MiltOnNotes Volume One

MILTONOTES

Volume One

© Milton [email protected]

An open-eared exploration of composition in theory & practice.

Sound, Music & Technology

Milton [email protected]

MILTONOTESAn open-eared exploration of

composition in theory & practice.

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Key Historical Events inContemporary Computer Music

Dawn of Music Notation

Iraq:1800BC Cuneiform (melody in 3rds)

The representation of music

Ancient Greece: c.600BC Pitch and rhythm


Teaching behind the veil-readopted by Schaeffer as the veil of speakersThe concept of sound as divorced from source

The appreciation of sound for its own sake regardless of originA numerical basis of sound

c. 500BC Acousmaticἀκουσματικοί

Pythagorus, Ionian philosopher, mathematician and musician (c.570-c.495BC)


Development of Music Notation

Byzantine Empire : c. 390AD differential pitch

The grid

Middle Ages Europe: c.850AD Grid system


Randomness in Music

Mozart’s Dice Game (1787)

A Musical game for composing minuets and trios from dice rollshttp://sunsite.univie.ac.at/Mozart/dice/


1857 E. Leon Scott’s Phonautograph

Sound can now be made permanent, with one slight problem.


1861 Philip Reis’ Telephone

Sound can now be transmitted across distances rapidly


1863 Helmholtz publishesOn the Sensation of Tone as a Physiological Basis

for the Theory of Music

Basis of additive synthesisAny sound can - in theory - be constructed


1874 Elisha Gray’s Musical Telegraph

Transmission of electronic polyphonic music


1876 Thomas Edison’s Phonograph

Sound can be recorded and reproduced


Solidified sound wave


Ocean of Sound and the birth of Ambient music

1889 Claude Debussy at L’Exposition Universelle


1895 Thaddeus Cahill’s Telharmonium

The first synthesiser


1907 Busoni’s Sketch of a New Aesthetic of Music

The promise of electronic music


1913 Russolo’s The Art of Noises

The democratising of all sound and the destruction of musical elitism


1913 Russolo’s The Art of Noises

Wicked noise-makers


1915 Varèse moves to New York in search of a new music

An organiser of sound

I dream of instruments obedient to my thoughts and which with their contribution of a whole new world of unsuspected sounds, will lend themselves to the exigencies of my inner rhythm

Our musical alphabet must be enriched, I refuse to limit myself to sounds that have already been heard...What I am looking for is new mechanical mediums which will lend themselves to every expression of thought and keep up with thought


1915 Lee De Forest patents vacuum tube

Miniaturisation of electronics


1929 RCA releases the Theremin

Commercialisation of electronic instrument and in the 1930s the Terpsitone and Rhythmicon


1924 Respighi’s The Pines of Rome

Blending of live and pre-recorded music


1930 Hindemith and Toch’s Grammophonmusik

Audio manipulation


1948 Schaeffer’s Etude aux Chemin de FerMusique Concrète

Found sound, sampling, looping, filtering reverb and the ‘sound object’


1948 Nancarrow’s Studies for Player Piano

Bionic virtuosity


1952 Cage’s 4’33”

All sound considered

4’33” live version


1952 Luening and Ussachevsky

Live effects


1956 Louis & Bebe Barron’s Forbidden Planet score

A working electronic music studio


1957 The IIliac Suite The Birth of Computer Music

Live effects


1958 Varèse’s Poème Electronique

Major display of electronic work a graphic score with a familiar look


1958 Dissevelt’s Whirling

Birth of pop electronic music


1959 Cindy Electronium

Raymond Scott (1908-94) was a Jazz musician, jingle writer, electronic artist and inventor, and one of the earliest to fully adopt the

music technology as a useful -and profitable-part of the composer tool-kit rather than esoteric experimentalism - similarly Stevie Wonderin the early 70s embraced the studio to make more efficient the

compositional process


1964 The Moog

The development of synthesis


1971 NHK first digital recording

The extraordinary rate of development of processors allows sound to bemanipulated beyond physical constraints. And what used to be housed

in 200 tons of hardware can be emulated while checking email.If cars developed like computers they would travel at 470,000 mph, get 100,000 miles to the litre, cost 2p, and could balance on a matchstick.


1983 MIDI patented

A musical language for computers


Now

Applied vs. ‘Pure Music’

How does computer composing differ from composing?

Additional Reading

Holmes, T., (2008) Electronic and Experimental Music, revised 3rd edition. New York: Routledge.

Manning, P. (2004) Electronic and Computer Music .Oxford: Clarendon Press.

Toop, D. (2001) Ocean of Sound. Serpent’s Tail.

MILTONOTES

Pulse, Tempo & Metre



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Pulse

Musical events in time

All music has some duration, and the occurrence of musical events over time-

rhythm. When there appears to be some

underlying regularity of events thisis the pulse or beat.

Generally ranging from 20-330bpm

Pulse

Tempo■ Larghissimo — very, very slow (20 bpm and below)■ Grave — slow and solemn (20–40 bpm)■ Lento — slowly (40–60 bpm)■ Largo — broadly (40–60 bpm)■ Larghetto — rather broadly (60–66 bpm)■ Adagio — slow and stately (literally, "at ease") (66–76 bpm)■ Adagietto — rather slow (70–80 bpm)■ Andante Moderato — a bit slower than andante■ Andante — at a walking pace (76–108 bpm)■ Andantino – slightly faster than andante■ Moderato — moderately (101–110 bpm)■ Allegretto — moderately fast (but less so than allegro)■ Allegro moderato — moderately quick (112–124 bpm)■ Allegro — fast, quickly and bright (120–139 bpm)■ Vivace — lively and fast (≈140 bpm) (quicker than allegro)■ Vivacissimo — very fast and lively■ Allegrissimo — very fast■ Presto — very fast (168–200 bpm)■ Prestissimo — extremely fast (more than 200bpm)

Pulse

Musical events in time

Some pieces or musical moments has no, little or an ambiguous sense of pulse.This will occur when there is insufficient regularity and/or if note events are ill-

defined

Zero gravitation, John Adams

Exercise 1: Compose an introduction to a piece where no pulse gives way to ambiguous and then clear pulse

Pulse

Tempo feel

Even when pulse exists, it may be experienced at more than one level.This can be exploited as half-time or

double-time feel. Where the music moves at the same rate, but the sense of pulse can alter.

Ray Charles, Wynton Marsalis

Exercise 2: Compose a musical section and arrange it with normal, half and double-time feel.

Pulse

Tempo Changes

Fixed SmallNatural

Fluctuations

GradualChanges

Sudden Shifts

Direction,shape,extent

duration.

rubatorallentandoritardendo

ritenutoaccelerandoprecipitando

etc.

During performance,unconscious or not.

Metronomic

Boulez’s conveyor belt

Adjacent tempi canexist in

simple rational relationships (double-time, half-time)

more complex rational (e.g. 3:4, 5:4)or irrational

Pulse

Tempo

Natural fluctuations inJames Brown, ‘I Got You’ Millyard SOS

Pulse

Tempo Curves

■ Accelerando — speeding up (abbreviation: accel.)■ Allargando — growing broader; decreasing tempo, usually near the end of a piece■ Calando — going slower (and usually also softer)■ Doppio movimento — double speed■ Meno mosso — less movement or slower■ Mosso — movement, more lively, or quicker, much like più mosso, but not as extreme■ Più mosso — more movement or faster■ Precipitando — hurrying, going faster/forward■ Rallentando — gradual slowing down (abbreviation: rall.)■ Ritardando — less gradual slowing down (more sudden decrease in tempo than rallentando)(abbreviation: rit. or more

specifically, ritard.)■ Ritenuto — slightly slower; temporarily holding back. (Note that the abbreviation for ritenuto can also be rit. Thus a more

specific abbreviation is riten. Also sometimes ritenuto does not reflect a tempo change but a character change instead.)■ Rubato — free adjustment of tempo for expressive purposes■ Stretto — in faster tempo, often near the conclusion of a section. ■ Stringendo — pressing on faster (literally "tightening")

(From wiki) what curves in terms of shape, duration, extent and direction might be associated with these terms?

Pulse

Metric modulation

A shift from one tempo (or meter) to another via a pivotal note value

For example

q=e

200bpm 100 bpm2:1

Pulse

Metric modulation

100bpm 150 bpm

q=q.2:3

Pulse

Metric modulation

100bpm 150 bpm

q=q.2:3

Pulse

Metric modulation

100bpm 80 bpm5:4

qx=q(

Pulse

Metric modulation

Tempo I

Tempo II

Tempo III

Tempo I

Exercise 3: Construct this tempo map in a short piece.Tempo I,II,III should exist in rational relationships of your

choosing, and modulations should be pivotal.Complete with melodic and harmonic elements.

Pulse

Metric modulation Exercise 2&3from String Quartet No.1 Elliot Carter

Exercise 4a: Sequence this metric modulation passage, using melodic and harmonic elements.4b: Design, notate as above and sequence your own metric modulation sequence

Pulse

Polytempo and Xenochrony

It is possible for two or more tempi to exist at once,even if they have a very complex relationship.

Charles Ives introduced the idea of polytempo and Zappa coined the term Xenochrony to describe

the studio equivalent of superimposing different tempi.

Exercise 5: Create a sequence with two superimposed tempi

Meter

Pulses or beats almost always existin logical groups and in a hierarchy of strengths.

This meter or time signature indicates how many beats - and what type of beat -exist in each measure.

Listening examples.

Grouping in 2s and 3s

Exercise 6:Write a 4-bar groove in 4/4 and reinterpret in 5/8 or 5/4 and 7/8 and 7/4

Be fully aware of 2 and 3 groupings

An introduction

Exercise 6:Write a 4-bar groove in 4/4 and reinterpret in 5/8 or 5/4 and 7/8 and 7/4

Be fully aware of 2 and 3 groupings

Exercise 5: Create a sequence with two superimposed tempi

Exercise 4a: Sequence this metric modulation passage, using melodic and harmonic elements.4b: Design, notate as above and sequence your own metric modulation sequence

Tempo I

Tempo II

Tempo III

Tempo I

Exercise 3: Construct this tempo map in a short piece.Tempo I,II,III should exist in rational relationships of your choosing, and modulations should be pivotal.

Complete with melodic and harmonic elements.

Exercise 1: Compose an introduction to a piece where no pulse gives way to ambiguous and then clear pulse

Exercise 2: Compose a musical section and arrange it with normal, half and double-time feel.

Lecture 1 Compositional Exercises

MILTONOTES

Meters, Patterns & Polymeter



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The Music There Is

@miltonline

The Music There Is

Tc There Is

.

The Music You’ve Heard

Make it a mission to expand this

The Music You Like butDon’t Understand

The Music You Like and Understand

The Music You Don’t Like But Understand

The Music You Don’t Like and Don’t Understand

Educational

Inspiring

Ideal

Understand =anything from being virtuosic in the idiom to appreciating

the mechanics, skill and artistry within it

Your best moves

NB. this circle is a continuum not 4 distinct spaces

There’s always more to learn and don’t take your musical

taste too seriously

Tc There Is

.So make this bigger,

and move left and up within it.

@miltonline

Meter

A Hierarchy of Pulse

The concept of pulse - an underlying unit of rhythmic regularity - has been established in Lecture 1. This

regularity may occur at different levels, a concept that can be exploited in, for example half-time or double-time feel, but there is usually one predominant ‘tap-

along’ pulse.However, this string of pulses - beats - are rarely

entirely equal. There is a hierarchy.

Meter

Types of Meters, Beats and Bars

Pulses or beats almost always existin logical groups and in a hierarchy of strengths.

This meter or time signature indicates how many beats - and what type of beat -exist in each measure.

