See and hear the differences between Equal Temperament, Precise, Just and Pythagorean at 432 Hz
ฝัง
- เผยแพร่เมื่อ 14 ก.ค. 2022
- More information at ToniMazzotti.com and robertedwardgrant.com
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“The problem with “Just” Scale Tuning is that while the mathematical intervals are considered “perfect”, due to the “Major 3rd Problem” (explained in slides), the octaves never quite double through Major 3rds. The mathematical ratio of the Major 3rd is 5/4 (1.25x). Well, 1(1.25^3) = 1.953 and ≠ 2.00. Whereas 1(1.26^3) = 2.00. This one ratio throws the entire Pythagorean Just Tuning out of whack despite its clear mathematical correspondences for all other notes. Equal Temperament is also problematic because it simply cuts the octave range of frequency into 12 equal parts (based on 2^.5), when there is slight variation between tonal transitions exhibiting yet again wave behavior. Also, equal temperament loses a lot of the benefit of the Base 9 mathematical system and depending on your sound system/software, the numbers may no longer sum to 9 in modular arithmetic. How to solve this conundrum? A potential solution: Precise Temperament Tuning. By simply replacing Major 3rd’s 1.25 with 1.26 (derived as 2^1/3 instead of 5/4), this brings the entire scale into very close equivalence with Equal Temperament tuning. Additionally, there is another consequence of this 1.26x usage seen on the very last slide: All of the notes create a decimal extension with “Just” undertone dominant chords represented in the decimal extension (for example Note D5: 576.108288hz, whereas 576 = D in Just Tuning); 108hz is an A3 in Just tuning and 288 is a D4 in Just tuning. This “BLOCKCHAIN-style” chordal representation appearing in the decimal extensions is one of the natural consequences of the 1.26x replacement for the Major 3rd when used with Pythagorean “Just” values (abandoning 1.25x). But how does it sound? Based on the ratios and the very close equivalence to Equal Temperament values in 432hz, I am quite sure it will sound great. Another plus is that all the new “Precise” frequencies Sum to 9 naturally just like the sum of angles of ALL regular polygons/polyhedra/polytopes!” - Robert’s announcement at 20 July 2022.
IMPORTANT _________________________________
1. Equal Temperament is considered the standard in Western music because it allows the use of all the root notes, making the distances between the intervals all equal, and thus allowing the transposition of the songs. However, the cost of this alignment is a small disharmony in all chords.
2. Unequal Temperaments are subdivided between the playable in all root notes, also called Well Temperaments, and the non-playable in all root notes. Unequal Temperaments playable in all root notes, will sound better than Equal Temperament in adjacent root notes in the Circle of Fifths, but will sound less harmonious in opposite root notes.
3. Precise Temperament is an unequal temperament considered playable in all root notes for most modern repertoire. When tuning an acoustic piano with it, you must choose the root note, which by default is C. Listen to Jason Martineau's improvisation "All Around the Wheel", where the playability around the Circle of Fifths is tested with a virtual piano tuned in C: / all-around-the-wheel-1
4. The choice of chords used in video comparisons are based on the four types of triads: Major, Minor, Augmented and Diminished, and on the contemporary use of the sevenths. The Diminished chord is not used directly, but is included in the Minor7b5 used in the tests; These are the chords used in this sequence: Major Augmented, Major, Major7, Minor, Minor7 and Minor7b5 (which includes Diminished). Being played in 4 octaves at the same time.
5. The Pythagorean and Just Intonation musical scales were included in the tests for illustrative purposes only. They are not useful scales for the context of contemporary Western musical harmony.
6. Is it possible to change the temperament of a polyphonic acoustic instrument previously recorded using the Melodyne software: / watch v=Xuu_6Y6t61M. Virtual instruments can be tuned using these scale files: tonimazzotti.com/how-to-creat... See the list of music software with microtone resources: en.xen.wiki/w/List_of_microto... - เพลง
Great job, Toni! Bravo to you and to Robert E. Grant !!!
