Im Digitalisierungsprojekt „Ernst Krenek lectures online: die musiktheoretischen Vorträge eines Exil-Österreichers“ wurden die im Archiv der Ernst-Krenek-Institut-Privatstiftung aufbewahrten Manuskripte und Typoskripte zu Kreneks Lehrveranstaltungen, Vorträgen und Radiosendungen in einer kuratierten Auswahl online verfügbar und durchsuchbar gemacht, sowie mit begleitenden historischen und biographischen Informationen kontextualisiert.
Digitalisiert wurden rund 90 Schriftgutobjekte mit einem Gesamtseitenumfang von rund 800 Seiten. 75% dieser Objekte sind Manuskripte, die restlichen 25% sind Typoskripte, wobei die Hälfte der Dokumente in deutscher, die andere Hälfte in englischer Sprache verfasst sind. Diese Dokumente stammen aus dem Nachlass Ernst Kreneks und stehen im Zusammenhang mit seiner Lehr- und Vortragstätigkeit sowohl in akademischen Institutionen als auch in Rundfunksendungen.
Textfehler und Schreibfehler wurden übernommen.
Fehlende i-Punkte, Umlautzeichen etc. werden stillschweigend ergänzt. Geminationsstriche werden aufgelöst. Leerzeichen und Abteilungszeichen werden standardisiert.
Fehlende Interpunktion wird nicht ergänzt. In Zweifelsfällen wird das den Rechtschreibregeln entsprechende Interpunktionszeichen erfasst. Striche werden immer als Bindestriche erfasst.
Es werden ausschließlich englisch Anführungszeichen verwendet. Es wird vorlagegemäß zwischen einfachen und doppelten Anführungszeichen unterschieden.
Die Silbentrennung wird vorlagegemäß übernommen.
Der Text wird in Seiten, Textfelder (Paragraphen, Überschriften, Seitenzahlen, Notizen) und Zeilen segmentiert.
Ernst Kreneks Unterweisung im zweistimmigen Kontrapunkt bietet einen umfassenden, wenn auch stark komprimierten Überblick über das Regelwerk der Vokalpolyphonie des späten Mittelalters und der Renaissance in Anlehnung an das Theoriewerk von Johann Joseph Fux, das schon die Grundlage für Kreneks eigene Kontrapunkt-Unterweisung während seines Studiums bei Franz Schreker an der k.k. Akademie für Musik und darstellende Kunst in Wien.
First Species
(Note against note)
1) Melody
* Available progressions:
Seconds (major and minor)
Thirds (major and minor)
Fourth (perfect only)
Fifths (perfect only)
Sixths (minor only, ascending only)
Octaves (perfest only)
* The tritone (a melodic progression involving an augmented fourth
or a diminished fifth) should be used only if it is continued
stepwise.
* The counterpoint must have one highest point, and should have
one lowest point.
* Sequences (consecutive repetitions of melodic elements) are to
be avoided.
The repetition of a tone is permitted occasionally; in such cases
the two notes are tied together.
2) Counterpoint
Available intervals between the two parts:
Unison (first and last measures only)
Thirds (major and minor)
Fifths (perfect only)
Sixths (major and minor)
Octave (perfect only)
Tenths, etc.
* Unison, Fifth and Octave are called perfect consonances, Thirds
and Sixths imperfect.
* In general, the parts should not be farther apart than a tenth.
One must begin
terpoint lies below the c.f. only actave or unison may be used
for beginning and ending.
* Fifths and octaves are not to be approached in parallel, or similar,
motion.
No more than three or four thirds or sixths should appear consecu-
tively.
* Crossing of the parts is permitted.
*Rules valid in all species
Two-part Counterpoint
Second Species
(Two notes against one)
1) Melody No more than two skips are available within an ascending, or descen-
ding, portion of the melody.
If two skips are used, the second skip has to follow the first one
immediately.
If the two skips are of unequal size, the larger skip has to be the
lower of the two skips, in either direction. (Usually no dis-
crimination is made between major and minor third, i.e. they
are considered as of equal size.)
Skips, following (in ascending motion), or preceding (in descending
motion), a skip larger than a third, should be smaller than the
skip which they follow, or precede.
Descending skips may be preceded, ascending skips followed, by step-
wise motion in the same direction, or the melody may turn back,
by skip, or stepwise.
After a skip of an octave the melody must turn back in the opposite
direction.
Immediate repetition of tones is not permitted.
2) Counterpoint On accented beats consonances only are available.
