{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3.2 Tuning and Temperament 07 - T uni ng a nd Temper a ment...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Tuning and Temperament An overview
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Review of Pythagorean tuning Based on string lengths Octave relationship is always 2:1 Fifth relationship is 3:2 “pure” or “just” intervals have no beats
Image of page 2
Building a Pythagorean scale…. Start with C = f =1 C to G is a fifth; G = 3/2 G to D is a fifth; D = 3/2 · 3/2 = 9/4; drop the octave and it becomes 9/8 D to A is a fifth; A = 9/8 · 3/2 = 27/16 A to E is a fifth; E = 27/16 · 3/2 = 81/32; drop the octave and it becomes 81/64
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The problem… C to E interval (Pythagorean third) is 81/64 - this ratio is too wide Pure third interval is 5/4, or 80/64 Using A=440 Hz as a base note: (80/64) A=440, C# =550 (81/64) A=440, C#=556.875 The small difference 80/81 is called the syntonic comma
Image of page 4
Another problem of internal consistency… Start with C and use 3/2 ratio to calculate the fifth (G), then go up another fifth, and continue until 12 fifths are built up You “should” get back to where you started - but you don’t!
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern