THE FOUNDATIONS OF MUSICAL SYSTEMS
Jean Louchet
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 1/104 Summary
1 Introduction 3 2 Some physics: harmonics, partials and inharmonicity 4 3 Pythagoreas and the classical musical notation 10 4 Zarlino: coming closer to Physics 21 5 The genesis of Harmony: Musica Recta, Musica Ficta 31 6 Time-frequency diagrams and the analysis of music 36 7 The organ and the synthesis of sound colour 43 8 Stringed keyboards: from the harpsichord to the pianoforte 52
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 2/104 1 Introduction
Is there any serious tonal theory behind music? or: why are there 12 notes on each octave on a piano?
Many interval systems in the world
7 note gamut (Occidental system) in reality 12 notes are used in modern music but many more have a name!
European Medieval and Renaissance music use more refined scales.
Middle-Eastern musical systems: 24 notes (“quarter tones”) and many others...
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 3/104 2 Some physics: harmonics, partials and inharmonicity
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 4/104 2.1 What is an octave?
Sound ‘modulo...’ a frequency factor 2.
Our auditory cortex has got a built-in “logarithmic modulo 2” is it reasonably accurate?
General philosophy: just like with vision, the audio information that comes to the conscious level: • is not the sound, • is not the frequencies, • it is actually an attempt at identifying the physical source of the sound.
Similarity with vision:
Human vision is the process of reconstructing a physical object from its image(s).
Human audition is the process of reconstructing an object from the sound(s) it produces.
Biological point of view...
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 5/104 2.2 Musical objects and the lattice of harmonics
Here, we assume a string is perfectly elastic.
Metal strings are relatively recent... • Gut • Copper • Brass • Bronze • Iron • Steel • Nylon • PVF (PolyVinylFluor) • Self overspinning (gut, PVF) • Classical overspinning: • metal (aluminium, brass, silver) over gut or PVF (plucked and bowed instruments) • metal over metal: annealed copper over iron or steel (pianos) • close or open
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 6/104 Fundamental frequency f , harmonic # n has frequency nf . Decomposition into a product of prime numbers: n = 2u × 3x × 5y × 7z × 11t... Striking point + internal damping → reduce higher harmonics Hearing modulo 2 → eliminate 2u The meaningful harmonics are given by n = 3x × 5y × 7z × 11t... Internal damping, choice of striking points and initial conditions (e.g. piano hammer curvature) reduce higher harmonics. Algebraists call this a lattice structure.
[Electronicians also work on lattice structures: Boolean algebras are defined as ’distributive complemented lattices’. Karnaugh diagrams are a consequence of this lattice structure]
The useful harmonics are given by n = 3x × 5y × 7z and even, in most stringed instruments, by n = 3x
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 7/104 2.3 String vibrating modes tension T = π ρ d2 F2 L2 1 T f requency F = d L π ρ For a perfectly flexible string, partial #n has frequency: n T F = n F = n d L π ρ thus each string produces a series of partials with relative frequencies 1, 2, 3, 4, 5, 6, 7, 8... ‘harmonics’ but in reality, due to string stiffness, the actual frequency of partial #n is higher than the harmonic: 1/2 ( 2) f n = n F 1 + B n using the basic inharmonicity coefficient π2 E S K2 B = T L2 E is the Young’s modulus, only depending on the string’s material. = d For a round section string, K 4 (gyration radius) and π2 E d2 B = 64 ρ For example if B = 0.005 the partials will be 1; 2 (1 + 4B)1/2 ≈ 2 × 1.01; 3 (1 + 9B)1/2 ≈ 3 × 1.022; 4 (1 + 16B)1/2 ≈ 4 × 1.039, etc.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 8/104 Reference: Fletcher (Neville H.), Thomas D. Rossing, The Physics of Musical Instruments, 2nd edition, Springer1998-99.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 9/104 3 Pythagoras and the classical musical notation
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 10/104 3.1 Pythagoras and the harmonic 3 We are working in frequencies ‘modulo a factor 2’ Let us choose a frequency FF (say = 1) and work out its harmonics 3x As we work modulo a factor 2, let us see how the numbers 3x × 2y are spread on the scale of frequencies.
