432 Hz vs 440Hz

[thevenusian]

Aaand, if you plot the Pythagorean tuning for the C-Major scale on a 360 degree wheel, the wheel is based on 16 divisions, and if you set middle C as 256Hz (A432 tuning), you get 16 sections of 16Hz in the wheel.

One thing that caught my eye was when I calculated the hertz frequencies for the C-Major scale in 432. I posted this on my facebook as well, but here it is... I find it fascinating that the cycles per second work out to whole numbers with A432 and NOT with A440. Seems to make sense that this tuning would "feel better" to the human ear.

Stradivari/Verdi Tuning (A = 432 hz, C = 256 hz)
Calculated using the Pythagorean method of 3:2 ratio for dominants, 11:8 for sub-dominants, 2:1 for octaves.

There is a little mixing of apples and oranges here, in that the Pythagorean ratios are 'just' tuning, in which all the mathematical relationships between notes are simple and 'pure', and the examples given for listening to later in the thread are 'equal-tempered' modern tuning just tuned down slightly. The composer Harry Partch used a 'just' system and made his own instruments in order to play in it. It sounds weird to most people. There are plenty U Tube examples of Partch. In 'just' tuning, the possibilities for making intervals are open and not limited as they are using the convention of equal-tempered tuning. If you start with a D note in Pythagorean tuning, the A note works out to be A-432, interestingly.

 

[combsbt]

Maybe I'm missing something but I guess it would make sense if the Hz or second unity is related to some intrinsic natural phenomenon, no?

Edit :
I mean all I can find about the definition of the second (or Herz by the same occasion) is from wikipedia :

The second (SI symbol: s), sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock.

Early definitions of the second were based on the motion of the earth: 24 hours in a day meant that the second could be defined as 1⁄86  400 of the average time required for the earth to complete one rotation about its axis. However, nineteenth- and twentieth-century astronomical observations revealed that this average time is lengthening, and thus the motion of the earth is no longer considered a suitable standard for definition. With the advent of atomic clocks, it became feasible to define the second based on fundamental properties of nature. Since 1967, the second has been defined to be

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.

I agree, hertz is based on cycles per second. And the definition of the second is essentially arbitrary^^.

The hertz (symbol: Hz) is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon.

So having whole numbers work for 432 tuning and not 440 tuning is based solely on convention.

 

[tridean]

I just listened to both versions of Pink Floyd Great Gig in the Sky.

when first listening through the computer I didn't notice much at all, 'except' that the 432 version had a slight vibrato that was more evident, and it was almost the sort you hear when two guitar strings are slightly out of tune (could be that my brain used to 440 was hearing a slightly out of tune version, who knows??)

I then listened to both through my stereo, same thing, not much difference, but could still detect the slight out of tune vibrato.

Then, I listened through my earphones and this is where I noticed a big difference.

The 432 version seemed to have a lot less muddyness to it, a sort of cleaner sound. In EQ terms, it felt and sounded like there was a lot more middle band EQ in the 440 version. Now I have to say here, that as a listener to music, and a player of music, and musical instruments, I have always disliked the middle bands of the EQ, in almost any sound or music I hear. All my stereos, amplifiers, mixers etc all have the mids right down and the bass and trebles up. When I record music, I am forever reducing mids, I hate the sound and muddyness of it, and when I heard the 440 version of Great Gig in the Sky after the 432 version through the earphones, this was very evident.

Just some thoughts, but I'd be very interested to hear other musos thoughts on what they think and do about their EQ's for all applications

 

[JonnyRadar]

There is a little mixing of apples and oranges here, in that the Pythagorean ratios are 'just' tuning, in which all the mathematical relationships between notes are simple and 'pure', and the examples given for listening to later in the thread are 'equal-tempered' modern tuning just tuned down slightly. The composer Harry Partch used a 'just' system and made his own instruments in order to play in it. It sounds weird to most people. There are plenty U Tube examples of Partch. In 'just' tuning, the possibilities for making intervals are open and not limited as they are using the convention of equal-tempered tuning. If you start with a D note in Pythagorean tuning, the A note works out to be A-432, interestingly.

Good call, venusian, thanks for pointing that out. :) Some fascinating stuff posted here... have been reading about the "Pythagorean Comma", the quarter-semitone difference that exists between octaves when using "just" tuning. I found a few of those discrepancies myself when trying all the different ratios on the relationships between the notes of the octaves. Seems you end up with more of a "range" for each note instead of an exact number. Or you can settle whole notes on whole numbers and utilize a range for semitones...

