This page is an illustration of What does means play in tune on violin
Harmonics technique yields eight notes out of the twelve chromatic scale notes.The four missing notes are in yellow
Cette œuvre (Intonation exercices on violin, de Alain lefébure) est libre de restrictions de droits d’auteur connues
Fortunately or unfortunately we can’t definitely answer : it depends on context.
The great french violinist Jacques Thibault was sometimes criticized for his « out of tune » intonation but, as pointed out by one of his famous students,Ivry Gitlis , : »playing the flat very low » he added color
In the art of violin , Laurent Korcia likes the slightly hoarse sound of Isaac Stern who « played out of tune but sounded in tune ».
Mind you, we are discussing international soloists, not amateur fiddler . Yet,their intonation was sometimes dissentious
So,let’s try to make things clearer
first let’s remind the deaf acoustician Joseph Sauveur’s discovery in 1701 on harmonics sounds ,
| Fundamental sound multiplied | By | gives |
| 2 | The octave | |
| 3 | The fifth | |
| 4 | The octave | |
| 5 | The Major third |
(division by 2 may be necessary to remain in a octave span)
Violinist ,violist ,cellist and double bassist have three choices
based on a string length division
and by
(actually a 12 th divided by 2 to get a fifth )
12 fifths slightly overtake 7 octaves ( B# is higher than C)
it consist of
adds division par 5 to the Pythagorean system to get natural Major third of the harmonic series .
This addition brought great disturbances into the system but enhanced the Major and minor chords (with no beats)
However this advantage est limited to 3 thirds the primary chords in major keys
.
In this system
Globally semi-tones are very large and therefore without or little attractive power
These inequalities make the system improper to modulations
NOTICE
These 3 systems are different from theory with its 4 commas diatonic semi-tone and its 5 commas chromatic semi-tone but values are near Pythagorean ones .
It must be pointed out that those systems are mainly based upon mathematics,not on physics.
From this summary ,we can draw some evidences
So « partly »is here an important word since we can’t use this system at any time .
Threfore, performer has permanently to make a choice
However , acoustic systems in the intonation work is relative
Since
Besides acoustical systems ,the most important thing to discuss.
are missing but the
Conclusion
As for harmonics 7, Tartini’s third tone is not really scientific since it is not easily reproducible but it’s a mean to search a clean intonation and a pretty sound.
The tonal system is supposed to be a simplification of the older modal system since it only consists of two modes namely the Major and minor modes. That is a kind of « swindle » since actually the so called minor mode consists of three derivative versions from old minor church modes.It would be more « honest » to state that key center has two possible tonics a major sixth apart. (CM-am)
It is not easy to define the tonal system which is a slow process so let’s assume few things
(all those chords are called perfect because the bottom – top notes form a perfect fifth ) –
We can represent the tonal system as a sliding rule with a long series of fifths from Cb(7 flats) to C#(7 sharps) on the fixed part of the rule and our seven fifths ( from IV to vii) on the sliding part of the rule. The tonality is I on the sliding part and the key signature is on the fixed part facing I
Notice that numbered 5-6-7 tones on the right sound like the 7-6-5 ones on the left thanks to enharmony So the chain is closed forming a circle.
Thank to the sliding,we can see how a chord can easily be reinterpreted for modulation.
Unfortunately minor mode obscures this very simple system.
If we want to write a mirror scale (opposite) to the major scale with respect to the key signature and Tone -semitone distribution we must start with the third degree of the scale which produces a minor descending scale .
No ascending minor scale fits to these two conditions; none respects the tone -semi tone distribution.
we must start the scale on II, III or VI to have a minor third but none would produce a leading tone which require a Major third . Therefore the second tetrachord can’t be symmetric to the first one and we must add some alterations.
Notice the symmetric D mode (Dorian) which was the most frequent minor mode used during the baroque era.
With our CM scale
II (D) needs C#, III(E)requires D#, and VI(A) G# which are not the direct continuation of the fifths circle.
Mind you, that is an explanation of the problem but not the reality:Both D and E modes are to be transposed on A so only G# and F# (coming from the B of the D mode) appear.
Adding a leading tone to the a minor scale creates an unmelodic augmented second interval so the VIth degree is altered (the borrowed B from D mode) to enhance the melody
So, the minor scale has three aspects
1-Natural or descending melodic or Aeolian mode A-BC-D-EF-G-A which does not have a leading tone.
2-Harmonic: A- BC- D -EF—G#A which provides a leading tone and a bad augmented second.