CD E F G A B C The sequence of the first 7 Pythagorean harmonics: FCGDAEB (natural order), or ABCDEFG (frequency order): tonality of C. This is one of the simplest possible musical systems. It is possible to make music using 7 tones. Their order of appearance is F C G D A E B. Actually they are named after the order of their frequencies: A B C D E F G. The tradition in the Western musical systems is to call C (the second tone of the sequence) the Tonic. F the Subdominant and G the Dominant. If we take the tonic C as a point of departure, the interval widths are: large, large, small, large, large, large, small. Now it is of course possible to use another note than F as a point of departure of the sequence FCGDAEB. For example lets take C. The new sequence is: CGDAEBX where X is a new frequency. We have to give a name to X; as the name F is no longer used in this new system, we recycle the name F and write the sign # to avoid any confusion with the old F. This is how key signatures are made – and why there is one # in G major, two ## in D major, etc.
X = F#
CD E F G A B C The new sequence using C as a point of departure (tonality of G)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 11/104 Reb Mib Solb Lab Sib Reb
Do Do# Re Re# Mi Fa Fa# Sol Sol# La La# Si Do Do# Enriching the scale: more tones upwards and backwards
This is the basis of the standard musical notation and the infinite Pythagorean scale:
... Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx ... tone of C: –––^––––––––––––––– no alteration tone of G: –––^––––––––––––––– one # tone of D: –––^––––––––––––––– ## tone of A: –––^––––––––––––––– ### tone of F: –––^––––––––––––––– one b tone of Bb: –––^––––––––––––––– bb tone of Eb: –––^––––––––––––––– bbb etc. hence the classical ‘key signatures’ which tell the tonality: here are the most frequent ones:
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 12/104 The most frequent key signatures and the corresponding tonalities.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 13/104 Tuning with pure "fifths" (harmonic no. 3) shows the Pythagorean comma: 312 / 2something
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 14/104 ...and some flats. This may be pushed to infinity, an endless story...
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 15/104 THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 16/104 The infinite system of music as it is written:
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 17/104 The Pythagorean scale is infinite. This is because the equation: − 3x 2 y = 1 has no solution with positive integers. However we should be so glad to be able to eventually fall back into our shoes rather than having an infinity of keys at each octave – in other terms, are there approximate solutions to this equation? The first solution is x = 7, y = 11. 2187 3x 2y = ≈ 1.068 2048 which is a very crude approximation. It would result in dividing the octave into 7 equal intervals. The second solution is x = 12, y = 19 . 531441 3x 2y = = 1.0136 524288 which is the basis for the ‘equal temperament’, a very old system (China, ca. 2000 B.C.?) that has re- appeared in Europe during the late 18th Century, as a simplification of the more refined previous systems. The third solution is x = 43, y = 68. 3.282569674 E20 3x 2y = = 1.1122 2.951479052 E20 and the fourth solution is x = 53, y = 84. 1.938324567 E25 3x 2y = = 1.0021 1.934281311 E25 The latter is remarkably accurate. It results into the octave being divided into 53 equal micro-intervals, called ‘Holder’s Comma’. The difference with the exact Pythagorean frequencies are smaller than anything audible. THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 18/104 Reb Eb Gb Ab Bb Db
C C# D D# E F F# G G# A A# B C C# The 53 interval system: a good approximation - one Pythagorean comma is not far from 1/53 octave (Holder comma). If we express the Pythagorean system into Holder’s commas, we have: C - D 9 commas D - E 9 commas E - F 4 commas F - G 9 commas G - A 9 commas A - B 9 commas B - C 4 commas
The interval between a note and the homologous sharp or flat note (e.g. between D and D#, or between Db and D) is called the ‘chromatic semitone’ in the Pythagorean system. Its value in Holder’s approximation is 4 commas.
The complement of a chromatic semitone to a tone (e.g. between D and Eb, or between C# and D) is called the ’diatonic semitone’. Its value in Holder’s approximation is 5 commas. The interval between a note and its close neighbour (as between Eb and D#) is called the ‘Pythagorean comma’ or ‘enharmonic interval’in the Pythagorean system, 312 / 219 ≈ 1.01364. Its value in Holder’s approximation is one Holder’s comma, or 1/53 of an octave, or 21/53 ≈1.01316.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 19/104 Unfortunately, while the musical notation is entirely based on the Pythagorean system, most keyboards only use 12 keys per octave. This does not necessarily imply that the instrument is tuned to the equal temperament!
Standard keyboard with x = 12
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 20/104 4 Zarlino: coming closer to Physics The Pythagorean system focuses on the harmonic 3 and proudly ignores higher harmonics. This is a heavy restriction to musical composition, as intervals like C - E, F - A and G - B (called ‘major thirds’) will sound badly on any instrument that produced harmonic 5 (i.e. about every instrument!)
