Chromatics

Chromatik ( old Gr. Χρῶμα ( chrṓma) = 'color') describes in tonal music the "re-coloring" of diatonic pitches by increasing or decreasing (high or low alternation) by a semitone . The chromatic variants of f, for example, are f sharp and f sharp.

In contrast to the autonomous chromatics of the 20th century ( free tonality , atonality , dodecaphony ), in which all levels of the chromatic scale, regardless of their notation, appear as independent and equal elements of the tone system, the term is used in the traditional major-minor system Chromatik precedes the seven-step diatonic as a basic part of the tone system. Chromatic is therefore subordinate to diatonic as its extension.

Example of a sequence of diatonic and chromatic semitones with five different accidentals .
Diatonic steps can be recognized by the fact that there is a progression to the neighboring position in the system of lines, while the position remains the same for chromatic steps.

If a voice moves between two variants of the same tone (e.g. f-f sharp, f sharp-f, f-f sharp), one speaks of chromatic progressions as opposed to diatonic (ef or f sharp-g). Externally, the difference between a diatonic and a chromatic tone step can be recognized by the fact that in chromatic steps the names of the tones involved have the same, in diatonic steps, however, different initial letters. (The only exception: h -b is also a chromatic step.)

With pure intonation there is a difference between chromatic and diatonic progressions (see, for example, the sound example for the passage duriusculus ). This distinction is important for a full understanding of musical processes (especially with classical music). Only with equal tuning - a compromise in intonation - there is no difference between chromatic and diatonic progressions, since all semitone steps are the same.

Chromatik types

The following types of chromatics are distinguished by WM Barskij and JN Cholopow:

Modulation chromatics
Subsystem-like (with tonal deviations)
keynote-like
altered
mixed (as a result of mixing different diatonic scales)
autonomous (or natural, or heptatonic )

In the standard work for classical harmony by Ludwig Thuille the following classifications can be found:

altered chords

chromatic semitone (excessive prime), diminished third , excessive sixth , diminished seventh chord with highly aged third, gypsy
scale
- Old age of the second stage
- Depression of the second stage
- Neapolitan sixth chord
- deep alteration of the subdominant in minor, combination of several alterations in one chord

modulation

Change of sex of the consonant triad
further chromatic changes in the consonant triad
chromatic change of dissonant triads in general

Chromatic alternating notes , leads and passages, random harmony formation

Encounter of chromatically different tones belonging to the same level
inserted chords of the same harmonies in the chromatic passage
Organ point - reclining voice
Syncopation - double harmonies

Enharmonic modulation

Confusion and reinterpretation
Reinterpretation of the diminished seventh chord
Reinterpretation of the excessive triad
Reinterpretation of the excessive fifth chord
further reinterpretations

Modulation chromatics

In the case of a chromatic progression with a given harmonic classification, the notation is clearly given.

Example 1 for a modulation in the minor parallel (chords here after "Blessed are you" EKG Württemberg No. 651 ) C-C sharp-D :

The C in the bass still belongs to the C major dominant chord of F major, the C sharp of the A major chord introduces the modulation to D minor, the minor parallel of F major.

Example 2 for increasing chromatic progression. C-Cis-D-Dis-EF :

Soprano: c 'a tone of the C major chord, c sharp' -> d 'modulation over dominant chord A major to D major, D flat' (-> e) Modulation over dominant chord B major to E major / e- Minor, whereby the E major / E minor chord does not sound, but is replaced by e '-> f' dominant seventh chord from C major to F major chord.

Example 3 for chromatic progression with lowering C-Des-D-Es-EF:

Soprano: c 'a note of the C major chord, des' a note of the Neapolitan, d' a note of the G major dominant chord, es' a note of the C minor chord, e 'a note of the C major -Dominant seventh chord of F major, f 'a tone of the F major chord

Diatonic and chromatic pitches in the score

In the case of individual pitches, the naming of the note alone cannot tell whether it is diatonic or chromatic. In the context of other notes, the tonal relationship is decisive for whether it is a diatonic or a chromatic tone. F is not automatically diatonic, just as F sharp does not have to be chromatic. In a C major setting, F is diatonic because it belongs to the C major diatonic scale and F sharp is chromatic. In a D major setting, F sharp is diatonic because it belongs to the D major diatonic scale, and F is chromatic.