My curiosity is with how this plays into the larger picture. Perhaps there exists some sort of tuning that resonates more harmoniously with the human body/ear, but I don't know how any empirical data could be applied to that theory. The metaphorical connections are kind of neat though, when you start looking at the numbers, ratios, meanings, etc...

Some of you may be interested in this guy's work - Reginald Brooks - he does research and artwork about the relationships between color and sound, and this page (http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/Gomas/gomas09.htm) was where I first encountered the wheel based on sections using the Pythagorean ratios. Brooks' work is fantastic, imo, and well worth a read-through. He makes some interesting proposals about the association of the C-note with the color Red, saying the nanometer wavelengths of the colors in the color wheel work out to the same proportions as the harmonics of the musical scale, and that using C and Red as the tonic on the wheel is the only configuration where the tonic and the dominant complement are 180 degrees across from each other vertically. Anyhow, it's worth a look if you have a few minutes...

 

[Human]

Maybe I'm missing something but I guess it would make sense if the Hz or second unity is related to some intrinsic natural phenomenon, no?
Edit :
I mean all I can find about the definition of the second (or Herz by the same occasion) is from wikipedia :

The second (SI symbol: s), sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock.
Early definitions of the second were based on the motion of the earth: 24 hours in a day meant that the second could be defined as 1⁄86  400 of the average time required for the earth to complete one rotation about its axis. However, nineteenth- and twentieth-century astronomical observations revealed that this average time is lengthening, and thus the motion of the earth is no longer considered a suitable standard for definition. With the advent of atomic clocks, it became feasible to define the second based on fundamental properties of nature. Since 1967, the second has been defined to be
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.

I agree, hertz is based on cycles per second. And the definition of the second is essentially arbitrary^^.

The hertz (symbol: Hz) is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon.

So having whole numbers work for 432 tuning and not 440 tuning is based solely on convention.

Yes, I agree, definition of a second is arbitrary and as such it's 'removed' from intrinsic natural phenomena.
Moreover if we look at the present-day definition of second

The definition of the second was later refined at the 1997 meeting of the BIPM to include the statement
This definition refers to a caesium atom at rest at a temperature of 0 K.
The revised definition would seem to imply that the ideal atomic clock would contain a single caesium atom at rest emitting a single frequency. In practice, however, the definition means that high-precision realizations of the second should compensate for the effects of the ambient temperature (black-body radiation) within which atomic clocks operate, and extrapolate accordingly to the value of the second at a temperature of absolute zero.

and for absolute zero

Absolute zero is the theoretical temperature at which entropy would reach its minimum value. The laws of thermodynamics state that absolute zero cannot be reached because this would require a thermodynamic system to be fully removed from the rest of the universe.

it can be seen that this definition has very little to do with Nature.

On the other hand, from the old definition of second

Early definitions of the second were based on the motion of the earth: 24 hours in a day meant that the second could be defined as 1⁄86  400 of the average time required for the earth to complete one rotation about its axis. However, nineteenth- and twentieth-century astronomical observations revealed that this average time is lengthening, and thus the motion of the earth is no longer considered a suitable standard for definition.

it can be said that second has been related to Nature through Earth's rotation.
(some things about 1/(24×60×60) choice for the definition of second are nicely explained in SHOTW, ch. 11 – Time)

Time as such is only a convention and I see it as a measure of interaction/change, especially associated with periodic changes/motions in Nature.
As we live on BBM and as such we are related to it, it's 'natural' that we're measuring time as it is 'seen' on Earth and common periodic motion on Earth is its rotation. So it's natural choice to relate definition of time to Earth's rotation.

This was probably 'little' off topic. To conclude I'll quote something that came to my mind today when pondering about time.

...
A man gets tied up to the ground
He gives the world
Its saddest sound,
Its saddest sound.
...

