432 or 440?

[R2-0G2]

If the mandolin is tuned to perfect fifths, which is in music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so, also known as Pythagorean Tuning which is 432 tuning. Why does everybody tune the mandolin to 440? The guitar can be 440, but the mandolin is setup and designed to be tuned to 432 just like the violin. So i guess what I'm asking is why would or should i tune to 440?

[Paul Busman]

Simplest reason is that if you want to play with anyone else, you'd better be in 440.

[DavidKOS]

You have it a wee bit confused.

Pythagorean Tuning is a tuning system based on whole number ratios for 4ths, 5ths, etc.; but it can be at any pitch, and is NOT the same thing as the current pseudo-science woo-woo metaphysics that claim one pitch like 432 is "better" than 440.

https://en.wikipedia.org/wiki/Pythagorean_tuning

"it is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2, "found in the harmonic series."[2] This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easy to tune by ear."

http://www.medieval.org/emfaq/harmony/pyth.html

It can be pitched anywhere, though and does not specify absolute pitch.


Why does everyone tune to A440 - because since the 30's it has been the agreed upon international standard for instrumental pitch. Before that you had pitches higher and lower than A440 - many old band instruments are marked "low pitch " or "high pitch" and vary by about a half step.

Here are some posts I've made on this issue on other forums, since this silly idea that A432 is metaphysically "better" irritates me because it is such bunk:

"I posted a long article before on another forum in relation to this post.

First off, there is a lot of unsupported evidence in those "A should be a lower pitch" metaphysical articles.

If one reads Hans Cousto's book "The Cosmic Octave" you will learn that there is no single pitch reference that is "mathematically consistent with the patterns of the universe."

Depending on what you are measuring you will find pitches ranging from 422.87 for the periodic cycle of Neptune adjusted to the audible spectrum to a high of 445.86 for the moon's synodic cycle.

Also if you read Juan G Roederer's "Introduction to the Physics and Psychoacoustics of Music" you will learn that how people hear and experience pitch is not as simple and straightforward as the low-A crowd would have you believe. Also, all the "partials" mentioned are harmonics, which are mathematically related to the root pitch and are always as such in proportion no matter what the pitch may be.

Also in the past pitch was not simply lower- it was all over the place even in the same cities. Choir tone and Chamber tone pitches could be off by as much as a 4th or so.

I have also heard the same sort of claims for music that is in "just intonation" rather than tempered tuning, again the nature of human psychoacoustics proves that to be wishful thinking too.

some references:

The Rise and Fall of English Pitch

Note that pitches were as high as 455 at one time

Wiki -"Some idea of the variance in pitches can be gained by examining old pitchpipes, organ pipes and other sources. For example, an English pitchpipe from 1720[2] plays the A above middle C at 380 Hz, (info) while the organs played by Johann Sebastian Bach in Hamburg, Leipzig and Weimar were pitched at A = 480 Hz (info) (a difference of around four semitones). "

Bach, a very spiritual composer, played on organs tuned as high as 480!

http://www.ling.ohio-state.edu/~mcgu...andTunings.pdf

Here's one for you:

Ancient chanting influenced temple designs

"In subsequent OTSF testing, stone rooms in ancient temples in Malta were found to match the same pattern of resonance, registering at the frequency of 110 or 111 hz. This turns out to be a significant level
for the human brain."

So this temple was designed for A440! (A110 is just 2 octaves lower than A 440. thus you can "prove" any pitch has spiritual significance.

In Indian music, which is closely tied to cosmology, there is no concept traditionally of a standard pitch - you tuned Sa, the tonic, to whatever sounded and/or felt right, and then everything was based on relationships to the tonic drone note. Believe me, if there was any specific "spiritual" pitch these guys would use it!

Anyway, I do not accept this belief, and I am definitely one of those that would if there was any real evidence.

....

Sorry guys this is well-intended bull****. Pitch has never had any special standard based on any "universal" issues. I've seen this article before, and it is just not true.

Even if you try to rationalize universal vibrations into some pitch reference, there is no one standard pitch to which everything resonates.

Cousto in "The Cosmic Octave" ISBN 0-940795-04-3, 1987, takes all sorts of planetary vibrations and by octave transposition figures out the pitch.

