.3.
Функция на Връзките-Релациите-Отношенията...^
2.
Експозиция на Елементите-образи
.................................75
2.1.
Множество, Принадлежност, Общо свойство
.....75
2.2.
Принадлежност на Елементите
-
тоналност
........76
2.3.
Специфика на начина на мислене в условията
на КСЕФ
................................................................................77
3.
Основни принципи на КСЕФ
............................................79
4.
Експозиция на Множествата
............................................80
5.
КСЕФ като техника на Комбинирането
.........................82
Глава яета.Композиционна последователност
в техниката на комбиниране
....................................................86
1.
Начално множество (М-во „А )
.......................................86
2.
Второ множество (М-во „В )
............................................88
3.
Трето множество (М-во „С )
............................................90
4.
Техниката на Включване на ЕО
в различните Множества
...................................................... 93
5.
Систематизация на въведените термини
......................94
Глава шеста.
Опериране
с множества
..................................96
1.
Обединение
...........................................................................96
2.
Сечение
...................................................................................98
3.
Множествена разлика.......................................................
100
4.
Крайно
множество
............................................................103
5.
За
нарушенията..................................................................
109
6.
Единство и центричност на формата
...........................110
7.
Завършване
на
композицията
........................................
Ill
7.1.
Движението
от частно
към
общо в КСЕФ
...........111
7.2.
Изчерпване
на
възможностите
за
Комбиниране.
...114
8.
За
принципите
на повторение
........................................118
9.
За
новия
начин на
музикално мислене.........................
124
Заключение
..................................................................................127
Библиография
.............................................................................129
Най-великото откритие
-
А 1.66/
G l.SO/ F 1.33/
£1.25... 131
1.
Началото
на
пътя
...............................................................132
1.1.
Поставяне на въпросите
..........................................132
1.2.
Гамата
-
най-древното научно откритие
.............134
1.4.
За Платон и геометрията
.........................................139
1.5.
Въпросите в историческа последователност
......140
1.6. ^2
и двойствеността „вълна-частица
.................141
2.
Как да построим геометрията на обертоновия ред...
143
2.1.
Вписаният в квадрата
равнобедрен
триъгълник....
143
2.2.
V5/2
и принципът на симетрия
..............................145
2.3.
„Нагоре (навън) и „надолу (навътре)
в структурата на звука
.....................................................147
2.4.
Развитие на въпросите
............................................. 148
3.
Геометрията на трептящата струна
...............................150
3.1.
Анализи в посоката-навън и посоката-навътре...
150
3.2.
Квантови числа и квантова симетрия на тоновете
....154
3.3.
Diabolus
in
musica
в квинтовия
кръг
на
гамите.
..155
3.4.
Правило на Леонардо да Винчи
.............................156
3.5.
Защо
„ла -то
е „ЛА ..................................................
158
3.6.
КОДЪТ
на диатоничната гама
................................ 160
4.
Как
са разпознати хармонията и мелодията
в
геометрията
на тона
...........................................................161
4.1.
Разбиранията
на
древните
за
хармонията
(акордите).....
......................................................................161
4.2.
Защо
терцата не
е била използвана
хармонически
....................................................................161
4.3.
„Терцата
2.5 -
едно изключително
математико-акустическо
събитие
.................................162
4.4.
Принципите
на
симетрия в Геометрията
на
струната (тона)
.............................................................164
5.
Геометрията
на
струната
-
източник
на дълбоките познания
.........................................................165
5.1.
Тризвучието „Ла-До-Ми
........................................165
5.2.
Двете различни по характер движения
на струната
.........................................................................167
6.
Обобщения и заключения
...............................................168
6.1.
Какво ново можем да кажем днес
..........................169
6.2.
Геометрията на струната и теорията
на струните
.........................................................................171
6.3
Легенда към заглавието
.............................................172
Приложения
................................................................................174
I.
Пълният ред на „сеченията-тонове
на диатоничната гама в триъгълника АЮ
.......................174
И. За „хиату^ -тетрахордите
...............................................175
III.
Квантова
симетрия
на тон-числата
по тетрахорди на бихармоничния минор
........................176
IV.