For example 4/4 120bpmThe crotchet is the predominant common pulse and they are grouped in 4 beats.

7/8 would imply that quavers are the common beats and are grouped in 7s

Meter

Types of Meters, Beats and Bars

What determines the groups?

Dynamic emphasis

Rhythmic repetition

Harmonic and melodic implications

Meter

Listening and transcribing

What determines a bar?

What repetition, harmonic and melodic exist?

Can the rhythm be broken logically into 2-beat and 3-beat division.

Clave

16 examples

Meter

Son Clave

Meter

Rumba Clave

Meter

Bossa Clave

( )

3-2

2-3

Meter

Bulgarian Folk Dance

The exploration of meter in folk music is hugely extensive. In Bulgaria folk music alone,a rich history of dance forms has amassed many metric forms.

Many may be considered additive, formed by an extension of beats.Here are 5 to transcribe

Paydushko horo

Chetvorno horo

Rachenitsa

Petrunino horo

Yovino Horo

Meter

Bulgarian Folk Dance

The exploration of meter in folk music is hugely extensive. In Bulgaria folk music alone,a rich history of dance forms has amassed many metric forms.

Here are 5: Transcribe your own.

Paydushko horo (2+3; 5/16 or 5/8)

Chetvorno horo 3+2+2 or 3+4; 7/16)

Rachenitsa (2+2+3 or 4+3; 7/16)

Petrunino horo (3+3+2+3=11/16)

Yovino Horo (3+3+ 2+2+3+ 2+2+3+ 2+2+2+2+3+2+2=35/16)

Meter

Playing with beat divisions: Hemiola

A meter can stay constant while groupings change.A hemiola is a musical figure where 2 groups of 3 notes

are followed or replaced with 3 groups of 2,implying-for example - a 6/8 to 3/4 change

Meter

Compás

Here we look at a more complex rhythmic interaction fromthe Flamenco style

The Flamenco compàs is a metric structureThere are several types- many of them containing 12 beats.

They are fully absorbed by the performers and this anchored, mutually felt rhythmic pattern

allows for a high degree of rhythmic sophistication

Meter

Compás

Soleares

1 2 3 4 5 6 7 8 9 10 11 12

Start

This is the basic pattern but there is a huge repertoire of counter-rhythm hand claps, endings and rhythmic devices

Meter

Compás

Siguriyas

8 9 10 11 12 1 2 3 4 5 6 7

Start

Short

ShortLong

Long

Short

A ‘rhythmic mode’ of Soleares

Meter

Compás

Alegrias

12 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 +

Start

Exercise 1: Clave/Compas. Select or better still, research/transcribe a metric template (from Bulgarian, South-American, Flamenco or other sources) and construct a groove/piece using the rhythmic structure.

Meter

Changing Meter

Meters can change, sometimes this is quite natural and can go unnoticedsimply adapting to accommodate a melody.

Beatles All you Need is Love.

7/4 (or 4 + 3) bars are used very naturally

Meter

Changing Meter

An example from the ‘classical’ repertoire is Mussorgsky’sPictures at an Exhibition (Promenade)

Notice how a simple melodic motif is developed perfectly accessibly using changing meters.

Exercise 2: Compose or select a clear melodic phrase, and use meters of different lengths to develop and reinterpret the melody into a longer

piece.

Meter

Changing Meter

Meter changes can be extreme lurching the pulse and messing with your musical brain.

Dream Theater Erotomania

From guitar entry

5/4 (3 bars) + 9/8 (1 bar)5/4 (3 bars) + 9/8 (1 bar)

5/4 (3 bars) + 3/4 (2 bars) + 2/4 (1 bar)5/4 (3 bars) + 3/4 (2 bars) + 2/4 (1 bar)

repeats

11/8 (3+3+3+2)10/8 (3+3+2+2)

4/4 (2 bars)

Solo in 5/4 etc.

2x

6x

Meter

Changing Meter

Complex changing meters has a long history,let’s look at the Sacrificial Dance from Stravinsky’s

seminal 1913 ballet The Rite of Spring

Exercise 3: Using the Sacrificial Dance (pick at least 2 consecutive pages) as a metric template, compose meter-specific material, and then compose material that occurs less dependently on the structure. The overall metric

implication may well be-for example 4/4 -with Stravinsky’smeter pattern embedded in some layer, or the meter pattern may be overt.

Polymeter

(not polyrhythm)Multiple meters may be implied at the same time.

SImple examples may be a delay set to a triplet or dotted quaver.Often, during solos, a soloist can use phrase that imply

different meters over an underlying groove, or rhythmic hits(Hancock -Hang Up Your Hang Ups 5:30 onwards)

However many compositional examples exist even from pop music:The Cars Touch and Go has in the verse a 5/4 bass and drum pattern and a

simultaneous 4/4 in the vocals and keys.

The use of polymeter in 20th Century ‘classical’ and contemporary metal is wide-spread.

For example, Ligeti’s Arc-en-ciel implies different and changing meters (as well as polyrhythms) in each hand.

Here are some more examples.

Polymeter

Hindemith - String Quartet no.3-II (0:05-0:19)analysis by Timothy Daust

Polymeter

Messiaen - La Verbe (2:18-2:23)analysis by Timothy Daust

Polymeter

Meshuggah - Rational Gaze (0:00-0:29)all Meshuggah analyses by Jonathan Pieslak

PolyMeter

Meshuggah - Stengah (0:16-0:48)

PolyMeter

Meshuggah - Humiliative (3:50-4:04)

PolyMeter

Meshuggah - New Millenium Cyanide Christ (0:00-0:25)

4+4+3 ostinato

Benjamin Britten, Peter Grimes -Interlude IVAll Britten analyses 2008 Timothy Daoust

Benjamim Britten, Peter Grimes - Interlude IV (1:16)

Benjamim Britten, Peter Grimes - Interlude IV (1:16)

Same passage re-scored

Exercise 4: Compose a piece with at least 2 simultaneous metric implications, make sure you understand how it interlocks.

Exercise 1: Clave/Compas. Select or better still, research/transcribe a metric template (from Bulgarian, South-American, Flamenco or other sources) and

construct a groove/piece using the rhythmic structure.


Exercise 2: Compose or select a clear melodic phrase, and use meters of different lengths to develop and reinterpret the melody into a longer piece.

Exercise 4: Compose a piece with at least 2 simultaneous metric implications, make sure you understand how it interlocks.

Exercise 3: Using the Sacrificial Dance (pick at least 2 consecutive pages) as a metric template, compose meter-specific material, and then compose material that occurs less dependently on the structure. The overall metric implication

may well be-for example 4/4 -with Stravinsky’smeter pattern embedded in some layer, or the meter pattern may be overt.

MILTONOTES

Elements of Groove



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Elements of Groove

Ensemble and feel

Another enormous topic, but we will focus attention on two extraordinary rhythmic ensemble disciplines:

Rhythmic patterns of Ashanti people of GhanaHartigan (1995)

andan analysis of several drum/bass/guitar grooves of

the James Brown Rhythm Sections (1968-1973)Slutsky & Silverman (1997)

Elements of Groove

Swing

Swing will be defined here as the difference in length betweenan on-beat and off-beat quaver (and on-beat and off-beat semiquaver). Rather than just a straight vs. triplet swung

concept of swing.

Elements of Groove

Swing

Elements of Groove

Latency

Elements of Groove

Time-feel

Elements of Groove

Syncopation

Syncopation is the emphasis of ‘weaker’ beats. By weaker beats we generally mean off-beat quavers and

semiquavers. Although stressing beats 2 & 4 over1 & 2 also falls into this category.

How can off-beats be relatively more emphasised than anon-beat?

No on-beat, or tied on-beat.Louder more articulated offbeat

Melodic/Harmonic emphasis

Elements of Groove

Identify the syncopated features

Elements of Groove

Rhythmic Repetition

An addition to feel, interesting rhythmic/melodic components can sense a groove through repetition.

Repeating phrase present a time-feel, and also create a sense of expectation allowing for musical variation.

Notice the repeated and slightly varied rhythmic device

Elements of Groove

Rhythmic DisplacementRepeating rhythmic figures tend to occur at 1, 2 or 4 bar

intervals. However a rhythmic figure can be repeated on a different beat of the bar. A simple displacement maybe 2

beats, where the beats ‘strength’ is similar. Three beatdisplacements also occur as well as at other subdivisions,

and create a subtle infectious polymetric feel.

Elements of Groove

Rhythmic Displacement

3 - beat (dotted minim) displacement

dotted semi-quaver displacement - disrupting any swing/weighting that may exist

Rhythmic/melodic figures can also be repeated and displaced between instruments

Elements of Groove

Elements of Ensemble Groove

Repetition/displacement of figures between instruments

Time-feel: What is the overall feel of the ensemble, Is feel (swing etc.) the same between instruments?

Are there any moments when a rhythmic gap in some instruments allowsanother instrument to feature? Is there a rhythmic interplay?

Are there moments when more than one instrument synchronise material and play a similar rhythmic/melodic figure (a sort of tutti)?

What are the roles of each instrument? Time-keeping, feel, texture, rhyhmic interest.Do these roles change?

West African Drumming

Ashanti People of Ghana

A richly syncopated drum tradition whose influencemay be heard in Cuban Son and Rumba, Haitian Vodun, Merengue of Dominican Republic, Brazilian samba and

American Jazz.

West African Drumming

Sikyi (Si-chee) Ashanti People of Ghana 1

Sikyi : Ashanti People of Ghana 2

Adowa : Ashanti People of Ghana 1

Adowa : Ashanti People of Ghana 2

Gahu : Ashanti People of Ghana 1

Gahu : Ashanti People of Ghana 2

Akom Style 1: Ashanti People of Ghana

Akom Style 2 (3/4)

Metric Illusions

Akom Style 2 (6/8)

Metric Illusions

Groove

James Brown Rhythm Section (1960-1973)

Identify the elements of time-feel, syncopation, repetition, displacement

and ensemble techniques in theseseminal grooves.

Imitate, assimilate, innovate.

Think (1960)

Think (1960)

I Don’t Mind (1962)

I Don’t Mind (1962)

Out Of Sight (1964)

I Got You (1965)

Don’t Be A Dropout (1966)

Cold Sweat Pt. 1 (1967)

Cold Sweat Pt. 1 (1967)

I Can’t Stand Myself Pt. 1 (1967)

I Got The Feelin’ (1968) - Verse

I Got The Feelin’ (1968) - Bridge

Licking Stick (1968)

Give It Up or Turnit A Loose (1968) - Verse

Give It Up or Turnit A Loose (1968) - Bridge

Mother Popcorn (1969) - Verse

Mother Popcorn (1969) - Bridge

Funky Drummer (1969) - Pattern 1

Funky Drummer (1969) - Pattern 2

Get Up (1970) - Verse

Get Up (1970) - Bridge

Got To Getcha (1970) - Verse

Got To Getcha (1970) - Bridge

Funky Women (1970)

Super Bad Pts. 1 & 2 (1970) - Verse (1/2)

Super Bad Pts. 1 & 2 (1970) - Verse (2/2)

Super Bad Pts. 1 & 2 (1970) - Bridge

Talkin’ Loud & Sayin’ Nothing (1970) - Verse

Talkin’ Loud & Sayin’ Nothing (1970) - Bridge (1/2)

Talkin’ Loud & Sayin’ Nothing (1970) - Bridge (2/2)

Give It Up or Turnit A Loose ‘Live’ (1970) - Verse

Give It Up or Turnit A Loose ‘Live’ (1970) - Bridge

Hot Pants Pt. 1 (1971)

Make It Funky Pt. 1 (1971)

Papa Don’t Take No Mess Pt. 1 (1973)

The Payback (1973) - Intro

The Payback (1973) - Verse

Exercise 1: Sequence the elements of an Ashanti Time-line of your choice.Make sure you can identify and have absorbed every part.