Very honored that you liked it my friend.
Toni, I did not like the chord progression that was selected. It was harsh on the ears. I put proper headphones on because I felt like that would be best and it was a discomfort. My hope is that you rework the exercise in a less percussive manner. I am in appreciation of your work. May your heart be seen and your work remembered.
There is some poetic freedom in this work. I tried to be minimalist, creating some variation with simple intervals or simple chords. I believe their progression is a matter of taste, or individual artistic preference.
But above all I always had in mind that these variations always needed to refer to the centrality of the fundamental tone, without proposing variations without end or harmonically more complex.
The rubato time, for me, is one of the strengths. Where some elements are in BPM 60, in 5/8, which is the only signature that fit when I divide 60 minutes into 24 equal parts, in the Logic Pro arrangement. But especially the constant variations of the times of musical phrases, in different layers. Time is constant in the fundamental tone but passes faster or slower in some simultaneous layers.
Fantastic job, precise sounds clear, pronounced and well far more precise.
And the most curious thing about this temperament is that Robert didn't know what he would sound like when he released it in July 2020. I spoke to his team who told me that I was the first to get to test his temperament in every key. And in these tests it is possible to clearly see and hear the sonic and geometric differences.
But there are more than 5000 proposed temperaments. And I plan to make another video comparing Precise Temperament against some other famous historical temperaments. Which also sound better than equal temperament.
On the other hand it is important to say that equal temperament has a great advantage against all other temperaments. As it has equal spaces between notes, it is compatible with any root note transposition.
If you tune your guitar to any temperament, you will have to choose the root note. And for all other root notes your guitar will sound a little out of tune. That's why equal temperament became the standard.
That's why I think that to play instruments the equal temperament ends up being the most suitable. However, to produce music, you can and should use more harmonious temperaments. Fine-tuning the pitch after recording acoustic or virtual instruments.
Great job! Thanks for the amazing work! I just have one question, why the choosing of the chords when doing the test? I myself is comparing Equal to Pythagoras for my bachelor research, but i can't find good information in which interval/chord progression that would work best to hear clearest difference between the two. Isn't also the 6th quite different between all temperaments?
Best regards
Victor
Hi Victorman, thank you for the compliment. Composer and writer Jason Martineau, who was the first to make songs using Precise Temperament, back in 2021, told me to use these chords when testing the differences. I think it makes sense because these are the starting chords in the harmonic sequence, they are also the closest to the top, in the circle of fifths. And they are also the most used in western music.
But your argument about sixths makes perfect sense and I'm going to test that too.
Starting to think about film versus HD comparison. Not sure between Equal and Precise which I prefer. I know the Precise has a more steady trajectory.
Hi great video, can you provide link to video in regards to crown sterling, show at start of video. It may be a Robert E Grant video I’m not sure.
Thank you very much :) Here is the video link:
th-cam.com/video/fPMxIt79PkE/w-d-xo.html
@@ToniMazzotti thankyou you are a star ⭐️
@@ToniMazzotti The first thing I notice is that video is 4.32 👌 These things don’t go unnoticed!
@@martinjones7884 Robert takes these alignments very seriously. His arguments were presented in recent years proving the importance of the number 432 in mathematics, geometry and cosmology.
@@ToniMazzotti So he should it’s one of the numbers I use in trading along with other sacred numbers along the same lines. 👍
Hi great video but how do I find this in logic i have the tuning window but I can’t find the precise temperament there :( want to test. Keep it up ❤
Hi Alex, did you check out my blog? I paste the link below with the explanation of how you should do to use the precise temperament in Logic Pro.
Basically you need to extract the SCL files from the zip (there are other formats in there but the one that works in Logis is SCL).
And then you need to put it inside user/applications/logic pro.app/content/resources/Tuning Tables.
To place the files inside the logic app you must right-click on the app icon and select "show package contents".
Logic's tuning panel does not update automatically and you need to close and reopen it to see the precise temperament in the list.
