Beginner impro Why are the perfect fourth and perfect fifth named as such?

[patrickintheforest]

I have heard one explanation as follows.

Before we all started using 12 Tone Equal Temperament, all the frequencies were mathematically correct. Nice simple ratios of the frequencies. But there were other problems in that to play in another key you would have to retune the piano. So a compromise was made in using 12 Tone Equal Temperament. So you could now play in any key without retuning your instrument. But of the nice simple ratios of the various intervals, most are now not accurate (with the exception of the octave), but you would have a job to hear the error. The only other intervals that are still accurate are the fourth and the fifth, so they are referred to as perfect.

Is this explanation true or is there another reason?

 

[Pete Thomas]

I might be wrong (I was once) but I always assumed perfect in regard to an interval meant it wasn’t diminished or augmented. Not to do with being a perfect mathematical ratio.

Note that we talk about a major or minor third whether it is equal temperament, just or meantone, so the descriptors perfect, major, minor etc are nothing to do with equal temperament.

 

[mizmar]

I have heard one explanation

Next time you hear an explanation from that source, nod, turn around while giving a sideways look as you slowly walk away

 

[skeller047]

2nds, 3rds, 6ths and 7ths have a major and minor version. There is no major or minor version of the 4th, 5th or octave. Hence the name "perfect".

Perfect and minor intervals can be reduced 1/2 step, in which case they are "diminished". Perfect and major intervals can be increased 1/2 step, these are "augmented".

 

[LostCircuits]

About the only thing to ad is that before the well tempered tuning was introduced, the frequencies were not mathematically correct. Yet you could play in any key without retuning, it would just give you a different temperament, sad, happy whatever.

But it's a good thing you asked rather than letting the bad info fester.

 

[skeller047]

Putting on my pedantic hat. Many people confuse “well temperament” with “equal temperament”. They are not the same.

Equal temperament is what we use today. All the intervals are slightly out of tune, with respect to the root frequencies; they are not exact integer multiples. Every note is exactly the same distance, logarithmically speaking, from the next.

Well temperament is also slightly out of tune, but each key is out of tune by a different amount. So thirds are sharper in sharp keys, and flatter in flat keys, compared to equal temperament. There are also occasional things that make your ears go “huh?” when modulating. There are actually several different well temperament tunings; Werckmeister is the one in widest use today. It was first described (in Europe) in the late 1600’s.

This tuning was coming into common use during Bach’s time. Equal temperament didn’t come into wide use until the 1800’s, although I think it was known much earlier.

 

[Tenor Viol]

Ugh a minefield… Yes, ET was known about much earlier but wasn’t in real use - mainly for performance with keyboard instruments- until well into the C19th. Evidence from early recordings in the late C19th suggest pianos were not in ET necessarily even then.

Well-tempered was in use and performers devised their own, including Bach.

We have Pythagoras to blame for most of this as if you have a vibrating string and divide it at various mathematic ratios e.g. 3:2, 4:5 etc you will create various intervals. Some are very difficult e.g. major third.

The problem Pythagoras found was if you stack 5 octaves you don’t end up at the same point as stacking 8 fifths… this is the Pythagorean Coma. ET loses the coma by splitting it amongst all the semi-tones using the ratio of 12th root of 2.

Whilst you can now play in any key on a piano and it sounds ‘ok’ nothing is truly in tune. The 5ths are narrow and the major 3rds are so wide they’re not really in tune.

When I tune my cello, the 5ths are pure and I use a specific tuner setting for this. If I used ET I’d get a beat between adjacent strings sounded together

 

[Woodpad]

The only other intervals that are still accurate are the fourth and the fifth, so they are referred to as perfect.

Equal temperament uses the twelfth root of two as a multiplier between two adjacent half tones. Only the octave is in tune with a multiplier of a perfect 2. The word perfect is probably used to destinguish the intervals from the wolf intervals in the prior tuning systems. It isn't used on the octave because they didn't change when going to equal temperament.