So, according to him, there are several pitches at which one can claim cosmic harmony; A435 is CLOSE to one of them based on the average solar day, 435.92; the sidereal day is A437.11, and so on. The "tone of Venus" is A442.457, while the moon is A445.86.

Plus there is a list of tuning sources from european history, and as many are ABOVE A440 and are below, and there was little standardization.

Don't let that article scare you.

The Ancient Temples Were Designed for 110 Hz Chanting + The Musical Scale Conspiracy (440 Hz Vs. 432, page 1

"It has been recently discovered that the Ancient temples were designed for 110 Hz chanting. The oldest temples examined by experts are about 6,000 years old. "

100...220....440.....so what's the problem - chant away!

Ancient chanting influenced temple designs

"In subsequent OTSF testing, stone rooms in ancient temples in Malta were found to match the same pattern of resonance, registering at the frequency of 110 or 111 hz. This turns out to be a significant level [right] for the human brain. Whether it was deliberate or not, the people who spent time in such an environment were exposing themselves to vibrations that impacted their minds."

"Findings indicated that at 110 hz the patterns of activity over the prefrontal cortex abruptly shifted, resulting in a relative deactivation of the language center and a temporary switching from left to right-sided dominance related to emotional processing. People regularly exposed to resonant sound in the frequency of 110 or 111 hz would have been "turning on" an area of the brain that bio-behavioral scientists believe relates to mood, empathy and social behavior."

From other folks:

"432 may be math
432 Hz is not.

There is no natural time interval called the second. If you make the second slightly shorter, than the current pitch we hear now as 440 cycles per SECOND would be 432 cycles per SECOND.

The whole division of a day (which IS a natural cycle) into 12 hours, and then into 60 minutes, then 60 seconds is simply based on numbering systems we don't use any more -
Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day? - Scientific American

If the Egyptians were on the metric system, we wouldn't be having this discussion. And even if you believe the Egyptians were on to something cosmic, since their day was longer in the summer, the hour was longer in the summer. The hour and second, being divisions using the number 60, would actually change how long they lasted depending on the season. So, in Winter, 432 would be a higher pitch, as he second would be shorter.

So, there is no magic in 432 Hz other than a historical accident on the way time is divided up.This right here debunks the idea that 432 Hz is more in tune with nature's mathematics simply because it's divisible by 12."

"S0 ... you do realize the second is an arbitrary measurement, correct?

What we call 432 cycles per second could easily be 440 cycles per second if you just made the second a little bit longer.

There is no natural division of time to make the second what it is.

Also, 440 was proposed as a standard, as were other pitches, long before it was widely accepted and it still is not standard. Lots of people tune to a different pitch."



Keep tuning to 440.​

[DavidKOS]

but the mandolin is setup and designed to be tuned to 432 just like the violin. So i guess what I'm asking is why would or should i tune to 440?

Where did you get the idea that the mandolin should be pitched at 432 "like the violin"? I've never heard that in my entire 4 decade plus musical career.

[Bertram Henze]

You can use any pitch you like as long as you play alone or with like-minded musicians only.
But do not try to prove it right or wrong with maths, because maths just won't give you that.

David said it all above, and more elaborately than I did. Listen to him.

[objectsession]

If the mandolin is tuned to perfect fifths, which is in music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so

Just wanted to add that the "very nearly so" part is significant. (Contemporary) mandolins are usually designed to use equal temperament tuning*. For a mandolin to be designed for Pythagorean tuning, which is a just tuning (and not even the more familiar 5-limit tuning), it would have to be fretted differently.

* and even that's an approximation because of the real world physics of an instrument.

[Polecat]

...So i guess what I'm asking is why would or should i tune to 440?