On a Pythagorean scale, the ratio E : C is 34 / 26 = 81 / 64. The sound of C will contain its harmonic 5, which will beat with E as the ratio is 81/80 this is called the syntonic comma.
Some European medieval systems consider the interval of third as dissonant and normally forbidden. This is a serious limitation.
To overcome this, Zarlino (1517-1590) introduced a slightly different scale, taking the harmonic 5 into account.
F→C, C→G, G→D factor 3 (‘pure fifths’) C→E, F→A, G→B factor 5 (‘pure thirds’) C D E F G A B C Pythagorean scale 1 9/8 81/64 4/3 3/2 27/16 243/128 2 Zarlinian scale 1 9/8 5/4 4/3 3/2 5/3 15/8 2 Easy to tune by ear...
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 21/104 The Zarlinian scale can be extended: here are the most useful tones.
A→C#, B→D#, Db→F, Eb→G, E→G#, Bb→D→F# factor 5 C C# Db D D# Eb E F F# G G# A Bb B C Pythagorean 1 2187/2048 256/243 9/8 32/27 32/27 81/64 4/3 1024/729 3/2 128/81 27/16 16/9 243/128 2 ≈1.0679 ≈1.0535 =1.125 =1.3333 ≈1.4047 =1.5 ≈1.5802 =1.6875 ≈1.7778 ≈1.8984 Zarlinian 1 25/24 16/15 9/8 75/64 6/5 5/4 4/3 45/32 3/2 25/16 5/3 9/5 15/8 2 ≈1.0417 ≈1.0667 ≈1.4062 =1.5625 ≈1.6667 =1.8 =1.875 With the Pythagorean scale, the Pythagorean ‘enharmonic’ comma (e.g. between C# and Db) is 312 / 219 ≈ 1.01364. 16 25 = 10 ≈ . Here, we find a new interval between C# and Db: 15 : 24 9 1 1111 As both D# and Eb are frequently encountered in musical compositions, many Renaissance instruments (especially at Zarlino’s time) had split accidentals. Same with G#/Ab.
Another interesting point is that flats and sharps are swapped: • in the Pythagorean scale, enharmonic sharps are higher than flats: C# > Db • in the Zarlinian scale, enharmonic sharps are lower than flats: C# < Db.
This system is the backbone of most Mediterranean antique, medieval European and traditional Amerindian music systems.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 22/104 However, complex polyphony arose from the late Middle Ages – Perotin and the Ecole Notre Dame in the 13th Century, then Binchois, Dufay, Ockeghem, very probably as the development of a Christian tradition to symbolise the multiple voices inspired by the Holy Spirit at the Pentecost, all of this having a considerable development during the 16th Century – Thomas Tallis’ Guinness record motet ‘Spem in alium nunquam habui’ with 40 singing voices is a telling example.
A 6-tone system, while well suited to plain-song, is a hard limitation when attempting to sing with more than two voices (cf. medieval Bicinis). It was necessary to find a way around this difficulty.
• the first route was a development of the Zarlinian system, leading to the multiple Hexacord system and Musica Ficta – an intonation system born in the 12th and 13th Centuries with l’Escole Notre- Dame (Maître Pérotin), further developed by the medieval poet and musician Guillaume de Machaut then through all the Renaissance period and the early Baroque (Monteverdi), ca. 1610.
• the second route, born in Italy during the late Renaissance (ca. 1560) abandoned the refined accuracy of Musica Ficta in favour of a circular system, at the cost of the importance of the term 5y – at least in theory. It only became the dominant system from the mid 19th Century.
• Most of the baroque, classical and early romantic music uses a mixture of the two approaches, through circular temperaments. J. S. Bach’s Das Wohltemperirte Klavier is an outstanding illustration of how it is possible to write into all possible tonalities while using an unequal circular temperament (this has often been misunderstood). In these temperaments, some thirds are pure or acceptable while other ones are terribly false, the trick is to use them only on extremely short values.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 23/104 A 16th Century Italian harpsichord (virginal) with split accidentals. St Cecila’s hall collection, Edinburgh/
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 24/104 This is D#, not Eb.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 25/104 Guarracino’s Renaissance ‘enharmonic’ keyboard with x = 53 (in fact only 19 keys per octave). It is playable!
