1. By Prof. Lydia Ayers

2. Bowed Strings (huqin) ErhuErhu 2 strings with a snake-skin sound box2 strings with a snake-skin sound box Wong On Yuen, erhu, performs Joshua Chan Kam Biu's Eternal Love Wong On Yuen, erhu, performs Joshua Chan Kam Biu's Eternal Love Wong On Yuen (gaohu)

3. Bowed Strings (huqin) GaohuGaohu 2 strings with a snake-skinsound box; higher than erhu2 strings with a snake-skinsound box; higher than erhu ZhonghuZhonghu lower than erhulower than erhu The shape of the resonator varies from circular to octagonal.The shape of the resonator varies from circular to octagonal.

4. Pythagorean Tuning in common use in Greek Antiquity and the Middle Ages in western musicin common use in Greek Antiquity and the Middle Ages in western music still used in Chinese music and some Indian ragas todaystill used in Chinese music and some Indian ragas today Pythagorean spiral of fifthsPythagorean spiral of fifths based upon pure 3/2 fifthsbased upon pure 3/2 fifths fifth 3/2

5. Pythagorean Tuning Ling Lun's Tuning of the Lu by Edward Wong paixiao first discovered by Ling Lun, a court musician of Emperor Huang-Ti, possibly as early as the 27th century B.C.first discovered by Ling Lun, a court musician of Emperor Huang-Ti, possibly as early as the 27th century B.C. used a length of bamboo called a "lu" similar to paixiaoused a length of bamboo called a "lu" similar to paixiao

6. [i:57] Zheng Tuning Example 13 927 81 12 816 64

7. Pythagorean Tuning [i:58] [i:58] Pentatonic (5-note) scale of Ling Lun's Tuning of the Lu. Chinese: 1 2 3 5 6 1

8. Pythagorean Spiral of Fifths 1111 27 16 C 9898 3232 E A D G, Db Ab Eb Bb F Gb/F# B 128 81 243 128 81 64 32 27 16 9 4343 729 512 256 243 1024 729 1111 9494 3232 x 3232 = 3232 x = 9898 1212 x = Pythagorean531441 Comma524288

9. Pythagorean Tuning [i:59] [i:59] Pythagorean Major Scale

10. [i:60]Comparing Tuning Systems for the Major Scale [i:60] Comparing Tuning Systems for the Major Scale

11. Pythagorean Tuning [i:61] [i:61] Pythagorean Major Chord major third is very sharp, so major chord is out of tunemajor third is very sharp, so major chord is out of tune

12. [i:65]Just Natural Minor Scale [i:65] Just Natural Minor Scale

13. Interval Flow Chart (major intervals on top) 9/8 15/8 9/8 15/8 / /\ / \ / /\ / \ / 10/9 5/4 5/3 \ / 10/9 5/4 5/3 \ / / / \ / \ \ / / / \ / \ \ 1 - - - - - -4/3 - 3/2 - - - - - 2 1 - - - - - -4/3 - 3/2 - - - - - 2 \ \ / \ / / / \ \ / \ / / / \ 6/5 8/5 9/5 / \ 6/5 8/5 9/5 / \ / \ / / \ / \ / / 16/15 16/9 16/15 16/9 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

14. [i:66] Pythagorean Minor Scale [i:67] [i:67] Comparing Tuning Systems for the Minor Scale

15. Minor Chords Pythagorean minor third is very flat, so chords are out of tunePythagorean minor third is very flat, so chords are out of tune [i:68] [i:68] Just Minor Triad [i:69] [i:69] Pythagorean Minor Triad

16. [i:70]Sometimes I feel Like a Motherless Child (Black American Spiritual) [i:70] Sometimes I feel Like a Motherless Child (Black American Spiritual) A Natural Minor ScaleA Natural Minor Scale

17. Leading Tone "leads" up to the tonic by a half step"leads" up to the tonic by a half step seventh scale degree from the major scaleseventh scale degree from the major scale [i:71] [i:71] Leading Tone in C Major Scale

18. [i:72]Harmonic Minor Scale [i:72] Harmonic Minor Scale natural minor scale pattern with seventh scale degree borrowed from major scale to give a leading tonenatural minor scale pattern with seventh scale degree borrowed from major scale to give a leading tone modified by accidental, not by key signaturemodified by accidental, not by key signature Harmonic Minor Scale - Key of C

19. [i:73]Melodic Minor Scale [i:73] Melodic Minor Scale natural minor scale pattern with raised tones going up and lowered tones coming downnatural minor scale pattern with raised tones going up and lowered tones coming down closes gap between sixth and raised seventh scale degreescloses gap between sixth and raised seventh scale degrees Melodic Minor Scale - Key of C Minor