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what is ROOT KEY?
Old 16th October 2018
  #1
Gear Head
 

what is ROOT KEY?

For 432 hz tuning I set my temperament to pythagorean because I read it was the best (unless you know better).

Below my pythagorean choice for "Type:" is "Root Key:". What would be the best root key for 432 hz tuned music?
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what is ROOT KEY?-screen-shot-2018-10-16-1.27.59-pm.jpg  
Old 16th October 2018
  #2
Gear Guru
 

UKM,

I would assume though that the "tuning" option simply shifts the entire scale by a set amount of cents, and that if each half step isn't equal then the non-equal tuning of the scale in question is relative to the root key, no?

And so if 432 is desired then whatever note it is the closest to should be the root, yes? Or am I misunderstanding how that software works?
Old 16th October 2018
  #3
Gear Head
 

Quote:
Originally Posted by UKMK00 View Post
With pythagorean temperament, the further you move from the root key, the stranger and more out of tune your chords and harmonies will become. its great for producing esoteric, slightly to harshly out of tune music. It does not matter what the "Root Key" is. What ever key you choose will act the same way. There is a reason Bach invented "equal temperament"....

Is that the sound you are after?

The 432 thing is a pantsload. Music does not sound "better" @ 432 hertz. 432 Hz was used as a tuning reference in the baroque era because stringed instruments sounded less harsh in the upper registers, and singers could last a bit longer without tiring or hurting their voices.

Do some research. There is ALOT of mystical nonsense attached to the 432 thing. How it makes your music sound, is completely subjective. It certainly is not "better"....
This is why I chose pythagorean: "from what I'm reading Equal temperament is NOT the purest form of 432 tuning. Pythagorean is. Read Roel Hollander Concert pitch vs Tuning System. Would love to know what you think..." & then "Roel explains that in order to obtain a true representation of 432 Hz then, one would have to compose not only in A = 432 Hz but in combination with Pythagorean Temperament or a close implementation of it like Just Intonation or Twelve True Fifths Tuning."

I'm after a sound in tune with the ratios found in nature/universe/everything, even though some won't think it's better.

No matter what I pick as root key, it will sound the same? Should I leave it as C? Or since A = 432 is what I'm going after, should I set the root key to A?
Old 16th October 2018
  #4
Gear Guru
 

Sounds like you need A.

I think UKM's point was simply that IF you move outside of the (root) key you'll possibly have issues with how the chords will now sound and work. A living breathing musician playing live can and will adjust to the circumstances, and so if I wanted to push my major thirds up a bit (rather than them being perfect) then I can do so regardless of which key I'm in, because I can adjust on the fly. But of course if it's a single piece of music that's entirely diatonic and sticks to the one key then tuning an instrument accordingly makes it easier to play.

In other words, if you run into chords not sounding right because they're not in the key of A then you may prefer to retune for that section according to that new key...

...is my hunch...
Old 16th October 2018
  #5
Gear Guru
 

Quote:
Originally Posted by UKMK00 View Post
Pythagorean Tuning is a fixed tuning scheme that was developed by Pythagoras in about the 6th century. It is based on the "perfection of 3", and all of the intervals are fixed at 3:2. If you play a perfect 5th, "the UNIVERSE and EVERYTHING is vibrating in perfect harmony. BUT, try to play a simple triad. Like a C major chord. Or a leading tone triad...You will find that the Universe starts to get really, really, weird. The Tuning reference is just that... A reference. Pick any number that you feel is the "UNIVERSAL IDEAL"... If you use the "Pythegorean Tuning" option, every thing outside a Pefect 5th will sound.....well, less than perfect. And forget chromaticism...You might just lose your lunch...
I'm not sure you understand my point (even though it might be wrong). Let me ask you this:

- assuming we have two grand pianos side by side... and both are using Pythagorean tuning... and one has a root key of D for tuning, the other Ab.... And the "D" on both is the same frequency....

Will any and all intervals sound the same when played simultaneously on the two pianos? In other words, will playing any fourth starting on the same note on both sound the same?
Old 16th October 2018
  #6
Gear Guru
 

Quote:
Originally Posted by UKMK00 View Post
So...if one piano is Root Key "D" that will mean that all the intervals an that piano will be "fixed" at a 3:2 interval from the Root. A flat will be "chromatic", and not "Diatonic" to the Root Key... Among other things, Pythegorean tuning does not do Tritone Intervals very well.

Conversely, moving to the A Flat Root key piano... With Ab as the Root Key, D is not with in the 3:2 fixed interval it is a "Chromatic", and will be horribly out of tune with the "Root Key".

For the above reasons, "D" on the D piano will be out of tune with the "D" on the Ab Piano.

