Perfect Tuning is a Mathematical Impossibility

[ashtray]

Because the note to note intervals are not equal, each musical key has it's own feel to it. It's subtle but it's definitely there.

My electric piano has the option of changing the tempering - I played around with it one day. Some songs sounded pretty normal, while others had notes here or there that just stuck out.

 

[BassBrass]

Never having passed a math class I'm more interested in The Implications (if there are any) of the split between math and nature. Einstein had to add a fudge factor to make his theory work but practically, as a trumpet player I'm always needing to use my ears and pull myself flat as I go higher or else I'll wind up too sharp (and why 2 or 3 trumpets work like piano strings, all slightly imperfect making a fat sound) Automatically (in Bb or any tuned brass) A and E in the staff are sharp, and C# and D below then staff are sharper, so that any non beginner horn has a trigger to lengthen the 3rd valve slide and pro horns may trigger the 1st and 3rd valve slides for intonation. That's 2/3 of the valves have slides on them just to stay in tune. Welcome to crazy world.

 

[lokikallas]

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[Frank Tuesday]

That's why fretless instruments can be played perfectly in tune ( not by me although I have a couple of uprights).

Someone recently posted the difference between F# and Gb. There is a difference because there are 9 divisions between F and G. Where's the "half way point."?

Just curious, but what are the 9 divisions between F and G? There are as many divisions as you wish to put between F & G. If you choose to make it 1 division between F and G, and make that division at precisely 2^1/12 more than F, you have F#/Gb. If you put it anywhere else, you have either an out of tune F#/Gb or you're not using the 12 tone scale, so F and G don't really have any meaning.

 

[Nev375]

The joke was since the 12 root of two was irrational, it does not terminate or repeat, it is always an approximation in a mathematical sense, even if you carry it out to a billion places.

Aren't jokes supposed to have... oh what's the word... rhythm?

No. That's not it. Where's the line to the punchbowl? I'm not drunk enough for this joke.

 

[redwingxix]

I'm by no means well-versed (illiterate) in music theory, but a couple years a go I read a book called Temperament by Stuart Issacoff that was a history of how western tuning standards arose over the last several centuries. I highly recommend it to anyone even remotely curious about this stuff. There was some math but even glossing over that it was a really good read.

 

[Slevage]

Just curious, but what are the 9 divisions between F and G? There are as many divisions as you wish to put between F & G. If you choose to make it 1 division between F and G, and make that division at precisely 2^1/12 more than F, you have F#/Gb. If you put it anywhere else, you have either an out of tune F#/Gb or you're not using the 12 tone scale, so F and G don't really have any meaning.

You'll have to consult the classical gurus on that one.
Musical divisions are not the same as mathematical divisions- then there's the issue of resolution and methods of proving the results (equipment accuracy).
I'm faced with that daily when taking voltage, current, and impedance measurements.

 

[Chrisk-K]

I'd love to invent a tuning system involving i (square root of -1).

 

[Spidey2112]

The precise mathematical value of the tuning of my bass going through my Boss TU-3 tuning pedal on stage in a bar about to play rock and country to at least 100 adoring fans is......

(Takes deep breath)



.....plenty close enough.

Yep.

 

[lfmn16]

The precise mathematical value of the tuning of my bass going through my Boss TU-3 tuning pedal on stage in a bar about to play rock and country to at least 100 adoring fans is......

(Takes deep breath)



.....plenty close enough.

Even if you could get your bass perfectly in tune, most basses are affected in some degree by the temperature, humidity and how hard or soft you play so the note you actually played still could be out of tune. I'm not saying we shouldn't tune our basses, but of all the things that will make you a great player, worrying about this has got to be at the bottom of the list.

 

[Oddly]

It really doesn't matter if we're in tune anyway.
The guitar player will be out.

 

[mcarp555]

No one has mentioned the fact that frets are not exact as well, only average approximations of where the pitch should be. I remember many years ago seeing a classical guitar with a removable fretboard so you could swap it out with ones that had the frets broken up for each string and correctly placed to give a closer approximation depending on the key you were going to play in.

 

[bassdude51]

Umm, we can take that even farther. There is no such thing as "perfect" anything.

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Also....................

 

[Paulabass]

Aside from tempered tunings on a piano, perfect tuning is impossible on a fretted (or fretless) because you must take into account that as a string is pushed down to a fret, it is stretching sharp.

 

[bassdude51]

Aside from tempered tunings on a piano, perfect tuning is impossible on a fretted (or fretless) because you must take into account that as a string is pushed down to a fret, it is stretching sharp.

Yes indeed!

Also, as our fingers transmit warmth to the strings and changing their temperature, the strings stretch. Constantly going out of tune as we constantly play.

Ya know, I don't think a perfectly in tune instrument is going to sound right anyway. That's what makes the violin section sound so beautiful. Everybody is a little bit out of tune.

 

[grisezd]

Nothing is mathmatically possible. I hope this helps.

 

[Paulabass]

^ This is why musicians get a break on the beer prices. It makes intonation discrepencies not as bothersome.

 

[FugaziBomb]

You misread it. It said no meth.
Maybe next week.

Well I'm from Florida, and that's unacceptable. Meth is our chief export.

 

[Gravedigger Dav]

Well I'm from Florida, and that's unacceptable. Meth is our chief export.

Wow, am I confused. I thought is was Florida's major import.

 

[vonbladet]

While I'm in charge of being boring, the problem with even temperament is simple enough to explain: the ratio between frequencies in a perfect musical fifth should be 3/2 (or 1.5 in decimal); the ratio you get with even temperament is 2 to the power of 7/12, which is 1.49830(...). So your "fifths" come out slightly flat, and ill-shod string quartets will point at you and laugh.

What you get in return is a compromise that works equally well (or badly) in all keys and chords at once, so you can modulate freely.