At the risk of getting into a youtube argument, Bach's Well Tempered Clavier wasn't written for equal temperament; it was written for well temperament. Some writers have suggested that Bach's treatment of dissonace etc varies depending on the character each key would have had in such a temperament.
The circle of fifth is closed, there are no wolf in a well-tempered temperament, so there can harmonics and a same key can have more than one name. No need for equal temperament And why would he have written in all keys if they all sounded the same, kind of meaningless
the just intonation sounds a little too perfect to me, with a mechanical edge. It'd fit well into some abrasive Aphex Twin type music, something like this works better without it.
@@DixieDee Woah, woah, easy there! I'm just saying this particular piece in JI sounds perfect, not JI is perfect. I also don't understand why you involve Christianity.
@@DixieDee God has given everyone Liberty to choose any tuning we want. As a consequence, though technically these are all equal temperaments, the Arabs chose 24edo, and the Turks chose 53edo. I suggest you to listen to some xenharmonic pieces. For example, Gleam (22edo), Desert Island Rain (313edo), and Droplets (53edo) by Sevish.
Those unequal stretches in meantone really brings out the emotion of pure major thirds lovely. It's sad that people only know that alright equal temperament.
When tuning an ensemble with experienced musicians, generally I find that just intonation falls into place naturally without consideration. Unfortunately, equal tempered instruments are hard to blend into those ensembles.
Rameau recommended that other instrumentalists attempt to imitate the temperament of the harpsichord in small ensembles. In fact, he thought that violinists who tuned pure fifths were lazy and that they should be narrowed to emulate keyboard tuning and improve the thirds.
I just love how flat those C naturals are in just intonation. Those 31 cents go a long way, and add a surprising spice to the ending of the piece that I find very exciting😂
In the meantone example, the higher voices to me seem "flatter". As in tuned flatter. More mellow. The thirds seems much more harmonious. I prefer it over the other two. I went to music school, and I don't have perfect pitch. So, while no, I probably wouldn't be able to tell tuning systems if you blinded me, it's interesting to hear the differences in tuning relationships side by side.
That's because the thirds are pure. If one were to tune all of the fifths in the circle as pure 3/2 ratios (except for one, of course, which would need to be narrowed to get all 12 pitches to fit into an octave), the thirds that would be produced would end up much wider than their pure 5/4 state- almost bordering on the line of dissonance. Therefore, in meantone, all of the fifths are slightly narrowed by just the right amount to get 8 of the (most commonly used) major thirds pure. However, one of the fifths, called the "wolf", (which is actually a diminished sixth) must be left conspicuously wide in order to get the fifths to "fit" the octave. Traditionally it is placed between G# and Eb. Any chord or key signature requiring that fifth is therefore sacrificed, more or less eradicating the idea of enharmonics. Try to use that accidental between D and E and it's a perfect Eb- more perfect than one would ever hear in equal temperament. But try to use it as a D# and it sounds hideous. So, meantone temperament sounds more in-tune than equal temperament, but only in key signatures that it allows for. If the wolf is between G# and Eb you have all key signatures not exceeding 3 sharps or 2 flats at your disposal: C, F, G, D, A, and Bb major, along with A minor, D minor, and G minor. If you really wanted to you could use F# minor, B minor, or E minor, but you would have no access to a raised leading-tone. Of course, one could easily duck this issue by a. moving the wolf around (which would just change which keys with which one would encounter problems) or b. not requiring that 12 pitches fit into an octave and instead use split sharps (on the keyboard) and get not a CIRCLE of fifths, but rather a SPIRAL so to say.
Of course, in theory, a series of meantone fifths can extend infinitely the same as Pythagorean fifths can, or any other size of fifths not found in ET.
PS. How would that "split sharps" keyboard look like? Are there any attempts to actually construct one (presumably electronic midi would be easier)? Or any mockups, to help visualise? In the realm of electronic instruments, I'm only aware of continuously-variable temperament, which uses an algorithm to automatically (in real-time) achieve the "cleanest" frequency ratios. Of course, that works with any midi keyboard. I don't remember the name it was marketed under.
That was fun. In my opinion, the melody comes out most clearly and strongly in meantone. The only exception is the first few measures where you can hear the comma. But after that, it's much stronger than either of the other two temperaments.