Choose the root note of the music you are producing and the temperament will adapt.
Another important detail is to set the slide called Tune to -31.75. This will put the master tuning at 432 Hz.
After entering this value of -31.75, the display will show -31.8. And this is normal. It's just rounding off the values on the display. But internally the values will be correct.
You can test the exact frequencies with Logic's native instrument called Test Oscillator.
tonimazzotti.com/how-to-create-and-use-the-precise-temperament-for-432-hz/
Is there any app or download that will allow me to convert mp3 files to that A=432 hz but in unequal temperament so I can change the major 3rd? Trying to get my music perfect
Unfortunately it is not possible yet, as far as I know, to change the musical temperament of complete songs. But, on the other hand, there are programs that can already separate the elements of each complete song. So I think it's a matter of time before a software appears that can change the temperament of complete songs.
Watch this video of the melodyne software, where it is possible to change the temperament of polyphonic instruments such as guitars and pianos.
th-cam.com/video/Xuu_6Y6t61M/w-d-xo.html
How about singing in precise temperament tuning. Is there anyone who has tried that? 💚
As far as I know, not yet.
These are exciting times! After Brahms and Paul Hindemith, I feel that harmony has had all of it's bases covered. If music is to "evolve" it is INWARDS, not outwards. This this what so many composers and musicians don't seem to understand, my opinion. I am sharing an incredible recording of JS Bach prelude in E-flat using the new Precise Temperament. I also explain my "acoustification" recording process using vibrations speakers on a resonant surface. I'll try to give the uTube link here, or find it here on my channel here at _The Acoustic Rabbit Hole._
Peace and love to all! - _The Acoustic Rabbit Hole_ th-cam.com/video/qRAqsZAhndM/w-d-xo.html
Thank you very much for the demanding work you do to share this knowledge! I tried it myself with the manual you share on your website. I used the Logic Pro test oscillator to test the tuning. If I hit A5 on the oscillator in standart 440hz equal temperament I would get 440.00hz . But if I would try it with 432hz (-31,8 cents) and precise temperament with root A I would get 431,9. I think it should show 432,08… I see you dit anything like I did. So do you have similar results or other methods to test the precisement of the tuning? Thank you
Hi, thanks for point me this. Site and PDF updated for Logic Pro users :):):)
"
When changing the fundamental note in Logic Pro tuning, you will need to readjust the Tune slider. For each selected note the slider will take on a slightly different value. This happens to rearrange the different proportions between the notes, while keeping the note A at 432.81 Hz. To confirm the frequencies in Logic Pro, use the internal plugin called Test Oscillator. Both in the Tuning window and in the Test Oscillator plugin the accuracy is 2 decimal digits.
The SCL tuning file, which is the one used by Logic Pro, does not contain the Standard Pitch information internally. It is the simplest type of tuning file and has only the number of notes, in this case 12, and their relative proportions. There is a file that can accompany the SCL called KBM, it contains this additional information. But Logic Pro is designed to, instead of loading this secondary file, adjust this Standard Pitch and Root Note information in its own interface. Use the values below for each root note. Attention: Logic Pro Tuning only has an effect on your internal instruments and plugins.
A -31.44
A# -35,52
B -35,57
C -29,29
C# -31,67
D -33,73
D# -31,13
E -29,50
F -31,55
F# -33,60
G -35,35
G# -29,38
"
Hey, thank you for your fast replay and your updated version, this solved the problem for me!!!
I still struggle to implement it correctly in Spectrasonics Omnisphere/Keyscape. If I choose the option 1 you mention, should I change the System Scale to the desired PT Scale and leave the Master Tune at 440Hz or should I only change the tuning to PT on the "MAIN" window and leave the Master Scale at default? This option may work, but for some reason when I do this, the note A5 sounds like a tinnitus tone with every single instrument in Omnisphere. Every other note is playable. Have you got similar issues?