The Danikey system: 22 keys per octave
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 26/104 August Forster’s enharmonic piano with 36 keys per octave.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 27/104 harmonic 5
small diesis =enharmonic comma -5 3 2 x5 = 125/128 diaschisma -11 4 2 2 x3 x5 =2025/2048
schisma -15 8 2 x3 x5=32805/32768
harmonic 3
Reference Pythagorean comma -19 12 2 x3 =531441/524288 ~12 schismas syntonic comma =Zarlinian comma -4 4 -1 2 x3 x5 =81/80 ~11 schismas Approximate meeting points and micro-intervals. Red = too high, green = too low.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 28/104 The Meantone systems: some pure Thirds, honour to the fifth harmonic! - the wolf tone.
The meantone temperament above (mesotónico) is but one among many practical solutions.
Well tempered ≠ equally tempered!
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 29/104 THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 30/104 5 The genesis of Harmony: Musica Recta, Musica Ficta
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 31/104 5.1 Solmization in theory
Mi contra Fa, diabolus in Musica
tetrachords, hexachords, solmization
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 32/104 D E F G A B B C
ut re mi fa sol la ut re mi fa sol la ut re mi fa sol la
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 33/104 5.2 Solmization in practice Example taken from William Byrd, O God that guides the cheerful sun.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 34/104 THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 35/104 6 Time-frequency diagrams and the analysis of music
Intensity and time-frequency diagram of a spoken sentence.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 36/104 Voice pitch and harmonics Pitch frequency: male 100-130, female 180-250
Vocal tract shape and formants – the envelope of the harmonics of the pitch frequency.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 37/104 “goes out as a great champion” itre.cisupenn.edu/~myl/languagelog/archives/002353.html
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 38/104 Characterising vowels by their first two formants.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 39/104 DIDEROT & D’ALEMBERT WERE WRONG!
THE RATIOS OF HARMONICS DO NOT MAKE THE SOUND COLOUR
THE FORMANTS MAKE THE COLOUR
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 40/104 Broman’s ‘monster harpsichord’ made after Diderot’s principles. • one string material • one string diameter • one string tension don’t make the sound timbre homogenous. Fortunately, the case gives its own formants.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 41/104 ‘Clavecin brisé’ de Jean Marius: three cases, three different sound colours
TRY A TAPE RECORDER...
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 42/104 7 The organ and the synthesis of sound colour
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 43/104 7.1 How an organ works • Flue pipes and reed pipes • Pipe scaling and denomination • Bellows, windchest, pipework, console. • Positive, great [organ], recit / swell, echo, pedal • Swell and expression.
First understand the ‘real’ pipe organ.
Flue pipes: a whistle (similar to a recorder’s) and a pipe. The pipe length determines the pitch Reed pipes: use a resonating reed (similar to the clarinet or saxophone)
At the heart ot the instrument: the WINDCHEST (‘sommier’) is basically a matrix. Air supplied by a bellows or electric pump. Air pressure stabilised by a bellows system. *tremblant
The windchest matrix is organised into • columns: one column per key • rows: one line per register. Each register can be switched ON (pulled) or OFF (pushed). Depressing any key opens a valve which provides air to the pipes at the intersections of the depressed key (columns) and the pulled registers (rows).
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 44/104 Cut view of an organ windchest (tracker action)..
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 45/104 Register, stop, rank
Windchest and pipework: general view. Pipework and denominations A row of pipes is described by a name and a number. The number is the length of the lowest pipe of the register (in feet). A 8ft stop is a register at the normal octave. a 4ft stop will sound one octave higher. a 16ft stop will soud one octave lower. etc. Usual range: 4 octaves (Renaissance/Early baroque) to 5 octaves (modern) Pipe lengths: on a 4 1/2 octave 8ft register, from 240cm to 20cm.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 46/104 7.2 Organ architecture
Cesar Franck at the console of Sainte Clotilde organ, Paris: 3 manuals, 1 pedalboard. THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 47/104 Several organs into one organ 1 to 5 manual keyboards, 0 to 1 pedal keyboard. One windchest for each keyboard
Continuo organs: 1 manual, 3 registers Small church organs: 1 or 2 manuals, 1 pedalboard Major church organs: 3 manuals, 1 pedalboard, couplers, swell, 40 to 70 registers May go up to 5 manuals, 1 pedalboard and 120+ registers
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 48/104 Grand-orgue positif de dos
buffet du grand-orgue soufflerie
buffet du positif
Le buffet du Clicquot de Souvigny (Allier), d'après un relevé de B. Aubertin. On distingue bien le positif du grand-orgue. A droite, un orgue français (D. Bedos).
