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Musical Intervals and Scales

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Chapter - 5B

Musical Intervals and Scales:


An " Interval" is said to have been played, when two notes are sounded together. It is the relationship between the pitches of two notes and is often measured in as their frequency ratio.
When two notes are played together, they constitute a "Vertical Interval" and when they are sounded separately, they are make up a "Horizontal Interval."

A special type of intervals needs to be mentioned here: Pitch Class -
A frequency with all its octaves is called a "Pitch Class." Thus the names of these notes are the same but their frequencies are either obtained by multiplying or dividing one of them by the number 2 (two). E.g.: g.: The middle C (written as "C4" but different in meaning from that in music sheet or chords) is 262 Hz. Its octaves C3 (131 Hz) and C5 (524 Hz) are all written, in general music notation, as "C" only as they belong to the same pitch class, viz. "C." So a scale, dividing any octave, begins and ends on the same pitch class.

The intervals in the 12-TET divided octave are as follows:

If we take any note to start with and take its frequency to be F Hz, the ratio

Semitones---------Interval-----------Just Intonation
from Unison:--------Name:--------------Equivalent:-
(1/2 steps)

-0-----------------Perfect Unison---------1:1
-1-----------------Minor 2nd-------------16:15
-2-----------------Major 2nd--------------9:8
-3-----------------Minor 3rd--------------6:5
-4-----------------Major 3rd--------------5:4
-5-----------------Perfect 4th------------4:3
-6------Augmented 4th/Diminished 5th--45:32/64:45
-7-----------------Prefect 5th------------3:2
-8-----------------Minor 6th--------------8:5
-9-----------------Major 6th--------------5:3
-10----------------Minor 7th-------------16:9
-11----------------Major 7th-------------15:8
-12----------------Perfect 8Ve------------2:1

(Intervals written out in staff notation)

Vertical intervals are often played as double notes in certain pieces where as the horizontal intervals make up the pieces themselves.

An augmented interval is one which is a 1/2 step longer than the perfect or major interval.
A diminished interval is one which is a 1/2 step shorter than the perfect or major interval.

Musical Intervals and Scales:

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