Квантова симетрия на тон-числата
по тетрахорди на бихармоничния
мажор
........................176
Библиография
.............................................................................177
Summary
........................................................................................179
SUMMARY
HRISTO
PITEV
TO PYTHAGORAS AND FORWARD
NEW MUSICAL KNOWLEDGE
motivation
-
ideas
-
creative work
THIS VOLUME contains two pieces of original research
and findings in the field of music theory. The ideas presented in
them constitute an attempt, on the basis of scientific knowledge
and the characteristic events in the development of Modern mu¬
sic, to reach a more profound understanding of the problems in
contemporary musical composition. These problems
-
of today
and tomorrow
-
are all problem of knowledge: of putting in or¬
der the separately wandering in time constituents of knowledge
-
creative work
-
reality, of seeing these constituents in their
proper perspective, and bringing them into a united whole
-
CONTEMPORARY MUSICAL KNOWLEDGE.
I. COMPOSITION WITH FREE ELEMENTS AND FORM
(CFEF) was conceived on the basis of mathematical set theory,
interpreted and understood in close relation to the character¬
istics of the radically changed, new musical reality. In this way,
the gist of this theory of composition is in bringing to the fore¬
ground the importance of the CONNECTIONS between the
separately distinguishable musical constructs-elements, while
assuming that each one of these is an Element with a form and
theme of its own
-
Element with capital E is a free element.
This means that the Elements in a composition (CFEF) are not
hierarchically arranged into primary and secondary ones, and
are not dependent on one and the same thematic succession
178
-----------------------------------
Summary
-----------------------------------
-
such as the building up of theme-parts in classical form. It
should be noted that the free element quality is not inherent in
itself, but is cultivated in satisfying certain conditions in each
positioning (differentiation) of an Element. These conditions
are the following: no Element is to be subject to shortening or
extension, to splitting or merging with other Elements, is not to
be changed internally, as well as not to be transposed or modu¬
lated. It is of extreme importance that these conditions are not
regarded as limitations to the structuring of the individual Ele¬
ment, but as a prime requirement of the reality of the free el¬
ement quality
-
the reality of this quality is expressed in the
potential of the Elements to freely come into contact with each
other, to combine, to establish various kinds of relations. So,
in their multifarious communication, the
Elemente
are able to
manifest various characteristic features of their own, thus add¬
ing to their presence in the composition.
A central role in realizing the free communication of the
Elements in a composition
-
in realizing its content
-
is played
by the functional connection (a concept almost unknown in
music theory). In stark contrast to the structural connection
-
the connection established by a certain similarity, identity,
or resemblance of the constituents
-
the FUNCTIONAL CON¬
NECTION is a spontaneously occurring attraction between
two formations differing in structure
-
a connection merely
by sympathy, by incidental occurrence, by contrast. This kind
of connection cannot be foreseen, nor can it be concretized in
any particular scheme. We can only say that its occurrence (ex¬
pectation
-
appearance) is provoked by the energy of internal
preservation, of defence in preserving the integrity of each Ele¬
ment. Therefore we can assume that the inwardly directed en-
ergy. is inevitably transformed into outwardly directed energy
-
into the energy of searching for ever new connections and
situations, new accelerations of the course of composition.
179
To Pythagoras and Forward
An important advantage of CFEF is that the Elements differ
in size. Ibis difference, in terms of recognizability and syntax
of musical speech, will· most often be within the sentence. How¬
ever, with the larger possibilities offered by operating with sets
in the composition, an Element may also fit into a few meas¬
ures or even (as an exception) into a single chord or sound-
rhythmic moment-complex.
A starting point in defining (distinguishing) each one of the
Elements in the composition becomes the fact that they are all
OF EQUAL STANDING (which is one of the conditions for the
importance of connections to come to the fore). Emphasizing
the necessity for the Elements not to be dependent on one or
another thematic sequence, we have to add that the Elements
in every composition (CFEF) are regarded as INDIVIDUALS,
as uniquely existing at a particular time and place. Beyond their
belonging in a particular composition, the Elements have no
significance or meaning whatsoever, no reality, being merely a
pure abstraction.