JS back had very good motivation for the Equal temperament system we use today...
Right, and so that's why I was saying that it actually matters which key you choose. If you want to compose in the key of X with this tuning then you can't set the virtual instrument to the root key of Y.

Correct?
Old 16th October 2018
  #7
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12tone's Avatar
 

Quote:
Originally Posted by UKMK00 View Post
There is a reason Bach invented "equal temperament"....
Bach might have written the definitive treatise on the possibilities of equal Temperament (The Well Tempered Clavier, books 1 and 2), but he didn't invent 'it'.
Old 17th October 2018
  #8
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open_source's Avatar
 

You don't understand the full implication of the tempered tuning system that our music is based on. You are going to need a lot of math to make everything work out at 432Hz.

And BTW, 432Hz doesn't sound better, at all. If you want to use it though, good luck to you. Here's some info for you. Make sure you watch all the way to 2:00.


Old 17th October 2018
  #9
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Quote:
Originally Posted by UKMK00 View Post
Yeah, I guess you are right. But that is implied, is it not?
I think the OP may have missed it.
Old 18th October 2018
  #10
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Quote:
Originally Posted by mattiasnyc View Post
I think the OP may have missed it.

Quote:
Originally Posted by open_source View Post
You don't understand the full implication of the tempered tuning system that our music is based on. You are going to need a lot of math to make everything work out at 432Hz.

And BTW, 432Hz doesn't sound better, at all. If you want to use it though, good luck to you. Here's some info for you. Make sure you watch all the way to 2:00.


so what would the math be?
Old 18th October 2018
  #11
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Quote:
Originally Posted by CuriousYearner View Post
so what would the math be?
Well frequency operates on a logarithmic scale, I know that much. You would have to recalculate every single note above and below 432Hz. He mentions it in the video.

An octave above 100Hz is 200Hz, but an octave above 5000Hz is 10000Hz. It works in integer multiples. You would start there, and then you have to do all of the tempered ratios to get other intervals like 5ths, 3rds, etc. Honestly there is probably a chart out there that lists all frequencies where A = 432Hz. Seriously though, watch the video.
Old 18th October 2018
  #12
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Quote:
Originally Posted by open_source View Post
Well frequency operates on a logarithmic scale, I know that much. You would have to recalculate every single note above and below 432Hz. He mentions it in the video.

An octave above 100Hz is 200Hz, but an octave above 5000Hz is 10000Hz. It works in integer multiples. You would start there, and then you have to do all of the tempered ratios to get other intervals like 5ths, 3rds, etc.
Why?

Read the first post: He's posting an image of a software. It gives the option to set a scale for "software instruments". Surely this implies that the software does all the math, yes?

So setting it to Pythagorean should give the intervals for Pythagorean within each octave.

Setting it to any specific key surely determines the root key that serves as the basis for that scale (since it's not equal temperament).

And finally setting the "tune" to anything but zero presumably offsets the entire scale from a default, which again presumably would be 440.

The software does all the work, no? No need for math...

Or am I missing something?
Old 18th October 2018
  #13
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teleharmonium's Avatar
 

Quote:
Originally Posted by UKMK00 View Post
There is a reason Bach invented "equal temperament"....
Bach neither invented it, nor used it in musical composition, nor heard it in his lifetime.



Quote:
Originally Posted by UKMK00 View Post
The 432 thing is a pantsload. Music does not sound "better" @ 432 hertz.
Agreed.
Old 18th October 2018
  #14
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Quote:
Originally Posted by open_source View Post
You don't understand the full implication of the tempered tuning system that our music is based on. You are going to need a lot of math to make everything work out at 432Hz.
Nah, the math of equal temperament is messy, if you like simple math. There are lots of numbers for the resulting intervals that have to be rounded, no matter what reference pitch you use. It's not more of a mess at 432 than it is at 440 or 438.69462 or whatever.
Old 18th October 2018
  #15
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Quote:
Originally Posted by teleharmonium View Post
Bach neither invented it, nor used it in musical composition, nor heard it in his lifetime.
He was the first to systematically compose in all 12 major and 12 minor keys, which was only possible through equal temperament, demonstrating the versatility and possibilities of it.

Sure he heard it in his lifetime, not only did he use it, it predates him by several centuries.
Old 18th October 2018
  #16
Gear Guru
 

Quote:
Originally Posted by CuriousYearner View Post
I'm after a sound in tune with the ratios found in nature/universe/everything, even though some won't think it's better.
Ratios are real in the sense that they are represented in natural phenomena. Objects that vibrate will vibrate in halves and thirds and so on. So the temperament that you choose will affect how your music fits together. How chords will clash or not clash. You may find it interesting to explore how these tunings handle (or don't handle) the compromises.