Exercise 2: Create a piece using some (not necessarily all) of the elements from Exercise 1. You may wish to turn one pattern into a bass-line and bind some of the

others to other melodic, harmonic and rhythmic instruments.

Exercise 4: Using features which you have absorbed from the James Brown templates, create your own 2, 4 or 8 bar groove, paying particular attention to

time-feel. syncopation, repetition, displacement and ensemble mechanics.

Exercise 3: Recreate as accurately as possible with MIDI one of the sample James Brown grooves, paying particular attention to articulation and swing values.

MILTONOTES

Melodic Structures



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Quick intermission before our scheduled

Episode

Conceptualise (or fully compose) piecesbased on each of the following images

This species of ant survive floods by hugging each other. The cluster floats but they would drown as individuals

Review

All episodes interlink, so frequent reviewing and re-contextualising of information is highly

beneficial

Polymeter Use

Alignments

When a polymeter appears there will be a point in time when the barlines coincide. The effect of

this event may be used musically.

Polymeter Use

Break out Clauses

A polymetric phrase may be held indefinitely, but often the implications is broken by added or

subtracted beats torealign the measures.

Polymeter Use

Melodic/Harmonic Adjustments

As polymetric phrases fall out of sync, some phrase can be adjusted at some point in their cycle to accommodate their new harmonic/

melodic environment

Polymeter Use

Lateral thinking of polymeter

A single line may embody several musical features subject to meter, and hence polymeter:

Note phrasing, dynamic emphasis, melodic emphasis, delay rate, pan rate, filter rate, trem

rate and so on.

MILTONOTES

Melodic Structures



Here we look deeply into the construction ofmelodies from a ‘classical’ perspective although its implications run beyond stylistic constraints

Arnold Schoenberg (1874-51)

A radical traditionalist2nd Viennese School,

Fundamentals of CompositionHarmonielehre

Melodic StructuresThe Phrase

The smallest structural unit is the phrase, a kind of musical molecule consisting a number of integrated

musical events possessing a certain completeness and well adapted to combination with other similar units.

...a unit approximating what one could sing in a single breath. Its ending suggests a form of punctuation such

as a comma. Often some features appear more than once in a phrase. Such ‘motivic’ characteristics will be

discussed [later]


Concentrated in one voice, implies an inherent harmony


Even with elaborate melodies, harmony (usually I and V) is clear.


Length of phrases can vary widely, depending on metre and tempo

Melodic StructuresThe Phrase from Chords

Phrases are often derived from skeletal chord forms


Simple elaborations of skeletal chord forms


Passing notes to chord forms

Melodic StructuresThe Phrase from Chords, Elaborated

Passing notes and note repetitions toelaborated chord forms

Phrase embellishment


Appoggiaturas and changing tones.


Exercise 1a-f Compose 2 different simple phrases using chord tones of 1-3 chords in a major key(1a,1b), a minor key (1c,1d) and the dorian mode (1e,1f). Keep them very simple, clear and memorable.

Exercise 2a-c Pick one phrase from each of the major, minor and dorian sets and elaborate using appoggiaturas, upbeats and other available devices.

Melodic StructuresThe Motive (Motif)


If a phrase is a molecule, the motif is the atom, the ‘smallest common multiple and greatest common factor’ providing unity, and through repetition, variation and recombination can form higher structures in the phrase and piece


Often the use of the motif is intuitive, though it needn’t be. It forms the invisible musical glue

that can unifies and forms higher level structures


Usually defined by a simple rhythmic and intervallic structure, a motif is maintained by

repetition of which there is:

Exact and Modified Variations.

Variations preserve some musical features and alter others


Note the simplicity of the motif, and how variations are slight but in different features

Melodic StructuresMotivic Transformations





Exercise 3 Write a simple motif, and create 12 variants (using for example, transpositions, elaborations, inversions, retrogrades, retrograde inversions, rhythmic changes, omissions and so on).

Exercise 4 Construct a phrase (or 2 or 3) using combined variant forms of your motif from Exercise 3. Try and outline a harmonic sequence.

Melodic Structures

Melodic Structures from Phrases and Motifs

Although it may pain Schoenberg, let’s look at phrase and motif construction over the course of

a whole piece in the work of the French composer of stunningly progressive minimal

work, Erik Satie (1866-1925)

Melodic AnalysisGnossienne I - P1

2 scales, 3 chords, 1 piece




Exercise 5 Listen to, and examine the score of, Gnossienne I (or any Satie piece) See if you can identify key motifs (and variations) through phrases, as well as phrases and their repetitions and variations are put together to make the whole piece.

Exercise 6 From the techniques observed in Exercise 4, choose a scale or 2, 3 or so chords, simple rhythms and limited motivic material, and a series of phrases. Create a short piece with a series of melodic phrases.

Exercise 1a-f Compose 2 different simple phrases using chord tones of 1-3 chords in a major key(1a,1b), a minor key (1c,1d) and the dorian mode (1e,1f). Keep them very simple, clear and memorable.

Exercise 2a-c Pick one phrase from each of the major, minor and dorian sets and elaborate using appoggiaturas, upbeats and other available devices.

Exercise 3 Write a simple motif, and create 12 variants (using for example, transpositions, elaborations, inversions, retrogrades, retrograde inversions, rhythmic changes, omissions and so on).

Exercise 4 Construct a phrase (or 2 or 3) using combined variant forms of your motif from Exercise 3. Try and outline a harmonic sequence

Exercise 5 Listen to, and examine the score of, Gnossienne I (or any Satie piece) See if you can identify key motifs (and variations) through phrases, as well as phrases and their repetitions and variations are put together to make the whole piece.

Exercise 6 From the techniques observed in Exercise 4, choose a scale or 2, 3 or so chords, simple rhythms and limited motivic material, and a series of phrases. Create a short piece with a series of melodic phrases.

MILTONOTES

Phrase, Contour & Melodic Forms



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for music and more

This episode

Entire serieshttp://open.spotify.com/user/miltonline/playlist/7El79d9SdfBxnSwNruyAeD

http://open.spotify.com/user/miltonline/playlist/0IIbAhOvRgGeKhtqc8NXaZ

The concepts of motif and phrase have been defined, as well as principles behind their

construction and transformation. Let’s see how these manifest to form successful melodies in the real world and how we might use these ideas in

composition.

Key terms: Motif, Phrase, Endings, Intervals, Phrase Hierarchy, CTs, NCTs, Devices, Range,

Contour, Diatonicism, Parallelism, Leaps & Lines, Accel/decceleration, Melodic forms.

EndingsSimilar

How a phrase ends is often of particular melodic importance. You may notice that different phrases

often have similar endings.Phrase 1

Phrase 2 has unequal length, different starting material but similar motifs and an identical ending, forming a link with Phrase 1

EndingsModified

Conversely, a phrase may be repeated with small modifications to the ending, to create different

degrees of resolution even with similar harmony

Phrase A1 Phrase A2

Phrase A1.2 Phrase A1.3Phrase A1.1 Phrase A1.1

This introduces the concept of phrase hierarchyPhrases made up of smaller phrases which can be modified and recombined

EndingsDegrees of Resolution

Here’s an impression of resolution level of diatonic notes in a major scale devoid of harmony (the same categories work for minor also)

It’s very dependent on content but is a reasonable starting point.Note that the idea of resolution here is independent from consonance/

dissonance - the sound of a note against the underlying harmony.

Major

Minor

ChromaticismDegrees of Resolution

Major

Minor

These are highly context dependent and not hard rules - there are also other settings other than major or minor that can be established,

but the idea of varying degrees of melodic resolution is fundamental.Again, this about melodic resolution not consonance/dissonance - the latter

being controlled by harmonic context.

Phrase ConstructionDegrees of Resolution

We can now see how a sense of resolution (from stable to unstable) can be established between phrases giving a longer arc to melodic construction.

This is a fundamental concept in 1000s of melodies.

Phrase A1 Phrase A2

from Gnossienne 1 - Satie

Unstable #4Resolution

Stable Root

EndingsDegrees of Resolution

Exercise 1 Write two different phrases that share identical resolving endings

Exercise 2 Write two phrases with the same (or no) harmony, but with a different note choices at the ending, creating different degrees of resolution.

Phrase Endings & HarmonyLinking phrases with similar or

modified endings

Sub-divide into 2 levels of phrases noting areas of stability/instability and how harmony accommodates the melody


modified endings

from Across the Universe - BeatlesNote that melody notes, melodic rhythm and harmony all combine

to create a multi-layer musical experience


modified endings

Note the use of varied phrase endings, motivic editing and transformation with harmony

from Angel Eyes - Matt Dennis


modified endings

Note the use of varied phrase endings, motivic editing and transformation with harmony

Phrase Endings & RhythmStrength of ending

Rhythm contributes to the sense of finality of a phrase (not that a phrase always needs it). The ‘strength’ of the beat on which the phrase ends contributes to a sense of continuity or finality.

1 32 4& & & &

Strong

Weak1 32 4& & & &

Phrases & Rhythm

Exercise 2a Write 3 similar phrases with different strengths of ending

Exercise 2b Write 3 similar phrases but starting on different beats

Melody Contour & Range

Melodic TypologyAlthough there are millions of possible melodies, analysts have proposed

systems to categorise them into various groups. We won’t favour one but at least look at the various identifying features.

Range (Highest to lowest notes)

Contour (Position of highest and lowest notes)

Leap & Line (Stepwise motion or intervallic leaps)

Long Term Goals (A journey between 2 notes) Chopin

Motivic Material(Identifying motifs or articulations)

Scale/Diatonicism/Chromaticism(Set of notes used)

Consonance/Dissonance(How the melody interacts with harmony)

Melody Contour & Range

Melodic Typology

Exercise 3a-b Write a melody with specific ideas for the features identified previously. Write another melody from the previous by changing. 2 of the features

Melody & Harmony

Consonance & Dissonance

In addition, to melodic resolution, there is another important musical layer:The consonance and dissonance of a melody against the harmony.

The most consonant melodic approach is to use only chord tones (CTs)

Melody & Harmony


NCTs of course can be used, and there are techniques for resolving dissonances.Here Passing Tones (PTs), Diatonic Sequences and Chord Tones Pivots.

Melody & Harmony


Melody & Harmony


Melody & Harmony


Melody & Harmony


Melody & Harmony


Melody & Harmony


Melody from a chord sequence.A Theme and Variations concept (Paganini Caprice 24)

This allows the creation of certain canonic forms where material that functions of the same harmony can be superimposed

Melody & Harmony


Exercise 4 Write a 4-bar chord sequence, and an accompanying melody using CTs, create 3 subsequent phrases on the chord sequence

Melody & Harmony


NCTs can be left unresolved as part of a melody and will produce a varying amount of dissonance against the underlying harmony, for which the next page give a general impression of this continuum.

Melody & Harmony


Melody & Harmony


This schematic shows the continuum of consonance and dissonance with reference tothe chordal context (ie if we are looking at a ii or a iii chord, a I or a IV etc.

There are some exceptions to this, for example the use of the b3(aka #9) in a major context, which is a stylistically perfectly accepted dissonance in many African-

American sourced music forms (Jazz, Blues and by assoiciation Rock, pop, funk etc.)

CTsDiatonic

Non-ClashNCTs

Non-DiatonicNon-Clash

NCTs

DiatonicClashNCTs

Non-DiatonicClashNCTs

Melody & Harmony


From another perspective we can look at common dissonances - also known as tensions or extensions and have a quick look at what contexts they are accepted,

other than a passing tone or other melodic device.

b9 (aka b2)

Melody & Harmony


b9 (aka b2) This can be sometimes found unresolved when it is a diatonic.

