3 schools of harm question

Question 1

Figured bass general opening

Answer 1

Practical concerns of performers, variety of type of treatise, Yes reflects bass driven, that is, harmony driven music, but starts of instucting the continuo player how to fill in voices.
This is reflected in variety of publication type. Appeared with published music–such as Viadana, (1602) as late as Telemann 1703.
Some focus more on performing figures
Others (the interesting onces I will discuss) apply all this to composition.

Question 2

Earliest in itself figured bass

Answer 2

Earlier sheet to itself–Biancardi 1607

Question 3

Distinction in treatise types

Answer 3

Focus on performance vs. composition would effect rules–Much looser in performance

Question 4

Compositional use pre Niedt

Answer 4

Antonio Brioschi, Le regole per il contrapunto… Rule of the octave leading to I by way of root position IV and V chords.
Penna, I primi albori musicali (1672), and Biancardi breve regole, give other harmonizations. Penna uses more inverted triads.

Question 5

First Figured bass writer

Answer 5

Friedrich Niedt Musikalische Handleitung, (1706)
Most detailed account of how mastery of figured bass can lead step by step to composition
(partimenti tradition a bit no?)

Question 6

Niedt details

Answer 6

Describes three triad spacings: Radix Simplex (closed), Radix Aucta (close plus octave), Radix diffusa (Open spacing).
Gives rules for voice leading, such as in a 6/5 chord, the “5th” must be prepared.
Rules for suspensions, 7-6, with 7th prepared.
However, the root position (seven chord) is seen as just a chord, and the 7th need not be prepared.
(Basic set of rules)
Its ninth chapter is titled “On Preludes and Chaconnes and How They May Be Made From a Simple Thorough-bass.” Niedt provides the student a “simple bass without great adornment,”

Question 7

Second figured bass writer

Answer 7

Johann David Heinichen, Der General Bass in Der Composition, (1711, 1728)

Question 8

Heinichen basics

Answer 8

MOST ENCYCLOPEDIC and thourough (960 pages!!)
Lists huge number of possible chords (Really chromatic onees too)
Organized not by inversion, but by figures:
This is a key element and shortcoming of figured bass

Question 9

Heinichen further

Answer 9

Hence, Triads, chords of the 6th (including 6/4/3), of the 4th, 5th, 7th 9th, etc.
Includes Augmented and diminished chords of various intervals, including what we call Augmented 6th chords.
Voice leading discussed on a chord by chord basis. But the rules are still those we teach today, just made much more complicated without the concept of chord inversion.
Also includes a rule of the octave but with more inversions of I IV and V, as the most important triads.
(Does recognize inversion as leading to the 6 chord (but does not reflect how he categorizes it)–this only appears in the later parts of the treatise from 1728)

Question 10

Short additional fb 2.5

Answer 10

François campion Traité d’accompagnement et de composition (1716)
Includes a fuller rule of the octave, for ascending and descending scales, involving inversions of triads and seventh chords.

Question 11

C.P.E. title

Answer 11

Versuch uber die wahre art etc. Part 2, on thorough bass, 1762

Question 12

CPE and Rameau

Answer 12

Claims to be contrary to Rameau;
But clearly does not ignore Rameau and chord inversion
Chapters grouped more according to chord type (all triad inversions first, then 7 chords, suspensions, etc.)

Question 13

Smattering of CPE rules: hence summary of figured bass tradition; basics

Answer 13

Many the same as in Niedt, and still taught today)
(memorize these details: Culmination of the traditions, so spit out some of the rules!)
First discusses chord spacing and doubling of triads.
Rules for avoiding parallel octaves and fifths, again, contrary motion in hands as good principle.
So similar stuff that we teach today in keyboard harmony

Question 14

CPE some nice subtle details still taught

Answer 14

Hidden octaves and fifths also mentioned (between one voice and upper voice, especially upper voice and bass).
Common exceptions still taught (5ths if top voice moves by step, 8vs if half step up or step down).

Question 15

DON”T FORGET

Answer 15

How the fact that these guys are composers influences

Question 16

More CPE suggestions

Answer 16

Chords succeed…in the most direct manner” (smoothest possible voice leading).
Discussion of pitfalls of parallel triads, formula for voicing them correctly (such as V-vi, with vi containing a doubled 3rd).

