Perfect intervals

Why are the 4th,5th and 8th considered perfect?

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Jul 28, 2017
Searching for rigor on this...
by: Anonymous

It's also the case that (in the C major scale / Ionian mode) the sum of the half-steps in the 4th and 5th is 12. You could also say that sum of half steps in the unison (0) and the octave (12) is 12. No other pair of notes have this property.

In other modes, some do. I worked out the following:

Lydian: 4th+4th
Ionian: 4th+5th
Mixolydian: 2nd+7th, 4th+5th
Dorian: 2nd+7th, 3rd+6th, 4th+5th (all notes)
Aeolian: 2nd+7th, 4th+5th
Phrygian: 4th+5th
Locrian: 5th+5th

Interesting pattern - seems like it ought to be telling us something. The unison+octave pair is present in all of them as well - that one is a "given."

Nov 06, 2016
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by: Joseph Dsouza

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Aug 26, 2016
Perfection and the overtone series
by: Rodger Schoonover

Another perspective: The lowest notes in the overtone series are the easiest to hear. And the first three intervals are (1) Octave [above the previous note], (2) Perfect Fifth [above the previous note], and (3) Perfect Fourth [above the previous note].

There is also a "hollowness" to the intervals which distinguishes them from the other narrower intervals.

Of note, the lower notes of the overtone series generate a major triad (the chord of nature?) and the lowers notes generate a mixolydian scale, but musica ficta causes our ear to generate a raised leading tone (or, phrased differently, by raising the seventh scale degree, it acquires "leading" characteristics.

Thank you, I enjoyed reading the discussion.

Rodger Schoonover
Virginia Beach, VA

Aug 16, 2016
Perfect Intervals
by: Simon

Hi there,

My answer would naturally have been: Perfect intervals are called 'perfect' because they have a high degree of consonance. It is more 'in perfect tune' than any other interval aside from the unison and the octave.

The group of perfect intervals also invert to form other perfect intervals whereas major intervals invert to form minor and diminished to form augmented intervals.

However, this is just something I believe to be true so I took to Google and a few other sites. If you want some more in depth discussion have a look on this

reddit page

I really like the sound of this answer half way down. Even if not true, it is a good way of thinking about it.

Think about the diatonic scale -- for simplicity, in C: C D E F G A B
There are seven seconds here, five bigger ones -- C D, D E, F G, G A, A B -- and two smaller ones -- E F, B C. Similarly, there are seven smaller sevenths and two bigger ones.
There are seven thirds here, three bigger ones -- C E, F A, G B -- and four smaller ones -- D F, E G, A C, B D. Similarly, there are three bigger sixths and four smaller ones.
Well, there are seven fourths, too, but one of them just sounds too different. That's the tritone. So we have C F, D G, E A, G C, A D, B E as normal fourths, and one weird one, the tritone F B. It doesn't sound similar to a fourth. Similarly, we have six normal fifths and one weird one.
There's obviously only one kind of unison in the scale, and since the scale repeats at the octave, only one kind of octave. That's the normal one.
So, there are bigger and smaller seconds and sevenths, bigger and smaller thirds and sixths, but unmodified fourths and fifths, unmodified unisons and octaves, and the odd-man-out tritone which is a modified fourth or fifth. Well, "major" means bigger and "minor" means smaller, and "perfect" means unmodified. When we say "perfect fifth", we're really only saying "unmodified fifth".

For further reading you could also look up the wolf fifth and Pythagorean tuning!

Hope this helped and didn't raise even more questions than the one you asked!

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