The reason why you would has been answered comprehensively - it is a convention nearly everyone agrees on, like driving on the right (in most countries).
As to why you should, opinions vary widely, as you will have noticed. Some see "mystical tuning" (or whatever) as psychobabble mixed with woo-woo, and no doubt some of it is. If you want to hear an example of music based on A=432 and pythagorean tuning, you can listen to it at Damian Halliwell's Metta bandcamp page. Sounds like normal "celtic"-based acoustic music to me. However, it bothered my stepson (who is a bass player) to the extent that he asked me to turn it off, because he perceived it as being painfully out of tune.
It is not just the new-agers who believe in alternate tunings - last Monday night I was listening to a very enjoyable concert of baroque music by Il Giardino Armonico on the radio which included a long pause whilst they retuned to (I think) A=428 hz for the second half. They are lucky not to have any instruments with frets - if you retune your mandolin by that much without moving the bridge, the result is fairly teeth-grinding.
There are even those who believe the A=440 hz convention was a nazi plot to set humanity's nerves on edge, which is obviously silly, but I wouldn't reject out of hand anybody's esoteric reasons for doing anything. There are documented examples of people diagnosed with terminal diseases who have been "cured" after bathing in what they believed were sacred pools, and similar stuff. If you believe that your quality of life and the quality of your music is improved by using an alternative tuning, you are probably right, at least as far as you personally are concerned. The danger only emerges if you start insisting that everyone else must also do the same. The same is true of the A=440 convention - it is convenient, but if you make it into a dogma, you've missed the point.

[Polecat]

I forgot to add that if you tune your mandolin to perfect fifths (which is easy to do, just compare the 2nd harmonic, above the 7th fret, with the 1st harmonic, above the 12th fret on the string a fifth above, and tune them until they are precisely the same), the result will not be very satisfactory, and most chords will sound badly out of tune, no matter what you use as a "base frequency" for the A.

Also, there is no sanity clause.

[DavidKOS]

Just wanted to add that the "very nearly so" part is significant. (Contemporary) mandolins are usually designed to use equal temperament tuning*. For a mandolin to be designed for Pythagorean tuning, which is a just tuning (and not even the more familiar 5-limit tuning), it would have to be fretted differently.

* and even that's an approximation because of the real world physics of an instrument.

I forgot to add that if you tune your mandolin to perfect fifths (which is easy to do, just compare the 2nd harmonic, above the 7th fret, with the 1st harmonic, above the 12th fret on the string a fifth above, and tune them until they are precisely the same), the result will not be very satisfactory, and most chords will sound badly out of tune, no matter what you use as a "base frequency" for the A.

.

Because as you point out, mandolins, guitars, electric basses, banjos, 'ukulele's and every other non-Middle Eastern fretted instruments use 12 tone equal temperament tuning, which calls for 4ths to be a bit sharper than "pure tuning", 5ths to be a bit narrow.

To make string instrument with the ability to play in all keys in pure tuning would require something like 44 frets to the octave.

[foldedpath]

I forgot to add that if you tune your mandolin to perfect fifths (which is easy to do, just compare the 2nd harmonic, above the 7th fret, with the 1st harmonic, above the 12th fret on the string a fifth above, and tune them until they are precisely the same), the result will not be very satisfactory, and most chords will sound badly out of tune, no matter what you use as a "base frequency" for the A.

One thing I've found fascinating about that, is how one can still get away with playing unison melody on a mandolin, or chord backing on guitar, together with a fiddler who tunes in perfect 5ths. And they all do, at least the ones I know in the local OldTime/Irish/Scottish trad scene.

I play music very often at home with my S.O. who plays fiddle. Whether I'm backing her on guitar or playing the same unison melody line on mandolin, it still works. There is no obvious clash (at least to my ears), even though the only time we're perfectly consonant is on the open A strings, where we're both tuned to A=440.

My current theory for why this works, is that the Irish and Scottish dance tunes we mostly play have notes that go by so fast, that you don't have a chance to register any subtle clashes on individual notes. The very fast note decay on mandolin also avoids hearing any "beats" from sustained notes compared against each other. You'd notice it more on airs, I suppose, but I don't play many airs with her on mandolin. When backing on guitar, the lower pitch underneath the fiddle probably masks some of the clashes.

I suppose when a fiddler plays in a band dominated by 12TET instruments (i.e. a Bluegrass or Country band), the fiddler is probably making an unconscious adjustment to stay closer to 12TET in their playing.

[Polecat]

Interesting, foldedpath,
If I tune to perfect fifths I can't stand to play the mandolin at all, it sounds so "wrong" to me in and of itself, let alone in the company of others.
There are probably dozens of programs (or apps) out there that do the same job, but anyone who uses a mac might be interested in http://www.katsurashareware.com/chro...chromatic.html. It's a shareware (10$) chromatic tuner that enables you to tune to a wide range of temperaments and pitches, so you can compare how they sound.