Even doubly raised or lowered tones need not necessarily be chromatic. For example, f sharp is the ladder's own, diatonic seventh degree of G sharp major. Such cases are by no means rare and occur already in the modulatory Schubert and even more frequently in the romantic harmony of Chopin, Liszt to Skriabin. Often the simpler spelling is chosen by means of enharmonic confusion , but this is not always correctly noted from a harmonic point of view. Thus, in theory, the ascending chromatic scale is realized with cross notation, while the descending chromatic makes use of Bes. In practice, however, this notation system does not necessarily apply. As such, there is no uniform understanding of how harmonic relationships are ultimately interpreted and correctly noted. Regardless of this, interval relationships can be interpreted differently.

Diatonic and chromatic intervals

Diatonic intervals are those that occur between the pitches of a diatonic scale, i.e. prime, major and minor second, major and minor third, (pure) fourth and fifth, minor and major sixth, minor and major seventh.

Chromatic intervals are all excessive and diminished intervals, e.g. B. Excessive prime, diminished and excess second, diminished and excess third, etc.

The tritone is a special case . Although it occurs in the diatonic as an interval between the fourth and seventh degrees of the major scale, on the other hand it is assigned to the chromatic intervals as an excessive variant of the pure fourth.

Chromatic scale

A chromatic scale is obtained through an ascending and descending melodic sequence of twelve semitone steps within an octave. Based on the equal tuning , its interval structure is independent of the note with which it begins. So it has no keynote and represents a material scale from which so-called usage scales can be obtained by selection. It is only in free tonality or atonal twelve-tone music that it becomes a scale of use and takes the place of the diatonic major and minor scales.

In classical instrumental music, the chromatic scale was also often used as a material for a virtuoso drive, which is why playing the chromatic scale is part of the basic technical training of every instrumentalist.

The notation of the chromatic scale can be done according to different principles. Since around the middle of the 19th century, a notation that tries to get by with the smallest possible number of accidentals became increasingly popular. In addition, however, there has long been an endeavor in the practice of composition to clarify the embedding in tonal contexts through the notation.

Simplified notation of the chromatic scale

With this notation, which is common today, the ascending scale is only notated with the help of heights and the descending scale only with the help of humiliations. The notation is particularly simple if you choose c as the starting tone:

Listening example : Chromatic scale from c: Play full octave ascending and descending ^?^/ⁱ .

Notation of the chromatic scale in the major-minor system

On November 16, 1864, there was a report in the Allgemeine musical newspaper about Simon Sechter's harmony system, which made it clear that even then there was by no means a uniform understanding of how the chromatic scale should be notated. The following notation was largely standard for Bach and other classical musicians, with a number of exceptions, which are not explained here, are also important.

In practice, the spelling of all diatonic levels is retained and is not replaced by enharmonically confused levels.

In an ascending, chromatically extended major scale ("chromatic major scale" for short), all diatonic pitches are raised up to the sixth. Instead of the sixth, the seventh diatonic pitch is lowered. Example: Chromatic major scale from c 'upwards

In a descending chromatic major scale, all diatonic pitches are lowered down to the fifth. Instead of the fifth diatonic pitch, the fourth diatonic pitch is raised. Example: Chromatic major scale from c '' down. If you add the F sharp from G major (dominant) and the D flat from F minor (subdominant) to the C major and C minor scales , you get these twelve levels.