Question 17

CPE on 6’s and

Answer 17

6’s and 6/4s
Discussion of Chord of 6th clearly describes it as an inversion of a triad, the bottom note being flipped upwards to become the 6th.
Rule 10 in this chapter (paralel 6 chords–doubling must be changed to avoid parallel 5ths).
But, rule 11, these are more easily performed in 3 voices. (Again, exactly what we teach today). (so great! So practical)
Mentions 5-6 and 6-5 LIP, but without sequencing them.
6/4 chord
Again, the still taught rules–double bass (5th), etc.

Question 18

Rameau Treatise

Answer 18

Traité de l’Harmonie (1722)

Big new things: Starts with equal div of string (theoretical)…(way way more theoretical than FB treatises at least)….Chord inversion….and chord succession

Question 19

Rameau INVERSION!!!!

Introduces the concept of chord inversion.

Answer 19

The root position chords are seen as basic. Rules given for their voice leading can be applied to inversions. The types of chords are finally organized as we now organize them, instead of by figure.

Question 20

Rameau foundations 1

Answer 20

Rameau divided strings into parts instead of comparing different string lengths and ratios.
Generated intervals of octave, 4th, 5th, 3rds and 6ths directly or indirectly from these intervals.
String divided into equal parts, generating what today we recognize as the harmonic series, but that phenomenon was not yet discovered.
Indirectly generated intervals: Minor 6th, “shadow of the 5th,” so partial (using our modern understanding) 3 to 5. Minor

Question 21

Rameau foundations 2

Answer 21

On Harmonic Division or the origin of chords
Divides a single string into proportions (instead of earlier approach of comparing string lengths) (older technique)
Major triad is 4:5:6, minor derived as 10:12:15
Comparison of both from multiplication and cross multiplication of the figures results in 20:25:30 for major and 20:24:30 for minor. (to compare rations)

Question 22

Usefullness of Rameau’s inversion theory seen…

Answer 22

We have “major” and “minor” dissonance, that always resolve the same way.
The Dominant 7 chord
Is described as having a major dissonance (the 3rd) and a minor dissonance (the 7th), which must resolve up and down by step respectively.

Question 23

Rameau more chromatic chords: case

Answer 23

Diminished 7 chords
These are described as occurring via borrowing:
The root of a dominant 7th is moved up by half step, this results in a vii4/2 chord. But this inversion is considered by Rameau as basic.
This does illustrate the function of the diminished 7 and its interchangeability with the dominant 7 quite well.

Question 24

Rameau . CHORD SUCCESSION!!! Why can he do it?

Answer 24

This is the first major discussion of rules of chord succession. Whereas in figured bass treatises, the voice leading issues of a given bass line and figures were discussed, here the question of which chords should follow which is taken up.
What allows Rameau to do this is his notion of chord inversion. Only with chord inversion can one talk about the progression not simply of chords, but of roots.

Question 25

Rules for chord successions

Answer 25

Some odd. Bass motion up by second is explained through double employment. The progression IV to V is seen as short for IV, ii, V (roots moving by third and fourth). OR IV is considered as an incomplete ii6/5.

Question 26

Rameau Cadences

Answer 26

Rameau defines a Perfect Cadence, which is what we call an authentic cadence. But goes further, describing any harmonic progression resolving down by fourth or up by 5th as a Perfect Cadence.

Question 27

Rameau later--1st new thing

Answer 27

Nouveau Système de Musique Théorique (1726) Generation Harmonique (1737) III. THE MINOR TRIAD PROBLEM AND IV Rameau’s effort is the first of many that comes up with an intriguing but scientifically false explanation of the minor triad.

Question 28

Minor triad issue lets Rameau...also quirks here

Answer 28

This idea allows Rameau to introduce IV as an important chord, and the I-IV-I progression as more basic. The progression I, IV, V, I, can thus be explained as I, IV, and V, I, with double employment again being used to explain IV to V. In the later writings, the notion that every progression of two chords is a cadence, is more emphatically stated and elaborated.