Eg. an F against an Eminor in the key of C, or against an E major in A harmonic minor.It is common against the one chord scales with a b2 eg. Phyrgian (F against E minor in E

phrygian) or in ‘Spanish’ Phrygian (F against E major) and the like. (Caravan, Miserlou for example)

It also appears on a major or dominant chord that is acting as a primary or secondary dominant, particularly (but not exclusively) when resolving to a minor chord. Other than this it

is rare when non-diatonic.

Melody & Harmony


9 This is the most common ‘dissonant’ non chord tone, and appears freely on a major, minor,

dominant, major 7 chord etc. It is only rare when non diatonic e.g. on a iii chord in a major key, but non diatonic examples are found particularly in a parallel context.

Every Breath You Take,(Police) or Twin Peaks Theme shows its diatonic usage, while Castles Made of Sand, Come On Pt.1 (1:16) and Little Wing (Hendrix) has parallel non-diatonic

examples.

Melody & Harmony


#9 Acting as a ‘blue note’ on a major or dominant chord is a commonly accepted melodic dissonance on any resolving dominant chord or over any I major or I dominant chord or

general tonality. It’s use on the IV or IV7 chord is actually quite rare due to the peculiarity of a b6 over b3.

Examples of a b3 in major/dominant context abound.

Melody & Harmony


11(4)Although traditionally a dissonance that requires resolution, the 11th (or 4) is often left

unresolved on a I chord a major or dominant context (being diatonic), and is common on minor chord as there is no clash with the 3rd. It is a little more rare, but still heard, in a non-diatonic form (e.g. on the IV chord in major, the IV chord in blues however tolerates it easily due to the

pentatonic context). All minor chords (and half-diminished chords) happily accept the 4th melodically although non-diatonic uses are a bit more rare.

Melody & Harmony


#11(#4)The #11 is a common NCT on major, major7 and dominant chords.

The least dissonan use is diatonic e.g. Chord IV in major, Chord I in Lydian or bVImaj in a minor (or borrowed minor) context. It is also often used on tritone-substituted dominant chords.

However it is common particular in jazz-tinged styles to include on major, major7 and dominant chords and on minor chords in a Satie-esque exotic moments.

(Blue 7 dominant, Satie minor, Blue in Green Major)

Melody & Harmony


b6(b13)The b6 or b13 with the presence of the 5th is quite a strong dissonance often

quickly resolvedThe exception being on resolving dominant chords (particularly to minor chords)

where it is often supported.

Melody & Harmony


6(13)The 6 or 13 in the melody, unless non-diatonic is readily supported by major, minor and

dominant chords alike.

Giant Steps - John ColtraneNotice how accepted NCTs are used alongside tomarry a memorable melody and a complex chord

sequence

Melody & Harmony

Intervallic Features

Exercise 5 Write a melody devoid of harmony. Harmonise it in 3 ways so that all notes are in example a) All chord tones b) Resolved dissonances c) Accepted NCTs

Melody & Harmony

Intervallic features

Traditional melodies usually have a few leaps using chord tones and devices, and the rest of the material step wise. However it is possible to use less traditional intervals as

important melodic motifs.

Melody & Harmony


Melody & Harmony


Melody & Harmony


Melody & Harmony


Melody & Harmony


Exercise 6 Write a melody based on extended intervals (4th,5ths and 7ths) or interval structures ( for example +2,+7,-1) using accepted NCTs

Melody & Harmony

Pedal Tone/Pitch AxisYou’ll notice that the more angular examples of intervallic tunes had less (or no chords)

Since harmony dictates consonance and dissonance, we can open up melodic possibilitiesby simplifying the harmonic context. For example a drone permits a wide array of scales to

be implied compositionally (or through improvisation). Indian classical music (discussed later) is monophonic and allows an enormous amounts

of expressive melodies unconstrained by even temperament.Even limiting ourselves to a 7 note system, even temperament, only one type of degree and no

b4, Satie’s F-minor chord (on which he uses Dorian #4 and Melodic Minor #4) actually has16 logically accompanying modes and scales.

b2or2

4or#4

b6or6

b7or7

R b3 5

Melody & Harmony

Pedal Tone/Pitch Axis

b2or2

4or#4

b6or6

b7or7

R b3 5

PhrygianAeolianDorian

Phrygian #4Aeolian #4Dorian #4

Melodic MinorHarmonic Minor

Harmonic Minor b2

Melodic Minor #4Harmonic Minor #4

Harmonic Minor b2/#4

Dorian b2Mel. Min b2

Dorian b2/#4Mel. Min b2/#4

Melody & Harmony


Ravel’s Bolero (1928) is an orchestral work based almost exclusively on a bass ostinato(bass loop) which includes only a C and G. This allows the insistent melody to

be transformed into several parallel beautiful scales while maintaining musical interest.

French composer Maurice Ravel (1875-1937)

Melody & Harmony


C Major(R,2,3,4,5,6,7)C Mixolydian b6 (Aeolian Major/Hindustani/Mode 5 of MM)(R,2,3,4,5,b6,b7)C Phrygian(R,b2,b3,4,5,b6,b7)C Phrygian Dominant(R,b2,3,4,5,b6,b7)

E Mixolydian b6E Phrygian

Bolero Modes

Melody & Harmony


.Take the bridge of Satch Boogie - Joe Satriani for example

The A acts as a pivot to a menagerie of exotic scales/harmonies.

Or no harmony whatsoever as in Debussy’s Syrinx unpublished in his life time.

Melody & No Harmony

“my favorite music is those few notes an Egyptian shepherd plays on his flute: he is a part of the landscape around him, and he knows harmonies that aren’t in our books.”

The opening phrase elaborates the notes of a whole-tone scale (Bb, Ab, Gb, E). The whole-tone scale is incompatible with common-practice harmony, because it contains no 5ths and no half steps, making traditional cadences impossible and eliminating tonic-dominant polarity. Debussy used whole-tone scales in many works as a way to confound his listeners’ tonal expectations and to explore new harmonic possibilities. Here, though, he does not limit himself to the whole-tone scale. He decorates it with chromatic neighbors and passing tones in the first two measures (A,B,G, F). In measure 4 he exchanges it for an ascending chromatic scale (Bb, B, C, Db).

In measure 11 he turns to a pentatonic scale (Gb, Ab, Bb, Db, Eb) with an added note (F). In measure 15, which begins the middle section of the piece, he uses a fully chromatic scale.

At measure 26 (the recapitulation) he returns to the initial whole- tone scale. Then in the very last measure he switches to the other possible whole-tone scale (B, A, G, F, Eb, Db), which is how the piece ends. In this very short piece Debussy exchanges pitch materials almost compulsively, but he steadfastly avoids the major- minor diatonic scale.

Melody & Harmony


Exercise 7 Write a melody over a 2, 1 or 0 note ostinato, exploring scales which the harmony allows.

Exercise 7 Write a melody over a 2, 1 or 0 note ostinato, exploring scales which the harmony allows.

Exercise 6 Write a melody based on extended intervals (4th,5ths and 7ths) or interval structures ( for example +2,+7,-1) using accepted NCTs

Exercise 4 Write a 4-bar chord sequence, and an accompanying melody using CTs, create 3 subsequent phrases on the chord sequence

Exercise 5 Write a melody devoid of harmony. Harmonise it in 3 ways so that all notes are in example a) All chord tones b) Resolved dissonances c) Accepted NCTs

Exercise 1 Write two different phrases that share identical resolving endings

Exercise 2 Write two phrases with the same (or no) harmony, but with a different note choices at the ending, creating different degrees of resolution.

Exercise 3a-b Write a melody with specific ideas for the features identified previously. Write another melody from the previous by changing. 2 of the features

MILTONOTES

Chance & Translation



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for music and more

This episode


http://open.spotify.com/user/miltonline/playlist/4XZkQfATo0nIycKYL91QTH

This episode we look at approaches to composition, that in some way have delegated

decisions to ‘outside’ influences such as the use of chance and indeterminacy in composition,

cryptograms and the ‘sonification’ of non-musical data and physical processes.

Why?

Indeterminacy (like improvisation) and chance could be a component (big of small) of composition. From making a

series of randomised chords, or predetermined motif ‘work’ or the

effective use of a noise wave-form LFO.

The transfer of non-musical data (for example someone’s initials converted to a motif, or a key from another piece) can

act as a form of tribute, signature or aesthetic link. It can also act as a compositional challenge and self-imposed to enhance creativity and

encourage new musical ideas.

The delegation of compositional control, has a philosophical implication. Can a composer create a piece that includes elements out of her control? At what

degree of uncertainty, white noise LFO or level of improvisation does it no longer

become the piece?Can we just point at a sound (like 4’33”)

and claim it as a piece?Which parts are important?

Cadenza to Jazz to Electronica

Chance and AleatoricMusic

The use of chance in composition has a varied and long heritage.

Defining chance or aleatoric music as“music in which some element of the

composition is left to chance”would imply many types and degrees of

chance music.

Chance

Types of randomness

Range

Step

Dotted or Drunk

Chance

Ockeghem’s Missa Culuvsis ToniA composition by Johannes Ockeghem (1410-97)

which allows a choice of modal interpretations.One composition: multiple realisations.

Chance

Determined Left to chance/Indeterminant

Using this very simple system allows a more nuanced and useful understanding

of chance music

Chance

Determined

Melodic contour, rhythms, structure, text etc.

Indeterminate

Which 1 of 4 Modes

Chance

Mozart’s Dice Game (1787)

A Musical game for composing minuets and trios from dice rollshttp://sunsite.univie.ac.at/Mozart/dice/

Chance

Determined

Harmonic structure

Form

Set of motifs

Left to chance

Which of theset of motifsare selected

Mozart’s Dice Game

Chance

DuChamp’s Erratum Musical (1913)Composition by the dadaist artist Marcel DuChamp.

A fixed number of pre-determined notes (and words in the vocal version) from a set of possibilities are randomly selected to form the work.

Chance

Determined

Prepared materials

Number of events

Left to chance

The order and which of the musical fragments are selected

Duchamp’s Erratum Musical

Chance

Cage’s Williams Mix (1952)Environmental sounds collected over 9 months by the Barrons,

then tape-spliced according to a set of rules determined by coin tosses.

Chance

Determined

Prepared environmental materials

Length of piece

Operations

Left to chance

Which operations on which tracks

Cage’s Williams Mix

Chance

Cage’s 4’33 (1952)

Measured ‘Silence’ Focusing attention on unintended sound

Chance

Determined

Duration(s)

Time

Place

Left to chance

Everything else

Cage’s 4’33”

Chance

The Use of Randomness in Synthesis

Noise wave as tone

Noise wave as LFO (with continuous and step values)

Chance

1 Layer of Randomness

Chance

2 Layers of Randomness

Chance

3 Layers of Randomness

Chance

Randomness and Creativity

The forcing of new ideas

Random Word Generator

Chance

Exercise 1 Write a musical passage which divides various musical features into determined, and randomly generated. Render some versions.

Exercise 2 Alter which of the features in Exercise 1 are determined or random and render some versions.

Exercise 3 Create a synth line (or several layers) experimenting with controlling LFOs with step and/or continuous noise functions.

Exercise 4 Randomly generate an adjective and noun, and create the opening (or all) of a work based on the phrase. Repeat with a different randomly generated phrase.

Chance

So compositions can allow areas and degrees of randomness and

indeterminacy. From interpretation, cadenzas, jazz to extremely random.