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 49/104 7.3 Register families and registration Unisons and octaves (flue pipes) Principals, flutes and diapasons: 16’, 8’, 4’, 2’, 1’ also called ’montre’, ‘prestant’, ’doublette’ (2’), ‘whistle / sifflet’ (1’), ‘cor de nuit’ (4’), gambas, etc. special case: stopped pipes. A 4’ long pipe will sound 8’: stopped diapason, bourdon, stopped flute etc. Stopped pipes don’t produce even harmonics. This is the backbone of the art of registration. Simple mutations Similar pipes, but synthesizing the other harmonics to the 8’ fundamental: 2’2/3 ‘fifth’, ‘quint’ or ‘nazard’ 1’3/5 ‘Third’ 1’1/3 ‘duodecima’ or ‘larigot’ Composite mutations (mixtures) Multirank stops, containing a combination of octaves and simple mutations, from 3 to 6 ranks: 4’, 2’2/3, 2’, 1’3/5, 1’1/3, 1’ with different balances, e.g.: • ‘plein jeu’ emphasis on 4’, 2’, 1’ • ‘fournitures’, ‘cymbals’, ‘ripieno’, • ’cornet’ (emphasis on 1’3/5 ) Some 19th century organs also include composite registers like salicional, unda maris, vox celeste etc. that combine slightly detuned or heterogenous pipe pairs. Reeds ‘solo’ stops, often inspired by ‘real’ instruments: crumhorn, dulcian, oboe, trumpet, gemshorn, regal, etc. THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 50/104 7.4 A classical organ: François-Henri Clicquot, Souvigny (France) 1783
Positif Dessus de flute 8’ Grand-orgue Montre 8’ Prestant 4’ Prestant 4’ Doublette 2’ Doublette 2’ Plein-jeu V Plein-Jeu VI Bourdon 8’ Bourdon 8’ Nazard 2 2/3’ Nazard 2 2/3’ Tierce 1 3/5’ Quarte 2’ Cromorne 8’ Tierce 1 3/5’ Trompette 8’ Cornet V (C3) Récit (C3 - D5) Bourdon 8’ Trompette 8’ Cornet IV Clairon 4’ Hautbois 8’ Voix humaine 8’ Pédale (F0 - A2) Flute 8’ Flute 4’ Trompette 12’ Clairon 6’
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 51/104 8 Stringed keyboards: from the harpsichord to the pianoforte
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 52/104 8.1 The clavichord
Minimalist
Schéma de principe du clavicorde. La corde vibre entre la tangente et le chevalet. Fretted or unfretted?
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 53/104 Fretted clavichord
Expressiveness
Plus faict doulceur que violence (Arnold Dolmetsch)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 54/104 8.2 The harpsichord Plucked strings
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 55/104 THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 56/104 THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 57/104 Italian action.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 58/104 French action: shift coupler (’accouplement à tiroir’)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 59/104 English action: dogleg.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 60/104 Registers and registration The instrument is built around its stringss steel, iron, brass, bronze, red copper, gut? The Lautenwerk
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 61/104 Clavicytherium-lautenwerk (1490), copy by Boinnard. Original: Royal College of Music, London. THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 62/104 The harpsichord in all shapes:
Spinets: Italian virginal, Flemish virginal, Flemish muselaar, “mother and child” muselaar, English bentside (Hitchcock).
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 63/104 Large harpsichords: clavicytherium, Italian and Flemish harpsichords. North vs. South: the bottom line... plane. • Southern (Italy, Spain, Portugal, Austria) built on the bottom plank.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 64/104 THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 65/104 • Northern: Flanders, Germany, France, England, re-Germany, Scandinavia first gets an internal bracing then a bottom plank.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 66/104 Power Inharmonicity Sound quality
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 67/104 Inharmonicité et qualité de timbre
La décadence: le clavecin expressif.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 68/104 8.3 Il clavicembalo con piano e forte The pionneer: Bartolomeo Cristofori, 1710. The follower: Gottfried Silbermann, 1740
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 69/104 8.3.1 Cristofori and the hammered harpsichord
Cristofori’s pianoforte
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 70/104 Cristofori’s action (copy) THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 71/104 Rough model of a push action (Stoßmechanik) by Cristofori.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 72/104 Stop action (Prellmechanik) by Zumpe & Buntebart (London)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 73/104 Square piano by Zumpe (ca. 1770)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 74/104 Silbermann’s inverted stop action, close relative to the (more recent) Wiener action.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 75/104 8.3.2 Play closer: the escapement (“English action”), Clementi, Broadwood
English action: Broadwood 1777. Invention of the pushing jack and the escapement dolly.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 76/104 Steinway 1860: an English action with a repetition lever (unconvincing).