Wow! So interesting to hear those C naturals that I always thought were such a terrible note choice all my 12EDO life. It sounds perfectly lovely in Just or Meantone, how it was presumably written.
No. This was either badly programmed in, or played and rendered using notation software therefore there is zero variation in tempo or dynamics. That’s why it sounds emotionless. MIDI is just a way of recording and playing back music data. The human has to put that emotion in themselves - the computer is not going to help you with that (although Noteperformer is making great strides to help in this area).
If this were recorded acoustically, the results would sound much different due to the ways sound waves work. The overtones produced by each pitch would line up with the other various notes in a way that MIDI cannot produce. But great video nonetheless!
You’re wrong about that. And honestly, your comment sounds like you know very little of what you’re talking about (“the way sound waves work”... do you mean interference?), neither about physics/acoustics nor what MIDI is. MIDI is a standard for representing music, not a particular technology for generating audio from it. There are more and there are less sophisticated ways to do the latter. In the simplest case, sine wave signals in the respective overtone mix are added(!). The interference happens there just as well. The only thing it will not capture is anharmonicity effects.
there would be emphasis of different frequencies, due to the self interference with the sound reflected by the environment, but that should be fairly static for a stationary sound; and it wouldn't invalidate the core effect of just intonation, which is that the *ratios* between frequencies are small and therefore produce short interference patterns - ones that don't have phasing effects from chromatic being slightly off.
I think I liked meantone the best, because it sounded warmer, darker, and fuller, which I guess helped the synths sound more like the real instruments :P It has always bugged me, those dissonant notes at the end, especially in just intonation where their dissonance is highlighted because of the perfectly consonant tones surrounding it. Meantone almost made that section sound almost bluesy though, I liked it. Equal temperament is, as with any situation, the middle ground :P
Interesting... I actually think the dissonant suspensions are more enjoyable in just intonation than in meantone temperament. The easier recognition of the dissonance I think is a virtue, because it makes things really expressive!
Chicken and egg, ladies and gentlemen. Music written in the past few centuries for 12TET is -- of course -- going to be best suited for performance in an ET musical framework. I should hope that makes sense to everyone. Why would anyone expect anything else? There is, however, music written for Just intonation that -- for those attuned to the sometimes piquant harmonic dissonance as well as pure and sweet consonances produced by true, mathematically correct intervals -- is balm to ears jarred by endless spew of out-of-tune ET intervals. I mean, take a 'perfectly' tuned 12TET digital keyboard and play a major third... and then listen to those beat tones... ugh.
Just all the way 3:00 to 3:50 tells exactly why JUST tuning reveals exactly where everynote is through all that overlaying very dense and the most densely you can construct tastefully.
It's fucking incredible if you think about it ... how music was derived from mere sound. Now we've made it so easy to dive straight into the realm of harmony. To understand what I mean, imagine you awake in the middle of a forest with nothing. How do you make music that is in any way complex?
Thank you so much for uploading this fascinating video. I can't believe how awful this piece sounds with equal temperament. The thing is, where would we be without Debussy and he needed equal temperament to get those unique harmonies.
I remember reading a while ago that younger people -- which I guess now includes people in their mid-20's or even 30's -- prefer the sound of music in MP3 format rather than the raw audio, even though MP3 is lossy and technically "not as good." You really can tell the difference with MP3s -- drum hits, for example, noticeably dull the rest of the music when they occur. There are better lossy formats out there, like Vorbis.
mightyNosewings Thats definitely not true, flac or wav sound so much better. That said listening on most earbuds, crappy laptop speakers etc. you probably can't tell the difference
Dantré Dogborsa, it actually is. There’s less “beating” because of the perfect ratios. There also seems to be less dissonance due to frequencies lining up to the harmonic series, or simply overtones of a note.
@@dantredogborsa7048 Why would it not be? Also, scientifically, it is easier to hear. The beating created by complex ratios is volume fluctuations. So in just intonation, everything is as close to being the same volume as possible.
A interesting fact, my hear phone speaker "broked" the sound much easier with 12-equal then the other 2 temperament. There is a actually a great dissonance between the "harmonics". But anyway, i prefer how the imperfection of 12-equal fill more the sound.