[k0k0peli]

One can select from numerous reasons for tuning to any specific key pitch. As a retired software engineer (burnt-out codemnkey) I naturally gravitate to C=256 where each octave of C is a power of 2. Heimholtz used C=256 in his analysis of sound, and generations of physicists and physicians have followed in his steps, so that's a well-established technical (non-musical) standard.

That's the key word: standard. An old electronics joke goes that standards are good; that's why we have so many of them. The C=256 standard lets audio professionals communicate, and the A=440 standard lets musicians communicate. Some musical organizations (like specific orchestras) have their own standards, with A=432 or A=444 or A=456 or whatever. BFD if it's not your standard. BFD if you can't play along to their recordings. BFD as long as everyone in the group tunes to the same standard. Any standard is as good as any other so long as it's recognized and used. Your group wants to tune to A=228? Glorioski! Have at it!

[foldedpath]

Interesting, foldedpath,
If I tune to perfect fifths I can't stand to play the mandolin at all, it sounds so "wrong" to me in and of itself, let alone in the company of others.

Right, to be clear, I'm not tuning my mandolin in perfect 5ths when I play tunes with my fiddler S.O., I'm in standard tuning. It just sorta works despite the theoretical clash on fiddles open G, D, and E strings (plus whatever she's doing to stay in a "pure" just intonation for Irish music).

When I play flute along with her fiddle, it sounds great and there is never a clash on long sustained notes between the fiddle and flute (unless I'm having a bad day). The flute isn't in 12TET, it's diatonic "in D", and with some weird idiomatic scale issues that fit well with Irish music. The flute and fiddle just lock in together because there are no 12TET compromises.

That's why a Classical string quartet can sound so amazing when they play together. They're all tuned in perfect 5ths and making micro-adjustments in the fingering to sound consonant with each other, in whatever key the music is in. No fretted instruments around (or a piano) to mess things up.


P.S. and this has nothing to do with whether our reference tuning is A=440, except that my flute is made to have a tuning range on the slide centered on 440, unlike the actual 19th Century, pre-Bohm flute the design is based on. The idea that we should all be playing with a reference of A=432 is a recent Internet fad, based on mystical woo-woo.

[EdHanrahan]

...how one can still get away with playing unison melody on a mandolin, or chord backing on guitar, together with a fiddler who tunes in perfect 5ths.

Forgive my touch of cynicism, but I've come to suspect that the fiddler's vibrato is something of an "easy out" from having to hit some specific micro-tone within one of the various scale & tuning conventions. Ya know... just sortta get in the general area and shake it around a bit?

Whoa, that sounded ugly!! I really do have HUGE respect & admiration for the fret-deprived among us!

[Bertram Henze]

Whoa, that sounded ugly!!

Back when I played the violin, that was exactly what I did. On the fretboard. Errhh the fingerboard

[journeybear]

"S0 ... you do realize the second is an arbitrary measurement, correct? ... There is no natural division of time to make the second what it is.
​

Well ... A few decades ago a bunch of scientists put their brains together and devised the atomic clock, which was based on variations in a particular isotope of cesium. This removed the definition of a second from an observation of repeating astronomical events, given to variances over time, and instead used a standard which was more consistent:

in 1967, the International Committee for Weights and Measures (abbreviated CIPM from the French Comité international des poids et mesures) changed the definition to:

the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom

This is a back-definition based on observations using the standard second at the time. So one could still argue it's arbitrary.

The very fast note decay on mandolin also avoids hearing any "beats" from sustained notes compared against each other.

This reminds me of the problems I had when I started using my EM-150 in a band. It was really hard to get it in tune, and if the strings in a pair were slightly out of tune the result was really annoying beats. Even if I got them in tune unfretted, the fretting action pulled them out of tune, unless I could magically stretch both string equally. My solution was to do away with pairs, opting for single strings instead.

[Bill Snyder]

Forgive me, I know this is a ridiculous question, but why does the OP think violins are tuned to A=432? I am sure that some are but I grew up playing viola and we tuned to A=440.
And Polecat no matter what A you tune to there is only one proper location for your bridge.