3- Ascending melodic A-BC-D-E-F#-G#A. with a leading tone and an altered VI th degree to correct the unmelodic augmented second
The complete minor scale (natural plus the two ascending scales)produces 13 triads
Why A rather than D or E?
From the natural minor scale the A scale need F# and G# to complete the ascending scale.
The D (Dorian)scale would request Bb and C# and the E (Phrygian) scale would need F# ,C# and D#
So A is the nearest from the Fifths circle.
Since the A minor scale has no alteration it’s associated to the C major and our sliding rule can be expanded like this
So, to find the key signature of a minor scale one must refer to the relative major scale or the third degree of the minor scale.
It must be pointed out the reverse image of the major mode
The major numeration is In yellow
Rationale in tonal music is to consider a scale as a Pentachord and a tetrachord (with a common tone)
For a given tonic, all notes of the pentachord but the Third are common to all tonal kind of scales
Tetrachord has two movable notes (The sixth and seventh degrees)
The Saxhorns group is the example of confusing writing previously discussed
This group has historically been subjected to addition and subtraction of instruments but the most common range includes
Flugelhorn Eb (or sopranino)
Flugelhorn Bb ( soprano or contralto )
Alto Saxhorn Eb ( or Ténor Horn)
Baritone Bb ( or Tenor Horn)
Basse Bb
Contrabass Eb
Contrabass BBb
Their theoretical range is similar to the trumpet one .Actually only Flugelhorn (Bb) and Baritone have a satisfying full range when played by a concertist.
All flugelhorns and Alto Saxhorn (Eb) share the same standard range but the Eb small flugelhorn is really efficient in a smaller range (One octave (E-E) .
Since these instruments are dedicated to the upper parts they logically use the treble clef
Bass and contrabass saxhorns (standard range below) playing the bass line are logically written with bass clef.
However Baritone (also named tenor and therefore written with treble clef) sharing Bass register a single sound are differently written ,while Bb Bass using the same written note and clef as BBb contrabass sound differently .
1 Flugelhorn Eb -2 Flugelhorne Bb 3 Alto (tenor Eb horn) 4-Contrabass Eb 5-Contrabasse BBb
An historical ambiguïty results from the old classification; Baritone beeing considered as a Bass should had been written with bass clef
Music notation software have solved most transposition problems. However the choice of a piece tonality according to a transposing instruments panel remains an issue; so does the choice of a transposing instrument according to the tonality of the piece.
Transposition is a simple transfer of the fifths cycle.Let’s imagine a sliding rule:The fixed (yellow) part reads tonalities of the piece while the sliding (blue) part reads the instrument tonalities.
So willing to write an obsolete Db piccolo part for an Bb (2b) melody
I place the instrument C facing Db(piccolo tonality) on the fixed part ;to Bb (piece tonality) tallies (A) instrument(blue) tonality.
This needless method for a single instrument becomes a precious tool when several transposing instruments are involved.
First of all it should be reminded that the writing confines tonalities to 7 accidentals(From Cb(7b) to C#(7#)) in order to keep a relative legibility; Beyond those limits we use enharmonic writing
.
« Forbidden » zones are in red but enharmonic choice is also advisable if an easier alternative tonality is available.
For example , let’s take an Ab Maj (4b) piece
For an A clarinet the chart reads 7b key signature
The best choice would be to switch to a Bb clarinet (2b)
But ,should we use an A clarinet for any reason ,we ‘d choose the B Maj (5#) enharmonic writing.
Below is a correspondence chart
Neglecting the classical double flats/sharps notation we suppose an unlimited number of flats/sharps instead.
The result is always 12.
Double sharps equivalence
Notice the reverse direction of increasing flats and sharps
It easy to explain transposing wood wind instruments but ambiguities occur when brass instruments are concerned.
This post attempts to clarify brass instruments.
Reminders: As far as transposing instrument is concerned, the eye (l’ oeil) and ear (l’oreille) doesn’t perceive the same thing .
For example a trumpet player reads then plays « C » but audience hears B flat.
The aim of transposing instruments is to keep the same fingering with different sounding instruments.
For example with saxophone.
In both cases written notes and fingerings are the same but sounds differently
Range of woodwind instruments is clearly established in the lower register.
There are few exceptions
-One key added on bari sax that can reach A instead on Bb on other saxophones.
-one missing key on English horn which cannot play the Bb of the oboe.
For any instrument, range in upper register is subject to variations due to player ability.
