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Perfect 5ths' aren't Really Perfect

KarateChris

KarateChris

Nov 18, 2018
156
193
Western North Carolina
chriscaruso.bandcamp.com
#1
Perfect 5ths' aren't really perfect, or are they?

On my musical journey I have encountered the terms "Perfect 5th" and "Perfect 4th". I am teaching myself to read music, studying music theory and learning a lot. I understand, describing the 4th and 5th notes of the scale as "Perfect" is because they are the same in the major scale and the minor scale.

I know that, for stringed instruments (especially piano) 4ths and 5ths aren't tuned perfectly. This is because of even temperment. 4ths are tuned narrower than perfect and 5ths are tuned wider. If tuning non-stringed instruments (like a pipe organ) the 4ths and 5ths can be tuned perfectly.

My point/rant? This can be confusing for people learning music theory. Those intervals aren't really perfect, stop calling them that! :D lol!

Am I wrong? Please educate me. :)
 
#3
KarateChris said:
I understand, describing the 4th and 5th notes of the scale as "Perfect" is because they are the same in the major scale and the minor scale.
Click to expand...

That's not really why. The actual reason is that when this terminology was developed, the 4th and 5th were considered the most consonant (and therefore "perfect") intervals, with the other intervals being less so to varying degrees.
 
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#5
KarateChris said:
Perfect 5ths' aren't really perfect, or are they?

On my musical journey I have encountered the terms "Perfect 5th" and "Perfect 4th". I am teaching myself to read music, studying music theory and learning a lot. I understand, describing the 4th and 5th notes of the scale as "Perfect" is because they are the same in the major scale and the minor scale.

I know that, for stringed instruments (especially piano) 4ths and 5ths aren't tuned perfectly. This is because of even temperment. 4ths are tuned narrower than perfect and 5ths are tuned wider. If tuning non-stringed instruments (like a pipe organ) the 4ths and 5ths can be tuned perfectly.

My point/rant? This can be confusing for people learning music theory. Those intervals aren't really perfect, stop calling them that! :D lol!

Am I wrong? Please educate me. :)
Click to expand...
Play fretless!

In just intonation a perfect 5th is 702 cents (frequency ratio = 3/2).

In equal temperament a perfect 5th is 700 cents. That is very, very close to just intonation. I believe no human can hear the difference.

3rds and 6ths in just intonation deviate much more significantly from equal temperament. Violin players, cellists, singers, fretless bassists can play just 3rds and 6ths.
 
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#9
KarateChris said:
I know that, for stringed instruments (especially piano) 4ths and 5ths aren't tuned perfectly. This is because of even temperment. 4ths are tuned narrower than perfect and 5ths are tuned wider. If tuning non-stringed instruments (like a pipe organ) the 4ths and 5ths can be tuned perfectly.
Click to expand...

There's no real difference between string instruments and others here. Pianos and organs are both capable of being tuned to whatever temperament you'd like.

Note it's not actually possible to nail *every* fourth and fifth at once, though--it's just a mathematical impossibility. If you want the cycle of fifths to work like it usually does, then stacking 12 fifths on top of each other should land you on the same note seven octaves up, so the final frequency should be 2^7 = 128 times the starting frequency.

In fact, if you stack up 12 fifths with each exactly a 3/2 ratio, the starting and ending notes end up in a ratio of (3/2)^12, which is about 129.75, a little bit more than 2^7.

So if you want your fifths to all be the same, and you want 12 of them to land you back at the same note, you need to flatten them slightly, to about 1.4983 instead of 1.5.
 
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#10
What you might be thinking about with when talking about string instruments is stretch tuning. Strings tend to be a little out of tune with themselves--the harmonics, instead of being exact multiples of the fundamental frequency, are a little sharper than that. The effect is especially pronounced with thicker heavier strings, which is part of the reason the lowest strings on a bass or a piano sound a little strange. Anyway, this means that if you want an octave played in the lowest range of the piano to sound good, you have to widen it a little, to prevent the first harmonic of the lower note from clashing with the fundamental of the higher one. At least, that's how stretch tuning has been explained to me.

But that's a different issue from the mathematical problem that keeps the intervals in an equal-tempered 12-tone scale from having intervals that are exactly nice simple ratios of each other.....
 
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#12
KarateChris said:
Perfect 5ths' aren't really perfect, or are they?

On my musical journey I have encountered the terms "Perfect 5th" and "Perfect 4th". I am teaching myself to read music, studying music theory and learning a lot. I understand, describing the 4th and 5th notes of the scale as "Perfect" is because they are the same in the major scale and the minor scale.

I know that, for stringed instruments (especially piano) 4ths and 5ths aren't tuned perfectly. This is because of even temperment. 4ths are tuned narrower than perfect and 5ths are tuned wider. If tuning non-stringed instruments (like a pipe organ) the 4ths and 5ths can be tuned perfectly.

My point/rant? This can be confusing for people learning music theory. Those intervals aren't really perfect, stop calling them that! :D lol!

Am I wrong? Please educate me. :)
Click to expand...

Context is important.

IMHO you are mixing theory and tempering. In equal temperament, pitches are intentionally detuned so you can play in all keys. This means that technically from a tuning standpoint you have tempered 4ths and 5ths rather than perfect 4ths and 5ths.

From a theory standpoint 4ths and 5ths are either diminished, perfect, or augmented. The difference between diminished, perfect, and augmented intervals is on the order of a half step, and you are not concerned if the note is adjusted by a few cents sharp or flat for tuning purposes.
 
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#15
KarateChris said:
I do play fretless sometimes. I'll try to hear the 2 cent difference in 5ths.

Isn't this the idea behind the fan fret design (Dingwall)?
Click to expand...
It's easy to hear with 5ths because of the beat that develops when they aren't perfectly in tune. However, yes, pianos are a compromise. Basses and guitar are also, unless you play fretless.... but then all music is a compromise.

I personally believe we should only ever play 372.3 Hz, and we'll call it Q sharp. It's safe, pretty simple, most of us can hit it on our instruments if we tune it right, and we'll always be in tune if we use, well, a tuner. Then no more worries about fretlines, how many strings.

Naw, forget it. There would still be arguments about how many strings. "Hey man, my B string sounds like crap on the Q#. Is it the tension/shape/gauge/wrap/material/age? Q# sounds SOOO good on my E string!"... "No man, you shouldn't use a B string... Jaco played Q# with a 4 string!"
 
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