Environment:      Siren
Superclass:         Object
Category:         Music-PitchClasses
Instance variables:   type semiTones

MusicalInterval commentStamp: '' prior: 0!
Intervalle represente un intervalle entre deux notes.
type represente l'ecart entre les deux notes extremites. Cet ecart ne tient compte
que des notes naturelles. Par exemple, les tierces (majeures ou mineures) ont comme type 3,
les quarte 4 etc.
demisTons est le nombre de demis tons entre les deux notes. Par exemple une tierce
majeure a comme type 3 et demisTons = 4.

computing notes

topIfBottomIs: aNote
   yields the note making the interval self with aNote

printing

isPrintable
   

printOn: s
   

printPrintableOn: s
   Watch out : all Intervals cant print themselves.
   You can convert a musicalInterval into a ChromaticInterval.
   E.g. : Interval between Cbb and C ## (super super augmented
   unison!!).
   There are here 40 printable intervals. Cf. method MusicalInterval allPrintableIntervals
(put in protocol constants)

storeOn: s
   

automatic access

orientedSemiTones
   

semiTones
   

semiTones: aValue
   

type
   

type: aValue
   

arithmetics

+ anInterval
   (MusicalInterval majorSecond) + (MusicalInterval perfectFifth)

testing

isA: anInterval
   

isAscending
   

isDescending
   

comparing

< anInterval
   

<= anInterval
   

= anInterval
   

> anInterval
   

>= anInterval
   

hasSameDirectionAs: anInterval
   

mutations

ascending
   

asChromaticInterval
   

descending
   

MetaClass:         MusicalInterval class

examples

allPrintableIntervals
   MusicalInterval allPrintableIntervals

example
   
   MusicalInterval majorThird inverse
   
   MusicalInterval perfectFourth topIfBottomIs: N C sharp -> Fa#
   MusicalInterval perfectFourth bottomIfTopIs: N F sharp -> Do#

   N do intervalBetween: N re -> Major second
   N do flat intervalBetween: N sol -> Augmented fifth   
   N do flat intervalBetween: N do sharp -> superAugmented unisson
   N do flat intervalBetween: N do sharp sharp -> non printable interval
   (N do flat intervalBetween: N do sharp sharp) asChromaticInterval -> Chromatic 3
   (N do intervalBetween: N sol) = (N re intervalBetween: N la) -> true
   (N do intervalBetween: N fa sharp) = (N do intervalBetween: N sol flat) -> false
   MusicalInterval allIntervalsType: 3 -> #(Major third Minor third )
   MusicalInterval allIntervalsType: 2 ->
   #(Augmented second Diminished second Major second Minor second )
   MusicalInterval allIntervalsType: 1 -> #(Augmented unisson Diminished unisson superAugmented unisson superDiminished unisson unisson )
   

exampleTranspositions
   three ways of of transposing pitch classes and od notes

creation

allIntervalsType: t
   MusicalInterval allIntervalsType: 2

type: aType semiTones: d
   

all-printable

augmentedEleventh
   

augmentedFifth
   8 semitones

augmentedFourth
   6 semitones

augmentedNinth
   15 semitones

augmentedOctave
   3 semitones

augmentedSecond
   3 semitones

augmentedTenth
   17 semitones

augmentedTwelvth
   20 semitones

augmentedUnison
   

diminishedFifth
   6 semitones

diminishedFourth
   5 semitones

diminishedNinth
   1 octave + 1 semitones

diminishedOctave
   11 semitones

diminishedSecond
   0 semitones

diminishedSeventh
   9 semitones

diminishedTenth
   15 semitones

diminishedThirteenth
   

diminishedTwelvth
   18 semitones

diminishedUnison
   MusicalInterval diminishedUnison topIfBottomIs: N C

majorNinth
   14 semitones

majorSecond
   2 semitones

majorSeventh
   11 semitones

majorSixth
   9 semitones

majorTenth
   14 semitones

majorThird
   4 semitones

majorThirteenth
   

majorTwelvth
   19 semitones

minorNinth
   1 octave + 1 semitones

minorSecond
   1 semitone

minorSeventh
   10 semitones

minorSixth
   8 semitones

minorThird
   3 semitones

minorThirteenth
   

octave
   

perfectEleventh
   5 semitones

perfectFifth
   7 semitones

perfectFourth
   5 semitones

superAugmentedUnison
   MusicalInterval superAugmentedUnison topIfBottomIs: N C

superDiminishedUnison
   MusicalInterval superDiminishedUnison topIfBottomIs: N C

unison
   

constants nick-names

aug11
   

aug4
   

aug5
   

aug9
   15 semitones

dim13
   

dim5
   6 semitones

dim7
   9 semitones

dim9
   

eleventh
   

fifth
   

flatFifth
   

flatNinth
   1 octave + 1 semitones

flatThirteenth
   

fourth
   

ninth
   

second
   2 semitones

seventh
   

sixth
   

thirteenth