In the ascending chromatic minor scale, all diatonic degrees are raised except the first. Instead of raising the first diatonic pitch, the second diatonic pitch is lowered. In contrast to this, however, some composers (e.g. Beethoven, Chopin) often write a raised first level instead of the lowered second level in ascending tone sequences. Example: Chromatic minor scale from A 'up

In the descending chromatic minor scale everything is as in the ascending minor scale or as in the descending major scale of the same name. Example: Chromatic major scale from a '' down

Tone assignment of a keyboard in a mid-tone tuning

Historical notation of the chromatic scale in a mid-tone tuning

Although the first well-tempered tunings appeared at the end of the 17th century , it was well into the 18th century before they were able to prevail against the previously common mean-tone tuning . Until then, the available tone supply and the corresponding notation was limited to what is shown in the adjacent illustration of a mid-tone keyboard. The tones of D flat, D flat, A flat and A sharp were not available at that time (or only as enharmonic variants that were unsatisfactory in terms of sound), so that certain keys could only be represented imprecisely. Correspondingly, Johann Mattheson described the basic triads of the relevant keys as follows in 1713: b major = b-e-flat-f sharp, f sharp major = f sharp-b-c sharp, g sharp minor = g sharp-b-flat, b minor = b-c sharp-f, g sharp major = g sharp-c-es, c sharp major = c sharp-f-g sharp, flat minor = eb-f sharp-b.

Diatonic and chromatic semitones

The semitones of the chromatic scale can be defined differently. If the equal-scale tuning that is most common today is not used, the diatonic and chromatic semitones are different in size. In singing schools that promote variable intonation with pure intervals, a distinction is made between diatonic and chromatic semitone steps because of their different sizes.

Diatonic semitone steps are: c-des, cis-d, d-es, d-e, ef, f-gb, f-sharp-g, g-a-flat, g-sharp-a, ab, a-sharp-b, hc.

Chromatic semitone steps are: c-c sharp, d flat-d, d-d flat, es-e, e-cis, f-f sharp, g-sharp, g-g sharp, a-flat-a, a-a sharp, bh.

Applied to our grading system, the following applies:

Semitones (actually not the tone, but the small second interval ) on adjacent positions in the staff are diatonic, semitones on the same position in the staff are chromatic.

Example Passus duriusculus . Chords here after WA Mozart Misericordias Domini in D minor Chromatic (KV 205 a).

The semitones in the bass are

c → h: diatonic
h → b chromatic
b → a diatonic
a → as chromatic
as → g diatonic

If the use of natural intervals occurring in the overtone series is assumed, the whole tone must be divided into steps of different sizes. Is z. For example, if a chromatic intermediate step (f sharp) is inserted between f and g, the whole tone fg splits into a chromatic (f-f sharp) and a diatonic semitone (f sharp-g). The size of these semitones depends on the tuning system used.

The frequencies of the chromatic scale in different moods

In the following, the frequencies and frequency relationships of the tones of the chromatic scale are enumerated and compared to the pure tuning in equal tuning. The concert pitch a 'is assumed to be 440 Hz.

Equal tuning chromatic scale:
Name of the tone	c	cis / des	d	dis / it	e	f	f sharp / total	G	g sharp / as	a	ais / b	H	c
Frequency [Hz]	261.6	277.2	293.7	311.1	329.6	349.2	370	392	415.3	440	466.2	493.9	523.3
In cents	0	100	200	300	400	500	600	700	800	900	1000	1100	1200
Descending chromatic scale of the pure tuning of C major:
Name of the tone	c	of	d	it	e	f	f sharp	G	as	a	b	H	c
Frequency [Hz]	264	281.6	297	316.8	330	352	371.25	396	422.4	440	475.2	495	528
In cents	0	112	204	316	386	498	590	702	814	884	1018	1088	1200

Pythagorean mood

The pitches differ depending on the tuning system, shown here using the example of F sharp and G flat. Compared to the equal tuning, the purely tuned F sharp is lower and the butt is higher. In Pythagorean or mid-tone tuning, the F sharp is higher and the butt is lower than with the same tuning.

