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Prof. Lydia AyersProf. Lydia Ayers

Intervals, Scales, TuningIntervals, Scales, Tuningand Melodyand Melody

Intervals, Scales, TuningIntervals, Scales, Tuningand Melodyand Melody

MelodyPitches, one after the other, which form a musical idea (a “tune”)

ScaleOrdered Set of Pitches

TuningPrecise Frequencies(Colors the Scale)

Supporting Raw MaterialIntervals

Tuning SystemTuning SystemTuning SystemTuning System• a way to select the a way to select the

frequencies of pitches frequencies of pitches to form intervals, to form intervals, scales and chordsscales and chords

• in tune = in focusin tune = in focus

[ii:34][ii:34] In Tune = In Focus In Tune = In Focus[ii:34][ii:34] In Tune = In Focus In Tune = In Focus

OUT OF TUNE(with fast beats)

IN TUNE(beats disappear)

Beats (Beating)Beats (Beating)Beats (Beating)Beats (Beating)• a periodic cancellation and reinforcement between a periodic cancellation and reinforcement between

waveforms as they interfere with each otherwaveforms as they interfere with each other• given two frequencies, 440 and 442 Hertz, the ear hears a given two frequencies, 440 and 442 Hertz, the ear hears a

single tone of 441 Hertz, fluctuating in amplitude at 2 single tone of 441 Hertz, fluctuating in amplitude at 2 beats per secondbeats per second

• [ii:35][ii:35] sine waves at: sine waves at: • 440 Hertz 440 Hertz • 442 Hertz 442 Hertz • 440 and 442 Hertz together (with 2 beats per second) 440 and 442 Hertz together (with 2 beats per second)

Symbol Name Effect

Double sharp

Raise the pitch by 2 half steps (= a whole step)

Sharp

Raise the pitch by a half step

Natural

Cancels any chromatic alteration

Flat

Lower the pitch by a half step

Double flat Lower the pitch by 2 half steps (= a whole step)

AccidentalsAccidentalsAccidentalsAccidentals

FlatsFlatsFlatsFlats

• Marks which look like small Marks which look like small "b"s that have been sat on."b"s that have been sat on.

• Their function is to lower a Their function is to lower a note by a semi-tone (more note by a semi-tone (more or less).or less).

David Barber and Dave DonaldDavid Barber and Dave Donald

A Musician's DictionaryA Musician's Dictionary

SharpSharpSharpSharp• A term for describing a note that has been A term for describing a note that has been

slightly raised in pitch (intentionally or slightly raised in pitch (intentionally or otherwise).otherwise).

David Barber and Dave Donald, David Barber and Dave Donald, Tenors, Tantrums and TrillsTenors, Tantrums and Trills

AccidentalsAccidentalsAccidentalsAccidentals• written to the left of written to the left of

the pitches they alter the pitches they alter • change all change all

subsequent subsequent appearances of the appearances of the pitch they alter in that pitch they alter in that octave until the bar octave until the bar lineline

AccidentalsAccidentalsAccidentalsAccidentals• Enharmonic equivalentsEnharmonic equivalents• different note spellings of the same pitch - different note spellings of the same pitch -

"synonyms""synonyms"• Bb = A#Bb = A#• C# = DbC# = Db

IntervalIntervalIntervalInterval

• the distance between two pitchesthe distance between two pitches

• the pitches of an the pitches of an interval may interval may sound at the sound at the same time or same time or one after the one after the otherother

IntervalsIntervalsIntervalsIntervals• we can find intervals between the we can find intervals between the

pitches of the harmonic seriespitches of the harmonic series

P

PP

Names of IntervalsNames of IntervalsNames of IntervalsNames of Intervals• come from the number of scale steps come from the number of scale steps

to count from the first oneto count from the first one

• ONE scale step counts as the SECOND (2) intervalONE scale step counts as the SECOND (2) interval

2 3 4 5 6 7 81

• two notes at the first pitch, or tonic, count as two notes at the first pitch, or tonic, count as the unison (1) intervalthe unison (1) interval

Types of IntervalsTypes of IntervalsTypes of IntervalsTypes of Intervals

• augmented intervalsaugmented intervals + 1/2 step + 1/2 step

• diminished intervalsdiminished intervals - 1/2 step - 1/2 step

• perfect intervalsperfect intervals

• major intervalsmajor intervals

(1/2 step)(1/2 step)• minor intervalsminor intervals