Also the piano is not perfectly tuned in equal temperament as the lowest and highest notes are slightly altered to make it sound more lively. Our minds like the simplicity of the equal temperament, but our ears want some chaos.

 

[Pete Thomas]

The only other intervals that are still accurate are the fourth and the fifth, so they are referred to as perfect.

As well as not being the reason for being called perfect, I would question whether equal temperament fifths are an accurate mathematical ratio anyway. Just being extremely close doesn’t count.

 

[mizmar]

We have Pythagoras to blame for most of this...

The mesopotamians. And I'm pretty sure they weren't trying to build a complete, multi octave tuning system. That would be the sort of thing done by those renaissance people and their flying machines... Who loved the mythology that every thing goes back to the Greeks.
And, anyway, folks almost everywhere we have evidence, would be more likely to be thinking tetrachords than octaves, right through to late medieval times.

I find it amusing to think about what it would have been like, for a music player, in antiquity. My little reed flute, with all holes closed, blows an octave (but the base notes are weak), a 5th, a 4th etc. It's not hard to find where to put a hole to reproduce the 5th "open" then trial and error to make holes for the 8 or 9 fingers producing notes that fit together.

I guess the equivalent stringed instrument would be the lyre and our colleague in the Fertile Crescent would be able to hear 5th as easily as we can.

When I tune my cello, the 5ths are pure

Some of the best mesopotamian mathematicians managed the breweries. So it's not a big stretch to imagine them, after testing the the latest batch while listening to some chart hits (eg 'By the rivers of Babylon"), to be "ok then, what's going on with these instruments... Hand me a stylus and hold my beer..."
Anyone one of us who've worked in the sciences will recognise that from boozy dinners.

 

[Woodpad]

As well as not being the reason for being called perfect, I would question whether equal temperament fifths are an accurate mathematical ratio anyway.

We are talking abouth the ninth power of the twelfth root of two. No mathemathician would consider that to be something perfect. It will be calculated to a certain number of figures behind the dot, but it is always an approximation.

Only marketing would consider to use the word perfect to discribe this approximation.

 

[Woodpad]

Who loved the mythology that every thing goes back to the Greeks.

Just because we don't want to know that the inventions that started the renaissance came from China.

 

[mizmar]

Just because we don't want to know that the inventions that started the renaissance came from China.

Some. Also.

 

[Targa]

Just because we don't want to know that the inventions that started the renaissance came from China.

Because China is so large the aliens could conceal themselves whilst implanting the knowledge.

 

[Woodpad]

Some. Also.

The trick was to call philosophy the mother of all sciences. The Greek have inveted a few things but the majority came from other places.

 

[Woodpad]

Because China is so large the aliens could conceal themselves whilst implanting the knowledge.

Yes, the great wall was just the signal to the alien headquarters that the mission was acomplished.


--------------


means wating for new orders to introduce the twelfth root of two on earth.

 

[PiccoloPirate]

Tunings on the Korg OT series.
Some piano tuning listening fun.

View: https://www.youtube.com/watch?v=63g9KV7sAvI

 

[Tenor Viol]

Pythagoras gets the credit because he wrote it down and records of that have persisted. Did he "invent" it? Probably not. He was probably codifying something already known about. And yes, tetrachords were the thing until about the C17th. It doesn't matter what the definition of an ET fifth is, the thing is that in ET it is not a pure fifth - it is slightly narrow and the major third is way too wide.

Some 'inventors' get credit for work that was not theirs, Edison being a prime culprit of that.

 

[mizmar]

Fine.
I was bouncing off your post to make a historic point.

The OP was framed as a historical argument but there are two possible questions, in general.
The "how did we get here" question and
The "what does it mean now" question.
Often people answer the second as a "progress" or even teleological poetics, charming or uplifting historeish story... But not history nor modern theory.

4 - The Man With The Golden Thigh: Pythagoras | History of Philosophy without any gaps

historyofphilosophy.net

 

[mizmar]

Pythagoras gets the credit because he wrote it down and records of that have persisted.

Have they?
Not according to wikipedia.