ByBy

Prof. Lydia AyersProf. Lydia Ayers

Bowed Strings (huqin)Bowed Strings (huqin)Bowed Strings (huqin)Bowed Strings (huqin)• ErhuErhu

• 2 strings with a snake-skin 2 strings with a snake-skin sound boxsound box

• <3:16><3:16> Wong On Yuen, erhu, Wong On Yuen, erhu, performs Joshua Chan Kam performs Joshua Chan Kam Biu's Biu's Eternal LoveEternal Love

Wong On Yuen(gaohu)

Bowed Strings (huqin)Bowed Strings (huqin)Bowed Strings (huqin)Bowed Strings (huqin)

• GaohuGaohu• 2 strings with a snake-skin2 strings with a snake-skin sound sound

box; higher than erhubox; higher than erhu

• ZhonghuZhonghu• lower than erhu lower than erhu • The shape of the resonatorThe shape of the resonator

varies from circular to octagonal. varies from circular to octagonal.

Pythagorean TuningPythagorean TuningPythagorean TuningPythagorean Tuning• in common use in Greek Antiquity and the in common use in Greek Antiquity and the

Middle Ages in western musicMiddle Ages in western music• still used in Chinese music and some Indian still used in Chinese music and some Indian

ragas todayragas today• Pythagorean spiral of fifthsPythagorean spiral of fifths

• based upon pure 3/2 fifthsbased upon pure 3/2 fifths

fifth3/2

Pythagorean TuningPythagorean TuningPythagorean TuningPythagorean Tuning

Ling Lun's Tuning of the Lu

by Edward Wongpaixiao

• first discovered by Ling Lun, a court musician of first discovered by Ling Lun, a court musician of Emperor Huang-Ti, possibly as early as the 27th Emperor Huang-Ti, possibly as early as the 27th century B.C. century B.C. • used a length of bamboo called a "lu" — similar to used a length of bamboo called a "lu" — similar to

paixiaopaixiao

[i:57][i:57] Zheng Tuning Example Zheng Tuning Example[i:57][i:57] Zheng Tuning Example Zheng Tuning Example11 33 99 2727 8181

11 22 8 8 1616 64 64

Pythagorean TuningPythagorean TuningPythagorean TuningPythagorean Tuning[i:58][i:58] Pentatonic (5-note) scale of Ling Lun's Tuning of the Lu

.Chinese: 1 2 3 5 6 1

Pythagorean Spiral of FifthsPythagorean Spiral of FifthsPythagorean Spiral of FifthsPythagorean Spiral of Fifths11

2716

C98

32

EA

DG

,DbAb

Eb

BbF

Gb/F# B12881 243

128

8164

3227

169

43

729512

256243 1024

729

11

94

32x

32=

32x =

98

12x =

Pythagorean 531441 Comma 524288

Pythagorean TuningPythagorean TuningPythagorean TuningPythagorean Tuning

[i:59][i:59] Pythagorean Major Scale

[i:60][i:60] Comparing TuningComparing TuningSystems for the Major ScaleSystems for the Major Scale

[i:60][i:60] Comparing TuningComparing TuningSystems for the Major ScaleSystems for the Major Scale

Pythagorean TuningPythagorean TuningPythagorean TuningPythagorean Tuning

[i:61][i:61] Pythagorean Major Chord

• major third is very sharp, so major chord major third is very sharp, so major chord is out of tune is out of tune

[i:65][i:65] Just Natural Minor ScaleJust Natural Minor Scale[i:65][i:65] Just Natural Minor ScaleJust Natural Minor Scale

Interval Flow ChartInterval Flow Chart(major intervals on top)(major intervals on top)Interval Flow ChartInterval Flow Chart(major intervals on top)(major intervals on top)

9/89/8 15/815/8

/ /\ / \/ /\ / \

/ / 10/910/9 5/45/4 5/35/3 \ \

/ / / \ / \ \/ / / \ / \ \

11 - - - - - - - - -- - -4/34/3 - - 3/23/2 - - - - - - - - - - 22

\ \ / \ / / /\ \ / \ / / /

\ \ 6/56/5 8/58/5 9/59/5 / /

\ / \ / /\ / \ / /

16/1516/15 16/916/9

1 2 3 4 5 6 7 81 2 3 4 5 6 7 8

[i:66][i:66] Pythagorean Minor ScalePythagorean Minor Scale[i:66][i:66] Pythagorean Minor ScalePythagorean Minor Scale

[i:67][i:67] Comparing Tuning Systems for the Minor Scale

Minor ChordsMinor ChordsMinor ChordsMinor Chords• Pythagorean minor third is very flat, so Pythagorean minor third is very flat, so

chords are out of tune chords are out of tune

[i:68][i:68] Just Minor Triad

[i:69][i:69] Pythagorean Minor Triad

[i:70][i:70] Sometimes I feel Like a Motherless ChildSometimes I feel Like a Motherless Child (Black American Spiritual)(Black American Spiritual)

[i:70][i:70] Sometimes I feel Like a Motherless ChildSometimes I feel Like a Motherless Child (Black American Spiritual)(Black American Spiritual)

•A

Nat

ura

l Min

or

Sca

leA

Nat

ura

l Min

or

Sca

le

Leading ToneLeading ToneLeading ToneLeading Tone

• "leads" up to the tonic by a half step"leads" up to the tonic by a half step• seventhseventh scale degree from the major scale scale degree from the major scale

[i:71][i:71] Leading Tone in C Major Scale

[i:72][i:72] Harmonic Minor ScaleHarmonic Minor Scale[i:72][i:72] Harmonic Minor ScaleHarmonic Minor Scale• natural minor scale pattern natural minor scale pattern

with with seventhseventh scale degree scale degree borrowed from major scale borrowed from major scale to give a leading toneto give a leading tone

• modified by accidental, not modified by accidental, not by key signatureby key signature

Harmonic Minor Scale - Key of C

[i:73][i:73] Melodic Minor ScaleMelodic Minor Scale[i:73][i:73] Melodic Minor ScaleMelodic Minor Scale• natural minor scale pattern natural minor scale pattern

with raised tones going up with raised tones going up and lowered tones coming and lowered tones coming downdown

• closes gap between sixth and raised seventh closes gap between sixth and raised seventh scale degreesscale degrees

Melodic Minor Scale - Key of C Minor