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 77/104 8.3.3 Wiener/German action: Stein, Walter, Streicher, Schantz, Graf... compulsory lightness.
Stein 1779,the first Wiener action, evolve from Silbermann’s stop action. THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 78/104 Walter’s piano. The first Wiener pianos (with Stein) – and Mozart’s choice.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 79/104 A modern copy of Schantz ca.1820 - lthe second Wiener school. Turqueries to forget... THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 80/104 Una corda, céleste, drommel, storm, forte (undamping).
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 81/104 8.3.4 Repetition actions: Sebastien Erard and the birth of the modern piano
‘Double échappement’ by Erard, invented 1819, patented 1821. Invention of the repetition lever asembly, the full development of Cristofori’s ideas!
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 82/104 8.3.5 Piano und übermenschen: when metallurgy helps. String tension and acoustical power Frame strength and string tensions Hammer mass and string tension
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 83/104 8.3.6 String structure String vibration T = 4 F2 L2 1 T F = 2 L We need heavier strings in the bass:
tension par note piano moderne
piano ancien
clavecin
grave aigu Tensions par note typiques sur un clavecin, un piano romantique et un piano moderne. Les discontinuités à la basse correspondent aux passages tricordes-bicordes-monocordes. Le graphique est qualitatif et ne représente pas des instruments précis. THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 84/104 Elastic limit, Young’s modulus and inharmonicity 1/2 ( 2) f n = n F 1 + B n π2 E S K2 B = T L2 for a simple string,, K = d / 4 It is necessary to reduce K – using materials or structures?
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 85/104 Hand spinning a piano bass string (usine Pleyel, Saint-Denis, 2008)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 86/104 English style overspun string loop (Broadwood 1853)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 87/104 Broadwood concert grand, 1853
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 88/104 A double overspun string.
Calculating a double overspun string requires the rsolution of a 6th degree polynomial equation:
ρ( 2 − D2)(D + 0.1d)(D2 + 2.2dD + 0.2d2) = 0.8d5 (dD2 + Dd2)(D2 + 2.2dD + 0.2d2) + σπ (2D3d + 12D2d2 + 16.8Dd3 + 2.4d4 + )(D + 0.1d) D
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 89/104 8.3.7 The piano structure Square piano and ‘harpsichord-shaped’ piano
Erard “en forme de clavecin” vers 1820 (Musée de Bruxelles), Erard carré grand modèle 1850, (Conservatoire de Tours)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 90/104 Console piano (Jean-Henri Pape), Swedish cabinet piano, giraffenfluegel (Schimmel) Piano frames: reinforcing bars Thermostable frames: William Stodart
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 91/104 William Stodart compensation frame
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 92/104 Broadwood with assembled frame (‘cadre serrurier’, locksmith’s frame) and parallel string s– ca. 1860
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 93/104 Erard’s parralel strung piano with an assembled frame.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 94/104 Cross strung Pleyel with an assembled frame
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 95/104 Single-piece cast iron frame sacrificing efficiency, sacrificing polyphony for more power. Cross-strung frame: sacrificing polyphony for more power (Babcock patent 1859).
Pleyel’s overstrung cast iron frame - small concert grand, ca. 1900.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 96/104 Pleyel factory, Saint-Denis 2008: a pre-strung frame.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 97/104 8.3.8 Repetition “downstriker actions”: Jean-Henry Pape, Nanette Streicher Variants of English action Thedeath of the square piano and the paradox of the upright piano’s survival.
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 98/104 8.3.9 Side inventions Felt hammers (Pape) Agraffes (Erard)
Agrafes Erard, premier type. Harmonic bar (Erard) - aka capodastro bar. The tonal pedal (Steinway) Aliquot segments and adjustable roofs
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 99/104 Aliquot strings (Blüthner) The Fourth Pedal (Blüthner)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 100/104 8.3.10 The future did not happen Yamasteinway, or the compulsory uniformisation
The Steinmaha. A good instrument in spite of its totalitarian option!
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 101/104 Malmsjö et le piano-banane Le Pleyel double
Duett piano: Pleyel’s double, collection of usine Pleyel, Saint-Denis
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 102/104 Creation of a 1825 Viennese style piano, by Christopher Clarke (octobre 2009)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 103/104 Between Schantz and Graf... (Christopher Clarke)
THE FOUNDATIONS OF MUSICAL SYSTEMS Jean Louchet 18th December 2012 Hogeschool Gent page 104/104