Course:PHYS341/2018/Calendar/Lecture 20

Phys341 Lecture 20: Summary and web references

2018.02.28

Textbook 14.1-14.12 (going light on the math)

Intervals and Scales Continued

1. Calculating equal temperament intervals
   • Equal temperament long seen as ideal in China
     • “Semitone” bells found in Marquis Yi’s tomb (5th C BC)
   • Prince Zhu Zaiyu of the Ming Court (Qinyang)
     • 30-year mathematical pursuit of equal temperament
     • Complete Compendium of Music and Pitch (Yuelü quan shu 乐律全书) 1584
   • Simon Stevin Van De Spiegheling der singconst (Bruges, c. 1605)
   • Thus, what we now call the semitone ratio was established at 21/12 = 1.05946
     • Each semitone step represents a ~6% increase in frequency.
2. Twelve tone Equal temperament (12-TET)
   • Advantages over Just Temperament:
     • String instruments can be fretted and played in any key.
     • Keyboard instruments can be played in any key with less keys (e.g. don’t need G# and A♭).
   • Disadvantages:
     • All intervals are slightly out of tune, but none badly.
   • Acceptance in the West was slow.
     • Early influential advocate: J. S. Bach
     • Complete by c.1850
   • J. S. Bach https://en.wikipedia.org/wiki/The_Well-Tempered_Clavier
   • Note: “well-tempered” is subtly different from “equal temperament” (but no time to go into all the math).
3. How to fix on an unfretted instrument
   • https://www.youtube.com/watch?v=buZOs-czOUg
4. Other ways of doing things
   • This is a big subject
   • South Asian scales
     • Basically modal, i.e. 7-notes to the scale
     • Some 22-note scales
   • Persian scales
     • Safi al-Din al-Urmawi born c. 613 AH (1216 AD), Urmiya (Iran), died in Baghdad on 693 AH (1294 AD)
       • Formalized a 17-note scale (intervals not equal)
     • More recently 24-TET (i.e. quarter-tone) scale has become standard
   • 20th century experimental scales
   • etc. etc.