The Pythagorean tuning wins all tones, including the large whole tone, only by combining the first two intervals of the overtone series, octave and fifth, and only knows the large whole tone (frequency ratio 9: 8). This is divided into a chromatic semitone with a frequency ratio of 2187/2048 (corresponds to approx. 114 cents ) and a diatonic semitone with a frequency ratio of 256/243 (approx. 90 cents). The Pythagorean chromatic semitone is also called the apotome , the diatonic Limma . Since the chromatic semitone is greater than the diatonic in the Pythagorean tuning, f sharp is higher than g flat here, for example . The theory that was widespread in the 20th century is based on this intonation that the leading tone (for example F sharp) should actually be intoned higher than in the equal pitch.

Pure mood

The pure tuning is based on the fourth (frequency ratio 4/3) and also on the pure major third (frequency ratio 5/4), which recurs an octave higher than the interval between the eighth and tenth partial tones of the overtone series. There the major third forms the product of the major whole tone (frequency ratio 9/8) and the small whole tone (frequency ratio 10/9) (9/8 * 10/9 = 90/72 = 5/4). The diatonic semitone of the pure tuning is the bridging interval between the major third and fourth. Its frequency ratio is calculated to be 16/15, which corresponds to about 112 cents. The major whole tone can be split into the diatonic semitone and the major chromatic semitone with (frequency ratio 135/128) (approx. 92 cents) and the small whole tone into the diatonic semitone and the small chromatic semitone with (frequency ratio 25/24) (approx. 71 Cent).

Both variants of the chromatic semitones in pure tuning are smaller than the diatonic semitone, so that now, for example, f sharp is lower than g flat . In the context of historical performance practice and based on the consideration that the consonance heard d-f sharp is based on the pure major third, this variant is preferred in tonal music today on instruments with flexible intonation.

Mid-tone mood

In mid-tone tunings , one theoretically uses an interval of 76 cents for the chromatic semitone and 117 cents for the diatonic semitone.

Unevenly tempered mood

So-called well-tempered tunings such as the Werckmeister tuning or the Kirnberger tuning lie in the intonation between the equal and mid-tone tuning.

Web links

Commons : Chromatik - collection of images, videos and audio files

Individual evidence

↑ Sheila Romeo: Complete Rock Keyboard Method: Mastering Rock Keyboard . 1999, ISBN 0-88284-982-4 , pp. 42 .

^ Rudolf Louis, Ludwig Thuille: Harmonielehre . Severus Verlag, 2012, ISBN 978-3-86347-306-8 ( books.google.at [accessed October 24, 2015]).

^ Richard Böhm: Symbolism and rhetoric in the songs of Franz Schubert. Volume 3 of Viennese writings on stylistics and performance practice . 2006, ISBN 3-205-77500-7 , pp. 148 ( limited preview in Google Book search).

↑ “There is also an insight into a plethora of unsolved problems posed by 19th century harmony, if we want to know about it at all (review by Detlef Gojowy In: DieMusikforschung. 1997, Heft. 1, pp. 126–127. ) “B. Hirszenberg: Chopin's Harmonics. Chromatics in relation to tonality . 1995, ISBN 3-931430-00-6 , pp. 204 .