But the starting pitch - be it 432 Hz or any other pitch - is not a ratio. It is not based on anything in nature/universe/everything! It's 432 Hertz and what is Hertz? It is cycles per second. But what is a "second" to Mother Nature or the Universe? Nothing. A second is something that some Babylonian king made up. The "second" is an arbitrary human cultural construct.

You might as well say that 432 inches is a "sacred length" or 432 ounces is a "cosmic weight". In fact, 432 inches = 10.9728 meters. Suddenly, just by changing the units, it's not so "cosmic" anymore! 10.9728 meters is an "ugly" number, but it is the exact same length as the more 'elegant' 432 inches. The only difference is what you want to measure it with.

If that ancient king hadn't been born with 12 toes, that same pitch would be called by a different number. Mother Nature does not give a damn about our units.
Old 18th October 2018
  #17
Gear Guru
 

Isn't the simple solution here to just help the person choose the settings they're after and then let them play around and judge for themselves how it sounds?
Old 18th October 2018
  #18
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12tone's Avatar
 

Quote:
Originally Posted by CuriousYearner View Post
so what would the math be?
Old 18th October 2018
  #19
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Quote:
Originally Posted by 12tone View Post
Where is that entered in the software?
Old 18th October 2018
  #20
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Quote:
Originally Posted by mattiasnyc View Post
Where is that entered in the software?
No idea...I just ganked it off of a site, run by a 432 adherent, of all things.
Old 18th October 2018
  #21
Gear Head
 

Quote:
Originally Posted by open_source View Post
Well frequency operates on a logarithmic scale, I know that much. You would have to recalculate every single note above and below 432Hz. He mentions it in the video.

An octave above 100Hz is 200Hz, but an octave above 5000Hz is 10000Hz. It works in integer multiples. You would start there, and then you have to do all of the tempered ratios to get other intervals like 5ths, 3rds, etc. Honestly there is probably a chart out there that lists all frequencies where A = 432Hz. Seriously though, watch the video.

Quote:
Originally Posted by mattiasnyc View Post
Why?

Read the first post: He's posting an image of a software. It gives the option to set a scale for "software instruments". Surely this implies that the software does all the math, yes?

So setting it to Pythagorean should give the intervals for Pythagorean within each octave.

Setting it to any specific key surely determines the root key that serves as the basis for that scale (since it's not equal temperament).

And finally setting the "tune" to anything but zero presumably offsets the entire scale from a default, which again presumably would be 440.

The software does all the work, no? No need for math...

Or am I missing something?

Quote:
Originally Posted by teleharmonium View Post
Nah, the math of equal temperament is messy, if you like simple math. There are lots of numbers for the resulting intervals that have to be rounded, no matter what reference pitch you use. It's not more of a mess at 432 than it is at 440 or 438.69462 or whatever.

Quote:
Originally Posted by mattiasnyc View Post
Isn't the simple solution here to just help the person choose the settings they're after and then let them play around and judge for themselves how it sounds?

Quote:
Originally Posted by 12tone View Post

Quote:
Originally Posted by mattiasnyc View Post
Where is that entered in the software?
Instead of Fixed, should I put the numbers in myself to User? What would I
put for Stretch Upper, Stretch Lower and Root Key?
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what is ROOT KEY?-screen-shot-2018-10-18-5.13.36-am.jpg  
Old 18th October 2018
  #22
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Owen L T's Avatar
Quote:
Originally Posted by mattiasnyc View Post

And finally setting the "tune" to anything but zero presumably offsets the entire scale from a default, which again presumably would be 440.

The software does all the work, no? No need for math...

Or am I missing something?
Nope; I think you're right on the money.
Old 18th October 2018
  #23
Gear Guru
 

Quote:
Originally Posted by UKMK00 View Post
Look, the software will do all the heavy lifting as far as calculations go. You already have your tuning reference ( A=432).

Select fixed and go with Pythagorean.
+1

And again, probably just set it to whatever key you want to compose in.
Old 18th October 2018
  #24
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Quote:
Originally Posted by 12tone View Post
He was the first to systematically compose in all 12 major and 12 minor keys, which was only possible through equal temperament, demonstrating the versatility and possibilities of it.

Sure he heard it in his lifetime, not only did he use it, it predates him by several centuries.
That is a very common misconception. In fact the Well Tempered Clavier was composed on a keyboard tuned to a then new tuning method called... wait for it... Well Temperament. (In fact it was one of two variants of Well Temperament.) It was intended to make it more practical to use all keys, hence the composition exploring them all. Equal Temperament did not come around until later.

Well v.s. equal temperament
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