This simplicity is due to the wood wind instrument sophistication through holes and keys which allow to select partials (or harmonics).
Difficulty of brass instrument paradoxically results from their simple construction
Brass are, historically speaking, a simple flared tube with an embouchure which allow the emission of a note ,the fundamental or pedal tone , and its partials or harmonics.Those added sounds are simply, if I may say, selected by the way the performer blows in the tube.
Sound 1 Fundamental or Pedal sound depends on the length of the tube.
A mere sight of the series reveals a first group of problems.
1-Lower notes progress by skip up to the seventh sound
2- The following conjunct notes are not necessary diatonic to the first sound.
3- Some diatonic sound are out of tune in our equal temperament system.
4-The series doesn’t provide all chromatic sounds.
Our modern instruments are
-The association of several tubes (trumpet, saxhorn) to supply the missing notes or the nearest notes of the equal temperament system.
This is done by mean of valves or slide that broaden the length of the initial tube
-or by fusion of two instruments, as seen in the french horn (F+Bb) or F-attached tenor trombone . The switching is made with a key.
Three valves provide seven combinations corresponding to seven bugles covering a tritone chomatically.
Therefore, a Bb trumpet is made of a (no valve) Bb trumpet, an A trumpet, an Ab trumpet.. and so on up to E (the lowest)
Those seven combinations are similar to the 7 positions of the slide of the trombone.
A crook is another possibility to lengthen the tube . We can,for example, turn a Bb trumpet into A trumpet but with many defects.
A fourth valve extends the tritone range to an octave (12 combinations) which ease the reach of pedal tones especially on saxhorns.
However, the fourth valve doesn’t necessary mean a larger range. It may only provide a better intonation but also bring new problems which possibly require more valves to solve the problem.
A second group of problems is due to the impossibility to cover the overall series with a single instrument.
Only instrument with large diameter can reach pedal tones.
Overcoming the harmonics 7 require a small diameter instrument
The Ratio diameter/length of the tube is also important to reach the pedal tones.
The shape of embouchure is another factor to select partials which determine the timbre. It may help to reach some pedal tone but too weak in strength to be efficient.
For instance a bass saxhorn (tuba ) can reach the contrabass ‘ lower notes but they are weaker, so the larger range of the bass is at the expense of the strength of lower notes.
However this instrument is only effective in the following range
It must not be confounded with the Bb low bass Tuba which uses a French horn embouchure. Its range is
sounding a second below.
That’s why we can hardly express the range of brass instruments. Furthermore,instrument makers have evolved lot of devices to enhance the playing which broaden the range and panel of instruments.
A third group of problems comes under instruments making and nomenclature.
The first difficulty is
-The name of instrument which doesn’t reflect the register. For example, the saxhorn Bass has the range of contrabass Eb but lower notes haven’t their strength.
-A given name correspond to different instruments according to countries For example » bombardons » mean either contrabass or include tenor bass. In an other hand the word tuba refer either to a non-homogeneous group of low brasses or a specific name for bass-saxhorn (in C or Bb) or Bb saxhorn contrabass.
–Confusion of register and instrumental group. Especially US Baritone (saxhorn) and euphonium Bb which is not a saxhorn; its timbre is different .
The complete range of Jupiter euphoniums should stops the confusion.
Another difficulty is to muddle tonality of the original tube and the concert tone.
For example, the trombone is a Bb instrument because in first position ( the shortest tube) it emits a Bb and its harmonics but it’s a C instrument (meaning non transposing) because the trombonist reads and hears Bb and so does the audience.
Caution:Modern tubas follow this logic contrary to former saxhorn- tubas that are transposing instruments.
At least some puzzling writing conventions
-No accidentals on the score for old instruments (Naturals)
-Treble clef for « tuben » according to the saxophones logic to keep a common fingering for different (lower Major sixth (Eb instrument ) or lower Major ninth(Bb instrument) Therefore transposing instruments). This practice is found in the salvation army brass band where all part but bass trombone part are written in treble clef
But the same part may be written in bass key sounding a higher minor third (Eb instrument ) or a lower major second(Bb) instrument
or -written in bass clef with concert tone ( non transposing instruments).
The problem often occurs with euphonium. The reason is more or less historical when trumpet players, only reading treble clef and playing three valve instrument, switched to euphonium especially with 4 valves.
Fingering of trumpet Bb is similar to the one of euphonium sounding a ninth lower.(An Eb euphonium would sound a sixth below)
(Figures refer to valves)
Another historical reason is the octaves determination according to Organ pipes length.
