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Pythagorean Comma

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That being said... How many "default points" should you associate with an exercise upon creation?
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But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
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Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/pythagorean-comma/

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Exercise:
abcliste abc Explain why an arbitrary number of just fifths will never add up to an eger number of octaves. abc On a piano keyboard a sequence of fifths corresponds to octaves. Calculate the ratio of these ervals asing just fifths. This deviation is known as em Pythagorean comma. abcliste

Solution:
abcliste abc Since a just fifth is given by the frequency ratio : any number of fifths corresponds to a ratio of an odd and an even eger. This can never be simplified to be an even eger. A number of octaves always corresponds to an even eger. abc fifths correspond to a ratio I_ leftfracright^Nf and octaves to a ratio I_ leftright^No The ratio is thus I_:I_ frac^Nf^Nftimes ^No frac^Nf^NfoP resultratio With equally tempered fifths seven half-tones there is no such problem: left^/right^ ^ abcliste

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Acoustics (BC) by by

2 | 16
Intervals and Scales by by

2 | 3
Acoustics by by

2 | 19

Attributes & Decorations

Branches	Acoustics
Tags	equal temperament, interval, just scale, scale
Content image
Difficulty	(1, default)
Points	0 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
Decoration
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