On unaccented beats consonances as well as dissonances may be used.
Dissonances must be introduced and left step wise in the same
direction, i.e. dissonances must be passing notes.
The counterpoint may begin on the first accented beat, or after a
half note rest. In either case the first note of the counterpoint
must form a perfect consonance with the c.f. If the counterpoint
is below the c.f., octave or unison only may be used for begin-
ning and ending. The last note of the counterpoint is always a
whole note. In the next to the last measure one may use two half
notes, or one whole note.
In addition to its use in the first or last measure, the unison may
appear occasionally on unaccented beats; it should be left in
the direction opposite to that in which it was introduced.
Fifts and octaves should be used but sparingly on consecutive ac-
cented beats.
3) Cadence If the counterpoint ends on the final of the mode, the final has to
be preceded by the lower, or the upper, leading tone, or by a
skip from the fifth step of the mode ("dominant"). In the Phry-
gian mode the leading tone approach only is available. The leading
tones themselves should be approached stepwise (in either direc-
tion), or by skip from the "dominant".
Two-part Counterpoint
Third Species
(Four notes against one)
1) Melody No more than one skip is permitted within an ascending, or descending
portion of the melody. (1)
Ascending skips larger than a third should be followed by stepwise
progression in the opposite direction. (2)
Ascending skips are permitted only from unaccented quarter notes
(2nd and 4th). (3)
In ascending melodies skips are permitted only at the beginning,
in descending melodies only at the end of the motion. (2), (4).
Repetition of the tone of the first quarter beat on the third, or
of the second on the fourth should be avoided as a rule, ex-cept
if the third, respectively fourth, quarter note is introduced
from below. (5)
2) Counterpoint The first and third quarter notes of each measure must be
consonant. The second and fourth quarter notes may be consonant
or dissonant; if dissonant, they must be introduced and left
stepwise, in the same direction (passing note), or in the op-
posite direction (auxiliary note); the latter, however, is
available only below. (6)
A dissonance on an unaccented quarter beat may be left by a skip
down exceptionally in the case of the cambiata, a melodic figure
consisting of five tones. After the skip the melody turns and
ascends stepwise. (7)
Fifths and octaves on accented beats should be separated by at least
three quarter beats. (8)
Unisons should not occur on the first beat of a measure, except in
the first and the last measure.
The counterpoint may begin on the first, or on the second (quarter)
beat. In the former case only perfect consonances may be used
(if the counterpoint is below the c.f., unison or octave only),
in the latter imperfect consonances are permitted.
The next to the last measure may have four quarter notes, or two
half notes, or one whole note.
Two-part Counterpoint
Fourth Species
(Dissonances on accented beats)
Two half notes are placed against one note of the c.f. The accented half
notes may form dissonances with the c.f., provided these dissonances
are prepared and resolved properly, i.e. that the note which is dis-
sonant with the c.f. is tied over from the preceding unaccented beat
where it has to form a consonance with the c.f., and that the disso-
nating note proceeds step wise down on the unaccented beat following
the dissonance, where it has to form an imperfect consonance with
the cf. Therefore, the following dissonances are available:
a) if the counterpoint is above the c.f.
7, resolving to 6;
4, resolving to 3;
b) if the counter point is below the c.f.
2, resolving to 3;
9, resolving to 10.
Wherever a dissonance can not be placed according to the above rules,
the rules of the second species will apply. They are also valid
with respect to beginning and end of the c.f.
Unisons may be used on both accented and unaccented beats.
Two-part Counterpoint
Fifth Species
(mixed, or florid, counterpoint)
1) Melody and Rhythm
If an ascending portion of the melody contains different rhythmic
values, shorter values usually precede longer values. (1)
If a descending portion of the melody contains different rhythmic
values, longer values usually precede shorter values. (2)
Sequences of quarter notes
begin in descending motion preferably on unaccented beats (3)
in ascending motion on both kinds of beats (4)
(in both directions with good effect after a skip
in the opposite direction);
end on a fully accented beat (first beat of a measure); if they
end on a relatively accented beat (second half note of a
measure), it is advisable to tie the half note over to
the next fully accented beat. (5)
In general, there should not appear more than 9 quarter notes in
continuous sequence.
Groups of two quarter notes ("isolated" quarter notes) are to be
avoided on fully accented beats, unless the following half
note is tied over to the next accented beat, preferably by
forming a dissonance there. (6) Groups of two quarter notes
on relatively accented beats (second half of a measure) are
correct. (7)
Within a section occupied by quarter notes the rules of the third
species apply.