Thanks thevenusian for clarification between 'just' and 'equal tempered' tuning. Partch sure sounds strange. ;)
Here is youtube clip about Just vs. Equal Tempered tuning
http://www.youtube.com/watch?v=BhZpvGSPx6w&feature=related
Those displayed figures remind me on Lissajous' curves from my Classical Mechanics course http://en.wikipedia.org/wiki/Lissajous_curve

Just intonation bass
http://www.youtube.com/watch?v=aekjzKg3B30&feature=related

Thanks JonnyRadar for Brooks' link. It's a long read but looks like it's worth reading it. :)

 

[ScioAgapeOmnis]

Ok so silly question, when everyone talks about tuning 440hz vs 432hz, you're not just talking about changing only the "A" key itself, but actually changing it along with the rest of the keys by the exact same amount up or down, right? I'm pretty sure that's the case I just want to make sure. It would seem weird if only the "A" key was switched from 440 to 432 because the distance between A and G is now not a complete "whole tone", and neither is the distance between A and B. So all other keys must then be brought down by 8 hz to match the change done to the A key, right?

Also, the differences in the tuning of the Pink Floyd song can also come from recording differences, which we should consider before ascribing any "likeability" to the 432 vs 440 thing alone. Every time a song is recorded it is a little bit different because the environment can be different, the instruments tuned imperfectly, the loudness and timing of playing can all be slightly different, and some background noise can be introduced and possibly the musicians "felt" differently that day so all kinds of possibilities. I think for an objective test it would have to be the same exact recording, and it actually should be confirmed that the original is in 440 before tuning it to 432. Because if the original is something like 439 or 441 then lowering it by 8 would not bring it down to a real 432 either.

 

[abstract]

I have always disliked the middle bands of the EQ, in almost any sound or music I hear. All my stereos, amplifiers, mixers etc all have the mids right down and the bass and trebles up. When I record music, I am forever reducing mids, I hate the sound and muddyness of it, and when I heard the 440 version of Great Gig in the Sky after the 432 version through the earphones, this was very evident.

I actually have an opposing viewpoint. :D

Midrange frequencies are essential for an instrument to have body and not be too thin sounding.

Guitar, for instance, relies heavily on midrange to cut through a mix, all the highs and lows get sucked out by other

instruments. I feel like the current trend of mid dumping can only last so long.

I in fact love the midrange frequencies, I feel they add clarity and impact and definition but only up to a point,

as too much mid will start to sound "honky".

 

[Mountain Crown]

[quote author=SAO]Ok so silly question, when everyone talks about tuning 440hz vs 432hz, you're not just talking about changing only the "A" key itself, but actually changing it along with the rest of the keys by the exact same amount up or down, right? I'm pretty sure that's the case I just want to make sure. It would seem weird if only the "A" key was switched from 440 to 432 because the distance between A and G is now not a complete "whole tone", and neither is the distance between A and B. So all other keys must then be brought down by 8 hz to match the change done to the A key, right?[/quote]

That’s correct. The A above middle C is also referred to as “concert A” because it is the pitch all instruments in an orchestra tune to. All other pitches are tuned relative to that A.

 

[WIN 52]

The mid is also where your voice is, or at least that is what I adjust when singing Karaoke.

u-tube vid on tuning

hope this works, or back to school for me!

They say the mathematics of the Kings chamber in the Great Pyramid works out to be 440 Hz. I am not sure of the implications of this fact, but it seems 432 Hz was dominant in other music at that time. This kind of points to some need for 432 Hz to be swept under the rug. The only problem is that for people who use their ear, 432 Hz is a much more preferable pitch to use. I play guitar by ear and after tuning the instrument by the pitch pipe at 440 Hz, I always fine tune it. I had always questioned why music didn't flow when the guitar was tuned, till I adjusted it. I thought it was just me, not hearing the proper tones. Now, I am thinking I have been tuning and singing at 432 Hz, naturally(by ear).

 

[thevenusian]

Ok so silly question, when everyone talks about tuning 440hz vs 432hz, you're not just talking about changing only the "A" key itself, but actually changing it along with the rest of the keys by the exact same amount up or down, right? I'm pretty sure that's the case I just want to make sure. It would seem weird if only the "A" key was switched from 440 to 432 because the distance between A and G is now not a complete "whole tone", and neither is the distance between A and B. So all other keys must then be brought down by 8 hz to match the change done to the A key, right?

Also, the differences in the tuning of the Pink Floyd song can also come from recording differences, which we should consider before ascribing any "likeability" to the 432 vs 440 thing alone. Every time a song is recorded it is a little bit different because the environment can be different, the instruments tuned imperfectly, the loudness and timing of playing can all be slightly different, and some background noise can be introduced and possibly the musicians "felt" differently that day so all kinds of possibilities. I think for an objective test it would have to be the same exact recording, and it actually should be confirmed that the original is in 440 before tuning it to 432. Because if the original is something like 439 or 441 then lowering it by 8 would not bring it down to a real 432 either.