With option 2 tbh. I don't quite understand where to put the semicolon or where to put the frequency in the text field of the file. Must I copy and paste the yellow frequencies below the errors only or with the numbers 60 - 71 and the Notes C - B? A short screen recording or more precise manual would be helpful. I think your explanation would help a lot of people with that. Thank you very much for your kind support Toni!!
@@ToniMazzotti
@Kingluui3613
Answer 1
Option 1 (AnaMark v2 for Spectrasonics .TUN) is already tuned to 432,081 internally. So you should leave the "Master Tune" field of the "System" page of Omnisphere/Keyscape at 440. That is, their interface will not change the tuning. Which will be maintained at 432,081 internally.
Answer 2
The second scale file option (AnaMark v2 .TUN) is tuned to 440,081 internally. When using this option, you must change the "Master Tune" field to 432.00 Hz. This way, you will use the Omnisphere or Keyscape interface to reduce everything to 8hz, resulting in 432,081hz. But for note 60 to work, you will need to open this scale file in a text editor and move the contents of the penultimate line to be part of the previous line. Thus, note 60 will be interpreted correctly on Spectrasonics instruments.
Okay thank you for your support. I think I kind of understand now. So for reference:
Answer 2: I edited the content of the penultimate line of the File of note a as follows:
; 69="! 440.081"
[Scale End]
And I removed the part with "Set reference key to absolute frequency (not scale note but midi key) "
Consequently, for example the file of F# would look like ; 66="! 369.599"
Is that the way it should look?
I really appreciate your help!
@@ToniMazzotti
@@kingluui3613 Here's how it should be in the case of the root note in A:
____________________
[Functional Tuning]
note 1="#=0 % 97.933000"
note 2="#=0 % 203.910000"
note 3="#=0 % 302.170000"
note 4="#=0 % 400.107000"
note 5="#=0 % 498.044000"
note 6="#=0 % 599.675000"
note 7="#=0 % 702.279000"
note 8="#=0 % 800.217000"
note 9="#=0 % 897.829000"
note 10="#=0 % 1004.126000"
note 11="#=0 % 1102.062000"
note 12="#>-12 % 1200.000000 ~999"
; Set reference key to absolute frequency (not scale note but midi key) note 69="! 431.950000"
[Scale End]
___________________
That is, the line you removed should come back. And the line below should come to the end of this one, that is back. In the same line.
Where is the plug-in if I want to tune my guitar in precise temperament 432? Thanks!! 💚
Oh I see the other comment answered. Thanks!!
Good:)
I feel the minor7b5 chord is not tuned correctly, but then how do you define correctly? It's D Minor, but the flat 5th makes the A# into an A. The interval from D# to A# is a perfect fifth (3/2) but D# to A? You get weird ratios like Diminished Fifth (64/45) or Augmented Fourth (54/32) to arrive at similar 'A" notes. The ratios for specific chords aren't exactly defined in just intonation because these chords come from an equal tempered system, right? Or am I wrong, because I'd love to be wrong and learn about what ratios make up specific chords.
TBH, the minor7b5 just sounds awful in general, like it's not actually a chord, but someone decided to call it one anyway.
All temperaments are ways to distribute the errors that emerge when we knead the spiral of the fifths. I dream of some way to unknead this spiral, maintaining polyphony and transposition.
This mathematics can help tuning Accrodion?
Logic X does the automatically or did you program it?
It is necessary to insert the values or upload scale files. Both in Logic Pro and in third-party virtual instruments.
Pythagorean is the closest I think , Is there a way to apply precise tuning to a digital piano ?
If your digital piano accepts the loading of scale files via SisEx MIDI, it will be possible. See more here: tonimazzotti.com/how-to-make-music-with-precise-temperament-tunings-for-432-hz-and-528-hz/
Do you know how to apply this tunning to a guitar?
Hi, thanks for your interest. The stringed instruments with frets are built in Equal Temperament. In other words, the distance of the notes is the same.
To use any other temperament in string instruments with frets, there are two solutions. The first one is to use a guitar with movable or crumpled frets. The second solution is to use applications such as Celemony's Melodyne to tune each instrument after it is recorded.