Eighth notes:
in groups of two only;
on unaccented quarter beats only;
stepwise only: as passing notes,
as alternating notes, below only. (8)
Only whole notes and half notes can be tied to subsequent notes.
The second of the two notes tied together may be of the same
value as the first one, or half as long. (9)
Two-part Counterpoint
Fifth Species (continued)
2) Counterpoint
A dissonance can not be resolved on an unaccented quarter beat, but
must always be resolved on the following relatively accented beat.
the resolving note itself may be of any rhythmic value (except
eighth notes). (1).
On the unaccented quarter beat between a dissonance and its resolution
one may interpolate either
a quarter note which is a third below the preceding dissona-
ting note, provided that this interpolated quarter note is
consonant with the other part, (2)
or a group of two alternating eight notes (below only). (3)
Alternating quarter notes above are permitted before longer rhythmic
values. (4)
The cambiata may appear in
(see ex. 5). The second, dissonant note must always be an unac-
cented quarter note. If the fourth note is a consonant half note,
the fifth note does not need to be one step above the fourth note.
When an accented note is approached stepwise from above, it may be anti-
cipated on the immediately preceding unaccented quarter beat, regard-
less of whether this anticipated note is consonant or dissonant.
Anticipations from below are unusual and only occasionally used
in final cadences. (6)
When an accented half note is followed by two quarter notes in stepwise
descending motion, the first of these quarter notes may be dissonant
in spite of its staying on a relatively accented beat ("accented
passing tone"). (7)
Two-part Counterpoint
Free Counterpoint
(without Cantus Firmus)
Additional rules and modifications of former rules:
Quarter notes may dissonate with each other on unaccented beats, provided
the dissonances are treated correctly in each part. (1)
The part against which the other part forms an accented dissonance (see fourth
species) may move on before the dissonance is resolved, provided an im-
perfect consonance is formed when the resolution takes place. Dissonan-
ces which would resolve into perfect consonances if the other part would
not move on are now available provided the motion in the other part
leads to an imperfect consonance. When the part against which the dis-
sonance is formed moves in half notes, its progression is subject only
to the general rules concerning melody. If this part moves in smaller
rhythmic values, the progression must be stepwise (passing, or altern.) (2)
In a figure of four quarter notes, beginning on a fully accented beat, de-
scending stepwise, and the last one followed by its upper second, the
third quarter note may dissonate with the other part, if this dissonance
is tied over and repeated on the strong beat following the last of the
four quarter notes and then resolved regularly ("Anticipated dissonance") (3)
Stepwise parallel motion in half notes, in both directions, may be modified
so that in one of the parts the tone destined for the relatively unac-
cented beat does not enter before the unaccented quarter beat following
the relatively unaccented beat, even if the delay causes a dissonance
on that beat ("Delayed parallel motion"). (4)
Parallel motion in quarter note sections may occasionally comprise more
than four consecutive notes.
The rule concerning the distance of the parts from each other is applied
less rigidly than heretofore, if the flow of the melodies requires an
exception.
Two-part Counterpoint
Double Counterpoint
Both parts shall be written in such a way that each of them can function
both as an upper part or a lower part in relation to the other part.
If one of the two parts remains in its place, one calls the double
counterpoint, according to the interval by which the other part is
transposed in order to change its relation to the fixed part, "double
counterpoint of" (or "to") "the octave","the tenth", "the twelfth", etc.
In order to insure correct procedure, one has to examine in what inter-
vals the original intervals are transformed by the transposition of
the movable part.
For the double counterpoint of the octave the transformation of the
intervals gives the following results:
1 2 3 4 5 6 7 8
becomes
8 7 6 5 4 3 2 1
For the double counterpoint of the tenth the results are:
1 2 3 4 5 6 7 8 9 10
becomes
10 9 8 7 6 5 4 3 2 1
The intervals of the original version must be treated with a view
of what becomes of them after the transposition. For example, in
the double counterpoint of the octave the fifth must be treated as
a dissonance, because it become a fourth after the transposition.
In the double counterpoint of the tenth parallel thirds and sixths
must be avoided, because they result in parallel octaves and fifths
after the transposition, etc.