"Not interested in technical details about tuning? See (link)... for Pachelbel's canon with mountain views from Switzerland" I couldn't stop laughing! Also, great video, and thanks for the technical details! I recently have been searching for those "lost" sonorities of music and training my ear to them :]
Hello again. I've been working on an programming project to explore musical tunings (and other departures from the everyday Western musical system). Have a look at some fun tunings here... :) Megruli Nana in different tunings
@fleebness i dunno, I get your point absolutely but I think that's a bit of an extreme :P. Equal temperament allows music to be whatever it wants to be with the full realization of a tonality that folds back into itself, and is thus equal on both sides (unlike just temperament, where music is VERY uneven on each side). There are tonal qualities of just temperament, but compositions in just temperament could never accomplish pieces from the 1700's(ish) on. It's more limiting than anything.
@BustTheNotes Hehheh... well, sometimes, it's fun to think of an extreme way to describe your point, just to add a little levity to the mix. I wonder, sometimes, with the advances we have made in digital instruments, etc. if we could perhaps create instruments that allowed you to specify the key in which to tune the instrument to a particular just/mean temperament, so as to allow for purer tones while having the flexibility of equal temperament.
12-TET has good perfect fifths, fourths, major seconds and minor sevenths, and tends to sound good in minor keys and with complex chords. That's why it caught on.
boptillyouflop 12-EDO doesn't have true perfect fifths. Yes, fifths are ok and semitones are good too. But tonal music doesn't need beautiful semitones. For most uses Valoti is superior to equal temperament - it has a range of thirds with distinct colours that are a joy to discern and actually make modulation purposeful.
Must say I like just temperament the best, I think the dissonance sounds more interesting as well between 2:55 and 3:30. More interesting squeaky things going on
Hi Scott I am just learning about about all of this stuff I have played guitar for about 8 years now and music in general since I was 5, I found your comment interesting and I was wondering if you meant anything by it or if it was just a joke (which is totally cool, just wondering if you meant there was a certain quality to septimal C)
George Pr Hey George, thanks for replying. Actually, I was quite serious: I love the sound of the sept, the pure harmonic seventh with the ratio of 7/4 to the fundamental. In the key of D that Pachelbel's Canon is in, the sept is flatter than an equal tempered C natural by quite a bit, and sounds strangely harmonious. You can't really play it on a guitar except by bending a B natural up a bit more than halfway to C natural. But you hear this interval all the time in blues: it's the so-called "blue note". cheers from cool Vienna, Scott
This is really interesting. The just intonation sounded the most "off" even though it is the purest, the meantone was most pleasing, even though I am obviously most used to equal temperament. How do figure that?
Adrian Bury just intonation sounded off because you are used to equal temperament. meantone was the most pleasing one because its not that far off from equal temperament, but still is better than equal temperament
Dixie Lynn you can't tune a piano in JI. it's called *just* intonation for a reason. you always have to tune the next note in the melody relative to the previous.
@@toniokettner4821 That's not true, that's one of the million problems with JI. The melody is wonky because only the harmony is valued, resulting in extremely uneven steps. If the notes were tuned relative to the previous, it wouldn't be JI.
This is, of course, an important subject to demonstrate (and discuss); however it is not quite effective due to the lack of the complex overtones produced by our traditional acoustical instruments. Thanks for the effort anyway.
@fleebness Yea definitely great point. I wonder how hard that would actually be... you should check out the fluid piano! I'm wondering if a similar system could be used for exactly what you're describing.
This demonstration would be a lot more effective is the music was less diatonic, i.e. more harmonically interesting. Perhaps the E-flat minor prelude from the Well-Tempered, book 1?
Hi, I'm currently studying the emotional responses that an audience may have between Just Intonation and Equal Temperament, would you mind if I used small bits of audio from this comparison in an A/B survey? Many thanks!
Meantone have pure thirds but worser 5:ths and 4:th . In acoustic situations and with acoustic instruments it sound much more pleasant. I had fast listening now, but I'm not sure if the order is correct. (I'm piano tuner).. but nice intepration...