Sound threshold tallies with a 64 feet pipe
-32 feet pipe corresponds with lower C of a 5 strings double bass
-16 feet correspond with lower C of cello
-8 feet correspond with lower C of viola
Since Tenor voice was written an octave above its sound,(baritone saxhorn) is written in treble clef but sounds as a 16 feet pipe (an octave lower) On the other hand a bass saxhorn is written (as a bass) in bass clef ; Being a 16 feet pipe its sound register is similar to the baritone’s one.
Double bass is written like a bass but as a 32 feet pipe sounds an octave lower .
To summarize
Baritone-Bass____ Different Clef —Same sound
Bass -Double bass—Different sound—-Same clef
« Real » tuba player read bass clef and play concert pitch with a specific fingering which is different according to the tuba tonality). In open, trumpet plays G (treble clef) while tuba plays F'(bass clef). the 1-3 valve combination yields D to the trumpet but C to the tuba that can possibly replace the 1-3 by 4
Treble clef writing presents an ambiguous zone due to the large compass of euphonium
In the above example , are the framed notes written in concert pitch for a tuba player or in transposed notes written for a trumpet player?
So I advise to use the tenor clef to write those notes in concert pitch.
Euphonium is Bb according to the trombone logic explained above and therefore non transposing in bass clef
Nowadays tuba scores are generally written in concert pitch (Non transposing)
Since tuba range is very broad, professional tuba players, king of the transposition choice the best tuba for the given tonality .
For the composer the difficulty concerns writing for wind orchestra especially for amateur,unaware of transposition .
From the trumpet range.
The three valves saxhorn baritone is written an octave lower
F contrabass is written a fifth below the baritone and the Eb contrabass a sixth below the baritone but start on G
Bb bass and contrabass are written an octave below the baritone but start on G with a smaller span (2 octaves).
Tenor trombone shares baritone range while ‘euphonium and bass trombone add a tritone to the lower register
French horn covers the range of the trumpet and of the baritone
However the whole range should theoretically be divided up into low horn (II-IV) and high horn (I-III)
Actually , the standard writing is as follow
Below is the advisable range (étendue) of brass instruments (in concert tone)
Avoid pedal tones in writing for trumpet and tenor trombone . Pedal tone should be assigned to bass trombone
French horn can emit pedal tones only through the Bb tube but only two pedal tones (B-A) are reliable.
When writing for a specific instrument
-it’s advisable to consult the player.
-Whatever the skill of the player one must never forget the general melodic rules: remain in the median register with a progressive reach by step of extreme notes .
More about transposition
Tables of brass instruments (notation and concert pitch equivalence
2° Masonic symbolism is part of the music material for the composer.
“Die Zauberflöte” (the magic flute), by Mozart and Schikaneder (both masons) is certainly the most convincing example –but most of the time the situation is rather unclear; the danger being to see symbol where there is not. The most striking example is the number 3 which commonly occurs in classical sonatas and others pieces .
The most evident situation is therefore songs based on an explicit Masonic text even though some doubts occur as far as Beethoven is concerned.
Occurrence of numerology or symbol in musical piece may be fortuitous or remains the, not necessary a Free Mason, composer ‘secret. Usage of the golden number is so frequent nowadays that it is no longer a secret.
A third situation embraces the two first ones.
Here I’m thinking to the opening of Mozart’s quartet K465 which expresses the impression of the apprentice’s initiation passing from dark to light. This piece « containing many mistakes that offend the good taste« * gave rise to to many critics and were largely rejected by his contemporaries . This is an illustration of the difficulty to export masonic idea outside from the lodge.
Conclusion: intricacies of symbolism do not allow perceiving a clear border between profane and sacred music.
*Prince Krazalkovicz
Disclaimer: this paper is a personal view on two- part writing way off the academic approach.
Two simultaneous notes form an interval while a greater number of simultaneous notes creates either chords or other terms such as Cluster that depend on school and music eras.
In a nutshell, counterpoint uses interval while harmony is based on chords; so Two-part writing is logically the concern of counterpoint.However,counterpoint is prior to tonal music and its rules, justified by Pythagorean intervals, are somehow obsolete with equal temperament. In an other hand, tonal harmony stems from counterpoint and therefore shares some rules with it but its at least three voices setting induces inaccuracy in two-part writing. That might be the reason of the scattered number of published methods
Hindemith is one of the most prominent contributors to tonal renewal of counterpoint but his sophisticated method might be hard to start with.
This paper is an attempt to draw some functional implications of intervals from tonal considerations .