Question 29

Followers of Rameau: general reflection

Answer 29

(Even fundamental to many recent textbooks--reviews Rameau vs. Schenker trend--chords and inversion vs overall counterpoint and prolongations)

Question 30

Specific followers:

Answer 30

Mozart’s pedagogical technique; concept of harmonizing with root position triads first, shows influence of Rameau. Fundamental bass, then elaborated with inversions. Georg Andreas Sorge, Vorgemach der musicalischen Composition, oder Anweisung zum General-Bass. (1745-47) Giuseppe Tartini:"Trattato di musica secondo la vera scienza dell'armonia'" (Padua, 1754) Profession as violinist aware of difference tone created by playing double stop. True root of inverted chord would be difference tone.

Question 31

More followers of Rameau

Answer 31

Johann Friedrich Daube, General Bass in Drei Akkorden. (1756) Posits three fundamental harmonies, Tonic, “fourth” and “fifth” chord. Other chords derived from them. IV to V considered normal ascending step progression. No need for other explanation. But does not allow IV to I progression This thought of as I to V in key of IV. Describes melody harmonization; first with root position, I IV or V chords. Then bass re-written with inversions. Other chords added. Christoph Nichelmann, Die Melodie nach ihren Wesen, (1755) Emphasizes independent voices Reflecting primacy of root position triads, rewrites Bach sarabande entirely with root position triads. Friedrich Wilhelm Marpurg (COMIC ASIDE) Considered himself the bearer of Rameau’s legacy in Germany and bitterly fought with all who sought to contest that with him But in reality, he had a imperfect understanding of Rameau, and his writing much more reflected the German figured bass tradition

Question 32

One more Rameau follower

Answer 32

J.P. Kirnberger, Die Kunst der Reinen Satzes (1771-79) Describes inversions of root position triads Leaves out the augmented triad but discusses the diminished. Describes “essential 7 chords” as opposed to inessential 7th dissonances. Also describes non essential dissonances such as suspensions; in this regard this is a major improvement on Rameau, for who treated suspensions as another group of chords. Kirnberger even discusses the 6/4 as a double suspension (hence, our cadential 6/4).

Question 33

Scale Step Theory and Roman Numerals | Basics

Answer 33

Especially Weber--empiricist/psychological type attitude, just observe how the phenomenom works and describe it. Don’t have to find scientific origins. Just describe! ALSO, OKAY, THE BIG POINT IS WE GET ROMAN NUMERALS! SO THINKING NOT IN TERMS OF SUCCESSION BY INTERVAL BUT IN TERMS OF IDENTITY AND FUNCTION OF EACH SCALE STEP

Question 34

First scale stepper

Answer 34

I. Georg Joseph Vogler, Tonwissenschaft und Tonsetzkunst (1776).

Question 35

Vogler's Innovation. Some conclusions of that.

Answer 35

Each scale degree given a triad, each of which is considered fundamental. That is vi6 is not an alternation of I, and ii6 not an alternation of IV. Uses Roman numerals, in this case, all large.

Question 36

More curiosities in Vogler, and one other thing...

Answer 36

Dissonance treatment: Suggests that any dissonant combination can be reduced to a triad (this taken from Vilotti). haha Mehrdeutigkeit Discusses this, which is what we call enharmonic reinterpretation of chords. Specifically, of leading tone diminished sevenths and of German sixth. (YAY ENHARMONIC REINT)

Question 37

2nd Scale stepper

Answer 37

Gottfried Weber, Versuch einer geordneten Theorie der Ton (1817-21).

Question 38

Weber's outlook

Answer 38

The preface states that the book will not attempt any attempt to derive harmony from string divisions or acoustics. Rather, the chords are simply taken as existent, and the job of the theorist is not to derive them, but to study how they are used and describe it.

Question 39

Weber's new terms and notations

Answer 39

Then introduces the scale, and names the scale degrees Tonic, supertonic etc…FINALLY GET THESE NAMES FOR SCALE DEGREES Uses large and small roman numerals, with the circle for diminished.FINALLY THE SMALL RN’S

Question 40

Weber on Chord succession

Answer 40

Does not give specific rules for chord progression (following the approach of simply analyzing what composers do), but gives the Tonic, Dominant and Subdominant central roles. Shows by example how ii, ii, vi or vii can substitute for or preceed I, IV and V. This is very much like our modern notion of Tonic, Dominant and Predominant functions.

Question 41

A final Weber innovation

Answer 41

Discussion of Modulation: Describes distance or closeness between keys by means of a Tonarten verwandtschaft. This diagram is close to Riemann’s Tonnetz. Uses this to analyze the highly chromatic opening of Mozart’s Dissonance quartet.