Pockets of chaos

But they can also includepre-determined material,

(overt or hidden).

The BACH motif

Translation

Cryptogram

(B = Bb H=B S= Eb)

B A C H

Acting as a tribute, or a test of compositional skill, the Bach motif has appeared in 100s of works since the 17th century.

The BACH motif

Contrapunctus V (2:20)

Contrapunctus IV

Translation

Cryptogram

The BACH motif

The unfinished Contrapunctus XIV, C.P.E. Bach’s("At the point where the composer introduces the name BACH [for which the English notation would be B♭-A-C-B ] in the countersubject to this fugue, the composer died."

Translation

Cryptogram

The BACH motif

Schumann: Sechs Fugen über den Namen: Bach No. 4 & 5 (1845)

Translation

Cryptogram

The BACH motif

Webern Tone Row String Quartet Op. 28

Translation

Cryptogram

The BACH motif

Translation

Cryptogram

1845 — Robert Schumann: Sechs Fugen über den Namen: Bach, for organ, pedal piano, or harmonium, Op. 601855 — Franz Liszt: Fantasy and Fugue on the Theme B-A-C-H, for organ (later revised, 1870, and arranged, 1871, for piano)1878 — Nikolai Rimsky-Korsakov: Variations on BACH, for piano1900 — Max Reger: Fantasia and Fugue on B-A-C-H for organ1910 — Ferruccio Busoni: Fantasia contrappuntistica for piano (first version; later versions 1912 and 1922)1926–28 — Arnold Schoenberg: Variations for Orchestra, Op. 311937–38 — Anton Webern: String Quartet (the tone row is based on the BACH motif)1968 - Alfred Schnittke: Quasi Una Sonata 1981 - Schnittke: Symphony No. 3 - used alongside the monograms of several other composers.1856 - Johannes Brahms: Fugue in A-flat minor for organ, WoO 81930 - Marios Varvoglis: Canon, Chorale and Fugue on BACH1932 - Alfredo Casella: Due Ricercari sul nome B-A-C-H, Op. 521932 - Francis Poulenc: Valse-improvisation sur le nom Bach for piano1934 - Hanns Eisler: Prelude and Fugue on B-A-C-H, Op. 46 for string trio1937 - Marios Varvoglis: Prelude, Chorale and Fugue on BACH1942-46 - Charles Koechlin: Offrande musicale sur le nom de B-A-C-H, Op. 1871952 - Jean Coulthard: Variations on BACH for piano1952 - Luigi Dallapiccola: Quaderno musicale di Annalibera for piano1954 - Dallapiccola: Variazioni ("Variations", orchestral version of Quaderno musicale di Annalibera)1951-55 - Dallapiccola: "Canti di liberazione"1964 - Arvo Pärt: Collage over B-A-C-H for strings, oboe, harpsichord and piano1974 - Rudolf Brucci: Metamorfosis B-A-C-H for strings1993 - Ron Nelson: Passacaglia (Homage on B-A-C-H) for concert band

What about other letters/notes?

Translation

Cryptogram

German System

A = AB = BbC = CD = DE = EF = FG = GH = BM = EL = A

R(e) = DS (Es) = Eb

T(i) = BAs = Ab

Ignore the rest

Translation

Cryptogram

French System

A B(or Bb)

C D E F G

H(or B)

I J K L M N

O P Q R S T U

V W X Y Z

Translation

Cryptogram

Alban Berg/Hanna Fuchs-Robettin

A, Bb, B, F

Berg’s Lyric Suite

Translation

Cryptogram

Arnold Schoenberg

A, Eb, C, B, Bb, E, G

Schoenberg’s Seraphita

Translation

Cryptogram

Brahms

Bb, A, B, Eb

Schnittke’s Quasi Una Sonata

Translation

Cryptogram

Haydn

B, A, D, D, G

Ravel’s Menuet sur le nom d’Haydn

Translation

Cryptogram

Béla Bártok

Bb, E, B, A

Translation

Cryptogram

Cage

C, A, G, E

Pauline Oliveros and Simon Jeffes of PCO in Cage Dead

Translation

Cryptogram

Dimitri Schostakovich

D, Eb, C, BIn many of Schostakovich’s work, and tributes to him.

String Quartet No. 8

Translation

Cryptogram

Sacher Hexachord

Swiss conductor and patron Paul Sacher,used by Babbitt and Boulez (Messagequisses)

Eb, A, C, B, E, D

Translation

Cryptogram

Robert Schumann

Used in Schumann’s Carnaval (in SCHA, ASCH and AsCH forms)

Eb, C, B, A

Translation

Cryptogram

Niels Gade

The monogram for Danish composer Niels Gade (1817-1890) is used in Schumann’s Nordische Lied No.41, Op.68

G, A, D, E

Translation

Cryptogram

Cross MotifSymbol from Gregorian Melodies

Franz Lizst (1811-86)

Translation

Cryptogram

Cross MotiveCrucifixion and star-crossed lovers

Tchaikovsky (1840-93)mm1-2 of Pathétique Symphony

Translation

Cryptogram

Exercise 5 Create your own monogram using the German or French system. Compose a phrase/passage/piece of your signature. Experiment with motivic transformations (R, I, RI), phrase constructions, harmonisations etc.

Exercise 6 Generate another cryptogram for someone (or something) else. Compose a phrase/passage/piece interweaving this, and your monogram.

Translation

Cryptogram

Translation

Other Mappings

Lettersin a name

Notenames

Amusical Musical

Translation

Other Mappings

Lettersfrom anywhere

Any pitch

Amusical Musical

Translation

Other Mappings

ASCII to midi note conversion

Translation

Other Mappings

DNA A C T G

ASCII 65 67 84 71

MIDI F3 G3 C5 B3

DNA to midi note conversion

Translation

Other Mappings

Codon permutations

AAAAACAATAAGACAACCACTACGATAATCATTATGAGAAGCAGTAGG

CAACACCATCAGCCACCCCCTCCGCTACTCCTTCTGCGACGCCGTCGG

TAATACTATTAGTCATCCTCTTCGTTATTCTTTTTGTGATGCTGTTGG

GAAGACGATGAGGCAGCCGCTGCGGTAGTCGTTGTGGGAGGCGGTGGG

Translation

Other Mappings

Lettersfrom anywhere

Rhythm

Amusical Musical

Translation

Other Mappings

h q ee xxe xex exx ‰e !x!x !x‰ ‰.x Œ

A B C D E F G H I J K

L M N O P Q R S T U V

W X Y Z

One of countless letter to rhythm mapping templatesLetter frequency and rhythmic sets will play a compositional role

Exercise 7 Create a rhythmic pattern from the given - or your own - mapping template using your name, initials or somesuch.

Exercise 8 Combine a rhythmic with a melodic mapping template, you may want to use two ‘source names’ so that for example all As aren’t the same length.

Translation

Rhythmic Mapping

Translation

Types of Mappings

Discrete/Continuous

One to One

One to Many

Many to One

Parallel

Translation

Villa-Lobos (1857-1959)

Brazilian Composer

Translation

Villa-Lobos’ millimetrization

New York Skyline

Translation

Villa-Lobos’ millimetrization

New York Skyline Melody (1939) and more

Exercise 9 Create a melody from an image. Harmonise.

Translation

Mapping

Translation

Other Mappings

Vertical Pitch

Amusical Musical

Horizontal Time/Rhythm

Translation

Data Sonificiation

Why stop at 2 discrete dimensions?

How much can be extracted?

What data can be used?

Primal Sound (2004,2007)The coronal suture of the skull (which should now be chiefly investigated) has

let us assume a certain similarity to the closely wound line that the needle of a

phonograph cuts into the receptive, revolving cylinder of the machine.

Suppose, for instance, one played a trick on this needle and caused it to

retrace a path not made by the graphic translation of a sound, but self-

sufficing and existing in nature – good, let us say it boldly, if it were (e.g.) even

the coronal suture – what would happen? A sound must come into being, a

sequence of sounds, music…Feelings of what sort? Incredulity, awe, fear,

reverence yes, which of all these feelings prevents me from proposing a name

for the primal sound that would then come to birth?

Ur-Geräusch (Rilke 1919, p 1087)

Translation

Data Sonificiation

Primal Sound (2004,2007)

Image ©2004 Palmer


Image ©2005 Supranowitz




Angela Palmer’s Inside Out exhibition

•!Ruskin Gallery, Oxford University, UK. 2 February 2004.

•!Royal College of Surgeons, Hunterian Museum, UK. 29 January – 19 May 2007.

Music of the Body exhibition

•!Science Circus, Guildford, Surrey, UK. 20 September 2008.

Translation

Data Sonificiation

Head Music (2004)

Translation

Data Sonificiation

Microcosmos (2007)

Generative Composition Emergent Music

Translation

Data Sonificiation

Exercise 10 Create your own mapping system from a data source and realise it compositionally.

Translation

Mapping

Exercise 10 Create your own mapping system from a data source and realise it compositionally.

Exercise 9 Create a melody from an image. Harmonise.

Exercise 7 Create a rhythmic pattern from the given - or your own - mapping template using your name, initials or somesuch.

Exercise 8 Combine a rhythmic with a melodic mapping template, you may want to use two ‘source names’ so that for example all As aren’t the same length.

Exercise 1 Write a musical passage which divides various musical features into determined, and randomly generated. Render some versions.

Exercise 2 Alter which of the features in Exercise 1 are determined or random and render some versions.

Exercise 3 Create a synth line (or several layers) experimenting with controlling LFOs with step and/or continuous noise functions.

Exercise 4 Randomly generate an adjective and noun, and create the opening (or all) of a work based on the phrase. Repeat with a different randomly generated phrase.

Exercise 5 Create your own monogram using the German or French system. Compose a phrase/passage/piece of your signature. Experiment with motivic transformations (R, I, RI), phrase constructions, harmonisations etc.

Exercise 6 Generate another cryptogram for someone (or something) else. Compose a phrase/passage/piece interweaving this, and your monogram.

MILTONOTES

Process



Listening list:



for music and more

This episode


http://open.spotify.com/user/miltonline/playlist/4YtsVORmc2f7BDYJGBBrNG

This episode deals with the use of compositional systems from the simple to highly complex, and

using physical and algorithmic processes. Compositional systems may be used quite freely to introduce creative options, or at the furthest extreme as a hands-off process that might be

heard clearly by the listener.

Process

Joseph SchillengerSystem of Musical Composition (1946)

Process

Comprehensive system on many musical aspects - beyond prevailing tutor books - an attempt at scientific unification

Process

Schillinger System: Permutations in melody and pitch scales

Process

Schillinger System: Permutations in scales, modulation and harmony

Process

Schillinger System: Rhythmic permutation (3+1)+(2+2)+(1+3)

Process

4:3 (3+1)+(2+2)+(1+3)

6:5 (5+1)+(4+2)+(3+3)+(2+4)+(1+5)

Realise in terms of rhythm, melody, harmony etc.

ProcessExercises

Exercise 1 Write a passage of music using the Schillinger system on rhythm, melody and/or harmony.

Process

Score for Metastasis (1953-54)Iannis Xenakis (1922-2001) deep mathematical and music connection.

Avant-Garde composer. Predetermined dragging of chairs and benches as well as drone music and

minimalism

La Monte Young - Poem (1960)

Process

Ligeti’s Poeme Mechanique (1962)

Process

Simultaneous tempi and wind down.

ProcessExercises

Exercise 2 Simulate musically a physical process (e.g. metronomes, drips, popcorn, tides, orbits etc.

Terry Riley’s In C (1964)

Process

Superimposition of 53 randomly started musical fragmentsFirst minimal piece.