Exactly right, and not a silly question at all. It is a really complicated subject. And very interesting in light of all the other things that are considered around here. The music we listen to has all been 'vectored' into one set of conventions to the exclusion of any others for the most part, and as a result we are all probably 'tuned' or conditioned in a certain way by that. Who knows what subtle effect that has produced. I am not aware of any serious scientific studies of the subject. Ancient musical systems were different- at least the ones we know about.
There was a fellow by the name of Tom Stone, who back in the 1980's was trying to market guitars that played in 'natural' scales based on Just tuning. He made removeable fret boards because the intervals following the natural progressions of harmonics from any given note do not match those produced by other notes. (The equal-tempered convention compromises these differences to make 12 equal half-tones that work in any key.) The frets did not go straight across the finger board like they do on modern guitars. They were in different spots for each string, and you would need to change to a different fret board to play in a different key. Very difficult to play, and very strange sounding. His notion never caught on with many people and he eventually went out of business.

 

[Mountain Crown]

[quote author=thevenusian] There was a fellow by the name of Tom Stone, who back in the 1980's was trying to market guitars that played in 'natural' scales based on Just tuning. He made removeable fret boards because the intervals following the natural progressions of harmonics from any given note do not match those produced by other notes. (The equal-tempered convention compromises these differences to make 12 equal half-tones that work in any key.) The frets did not go straight across the finger board like they do on modern guitars. They were in different spots for each string, and you would need to change to a different fret board to play in a different key. Very difficult to play, and very strange sounding. His notion never caught on with many people and he eventually went out of business.[/quote]

Years ago a piano tuner asked if I would like to hear my piano tuned with pure fifths and thirds. I agreed, and then he played some pieces (he kept the sound board exposed and used his tuning wrench when needed for changing keys). I remember being astonished by the colors I heard. It was like seeing color TV for the first time.

I hold that equal temperament, however useful, significantly reduced the Western Music aesthetic.

 

[Mikey]

Here is youtube clip about Just vs. Equal Tempered tuning
http://www.youtube.com/watch?v=BhZpvGSPx6w&feature=related

I always thought that tempered tuning was a superior form of tuning, because of the 'mathematical precision', but - wow! - this video absolutely convinces me otherwise! Tempered tuning really looks inharmonious. It would not surprise me if all of western music works with tempered tuning; it would just emulate true harmony, OSIT.

 

[abstract]

always thought that tempered tuning was a superior form of tuning, because of the 'mathematical precision', but - wow! - this video absolutely convinces me otherwise! Tempered tuning really looks inharmonious. It would not surprise me if all of western music works with tempered tuning; it would just emulate true harmony, OSIT.

Maybe this could by why so much western music just turns me off nowadays?

The fact that the tempering doesn't resonate correctly...very, very intruiging.

 

[ScioAgapeOmnis]

always thought that tempered tuning was a superior form of tuning, because of the 'mathematical precision', but - wow! - this video absolutely convinces me otherwise! Tempered tuning really looks inharmonious. It would not surprise me if all of western music works with tempered tuning; it would just emulate true harmony, OSIT.

Maybe this could by why so much western music just turns me off nowadays?

The fact that the tempering doesn't resonate correctly...very, very intruiging.

I can't hear a difference :( I'll give it a listen at home on a better system maybe it's my cheap headphones at work that fail me. But what is different - is the hz different between tempered and just tuning? I have heard that an experienced piano tuner can tune a piano "better" than using a machine to tune it precisely. Supposedly there is a way to tune it very slightly "imperfectly" to actually make it sound better than with machine-like precision. The human ear that supposedly has slightly different preference than perfectly tuned hz values. At least that's something a much more experienced musician told me. I wonder if the just vs tempered thing would explain it, or the 432hz might, or a combination?

 

[Rhys]

As useful as tempered tuning is, I was really hoping I could play in just tuning but as thevenutian says its impossible to retune this way because of the fret positions, and I cant alter my keyboard settings either :(

I'll scour the net for some cheap, easily accessible instruments that can be played in just tuning, if anyone's interested. I have a few Chinese insruments at home, too, so I'll check those out as well. It would be nice to create some music with a natural harmony. Looks like I'll have to read Reginald Brooks' page as well to get a better idea of what it is im looking for!

Anybody else know of anything we could play other than a retuned Piano or expensive synthesizer equipment