↑ "Theoretical About Sixth's Harmony System [...] Of no less importance in its details, almost too minute, but definitely new is Sechter's theory of chromatics, which he bases on the relationship with minor keys and on the degrees occurring twice in the same. In A minor, as noted earlier, F, F sharp, G and G sharp are entitled to their homeland and allowing them to follow one another in a consistent direction (up or down) contradicts neither the properly understood theoretical (fundamental) law nor the ear. However, in addition to A minor, E minor and D minor are also related to C major. This means that the tones and sequences c, c sharp, d, dis (e), such as b, b, c, c sharp, (d) appear in a relationship to C major. It will not be difficult for the reader to construct the whole upward chromatic scale of C from the above sequences. For the descending one, the sixth has minor keys ready, which, although in a different kind, are related to C major. The keys are C minor, F minor and G minor. In a broader sense, all those are related after sixth to a certain key which contain the tonic chord of the first key at some level with the same name (even if not always internally the same, e.g. as "impure"). The occurrence of the C major accord in F minor is evident - in G minor it is evident from the above; The fact that C major is related to C minor does not require further discussion, although Sechter gives reasons for this as well. Now the downward-going chromatic scale of C is constructed from C minor: (c), b, b, a, a flat, (g), - from G minor: (g), f sharp, f, e, es, d, and from F minor: f, e, es, d, des, c. We do not want to try to authenticate the unity established in this way as an absolute one, but no one will deny the family relationships of the three groups. Sechter builds a formal teaching of chromatic chord progressions on the above chromatic scale (which is also produced in minor according to similar laws), and with great acuteness. But we do not want to deny that in this area the boundary between what is permissible and what is inadmissible is becoming a very fluid one, since other circumstances are too important. The essential benefit of all these studies, which necessitate a great deal of elaboration, is that, first, the pupil is led out of certain constantly trodden paths to many less frequently used ones, but without being able to get lost. Furthermore, the study of chromatics in particular grants a great deal of certainty in musical spelling, which is known to be not at all easy for beginners and which has not yet been treated equally in all points in the music world. Especially in the more difficult keys of chromatic steps, the strangest inaccuracies can often be found in printed music with regard to whether a tone is e.g. B: to be noted as ais or b, cis or f. According to the doctrine of the Enharmonik, Sechter leads the pupil, as it were, to the highest points of the harmonic, to the watershed of three areas, where one overlooks the realm of all keys. Each diminished seventh chord allows for a resolution into eight *) essentially different keys; but since there are only three differently sounding accords of this kind in the tempered system, this denotes the entire area of the 24 keys. "Frits Knuf (Ed.): Allgemeine Musikische Zeitung . tape 2 , no. 46 . Michigan 1864, p. 9 ( limited preview in Google Book search).

^ Rudolf Louis, Ludwig Thuille: Books of Music . tape 2 , 2012, ISBN 3-86347-306-X , pp. 282 ( limited preview in Google Book search).

↑ Hans Zacharias: Books of Music - Diatonic Composition Theory - collection of examples of early music . tape 2 , 2008, ISBN 3-938622-27-X , pp. 168 ( limited preview in Google Book search).

↑ NG Halt: Textbook of Harmony . Ripol Klassik, 1986, ISBN 5-458-33218-0 , p. 296 .

^ Johann Mattheson : The newly opened Orchester . Benjamin Schiller's widow im Thum, Hamburg 1713, p. 60 .

↑ (more precisely) table: intervals of pure mood

↑ Modern strings are taught to sharpen leading tones (to approximate the leading tone G sharp in G sharp A or the A flat in A flat G to the root note). This "expressive intonation" is said to go back to Pablo Casals. After Ross W. Duffin: How Equal Temperament Ruined Harmony (And Why You Should Care). WW Norton & Company , New York NY 2007, ISBN 978-0-393-06227-4 ( Excerpt ( Memento of the original from March 16, 2015 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original - and archive link according to the instructions and then remove this note. ). @1@ 2Template: Webachiv / IABot / kilchb.de

[Romeo-1] Sheila Romeo: Complete Rock Keyboard Method: Mastering Rock Keyboard . 1999, ISBN 0-88284-982-4 , pp. 42 .

[2] Rudolf Louis, Ludwig Thuille: Harmonielehre . Severus Verlag, 2012, ISBN 978-3-86347-306-8 ( books.google.at [accessed October 24, 2015]).

[Richard-3] Richard Böhm: Symbolism and rhetoric in the songs of Franz Schubert. Volume 3 of Viennese writings on stylistics and performance practice . 2006, ISBN 3-205-77500-7 , pp. 148 ( limited preview in Google Book search).