Tape piece for phased vocal phrase. Slow technological phasing.Aural examination of a preacher’s voice and pigeon.

South Bank Show documentary (Rain) http://www.youtube.com/watch?v=q0DQRfm0uL8 or start watching entire documentary here (recommended): http://www.youtube.com/watch?v=e_pR1sHHeQU&feature=related

Complete piece http://www.dailymotion.com/video/x90h1r_steve-reich-its-gonna-rain-part-1_music

Steve Reich - It’s Going to Rain (1965)

Process

Ligeti’s Lux Aeterna (1966)

Process

Canonic structures and superimpositions that don’t fit traditional harmony, but form powerful compelling textures

Ligeti’s Lux Aeterna (1966)

Process

analysis ©Jarviepp

Process

Process

Algorithmic cyclical process whereby motifs are micro-rhythmically transformed to rhythmic displacements. 12-note, 8-note, 4-note phase

Steve Reich - Piano Phase (1967)Violin Phase (1967) Phase Patterns (1970)

Process

"I am interested in perceptible processes. I want to be able to hear the process happening throughout the sounding music.…

What I'm interested in is a compositional process and a sounding music that are one and the same thing" - Steve Reich

Piece formed by the gravitational pull of swinging microphones and feedback responses

Steve Reich - Pendulum Music (1968)

Process

Frederic Rzewski - Les Moutons des Panurge (1968)

Process

Written “for any number of musicians playing melody instruments, plus any number of nonmusicians playing anything,” contains a 65-note melody in F played in a cumulative sequence (1, 1-2, 1-2-3, and so on) by the entire ensemble in unison; once the entire melody is played, the sequence is reversed with the melody continued, but with notes from the beginning shed with each repetition (2-3-...65, 3-4-...65, and so on), until only one note remains. That final note is held until all the players have reached it, at which point all begin improvising. Rzewski’s instructions are: “Always play loud, never stop or falter, stay together as long as you can, but if you get lost, stay lost. Do not try to find your way back into the fold. Continue to follow the rules strictly.”

Carter & Rzewski

Karlheinz Stockhausen - Spiral (1968)

Process

A composition as a series of fixed transformations rather than a fixed structure.

Shepperd Tone piece

http://www.youtube.com/watch?v=RqRd555v0Hg

James Tenney - For Ann (Rising) (1969)

Process

Piece for 2 performers formed by 12-point displacement of rhythmic motif.

Steve Reich - Clapping Music (1972)

Process

Degradation through room resonance

Alvin Lucier - I Am Sitting In a Room (1974)

Process

With delay and varying EQ a motivic phrase automatically generates an ambient soundworld.

Album also includes pieces derived from fragments of Pachelbel’s Canon in D

Brian Eno - Discreet Music (1975)

Process

Oscillations and interferences on a wire

Alvin Lucier - Music on a Long Thin Wire (1979)

Process

Tone Row slowly unfolded then collapsed

James Tenney - Chromatic Canon (1980)

Process

Process Principles attached to longer scale harmonic form (See New York, and Cello Counterpoint)

Steve Reich - Electric Counterpoint (1987)

Process

ProcessExercises

Exercise 3 Write a piece of music based on an overt Reichian process.

Algorithmic Construction

Process

Thomas Tallis (1505-1585)

Spem in Alium


Process


Process

O M N I A 5 5 8

5,8


Process


Process


Process


Process

Process

Digital Technology and Process

Process

Computer processing has been harnessed since the 50s in order to provide composers with new ideas as well as algorithmically generated

pieces. Even creating millions of version of the same ‘piece’.

Digital Technology and Process

Process

Computer processing has been harnessed since the 50s in order to provide composers with new ideas as well as algorithmically generated

pieces. Even creating millions of version of the same ‘piece’.

Process

http://vimeo.com/25041544

Process

Iannix - software that harnesses computer processing to musical algorithms

ProcessExercises

Exercise 4 Construct an algorithm for a piece (with or without computer assistance) operating on more than one musical layer

ProcessExercises

Exercise 1 Write a passage of music using the Schillinger system on rhythm, melody and/or harmony

Exercise 2 Simulate musically a physical process (e.g. metronomes, drips, popcorn, tides, orbits etc.).

Exercise 3 Write a piece of music based on an overt Reichian process.

Exercise 4 Construct an algorithm for a piece (with or without computer assistance) operating on more than one musical layer

MILTONOTES

Tuning



Listening list:



for music and more

This episode


http://open.spotify.com/user/miltonline/playlist/1vWvLOvDYElkzQkuZr7Fp7

This episode deals with the scientific principles and creative possibilities of tuning from concepts

of just intervals, expressive intonation and electronic realisation of microtones.

Tuning

Tuning

• Wavelength & Frequency

• Hz. The Frequency of Human Hearing

• The Law of Octave Equivalence

• Harmonic Series

Tuning

How many octaves from 20Hz-20,000Hz?

Tuning

A reference pitch

Pitch inflation and variation for centuries.

In 1939 a standardised system of 440Hz was agreed although some European schoolhs go up

to 442Hz or 443Hz

Tuning

Harmonic Series

1/2 1/4Wavelength: !2/3

Frequency:

1/1

2/1 4/1!3/2 1/1

What division of the string?

How much faster does the string oscillate?

Note that frets (and pitch steps) are based on division rather than absolute length of a string. Hence, pitch is a logarithmic function with the perception of steps based on multiplications (and divisions).

We can however use the handy cent with using a logarithmic function turns the octave into1200 equal steps, with 100 cents equalling a 12th of the octave (equal semitone).

Tuning

Harmonic Series

Note that frets (and pitch steps) are based on division rather than absolute length of a string

(e.g. Frets are !5.61% of the remaining string).Hence, pitch is a logarithmic function with the perception of steps

based on multiplications (and divisions) of frequency (or wavelength).We can however use the handy cent with using a logarithmic function turns the

octave into 1200 equal steps, with 100 cents equalling a 12th of the octave (equal semitone), and 600 cents dividing the octave.

Tuning

Harmonic Series

String players can touch the string at any of these nodes to reveal the harmonic.

ƒλ1/1

1/2

1/3

1/4

1/5

1/6

1/7

1/8

1/9

1/10

1

2

3

4

5

6

7

8

9

10

NearestPitchHarmonic

1/1

2/1

3/1

4/1

5/1

6/1

7/1

8/1

9/1

10/1

C

C’

G’

C’’

E’’

G’’

Bb’’

C’’’

D’’’

E’’’

Tuning

Harmonic Series

Memorise this pattern up to the 11th harmonic including cent discrepancies.

Observe the narrowing of the intervals. Chord voicings respond well to a similar pattern which

will be looked at in more detail in Voicings.

-49-32 +41-14+2 -12+4+2 -14 +2 -32Cent deviation from Equal temperament

Tuning

Harmonic Series

If we imagine that the harmonic series tells us something about the nature of music - although one doesn’t have to believe that - then we can

propose some ‘natural’ outcomes.

-49-32 +41-14+2 -12+4+2 -14 +2 -32Cent deviation from Equal temperament

Tuning

Harmonic Series

The first triad to emerge is a major triad. (With a major 3rd 14c flatter and a 5th 2c sharper

than ET (Equal Temperament).

The first seventh chord to emerge is a dominant 7th (with a significantly flatter 7th (-32c) than ET)

‘Natural’ voicings are large in the bass register and progressively closer at higher registers

The first heptatonic scale is Lydian Dominant (aka Lydian b7, Mixolydian #11, or the Overtone or

Harmonic scale). The 3rd, b7 and especially the #11 (-49c) significally flatter than ET

The first common pentatonic scale to emerge is the major pentatonic

Exercise 1 Electronically realise the first 16 notes of the harmonic series. You can create these with cent deviations from Equal temperament or by generating tones as multiples of a fundamental frequency. Listen to each harmonic against a drone to appreciate its sonority. Sketch an opening of a piece that is somehow linked to the harmonic series.

Tuning

Exercise

Tuning

Acoustic Purity

• The Pythagorean concept of Acoustic Purity: Intervals from simple ratios

• Selecting notes and constructing scales from the Harmonic Series

Tuning

The Just 5th

1/1 2/1 3/13/2 Struck

Tuning

The 3-Limit Scale

1/1C

Root

2/1C’

8ve

3/2G

5th1

9/8D

Maj 2nd2

27/16A

Maj 6th3

81/64E

Maj 3rd4

4/3F

4th-1

Tuning

The Pure 5th vs. Even Tempered

3/2G

5th702

700E.T.5th

2 cents

Tuning

The Pure 5th vs. Even Tempered

3/2G

5th702

700E.T.5th

9/8D

Maj 2nd204

200E.T.2nd

27/16A

Maj 6th906

900E.T.5th

81/64E

Maj 3rd408

400E.T.2nd

2 cents 6 cents8 cents4 cents

4/3F

4th498

-2 cents

500E.T.2nd

Tuning

3-Limit Concept

Cent deviation from Equal temperament -14+2

Tuning

The 3-Limit Major Scale (Pythagorean)

Pitch Ratio Cent +/-C 1/1 0 0D 9/8 204 +4E 81/64 408 +8F 4/3 498 -2G 3/2 702 +2A 27/16 906 +6B 243/128 1110 +10C 2/1 1200 0

Ascending Pure 5ths (except F)

Tuning

The 3-Limit Locrian Scale (going down pure 5ths)

Pitch Ratio Cent +/-C 1/1 0 0Db 256/243 90 -10Eb 32/27 294 -6F 4/3 498 -2

Gb 1024/729 588 -12Ab 128/81 792 -8Bb 16/9 996 -4C 2/1 1200 0

Tuning

The Pure 5thFrom the 5th Harmonic

5/4

Tuning

The Pure 5th vs. Even Tempered vs. Pythagorean

5/4G

5th386

400E.T.5th

-14 cents

81/64E

Maj 3rd408

+8 cents

22 cents ! 81/80

Syntonic Comma ! 22 cents

Tuning

The Pure Major Triad

1/1

5/4

3/2

ET - 14 cents

ET + 2 cents

Exercise 2 Construct a major triad with a clear electronic tone and using cent discrepancies (-14 cents on major third) (+2 cents on fifth)

Tuning

Exercise

Tuning

5-Limit Concept

-14+2Cent deviation from Equal temperament

5ths from 3rd Harm.

Tuning

5-limit chromatic scale

1/3-2c

1+0c

3+2c

9+4c

5-14c

A5/3

884c

E5/4

386c

B15/8

1088c

F#45/32590c

1F

4/3498c

C1/10c

G3/2

702c

D9/8

204c

1/5+14c

Db16/15112c

Ab8/5

814c

Eb6/5

316c

Bb9/5

1018c

3rdsfrom5th

Harm.

Tuning

5-limit chromatic scale

1/3-2c

1+0c

3+2c

9+4c

5-14c

A5/3

884c

E5/4

386c

B15/8

1088c

F#45/32590c

1F

4/3498c

C1/10c

G3/2

702c

D9/8

204c

1/5+14c

Db16/15112c

Ab8/5

814c

Eb6/5

316c

Bb9/5

1018c

Pure major triad

Pure minor triad

Pure major 7th

Pure minor 7th

Exercise 3 Alongside the major triad, construct a minor triad, and other triads, 7ths and other chords using just intonation using cent discrepancies from the previous page. Create a chord sequence using carefully tuned chords. Compare to an even-tempered rendition. Consider if the moving bass line skips to even tempered or just intonated scale degrees.

Tuning

Exercise

Pure major triad Pure minor triad Pure major 7th Pure minor 7th

Tuning

Types of Degrees

As we saw with the major 3rd, different routes are available to

get to closely related scale degrees, and so there are different types of pitches

depending on which harmonics are used.