Many people asked me about the use of Precise Temperament on guitars and I think I'll make a video with this example soon.
I am sending below some links to help you understand the subject.
In this video the guitarist shows another temperament, but the concept is the same. With crumpled frets to reach the exact frequencies of the desired temperament on each note of each string. th-cam.com/video/D8EjCTb88oA/w-d-xo.html
In this video the guitarist shows how guitars are slightly out of tune instruments and how to solve this using a mobile fret guitar. Https://th-cam.com/video/OUoo1FKCs2I/w-d-xo.html
In this video, the Melodyne application is used to change the scales and temperaments of polyphonic audios already recorded. That is, this application can change the distances of different notes recorded in a single audio file. But that doesn't work for whole mixed songs. It only works well to change the notes of each instrument, each at a time. Https://th-cam.com/video/Xuu_6Y6t61M/w-d-xo.html
@@ToniMazzotti i found out about that doing more research, but im stuck... Do you think it would require a great modification for the fretboard to be made into that temperament? Because the gaps are very similar to equal temperament... The only difference seems to be in the 5/4 wich is 1.26 in precise temperament. Isnt it?
@@sk8pkl On page 8 of the pdf guide that I make available on the site including the scale files, there are the deviation numbers from the equal temperament of each of the twelve notes. I will paste below:
0,000
-2,063
3,910
2,170
0.107
-1.956
-0.325
2,279
0.217
-2,171
4,126
2,062
These numbers are measured in cents, where each semitone is divided into 100 parts. So, as you can see above, no note is exactly equal to equal temperament. And this should happen in all octaves. That's why a guitar needs to have movable or bent frets to sound in any other temperament.
In terms of curiosity, there are more than 5000 proposed temperaments. But Precise Temperament is one of only 2 made for 432 Hz.
@@ToniMazzotti hmm i see thankyou very much! I really want a precise temperament tuned guitar... or a hang drum maybe.
@@sk8pkl A Hang Drum works perfectly because it has few notes. And the resonance in the metallic body must be wonderful!
im here because of Robert Grant
this isn't a fair comparison because this is conducted at 432 Hz. If you can do this in 440 Hz with the different types (and ignore just intonation) your video would be credible.
The difference between the notes that is created by temperament, is maintained independently of the Standard Pitch at 432 Hz or 440 Hz. It is possible to perceive the same differences in beats per second, between the chords, when we use 432 Hz and 440 Hz.
About Just Intonation, I talk about it in the description. It was included for illustrative purpose only, because it does not work harmoniously in the context of Western music.
@@ToniMazzottiWhat's this guy's problem? he Strawmans 432 Hz (I prefer 440 Hz) but he makes 432 Hz sound very bad.
th-cam.com/video/ghUs-84NAAU/w-d-xo.html
Sorry, but your examples are biased in the way they are ordered - including Just and Pythagorean temperament in the examples, and following those with a replaying of "Precise" tuning - of course it is going to appear to sound better...
If you compare only "Precise" temperament with Equal temperament, you will find that the differences are fairly negligible.
Exactly, the difference is small, but it is noticeable. But I agree with you that the order did not help to compare equal temperament with precise temperament. That's why I'm going to make another video comparing just the 2 and giving you credit for noticing this.
The difference is small but it is possible to notice it. In the end I show a song produced only in equal vs precise. And it is also possible to notice the slight differences.
Thanks:)
@@ToniMazzotti no thanks, I'm not after credit..
Some of the differences are smaller than the tolerances for tuning to Equal Temperament (e.g. if you were tuning a guitar by ear, you might be within +/- 3 cents (or more) of the actual notes. Some of the notes are closer to Equal Temperament than this tolerance).
Also, the more I look into Robert Edward Grant, the more he looks to be a scammer/charlatan with some of his wild claims without any rigorous proofs (squaring the circle for one)...