1°) Scales
Tonal music consists of two modes: the Major mode and the minor mode which can appear under three aspects :
-The natural scale or descending melodic scale similar to eolian mode with a subtonic instead of leading tone.
-The harmonic minor scale ;a leading tone replace the subtonic.
-The ascending melodic scale with a sharped sixth degree to correct the augmented interval created by the leading tone.
2°) Triads
Stacks of thirds over each scales degrees yield four kinds of triads
3°)Scale degrees
Scale degrees are not equal in importance
The most important are I-IV-V known as primary or tonal chords which support either a major or a minor triad according to the mode.
others chords are secondary chords that may be of any kind according to the scale.
4°) Chord inversion.
Any triad has two inversions but some are uncommon . As a rule, only primary chords can non-restrictively be inverted. II and VII can be inverted under some conditions.Other chords are normally not inverted but in sequence
Inversions result in chord structure changes.
5°) Omission of note
When an incomplete chord is needed the fifth is generally omitted. Therefore, chords in root position appear under a third form (either Major or minor).
The third is obviously omitted in diminished fifth chord.
In tonal harmony the third can be omitted
-in the Dominant chord and the Tonic chord if the key is well established. Thus, a perfect fifth means V or I
–in sixth chords so first inverted chords are under the form of a Sixth interval
The fourth can be omitted in 4/6 cadential chord or the passing VII (b) on a weak beat
Removal of the sixth may occur in I6 ,V6 and VII4/6 which occur under a minor third structure
6°)Analysis
3 means either 5/3 or 6/3. Thus, CE can CEG or CEA
6 is 6/3 or 6/4. EC can be EGC or EAC
Primary chords prevails when interpreting an Interval .Therefore, with CE in CM we choose CEG=I5 but in minor we’d choose CEA=I6
The precedence is
I >VI>III so EG is I6 ,not III5 (In CM)
V>III GE is I4/6,not III5
IV>VI
but IV is equal II
From all those considerations we can establish the following guideline
7°) Rhythmic position
is the last consideration to take into account: Especially secondary chords should be on weak beat.
Postlude:
Although the logic is different from the classical taught counterpoint, usage shows a similar result with the classical writing rules so Much ado about nothing but I did try.
Mirrors tally ascending scale with descending scale (and vice versa).
For better comprehension few notions has to be kept in mind.
1°) Each scale degree is equivalent to a two fifths skip
with a slight default : F is sharp (#)
To remedy this we have to start our series a fifth below the tonic (F)
Starting on F results in a 7 diatonic notes series bordering the tonality
So C major scale limit are F and B : forming the Triton
2°) A note belongs to 7 tonalities according to an immutable order:
7 3 6 2 5 1 4 . So C is the seventh degree of Db,third degree of Ab and so on….
Notice the fifth series forms the triton Db -G ( triton of D Maj) which is symmetric to F-B and able to resolve on C
The seven fifths series forming a triton on C can be copied on the seven notes of the scale.With a two fifths shift we obtain the following table.
Notice
3°) Pivots (common notes) appear only with pair number of accidentals scales
From the C major scale, we can write a scale in opposite direction that respects the tones and semitones position (mirror).Any chromatic note can start the mirror scale but only scale with pair number of accidentals(and 0) has common note (pivot) associated with a tonality
Mirrors adhere to the tones and semitones distribution according two options
Actually the two options rests on : pivots.
Since modes have no accidentals, D (associated with 0 accidentals) as pivot places the two scale in the same tonality.
The mirror of the ionian scale (C maj) is E min (with no accidentals) ( E phrygien) that’s why Vincent d’Indy considered it as « true minor relative »
The reverse is also true
We’ll use two tables to write mirrors.
The first table states the 12 tonality of C with the seven scale notes according to the normal fifths series order
The prime scale is always in C whatever the mode since mode is only a different departure of the C scale
Table 2 indicates which degree of the tonality the mirror starts on(bottom line)
Pivot is the junction-point of the two scales but usually neither the tonic nor the starting point(finale) of the mirror (Finale)explaining the table 2 necessity.
The two first lines correspond to the ascending C Maj scale and define modes.
The two next lines are the descending C maj starting on E which is the true mirror (same tonality as the prime scale (given by the D pivot )
The bottom line figures are the interval between C and the tonic of the other tonalities.
This table shows how it is built but practically we need only two columns
We can see that each mode has its only one mirror mode
Summing up table
Example :To write the mirror of a Phrygian (E) scale with G as common note
G tallies with the Bb scale (column G) which starts on the first degree( Line E) (Bb).
