The Science and Art of Tuning

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December 2010 December 2010

The

The Scien

Science

ce and Art

and Art of

of

T

unin

uning

g

Milton Mermikides Milton Mermikides Dr

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Wh

What

at

is

in

T

un

une?

e?

How Long is a Piece of String? How Long is a Piece of String?

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How

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Concepts

•

• WWavavelength elength & F& Frequencyrequency •

• Hz. Hz. The The Frequency Frequency of of Human Human HearingHearing •

• The Law of Octave EquivalenceThe Law of Octave Equivalence •

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5 5

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Assumptions

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Acoustic Purity

•

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

Acoustic Purity: Intervals from

simple ratios

•

• Selecting notes andSelecting notes and

constructing scales from the

Harmonic Series

Sunday, 23 January 2011 Sunday, 23 January 2011

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The Pure 5th

1 1//1 1 3/23/2 22//1 1 33//11 Struck Struck

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The 3-Limit Scale

1/1 1/1 C C Root Root 2/1 2/1 C’ C’ 8ve 8ve 3/2 3/2 G G 5th 5th 9/8 9/8 D D Maj 2nd Maj 2nd 27/16 27/16 A A Maj 6th Maj 6th 81/64 81/64 E E Maj 3rd Maj 3rd 4/3 4/3 F F 4th 4th

Just intonation

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The Pure 3rd

From the 5th Harmonic (5-limit) From the 5th Harmonic (5-limit) 5/1: 2 octaves and a major 3rd 5/1: 2 octaves and a major 3rd 5/4: Major 3rd 5/4: Major 3rd 1/1 1/1 C C Root Root 2/1 2/1 C’ C’ 8ve 8ve 5/4 5/4 E E Maj 3rd Maj 3rd 81/64 81/64 E E Maj 3rd Maj 3rd 25/16 25/16 G# G# Aug. 5th Aug. 5th 8/5 8/5 Ab Ab Min 6th Min 6th

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Shrutis of Hindustani

Classical Music

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Raga Bhairav

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Monophonic vs.

Polyphonic

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Enough Physics, let’s

make 12 Notes.

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The Cycle Spiral of 5ths

(3/2) (3/2)1212=129.746=129.746 2 277₌₁₂₈₌₁₂₈ Pythagorean Pythagorean Comma Comma 129.746/128 129.746/128

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Temper, temper

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Eq

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Eq

Equa

ual T

l T

em

empe

pera

rame

ment

nt

Makes Cents

Cents = 1200 * log(ratio)

log(2)

Ratio = 2

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The

Third

Third Issue

Issue

(5/4) (5/4)33== 125/64 125/64 ≠ ≠128/64128/64

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The

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C Major Prelude

Eq

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C Major Prelude

W

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Another Solution

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Mozart’s Semitones

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Another Solution

1/9=11.1cents 1/9=11.1cents

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Clockwise from left: Clockwise from left:

Campagnoli’s ﬁngerboard diagram (1797) Campagnoli’s ﬁngerboard diagram (1797) W

Woldermar’s oldermar’s Violin Violin Method Method (1803) (1803) andand Split key harpsichord 1715

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Where Did It Go?

•

• Complexity of Instrument DesignComplexity of Instrument Design •

• Challenges of pedagogy Challenges of pedagogy and wider interest inand wider interest in

performing music, owning a piano performing music, owning a piano

•

• The drive through rThe drive through romantic harmony into 12omantic harmony into 12-

-tone serialism tone serialism

•

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Le

Lead

ad

in

ing T

g T

on

ones

es?

?

Consideration of the vertical and the horizontal. Consideration of the vertical and the horizontal.

A time for harmonic sonority, A time for harmonic sonority, and a

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Microtones & the Blues

The Neutral 3rd The Neutral 3rd The Neutral 7th The Neutral 7th 4-b5 4-b5 b5-5 b5-5

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Blues Inﬂection

•

• Thelonius Monk Thelonius Monk •

• Guitarists (Bends, Slide Guitar)Guitarists (Bends, Slide Guitar) •

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Tuning Systems

Harry Partch (1901-1974) Harry Partch (1901-1974)

American microtonal composer American microtonal composer

and instrument

and instrument makmakerer

11-limit 43 tone system 11-limit 43 tone system

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11-limit (43 tone)

•

• 11th harmonic chosen as the boundary of our11th harmonic chosen as the boundary of our

tolerance - falling

tolerance - falling betweebetween 2 n 2 equal temperedequal tempered pitches (F#- 49cents).

pitches (F#- 49cents).

•

• 43 divisions of the 43 divisions of the scale are constructed withinscale are constructed within

this boundary. this boundary.

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Micr

otonal adjustment

of

pr

e-existing

instruments

Tolgahan Cogalu Tolgahan Cogalu

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Technology and

Microtones

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•

• Busoni (1866-1924) In response to CahillBusoni (1866-1924) In response to Cahillʼʼs Telharmoniums Telharmonium "Let us take thought," he

"Let us take thought," he exulted, "how music may beexulted, "how music may be

restored to its primitive, natural essence; [...] let it follow the

line of the rainbow and vie with the

line of the rainbow and vie with the clouds in breakingclouds in breaking

sunbeams.”

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Autotune

•

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Autotune (Ab)use

Dixie Chicks

Dixie Chicks––The Long Way Around The Long Way Around – Noticeable on “parents” and “but I.” – Noticeable on “parents” and “but I.”

T-Pain

T-Pain –– I’m SprungI’m Sprung– Especially obvious on “homies” and “lady.” – Especially obvious on “homies” and “lady.”

Avril Lavigne

Avril Lavigne–– Complicated Complicated – Li– Listen to sten to “way“way,,” “when,” “driving” “when,” “driving,,” “you’re.” ” “you’re.”

Uncle Kracker

Uncle Kracker–– Follow MeFollow Me

The whole vocal sounds strained, but especially the word “goodbye.”

Maroon 5

Maroon 5–– She Will Be Loved She Will Be Loved – Listen for “rain” and “smile.” – Listen for “rain” and “smile.”

Natasha Bedingfield

Natasha Bedingfield ––Love Like ThisLove Like This – “Apart” and “life.” – “Apart” and “life.”

Sean Kingston

Sean Kingston ––Beautiful girlsBeautiful girls – “OoooOver” doesn’t sound human.– “OoooOver” doesn’t sound human.

JoJo

JoJo ––Too Little Too LateToo Little Too Late – Appropriately, “problem” stands out.– Appropriately, “problem” stands out.

Rascal Flatts

Rascal Flatts–– Life is a Highway Life is a Highway

Every vocal, foreground and background, is treated, but “drive” in particular.

New Found Glory

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Auto

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Auto

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Hiding vs. Hearing

•

• Corrective technology (Pristine vs. sterile)Corrective technology (Pristine vs. sterile) •

• ExpressivExpressive technologe technologyy •

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Practical

Democratic tuning

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Milton Mermikides

miltonmermikides.com miltonmermikides.com miltonline@me.com miltonline@me.com