Two-part Counterpoint
Imitation
The second part enters, after the first part has set forth a characteristic
motif of at least one measure and not more than two measures length,
by repeating the same motif, at any desired interval. Unison, octave,
upper fifth, or lower fourth are more frequently used. The first part
goes on with a counterpoint, and the piece develops and ends like the
previous exercises in free counterpoint. The imitating part may enter
at either a perfect, or an imperfect, consonance, or producing a syn-
copated dissonance against the other part. (5)
The imitation may be strict (all intervals imitated exactly) (1),
or free (minor intervals may be represented by major
intervals, or vice verse, or other alter-
ations may occur, provided the characteristics
of the original motif remain recognizable) (2)
tonal (in the imitation special attention is given
to reproducing characteristic final-dominant,
or dominant-final, progressions by correspon-
ding dominant-final, or final-dominant, pro-
gressions; adjustments of the motif will be
necessary, so that tonal imitation usually
is a case of free imitation) (3)
real (if the principle of tonal imitation is not
applied) (4)
Two-part Counterpoint
Inversion
The imitation in the second part answers the opening motif of the first
part by inversion, i.e. ascending intervals are transformed into
equivalent descending ones, and vice versa (with the adjustments
necessary for staying within the chosen mode). In the original
motif one has to avoid everything that would be inadmissible in
the opposite direction (see rules on sixth skips, skips in quarter
note motion, alternating notes, etc.)
Augmentation
The imitation in the second part answers the opening motif of the first
part in twice as long rhythmic values.
Diminution
The imitation presents the opening motif in rhythmic values half as
long as those of the original motif. In the original motif one
has to avoid everything that would be inadmissible in the smaller
rhythmic values. In treating half notes, or quarter notes, one has
to keep in mind that they will be transformed into quarter notes,
or eight notes, respectively.
Canon
Imitation not confined to the opening motif, but carried through the
whole length of the composition, except for the last measures
where arrangements for the simultaneous ending of both parts must
be made.
The devices of inversion, augmentation and diminution can be used si-
multaneously in various combinations.
Treatment of Text
Any note longer than a quarter note may carry a syllable. Several notes of
any value may carry a syllable. (1)
A quarter note may carry a syllable if it is preceded and followed by larger
values, or by groups of several quarter notes carrying one syllable. (2)
Notes may be repeated on new syllables. (3)
Linguistic accents coincide with the accents of the musical phrase.
Phrases of the text, or parts thereof, may be repeated.
New phrases of the text should be introduced by new musical motifs. Especially
in two-part writing each new section of the music should begin with imita-
tion.
The two parts should not cadence simultaneously, except at the end of the piece.
Each section of the composition should end with a clearly articulated melo-
dic
Any interval may occur between the last tone of a section of the melody and
the first tone of the next one, especially if these tones are separated
by rests, which should always be the case between sections of the text. (4)
Three-part Counterpoint
Additional Rules for Three-part Writing
1. Consonant three-tone combinations:
Major and minor triads in root position and first inversion.
Diminished triad in first inversion.
Major and minor sixth-four chord exceptionally, on unaccented half-beats,
provided the fourth is tied over into another dissonance which is to
be resolved regularly.
2. "Borrowed" dissonance: If a dissonance is in normal progress between two parts
as a tied-over syncopation, the third part may, on an unaccented quarter beat
jump into this dissonance and again out of it.
3. Half notes on relatively unaccented beats may form passing dissonances against
a second part with larger rhythmic values (according to second species rules),
even if the third part has quarter notes. These quarter notes, however, must
be correct in regard to both parts. Generally speaking, each part must agree
with all other parts carrying larger rhythmic values than itself does at any
particular place.
4. Quarter notes on unaccented beats may dissonate with each other provided the dis-
sonances are treated correctly in each part and/or with respect to any part
carrying larger rhythmic values.
5. The "anticipated" dissonance may be used whenever the third and fourth notes of
the four-note figure explained earlier are introduced stepwise from above,
by no matter what rhythmic value.
6. Fifths and octaves may be approached in similar motion except between outer
parts (crossing of parts makes the middle part frequently an outer part!).
They are particularly acceptable if accompanied by contrary motion in the
third part.
7. The distance between the upper parts should not exceed an octave, as a rule.
37.
Two Part Counterpoint
Text for the Christmas Motet
Rorate, caeli, desuper, et nubes pluant justum:
aperiatur terra, et germinet Salvatorem.
(Isai. 45,8)
Caeli enarrant gloriam Dei:
et opera manuum ejus annuntiat firmamentum.
(Ps. 18,2)
Tollite portas, principes, estras:
et introibit Rex gloriae.
(Ps. 23, 7,3,4)