A practical trick :The tonic of the mirror always correspond to E of the other scale (whatever the mode)
( E is the only pivot with common tonality;
Some more examples
Both examples having the same pivot share the Bb mirror scale but with a different starting note (tonic) coinciding with E of the prime scale
The pivot being D the mirror has no accidentals
Perfect mirror that share tonic and tonality but contradict the E rule
Another difficult and confused topic . Ancient church modes were declamatory melodies, sang in unison, which phrases ended with fixed melodic and rhythmic formulas and therefore had no cadence, as we understand with our tonal mind.
The first real cadences (clausules) appeared with polyphony which caused: the disappearance of modes
We can trace back modal harmonic cadences to the 19th century when composers tried to destruct tonality .However,Tonal culture is so deep-rooted in our mind that we want to make modal music a kind of tonal music transcription ( especially due to functional harmony).
Modal cadences are not conclusive as would be tonal cadences and are generally used to « add an transitory color » to a phrase.
But let’s first remind some tonality elements
.
Modern harmonic modality can be approach from different point of view.
The most intuitive is the minor mode without leading tone like the Aeolian mode with a minor Vth degre) for both ascending and descending scales resulting in change in degrees numeration . Cadence traces tonal cadence (v-I) for ascending scale or plagal (iv-I) for descending scale
We may consider semi tones as leading tone : ascending LT B-C and descending LT F-E
According to the slope direction , two possible dominantes and two possible leading tones are available.
Remark :In tonal music progression B -C, B is leading tone because the semitone leads to a strong degree (The tonic ) while F is not a leading tone because it leads to a weak degree (III).
In the tonal progression F -E, F is not a leading tone because the semitone lead to a weak degree however E,as descending mirror, is the tonic and therefore a strong degree : thus F becomes a descending leading tone .
Let’s place a triad on the Vth degree of each scale in ascending and descending forms
Among those V degree chords let’s select those with one of the two possible leading tone F or B which is not at the bass
Besides the ascending Aeolian mode,only two chords appear
Dominant 7 chord appears under two forms GBD and BDF
BDF can’t be used due to the triton that would resolve to C maj.However, adding the sixth from the descending Aeolian scale enable the BDF chord to form a common dominant chord (DFAB) to Ionian(CM )and Aeolian (am) scale.
Notice that the sixth (B) placed on the( II chord ( dfa) is the leading tone of the ascending scale.
Let’s generalize the method by adding ascending leading tone to descending scale and reversely
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As discussed in old church modes, Octave were divided into two tetrachords. There are different kinds of tetrachord:Four are part of old church modes (3 with perfect fourth and 1 with augmented fourth) and one perfect fourth tetrachord that does’nt belong to church mode:The harmonic tetrachord
The place of the semitones gives the direction of the slope,ascending on the right,descending on the left ,no slope in the middle
Considering Modes as two associated tetrachords
Lydian and Locrian modes do not allow two disjunct tetrachords and therefore those modes are the association of a pentachord and a tetrachord
Notice
Association of two opposed sloped tetrachords
Lydian and Locrian modes concentrate semitones in a tetrachord
It should be observed
This last approach helps to choose progression according of the slope of the scale and a tool for counterpoint which is by essence related to mode
Another hint
Let’ s write our scale as triads , not as a succession of triads but rather like a three voices counterpoint to take into account the respective location of semitones
The three minor scales share those three chords
The three Major scales share those three chords
However those chords do not necessary content the characteristic tone of the mode.
Adding a 6 th , 7th or 9th make things very interesting provide they don’t create the triton F-B which suggest the C scale.
We also may use medieval cadences discussed in
disappearance of church modes and the Baroque cadences which are similar to the medieval cadences but they may lead to a third interval (instead of octave or fifth)
We can make a tracing of functional Harmony according to two schools
1-The Niedermeyer-Ortig’s french school which uses tonal progression but chords building abides by the mode (so V can be a minor chord)
2- The Persichetti’s american school which makes a distinction between three kinds of chords
-The primary chords :The tonic chord and chords that contains the distinctive note of the mode.
-The secondary chords :chords that don’t contains the distinctive note of the mode.
-The Chords to avoid because of tritone that lead to major mode.(It can be a primary chord with an added 7th or 9th
Modal music is mostly melodic based on intervals and two functions Teneur (kind of dominant) and Final (Tonic). Its harmony is rather static and baffle functional harmony