[DavidKOS]

Forgive me, I know this is a ridiculous question, but why does the OP think violins are tuned to A=432? I am sure that some are but I grew up playing viola and we tuned to A=440.
.

I wondered the same thing.

[foldedpath]

Forgive my touch of cynicism, but I've come to suspect that the fiddler's vibrato is something of an "easy out" from having to hit some specific micro-tone within one of the various scale & tuning conventions. Ya know... just sortta get in the general area and shake it around a bit?

Whoa, that sounded ugly!! I really do have HUGE respect & admiration for the fret-deprived among us!

I think there's maybe a little truth in that, at least for the lower tier of fiddlers who are still working on their intonation, or just don't have a very good ear.

By the way, vibrato is something very rarely used in Irish traditional fiddling, and the quickest way to spot a Classical player "faking it" with the music. All the sustained-tone instruments used in Irish trad -- fiddles, flutes, pipes, accordion, and even Sean-nós singing are usually played with no vibrato, just a pure sustained tone. Maybe that's the historical influence of the pipes, or something. I've noticed more occasional use of vibrato with Scottish and Cape Breton fiddlers, where there often seems to be a bit more Classical influence.

[foldedpath]

Well ... A few decades ago a bunch of scientists put their brains together and devised the atomic clock, which was based on variations in a particular isotope of cesium. This removed the definition of a second from an observation of repeating astronomical events, given to variances over time, and instead used a standard which was more consistent:

Yep, and even the atomic clocks have a problem with that arbitrary definition of "a second," because they're getting accurate enough now that identical clocks will drift apart due to the change in the local gravity field (i.e. relativistic effects), with only a small change of height from one another. It's the reason GPS satellites are programmed with an adjustment to keep their clocks in sync with the ground, since they're in such a low gravity field.

This also means your mandolin and mine can never be perfectly in tune, if you're at sea level there in Key West and I'm playing mine at 5,000 feet in a local National Park. Due to relativistic effects, my 440 cycles per second at 5,000 feet is running faster than yours at sea level. You're also aging slower than me.


So there's a good excuse if anyone ever says you're playing out of tune. "Oh yeah, in reference to what distance from the local gravity well?"

[journeybear]

Temperature is also a factor, and I expect so is atmospheric pressure. But these variations probably don't add up to 8 cycles per second. I say, split the difference, tune to A 436 and be done with it.

No, I don't. A 440 Or Fight!

[Eric C.]

I use Snark tuning on my mandolin. Whats these numbers everyone speaks of?

[R2-0G2]

Thank you, I wasn't trying to start anysort of spiritual argument, I didn't know 440 folks are so hateful to other tunings. This is the kinds of answers i was looking for, I don't care about peoples woo-woo ideas or their metaphysics. I am so glad I got answers. Its good to know so many musicians keep themselves fluid instead of stagnant. The 18th century violins Stradivarius, Guarneri which are considered the greatest ever made were all made and designed for the 432 tuning, Mike Marshall, Chris Thile, and Avi Avital have all said that mandolin is tuned the same as violins. So i just didnt get why the standard became 440 when music is so diverse. I'm happy to know that I can play whatever tuning i want and will find kindred spirits. Thank you everybody for your responses.

[Beanzy]

Normally you'd tune an orchestra to the instrument that can't be easily tuned, so even modern orchestras will tune to an organ etc. and those could be built to a wide range of tunings. In general most decent players nowadays have a fairly good idea of what 440Hz will be on their instrument. Once you start playing you're tuning to the intervals and a consensus pitch and not any absolute pitch.

As for 'hateful' , I'd read it differently and think people get fairly short when the same subject gets dragged up time after time, even though it has been very thoroughly covered in previous posts. It is probably a reaction to the discourtesy shown by those who just post it again without bothering with a search to see the effort people have put in when answering previously. I often wonder how many times people are expected to re-hash the same answers just because the same old question gets dragged up again with nothing new added. If there is something new, then a new post makes sense, but if there's nothing new it's hardly worth yet another post.

[mandroid]

Modern standard A above middle C on a concert pitch tuned piano is 440Hz.
https://en.wikipedia.org/wiki/Concert_pitch

If you are the Band leader, and sign the paychecks, if you want 432
then I'd Expect the other players will say 'Yes, sir'.