[Hirszenberg-4] “There is also an insight into a plethora of unsolved problems posed by 19th century harmony, if we want to know about it at all (review by Detlef Gojowy In: DieMusikforschung. 1997, Heft. 1, pp. 126–127. ) “B. Hirszenberg: Chopin's Harmonics. Chromatics in relation to tonality . 1995, ISBN 3-931430-00-6 , pp. 204 .

[Allgemeine-5] "Theoretical About Sixth's Harmony System [...] Of no less importance in its details, almost too minute, but definitely new is Sechter's theory of chromatics, which he bases on the relationship with minor keys and on the degrees occurring twice in the same. In A minor, as noted earlier, F, F sharp, G and G sharp are entitled to their homeland and allowing them to follow one another in a consistent direction (up or down) contradicts neither the properly understood theoretical (fundamental) law nor the ear. However, in addition to A minor, E minor and D minor are also related to C major. This means that the tones and sequences c, c sharp, d, dis (e), such as b, b, c, c sharp, (d) appear in a relationship to C major. It will not be difficult for the reader to construct the whole upward chromatic scale of C from the above sequences. For the descending one, the sixth has minor keys ready, which, although in a different kind, are related to C major. The keys are C minor, F minor and G minor. In a broader sense, all those are related after sixth to a certain key which contain the tonic chord of the first key at some level with the same name (even if not always internally the same, e.g. as "impure"). The occurrence of the C major accord in F minor is evident - in G minor it is evident from the above; The fact that C major is related to C minor does not require further discussion, although Sechter gives reasons for this as well. Now the downward-going chromatic scale of C is constructed from C minor: (c), b, b, a, a flat, (g), - from G minor: (g), f sharp, f, e, es, d, and from F minor: f, e, es, d, des, c. We do not want to try to authenticate the unity established in this way as an absolute one, but no one will deny the family relationships of the three groups. Sechter builds a formal teaching of chromatic chord progressions on the above chromatic scale (which is also produced in minor according to similar laws), and with great acuteness. But we do not want to deny that in this area the boundary between what is permissible and what is inadmissible is becoming a very fluid one, since other circumstances are too important. The essential benefit of all these studies, which necessitate a great deal of elaboration, is that, first, the pupil is led out of certain constantly trodden paths to many less frequently used ones, but without being able to get lost. Furthermore, the study of chromatics in particular grants a great deal of certainty in musical spelling, which is known to be not at all easy for beginners and which has not yet been treated equally in all points in the music world. Especially in the more difficult keys of chromatic steps, the strangest inaccuracies can often be found in printed music with regard to whether a tone is e.g. B: to be noted as ais or b, cis or f. According to the doctrine of the Enharmonik, Sechter leads the pupil, as it were, to the highest points of the harmonic, to the watershed of three areas, where one overlooks the realm of all keys. Each diminished seventh chord allows for a resolution into eight *) essentially different keys; but since there are only three differently sounding accords of this kind in the tempered system, this denotes the entire area of the 24 keys. "Frits Knuf (Ed.): Allgemeine Musikische Zeitung . tape 2 , no. 46 . Michigan 1864, p. 9 ( limited preview in Google Book search).

[Rudolf_Louis-6] Rudolf Louis, Ludwig Thuille: Books of Music . tape 2 , 2012, ISBN 3-86347-306-X , pp. 282 ( limited preview in Google Book search).

[Hans_Zacharias-7] Hans Zacharias: Books of Music - Diatonic Composition Theory - collection of examples of early music . tape 2 , 2008, ISBN 3-938622-27-X , pp. 168 ( limited preview in Google Book search).

[NG_Halt-8] NG Halt: Textbook of Harmony . Ripol Klassik, 1986, ISBN 5-458-33218-0 , p. 296 .

[9] Johann Mattheson : The newly opened Orchester . Benjamin Schiller's widow im Thum, Hamburg 1713, p. 60 .

[10] (more precisely) table: intervals of pure mood