Even limiting to the the 5th harmonic a large array of scale

degrees emerge.

A fraction of the scale degrees which emerge from harmonics 3 & 5, the yellow block are the most common. Warmer & cooler colours represent sharper & flatter groups. The cream colour is the most common just intonated scale.

5-Limit Chromatic Palette

1/27-6c

1/9-4c

1/3-2c

1+0c

3+2c

9+4c

27+6c

81+8c

125-42c

Bb--125/72954c

F--125/96458c

C--125/641158c

G--375/128

640c

25-28c

B-50/271066c

F#--25/18182c

Db--25/24884c

Ab-25/16772c

Eb-75/64274c

Bb-45/32590c

F-135/128

82c

C-405/256

794c

5-14c

G-40/27280c

D-10/9182c

A5/3

884c

E5/4

386c

B15/8

1088c

F#-45/32590c

C#-135/128

92c

1Eb

32/27294c

Bb16/9996c

F4/3

498c

C1/10c

G3/2

702c

D9/8

204c

A+27/16906c

E+81/64408c

1/5+14c

F#64/45610c

Db16/15112c

Ab+8/5

814c

Eb+6/5

316c

Bb+9/5

1018c

F+27/20520c

C+81/8082c

1/25+28c

D+256/225

224c

A++128/75924c

E++32/25428c

B++48/251130c

F#+36/25632c

Db+27/25134c

1/125+42c

F++512/375

540c

C++128/125

42c

G++192/125

744c

Tuning

5-Limit Chromatic Palette

Even limiting to the first 5 harmonics, an indefinite number of degrees may be generated.

1/729-12c

1/243-10c

1/81-8c

1/27-6c

1/9-4c

1/3-2c

1+0c

3+2c

9+4c

27+6c

81+8c

243+10c

729+12c

625-55c

Bb.1250/729

934c

F.625/485

435c

C.625/3241137c

G.625/432

639c

D.625/576

141c

A--625/384

843c

E--625/512

345c

B--1875/1024

1047c

F#+5625/4096

549c

Db+16875/16384

51c

Ab>50625/32768

753c

Eb>youdontwant

255c

Bb>toknowsrsly

957c

125-41c

F#.1000/729

547c

Db.250/243

49c

Ab--125/81751c

Eb--125/108

253c

Bb--125/72955c

F--125/96456c

C--125/641159c

G--375/256

661c

D--1125/1024

163c

A3375/2048

865c

E10125/8192

367c

B135/1281069c

F#>729/512

571c

25-27c

D---800/729

161c

A-400/243

863c

E-100/81365c

B-50/271067c

F#--25/18569c

Db--25/2471c

Ab-25/16773c

Eb-75/64275c

Bb-225/128

977c

F-675/512

478c

C-2025/1024

1180c

G6075/4096

682c

D18225/26384

184c

5-14c

Bb-1280/729

974c

F-320/243

476c

C-160/811118c

G-40/27640c

D-10/9182c

A5/3

884c

E5/4

386c

B15/8

1088c

F#-45/32590c

C#-135/128

92c

Ab>405/64792c

Eb>1215/1024

294c

Bb>3645/256

998c

1F#<

512/729588c

Db<256/243

90c

Ab128/81792c

Eb32/27294c

Bb16/9996c

F4/3

498c

C1/10c

G3/2

702c

D9/8

204c

A+27/16906c

E+81/64408c

B+243/128

1110

F#>729/512

612

1/5+14c

D-/4096/3645

202c

A+<2048/1215

904c

E+<512/405

406c

B+<256/1351108c

F#64/45610c

Db16/15112c

Ab+8/5

814c

Eb+6/5

316c

Bb+9/5

1018c

F+27/20520c

C+81/8022c

G+243/160

723c

D+>729/640

225c

1/25+27c

Bb+<32768/18225

1016c

F+<8192/6075

518c

C+<2048/2025

20c

G+<1024/675

722c

D+256/225

223c

A++128/75925c

E++32/25427c

B++48/251129c

F#+36/25631c

Db+27/25133c

Ab>81/50835c

Eb>243/200

337c

Bb>729/4001039c

1/125+41c

F#+<silliness

629c

Db+<32768/30375

131c

Ab++16384/1125

833c

Eb++4096/3375

335c

Bb++2048/1125

1037c

F++512/375

539c

C++128/125

41c

G++192/125

743c

D++144/125

245c

A+>216/125

947c

E+>162/125

449c

B+>243/1251151c

F#>729/500

653c

1/625+55c

D/don’t ask

243c

A++<long

945c

E++<65536/50625

447c

B++<32768/16875

1149c

Bb++2048/1875

651c

Db++16/15153c

Ab+>1024/625

855c

Eb+>768/625

357c

Bb+>1152/625

1059c

F+>864/625

561c

C+>648/625

63c

G+>972/625

765c

D+>729/625

266c

Shrutis

C Db-- Db- Db Db+ D- D D+ Eb- Eb Eb+ E- E

1/1 25/24 256/243 16/15 27/25 10/9 9/8 256/225 75/64 32/27 6/5 100/81 5/4

0 70 90 112 133 182 204 223 275 294 316 365 386

E+ F- F F+ F#- F# F#+ G- G G+ Ab- Ab Ab+

81/64 320/243 4/3 27/20 45/32 64/65 36/25 40/27 3/2 243/160 25/16 128/81 8/5

408 477 498 520 590 610 631 680 702 723 773 792 814

A- A A+ Bb- Bb Bb+ B- B B+ B++ C

400/243 5/3 27/16 225/128 16/9 9/5 50/27 15/8 243/128 48/25 2/1

863 884 906 977 996 1018 1067 1088 1110 1129 1200

Pitch Name

Ratio

Cents(rounded)

Tuning

Shrutis and Ragas

A Raga is a an Indian Classical Music form that includes specific

rhythms, feels, motifs and microtonal scale forms. We’ll

concentrate on the latter here.

Since they occur over a drone and are essentially monophonic this allows for very specific and

expressive tuning

Tuning

Suha Raga

Second quarter of the night

Expression: Graceful, loving, night

C D Eb+ F G Bb+ C1/1 9/8 9/5 4/3 3/2 9/5 2/10 204 316 498 702 1018 1200

Descending only

(Tonic Bb on recording)

Tonic Confident, joyful Tender, loving Moonlight, peace Joy Desire Octave

Tuning

Bhairav Raga

Late Morning Raga

Expression: Calm and Loving

C Db- E F G Ab B C1/1 256/243 5/4 4/3 3/2 128/81 15/8 2/10 90 316 498 702 792 1088 1200

(Tonic E on recording)

Tonic Tender Calm Peace Sun Desire OctavePleasure

Tuning

Sohini Raga

Deep into the night before dawn

Expression: Effort to remain

C Db- E F F# A B+ C1/1 256/243 5/4 4/3 64/45 5/3 243/128 2/10 90 316 498 498 1018 1110 1200

DescendingOnly

DescendingOnly

Tonic Tender Conscious,effort to stay awake

Moonlight, peace Active,sensuous

OctaveIntense,

mysterious Soft,Callm

Tuning

Exercise

Exercise 4 Render one of these ragas (or research and invent one), carefully tune the shrutis - building a virtual instrument or set of instruments to achieve this. Play to a drone and compare to ET counterparts. Compose an opening of a piece in an alap style, slowly introducing and enjoying each of the shrutis and revealing the character of the raga.

Tuning

11-Limit

What of the other harmonics?We can reach other divisions by

using the 7th and 11th Harmonic,again from ET.

-49-32-14+2 +4+2 -14Cent deviation from Equal temperament

Tuning

11-Limit

Harry Partch’s (1901-74) 43-note universe

Tuning

11-Limit

Harry Partch’s microtonal dissonance

Tuning

Polyphonic Tuning Systems

Tuning

The Spiral of Fifths

(3/2)12=129.746

27=128

Pythagorean Comma129.746/128

!23.5 cents

Tuning

Temperament

Temper, temper

Tuning

Quarter Comma

!24centsover 4 5ths

4 quartercommas

Pure 5th=702c

Tempered=696c

-6c

-6c

-6c

-6c

696c

C 0

Db 90

D 192

Eb 294

E 390

F 496

F# 588

G 696

Ab 792

A 888

Bb 996

B 1092

C 1200

purer 3rd

purer 3rd

702c

Tuning

Sixth Comma

!24centsover 6 5ths

6 1/6commas

-4c

-4c

-4c

-4c

-4c

-4c

C 0

Db 94

D 196

Eb 298

E 392

F 502

F# 592

G 698

Ab 796

A 894

Bb 1000

B 1090

C 1200

More 3rds tempered, to a lesser degree than 1/4 comma

3rd3rd

3rd

3rd

698c

702c

Tuning

Bach’s Well Tempered Clavier

Tuning

Bach’s Well Tempered Clavier

Tuning

Equal Temperament (ET) 12-TET

-2c

-2c

-2c

-2c

-2c

-2c-2c

-2c

-2c

-2c

-2c

-2c

C 0

Db 100

D 200

Eb 300

E 400

F 500

F# 600

G 700

Ab 800

A 900

Bb 1000

B 1100

C 1200

!24centsover 12 5ths

12 twelfthcommas

-2c

700c700c

700c

700c

700c

700c

700c 700c

700c

700c

700c

700c

Tuning

Equal Temperament makes Cents

Cents = 1200 * log(ratio)

log(2)

Ratio = 2(Cents/1200)

Tuning

Another Solution

Tuning

Mozart’s semitones

Tuning

Splitting Accidentals

Clockwise from left: Campagnoli’s fingerboard diagram (1797)Woldermar’s Violin Method (1803) and Split key harpsichord 1715

Tuning

55-division tuning

1/9=22.2cents

88.8cents 100cents

111.1cents

Tuning

55-division tuning

C 0C# 88.9

Db 111.1D 200D# 288.9

Eb 311.1E 400F 500F# 588.9

Gb 611.1G 700G# 788.9

Ab 811.1A 900A# 988.9

Bb 1011.1B 1100C 1200

E-G# 388.9c(Pure is 386c)

3rd

3rd

Ab-C 388.9c(Pure is 386c)

Tuning

Exercise

Exercise 5 Recreate or invent a 7-note (or split accidental) tuning system using cent discrepancies. Write a passage of music that exploits the vertical possibilities.

Tuning

Where did it go?

• Complexity of Instrument Design

• Challenges of pedagogy and wider interest in performing music, owning a piano

• The drive through romantic harmony into 12-tone serialism

• Filtered out of the system

Tuning

Vertical vs. Horizontal

Consideration of the vertical and the horizontal.A time for harmonic sonority,

and a time for expressive intonation.

Microtonal infection, bends, glides, dips, portamento, vibrato etc. are hugely expressive devices but their extensive discussion will be

saved for another episode. Here we concentrate on the destinations of such motions, but here is a

brief overview of ideas.

Tuning

Expressive intonation: Bends

Direction

Contour & Pattern

Duration

Start/End/Stopping Points

Tuning

Expressive intonation: Vibrato

Shape

Width

Frequency

Tuning

Expressive intonation: Vibrato

Tuning

Other divisions

24-TET

24 quarter-tones

50 cents each

or+50c +100c +150c -50c -100c -150c -150c

Tuning

Other divisions

48-TET

48 eighth-tones

25 cents each

Tuning

Other divisions

7-TET

14-TET

n-TET

Each 1200/n cents

Tuning

Other Divisions

Tuning

Exercise

Exercise 6 Recreate or invent an atypical ET system, and compose a passage of music exploiting the intonation possibilities.Experiment with expressive intonation.

