scales and temperament

Question 1

What sensation replaces distinct beats when the beating frequency fB is increased?

Answer 1

Roughness

Roughness is perceived most intensely in the frequency range of ~300 - 400 Hz with an fB of 20 Hz.

Question 2

What is the relationship between dissonance in an interval and roughness according to Helmholtz’s theory?

Answer 2

The degree of dissonance is related to roughness due to interactions between harmonics

This theory explains how simultaneous notes can create a sense of roughness.

Question 3

What are JI intervals?

Answer 3

Pitch intervals found in the harmonic series

JI stands for Just Intonation.

Question 4

How many cents are in 12 JI perfect 5ths?

Answer 4

8424 cents

This is equivalent to 7 octaves + 24 cents.

Question 5

What is the 24 cent difference in tuning called?

Answer 5

Pythagorean comma

This difference arises when tuning based on JI perfect 5ths.

Question 6

What is the definition of temperament in music?

Answer 6

A way of defining musical scales by compromising the just intonation of some intervals

Different temperaments affect how intervals are perceived in tuning.

Question 7

What is Pythagorean tuning based on?

Answer 7

Tuning successive perfect 5ths in just intonation

This method is foundational in certain musical traditions.

Question 8

What types of triads are found on the tonic, subdominant, and dominant scale degrees in just diatonic scales?

Answer 8

Major triads (frequencies 4:5:6)

These triads are fundamental in Western music harmony.

Question 9

What is the syntonic comma?

Answer 9

The difference of 22 cents between the 5th D-A and JI

The JI perfect 5th is 702 cents, while the D-A interval is 680 cents.

Question 10

What characterizes meantone temperament?

Answer 10

Only one type of tone, the average of JI major and JI minor tones

This tone equals half a JI major 3rd.

Question 11

What are the pros of meantone temperament?

Answer 11

• Major 3rds are JI

This temperament offers a pleasing sound for major chords.

Question 12

What are the cons of meantone temperament?

Answer 12

• Most perfect 5ths are JI - 5.5 cents
• One perfect 5th is JI + 36.5 cents

These discrepancies can lead to dissonance in certain contexts.

Question 13

How is equal temperament obtained?

Answer 13

By dividing an octave into 12 equally tempered (ET) semitones of 100 cents

This method allows for consistent tuning across all keys.

Question 14

What is a pro of equal temperament?

Answer 14

• All keys have the same intervals

This uniformity simplifies playing in different keys.

Question 15

What is a con of equal temperament?

Answer 15

• Only the octave is JI
• The 3rd has a noticeable difference to JI

This can affect the harmonic richness of music.