The PROBLEM OF THE FORM IN CFEF is solved on the
principle of an always original self-adjustment and self-deter¬
mination
-
a principle which in its turn is activated by the rules
of differentiation and grouping of the Elements. It is perfectly
clear that the different elements in their succession in a compo¬
sition will have some common feature, will share a certain kin¬
ship (direct and indirect). It is also clear that this kinship will
perform the role of a COMMON QUALITY in the ways the El¬
ements communicate . This common quality/common feature
urges the Elements to combine and group together: some Ele¬
ments to belong in one grouping, other Elements to belong in
another grouping, as well as to regroup from a smaller group¬
ing into a larger one, from the larger one
-
into another still
larger grouping etc until the memory of kinship is exhausted
180
-----------------------------------
Summary
-----------------------------------
or worn off, thus new connections and relations becoming no
longer possible.
The rule that each Element is an Individual also involves
the rule that each connection is an individual connection. This
means that two or more Elements are NOT TO BE REPEATED
in one and the same sequence. Thus, building up the compo¬
sition is basically a process of a CONSTANT SEARCH FOR
EVER NEW CONNECTIONS. And since this inevitably ac¬
celerates the very connection dynamics, and the space whirls ,
a process of CENTRIC STRUCTURING OF FORM starts up.
And the rule that each Element is regarded as a free individual
quite simply and logically leads to the conclusion that the re¬
sulting recognizable whole will ultimately be a FORM which
is FREE, INDIVIDUAL, AND ALWAYS ORGANIZED IN A
CERTAIN WAY.
II. THE GREATEST DISCOVERY: A 1.66/ G l.SO/ F 1.33/
ΕΊ.25
From the point of view of modern experimental science,
the musical scale is considered to be the most ancient scientific
discovery, the credit for which goes to Pythagoras. However,
the Pythagorean scale could not come into use , as the purely
mathematical relations of tones proved to be foreign to hearing
perception and voice. It was only after the natural, harmonic re¬
lations of tones in the so-called diatonic scale were discovered
that the seven-note scale became the foundation of the tonal
system in music. Our assumption is that the diatonic scale
-
the true scale, is based on the DISCOVERY OF THE TETRA-
CHORD LA-SOL-FA-MI
-
a fact completely unknown today,
about which we find indirect evidence in Vitruvius, the great
Roman architect
(1st
century
ВС/
AD), in his commentary on
the significance of the tetrachord in the ancient Greek musical
system.
181
To Pythagoras and Forward
Tracing the events from that time and their logic leads to
the conclusion that had it not been for this discovery, Euro¬
pean music might have not followed that particular course in
its development which has taken MUSIC to such unimagina¬
ble heights of greatness and beauty. It is, however, more than
that: the present study demonstrates that the discovery of the
tetrachord La-Sol-Fa-Mi can prove to be „...one-of the most
beautiful and singular discoveries made 1 in the whole history
of human knowledge and culture. Historical facts and docu¬
ments clearly indicate that the identification of the tetrachord
was made by means of GEOMETRY and, more precisely, in the
Geometry of Tone.
The ancient Greek music theory contains a passage-postu¬
late by Aristoxenus (in his
Elementa
harmonica, translated into
Latin by Vitruvius) which has not been considered or quoted at
all in the existing studies on music history. Yet, judging by the
ideas it conveys, it can be defined as the very beginning of mu¬
sic theory. This passage is the following: „...these intervals of
tones and semitones of the tetrachord are a division introduced
by nature in the case of the voice, and she has defined their lim¬
its by measures... 2 At first sight, and bearing in mind todays
quite arbitrary use of the word nature, it may seem that there
is nothing of particular importance in this passage. However,
in stark contrast to our current obsession with the computer,
in antiquity people had an extravagant mania for geometry
-
for thinking and reasoning, and it seems that they knew better
what Nature is!... And if we ask why the ancients expressed the
1
Hermann Weyl about the discovery of the Platonic solids pen-
tagondodecahedron and icosahedron: Weyl, H. Symmetry, Princeton
University Press, Princeton, NJ,
1952 (1989), 74.