Tuning

Blues microtones

C7 C7F7 G7

Tuning

Blues microtones

Tuning

Blues microtones

Tuning

Technology and Microtones

Tuning


Busoni (1866-1924) In response to Cahill’s Telharmonium "Let us take thought," he exulted, "how music may be restored to its primitive, natural essence; [...] let it follow the line of the rainbow and vie with the clouds in breaking sunbeams.”

Tuning


Tuning


• Corrective technology (Pristine vs. sterile)

• Timbral expression

• Non equal-tempered auto-tuning?

Tuning

Exercise

Exercise 7 Compose a passage of music using autoned vocals to a non 12-TET system.

Tuning

Compositional Exercises

Exercise 1 Electronically realise the first 16 notes of the harmonic series. You can create these with cent deviations from Equal temperament or by generating tones as multiples of a fundamental frequency. Listen to each harmonic against a drone to appreciate its sonority. Sketch an opening of a piece that is somehow linked to the harmonic series.Exercise 2 Construct a major triad with a clear electronic tone and using cent discrepancies (-14 cents on major third) Exercise 3 Alongside the major triad, construct a minor triad, and other triads, 7ths and other chords using just intonation using cent discrepancies from the previous page. Create a chord sequence using carefully tuned chords. Compare to an even-tempered rendition. Consider if the moving bass line skips to even tempered or just intonated scale degrees.Exercise 4 Render one of these ragas (or research and invent one), carefully tune the shrutis - building a virtual instrument or set of instruments to achieve this. Play to a drone and compare to ET counterparts. Compose an opening of a piece in an alap style, slowly introducing and enjoying each of the shrutis and revealing the character of the raga.Exercise 5 Recreate or invent a 7-note (or split accidental) tuning system using cent discrepancies. Write a passage of music that exploits the vertical possibilities.Exercise 6 Recreate or invent an atypical ET system, and compose a passage of music exploiting the intonation possibilities.Exercise 7 Compose a passage of music using autoned vocals to a non 12-TET system.

MILTONOTES

Structure



Listening list:



for music and more

This episode


http://open.spotify.com/user/miltonline/playlist/7EsGc9soCKgCZJqCcdk1GX

This episode looks at concepts of structure (and form) in composition.

By looking at examples of folk and popular songs, jazz charts, classical forms, electronic pieces and

indeterminate and process works, we’ll build a catalogue of structures and structural concepts for

analysis and compositional application.

StructureLevels

Firstly we need to address what factors contribute to our perception of structure.

In fact as we saw in Pulse and Meter, Melodic Structures and Phrase, Contour

and Melodic formsthere are several levels on which

structure is based. On the following simple example

you can seethe different levels of

motif/phrase/section/piece

StructureLevels

Structure is achieved by the repetition of similar events, as well as the disruption of repeated events.

StructureLevels

StructureMeter Level

StructureMotif Level

StructurePhrase Level

StructurePassage (Higher Phrase) Level

StructureSection Level

StructureLevels

In this episode we will look at the ‘higher level’ structure of sections, but we should

always be aware that structure is achieved by the repetition of similar events, as well as the disruption of

repeated events.


2 scales, 3 chords, 1 piece

A


B

B

C


A

B

B’ C


B

B’’

StructureForm

A A

B B

C C

B B

A A

B B’

C C

B B’’

Three sections,the most famous A only occuring at two points.

The ending is given an effective poignancy by omitting the last bar. B has three versions (B’ is quieter, and B’’ is quieter and

shortened).

8 x 2

4 x 2

6 x 2

4 x 2

6 x 2

4 x 2

8 x 2

4 + 3

StructureLevels of Organisation

Pulse

Accented Beats

Meter

Motif/Figure

Phrase

Passage

Section

Piece

Cycle/Album/Set/Symphony

StructureForms

Charles Keil divides all musical forms into 3 types

Sectional

Developmental

Variational

StructureForm

We’ll look at some specific forms but will open up the idea that

sections can be created not just by traditional

melodic structures but by timbre, texture and

feel

Structure

Clear cut sectional units (A, B, C, Verse, Middle 8,

coda etc.)

Sectional

Structure

Strophic Form

Sectional

Unrelieved repetition, chain, medley.

AAAAAAAA

ABCDEFG(A)

AABBCCDDEE

e.g. Blue Danube - Strauss

Medley

Unrelieved repetition

Unrelieved variation

Unrelieved variation with repeats

Structure

Binary Form

Sectional

A piece made up 2 sections A & B complementary and of roughly similar lengths.

Traditionally major binary forms have A in the tonic key

B in dominant key, ending in tonic

Traditionally minor binary forms have A in the tonic key

B in relative major key, ending in tonic

AB or AABB

Structure

Ternary Form

Sectional

ABA De Capo operatic aria form

or AABAe.g. 32-bar form with middle eight

Structure

Rondo form

Sectional

A recurring theme with contrasting episodes

ABACABAC ‘Symettrical’

ABACADAE‘Asymettrical’

ABCBAArch form Special case of symettrical rondo without

intermediate themes

See Mozart examples

Structure

Palindromic

Sectional

Rondo forms can be palindromic on a sectional level

ABACABA

But palindromes needn’t be rondo forms

ABCADEDACBA

Palindromes can even exist on the note level...

Structure

Palindromic

Sectional

Haydn Symphony No. 47

Structure

Palindromic rhythms

Sectional

The Afro-Cuban rhythm Cáscara

x0xx 0x0x x0x0 xx0x

2-3 Cuban Son

Structure

Crab/Table Canon

Sectional

Structure

“Dammit I’m mad.Evil is a deed as I live.

God, am I reviled? I rise, my bed on a sun, I melt.To be not one man emanating is sad. I piss.

Alas, it is so late. Who stops to help?Man, it is hot. I’m in it. I tell.

I am not a devil. I level “Mad Dog”.Ah, say burning is, as a deified gulp,

!In my halo of a mired rum tin.I erase many men. Oh, to be man, a sin.

Is evil in a clam? In a trap?No. It is open. On it I was stuck.

Rats peed on hope. Elsewhere dips a web.Be still if I fill its ebb.Ew, a spider… eh?We sleep. Oh no!

Deep, stark cuts saw it in one position.Part animal, can I live? Sin is a name.

Both, one… my names are in it.Murder? I’m a fool.

A hymn I plug, deified as a sign in ruby ash.A Goddam level I lived at.

On mail let it in. I’m it.Oh, sit in ample hot spots. Oh wet!

A loss it is alas (sip). I’d assign it a name.Name not one bottle minus an ode by me:

“Sir, I deliver. I’m a dog”Evil is a deed as I live.

Dammit I’m mad.

Structure

Theme and Variations

Variational

A theme with related variations traditionally based on the harmonic progression and motivic material

A A1 A2 A3 A4 A5 A6 e.g. Theme and Variations on a Theme by Mozart - Sor

Note that each section may itself have an internal structure (AABB) and the whole form may have an

intro/outro and/or elaborated outro/coda.See also Paganini - Caprice 24 and many others.

The Rondo may also include intermediate variations:

A B A1 C A2 D A3

Structure

Theme and Variations further ideas

Variational

Britten’s Young Person’s Guide to the Orchestrahas each variation showcasing a different section of

the orchestra, and his Nocturnal for Solo Guitar, starts with the variations, only revealing the Dowland’s

underlying theme in the last section.

Elgar’s Enigma Variations is a set of 14 variations on an original theme - each a musical portrait, capturing

the personality of his close circle of friends.Variations include rhythmic, harmonic & melodic

references and even a Dorabella’s stutter, W.N.’s laugh and particular experiences they shared.

Elgar claimed all a based on a hidden theme that is “not played” and took the secret to the grave.

Structure

Variational

The Enigma theme - note the motivic variants. Pi?

Structure

Stylistic Variational

The common Blues and Jazz forms involving improvisation may be considered a special type of

theme and variation.

Typically a melody is played over a specific harmonic structure (A, AB, ABAC, AABA’ etc.) and then that

harmonic form (and perhaps some motivic and rhythmic material from the melody are used for improvised solos, and another realisation of the

melody is used to end the piece. The whole form may be topped and tailed by an intro, outro or intermediate

sections (see All Blues).

The stylistic forms you need to know are a 12-bar blues (sometimes interpreted as a 24-bar blues), an 8, 16-bar blues (Need Your Love So Bad) or other (Come

On Pt. 1), and a rhythm changes (many examples)

Structure

12-Bar Blues (major)

I7 IV7 I7 I7

IV7 I7 I7IV7

V7 IV7 I7 V7

Note this form wasn’t decided a priori it evolved, and still many structures have an indefinite length on the I chord,

moving to the IV on cue

Structure

12-Bar Blues (minor)

i7

iv7(IV7)

bVImaj7 V7

i7

V7 i7

Structure

8-Bar Blues (major)

I IV7I7

V7/II ii7 V7

#IVº7

I I7 IV7 I7 V7

StructureRhythm Changes

I

IVI7

V7/II ii7 V7

I

iii V7/II ii7 V7

iv V7/II ii7 V7iii

V7/VI

V7/V V7

I

IVI7

V7/II ii7 V7

I

iii V7/II ii7 V7

iv V7/II ii7V7iii I

V7/II

I

IVI7

V7/II ii7 V7

I

iii V7/II ii7 V7

iv V7/II ii7V7iii I

A

A’

B

A’

Structure

Developmental

Built directly from smaller units - the most established in Western Art music being the Sonata form. This is

beyond the scope of this episode.

However the idea of a structure that is ‘through-composed’ an unfurling stream of

consciousness with no clear sectional delineations is well established in ambient electronic music

Structure

Structural Components

Here are some of the devices that through repetition and variation starting with the most common

Melody

Lyrics

Key

Harmony

Orchestration/Instrumentation

Meter

Rhythmic Subdivision/Groove/Feel

Dynamics

Timbre/Texture

Structure

Popular Song Form - Building Blocks

Intro

Verse

Prechorus

Chorus

Bridge

Collision

Solo

Vamp

Outro

Note that features may be shared - an intro can use the chorus’s chords for example

Interlude

Structure

Wind Cries Mary - Hendrix

Intro

Verse

Prechorus

Chorus

Solo

Verse

Prechorus

Chorus

Verse

Prechorus

Chorus

Verse

Prechorus

Chorus

based on intro

ends with material and similar to

CriesWhispers Screams Cries

Outro

Structure

Better Be Home Soon - Crowded House

Verse

Prechorus

Chorus

SoloInterlude

Verse

Prechorus

Chorus

Verse

Prechorus

Chorus’

Chorus’’(short)

Bridge

Structure

Grow Your Own

Intro

VersePrechorus

ChorusBridge

Collision

Solo

Vamp

Outro

Interlude

Structure

Intro

Break

DropBuild

Mid-8

Outro

Electronic Structural ComponentsIn the absence of traditional key areas, melodic and harmonic expectations, lyrics and forms,

electronic dance music and IDM has developed structural components and forms based more directly on instrumentation,rhythmic components and feel, dynamic changes and timbre

SoloKey Sample

Hook

Arhythmic

Structure

Introductions

SectionalA unique section that only appears once such as the

original jazz form arrangements.Starting directly on a section that features throughout the

track.Or an adapted (usually thinned and/or shortened) variation of a

later important section or components

FadeDuration, curve

or...

Structure

Endings

Sectional (New)A modified section breaking expectation, new material or

a logical conclusione.g. Syrinx ends with the other whole

tone scale

Sectional (Recap)A repeat of an earlier section

with minimal alteration

FadeDuration, curve

or...

Exercise 1 Take an existing piece/section of yours (or write a new one) and rewrite in 7 different structures (including at least one from each of the 3 categories of sectional, variational and developmental).

MiltOnNotes Volume One

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