@@mrshr3d To me, Robert's reputation for his discoveries and inventions seems very solid. He now has 23 patents and really cracked the age-old mystery of prime numbers used for cryptography.
I've followed him long enough to know how to differentiate what his most solid discoveries and inventions are, from those that are still speculations and theories.
Equal temperament is best for performance and training. But that versatility costs a little bit of harmony. This is a known deficiency about equal temperament. But this question also depends on whether we use real or virtual instruments. It is much easier to test these differences with computers than with real instruments. It is also possible to re-tune a real instrument recorded in any temperament, to any other temperament, using an app called Melodyne.
In short, many other temperaments sound better than equal temperament. And equal temperament was chosen as the standard for its versatility. Because when all the slight differences between the notes are equalized, it becomes possible to transpose any harmony in real time without any tuning required. On the other hand, renowned historical temperaments sound better because they accentuate these differences, once equaled by equal temperament. With these temperaments the music will sound more harmonic on its root note, but will sound more disharmonious than the equal temperament on the other root notes.
I compared the precise temperament against the main historical temperaments and it also sounded slightly better to me. In the video I intend to make, I will include them as well.
@@ToniMazzotti Having patents is not proof of intelligence.
"It is also possible to re-tune a real instrument recorded in any temperament, to any other temperament, using an app called Melodyne." - You are showing a real ignorance of how pianos and other real instruments are tuned.
I am curious, did you compare your real tuning to the youtube playback of your recordings? Didn't youtube "autocorrect" "autoadjust" any of your real tuning(s) to whatever its auto-settings are set to? Or, is it intervening only with the dynamics? Anyway, the main question is - how the hell did musicians tune precisely to 432 or 440 or whatever during those times??? How did they even establish that very pitch (the accuracy of) no matter what the pitch was??? Does anyone know??? Any good book to read on various (cultural) tunings?
Hi, your questions are very good. First about TH-cam. It doesn't change the pitch at all. The process of changing pitch is cumbersome. Even the most evolved plugins cannot change the pitch with full quality when it comes to entire songs, polyphonic (with many instruments).
TH-cam also does not interfere with the dynamics of the audio of the posted videos. Social media and streaming are adopting a new standard for leveling the playback of their content, to improve the experience of Internet users. But this process only affects the volume and does not compress, equalize or tune anything.
432 is a very important number in mathematics, geometry and cosmology. In music it seems to be the midpoint of the mellow spectrum, which goes from 20hz to just over 4000 Hz. (these are the 7 octaves of the piano).
The midpoint of hearing and the human voice, as well as all musical instruments, is the middle octave of the piano. And the note that all cultures have listed as the central one is what we know in the West as A (A4), which today is tuned just 8 Hz above the 432 Hz.
That is, humanity almost found 432 Hz by ear.
@@ToniMazzotti Thanks for your response. But, the "midpoint of hearing" would rather be around 2.6 KHz, which is the resonance frequency of the human aural channel, being the most sensitive frequency for the human ear. Plus, the experience of listening, from the scientific point of view, is a messy conundrum, which, nevertheless, entirely depends upon the harmonics evolving from the source of sound. This conundrum is a mess to such an extent that apparently human ear does not even have the physical capability to catch frequencies below about 100 Hz, which are determined apparently by the psychoacoustic processes based entirely on the harmonics of the sound. All of these make me wonder how the hell did people in the past determine any accuracy whatsoever (not the relative accuracy) of any pitch (especially with such a little difference - 8 Hz - not noticeable to most ears) without having an oscillograph.... Though, the proportions related to the number 432 are indeed very interesting...
@@vardanhovakimyan7633 Hi, I think you misunderstood what I meant.
We hear frequencies exponentially and the middle octave of a piano is the middle range of the MELODIC spectrum. From 4000 Hz onwards, we gradually begin to hear more sibilance than tones.
The truth is it's much easier understanding in cents and xenharmonics (1 cent = linear 1/1200th of an octave) you never hear it bcuz 432hz people are obsessed with doing everything in hz which is the hard way lol.