2
Aristoxenus, Elements of Harmony, quoted in: Vitruvius, Ten
Books on Architecture, Book V, Chapter IV Harmonics.
182
-----------------------------------
Summary
-----------------------------------
general doctrine of quantities in geometric rather than algebra¬
ic terms, the answer will be in Plato s phrases which have come
down to us through the centuries: God always geometrizes .
..
Geometry will draw the soul towards truth.
..
What do geometry and music have in common? The be¬
ginning is in the clear and pleasant-sounding harmonious
tone: only bodies with regular geometry, with geometrically
regular form and structure can produce such a sound. The
slightest inexactness, distortion, or irregularity of the form of
the vibrating body will disturb the harmonious balance and
purity of the sound. The STRING has the most regular, ideal
geometry
-
the geometry of the vibrating string. Then
-
if
Plato is right
-
what is the main thing which this geometry
should necessarily contain? Certainly, it is the disposition and
scheme of the order of overtones (from the first overtone to
the infinitely high one). And in order for Plato to convince us
completely, this geometry should also contain the very tet-
rachord La-Sol-Fa-Mi. To our surprise (or not...) both one
and the other are clearly found in it. And in such a definite
way so as to prove without a shadow of doubt that the ancient
Greek music theory was developed on the basis of the geom¬
etry of the string
-
the geometry of the complete structure of
the sound, consisting as a whole of OVERTONES and (the
hitherto entirely unknown)
INTERTONES.
Only one thing
remains missing and that is the answer to the question: why
has this geometry been hidden for so long, together with the
passage-postulate, quoted above? Has it been because it had to
be that way or because we needed to walk the longest way to
trace the GREATEST discovery!?
183
|
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| author_sort | Pitev, Christo 1930- |
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| ctrlnum | (OCoLC)711857039 (DE-599)BVBBV037273668 |
| format | Book |
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| id | DE-604.BV037273668 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:59Z |
| institution | BVB |
| isbn | 9789544003555 |
| language | Bulgarian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021186592 |
| oclc_num | 711857039 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 183 S. graph. Darst., Notenbeisp. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Izdat. Faber |
| record_format | marc |
| spelling | Pitev, Christo 1930- Verfasser (DE-588)143726900 aut Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo Christo Pitev V.Tărnovo Izdat. Faber 2010 183 S. graph. Darst., Notenbeisp. txt rdacontent n rdamedia nc rdacarrier In kyrill. Schr., bulg. - Zsfassung in engl. Sprache u.d.T.: To Pythagoras and forward Kompositionslehre (DE-588)4164918-7 gnd rswk-swf Tonalität (DE-588)4185654-5 gnd rswk-swf Musiktheorie (DE-588)4040876-0 gnd rswk-swf Musiktheorie (DE-588)4040876-0 s Tonalität (DE-588)4185654-5 s Kompositionslehre (DE-588)4164918-7 s DE-604 Digitalisierung BSB Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021186592&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung BSB Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021186592&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Pitev, Christo 1930- Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo Kompositionslehre (DE-588)4164918-7 gnd Tonalität (DE-588)4185654-5 gnd Musiktheorie (DE-588)4040876-0 gnd |
| subject_GND | (DE-588)4164918-7 (DE-588)4185654-5 (DE-588)4040876-0 |
| title | Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo |
| title_auth | Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo |
| title_exact_search | Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo |
| title_full | Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo Christo Pitev |
| title_fullStr | Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo Christo Pitev |
| title_full_unstemmed | Do Pitagor i napred novo muzikalno poznanie ; motivacija, idei, tvorčestvo Christo Pitev |
| title_short | Do Pitagor i napred |
| title_sort | do pitagor i napred novo muzikalno poznanie motivacija idei tvorcestvo |
| title_sub | novo muzikalno poznanie ; motivacija, idei, tvorčestvo |
| topic | Kompositionslehre (DE-588)4164918-7 gnd Tonalität (DE-588)4185654-5 gnd Musiktheorie (DE-588)4040876-0 gnd |
| topic_facet | Kompositionslehre Tonalität Musiktheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021186592&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021186592&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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