@elgaed69 Yeah, I'm of two minds about equal temperament. On the positive side, it has made it possible to write music for keyboards that changes to various keys quite easily without a tremendous amount of fuss. On the other hand, it has deprived generations of people of the opportunity to hear the beauty of pure intervals. In a way, showing people these nicer temperaments is like revealing that your ears have been raped for centuries.
As he did it quite impossible, as you'd need three hands and pedal, but you could, for example, leave out the tierce stop and play its melody line with the left hand together with the melody line of the larigot. or any combination of these. Anyhow, you need pedal for the principale 16'+8' because i've never seen an organ capable of coupling ("koppeln" i don't know to say it in english^^) the pedal pipes on manual.
ji is too pure and sterile for me, less pure tunings such as equal temperaments provide the best sound, especially ones that don't approximate any simple ji intervals closely
@@cellularautomaton. it depends on the song don't you know that? Diatonic major scale music actually should be just temperament. Peices are written in the intonation it should be played in. Just Intonation only works when its a purely diatonic song like this one is except for like a note at the end?
The piece is not a very good choice for comparing the temperaments. In particular in meantone thirds are sweeter but it is really the chromatic scale that makes a difference compared to 12ET.
true, but you ca only play on two manuals at the same time...so either you take the same stop (register) for two of the three violins, or you take both stops for each one. Either way, you have to play at least two on the same manual...
changing the pitch does not solve the non-harmonic ratios of 12-TET but it helps with vocal delivery as the 12-TET has some pretty sharp major notes (except the major second, Re) compared to the "pure" just intonation. If Scheribler back in 1810s suggested the pitch A4 to be 439.5Hz with just intonation, you need to tune down the pitch at least 6.2 cents to be able to execute the vocal delivery. 6.3 cents down from 439.5Hz is 437.9Hz. I am a singer and in my experince the A4 tuning with 440Hz/12-TET is too high for the voice.. Most singers are flat not sharp... 12-TET will always be a comprimise but with its "vibrant" sound it needs a lower pitch... It is obivious if you listen to a large choir singing in 12-TET at 440Hz,, a lot will strain an naturally be a little flat of the required note.. My solution is that we lower the standard pitch in contemporary music where we use 12-TET that we tune our A4 to 437Hz (-11.84 cents).. Voices sound better and have less problems at the passaggios.. 216Hz/432Hz is the relaxed natural resonance for A3/A4 for the human voice..but a bit calm for rock and pop music.. 437Hz will give you the lift but not out of reach (which 440Hz in 12-TET is)... Former European pitch with 12-TET (from ~ 1860 to late 1930s)was 435Hz,, a really good average pitch with 12-TET,, It was agreed upon by dozens of singers, composers, physicians back in France in 1859... 440Hz (12-TET) has no such agreements or argument for its installment.
If you're using equal temperament, why does the base frequency matter? It's not like A4 is the only note you'll be singing. Just write in a lower key if it's too high.
Just 8 notes are used in Pachelbel's Canon: the Just Intonation scale, with respect to D, is: D = 1 E = 9/8 F# = 5/4 G = 4/3 A = 3/2 B = 5/3 C = 7/4 C# = 15/8 🙂
@@grahamthomason8796 This would imply to use two different G's, which is undoubtedly legitimate. For some reasons, when I rendered this piece in 2011, I preferred to establish a 1-1 correspondence instead 😊
Just intonation starts off nice, mellow...but becomes totally chaotic seeming at the end. The intervals totally stick out like a sore thumb at the end. Mean doesn't have much personality but the dissonance seems much more controlled. All the intervals, even seconds, blend into the whole a lot better. It melts into one gooey mass. Classical tuning really brings out the different voices the most with the least dissonance. or maybe it's just me?
I like meantone better as each key has a different mood. However, you can only play in a limited number of keys and modulations were limited to a small range of keys. Some keys would sound awful if used.
I made this a bunch of years ago ;) if I recall correctly, I set up G-D-A-E Pythagorean, B-F#-C#-G# Pythagorean as well, with B-F#-C#-G# = 5* G-D-A-E, thus with a wolf between E and B, which is not used in the Canon as a fifth. Then I added C = 7*D.
It is often wrongly assumed that there is only one kind of meantone, but this is not true. The example here is obviously quarter comma meantone, but the historical evidence, and the musical evidence of our own ears, shows that quarter comma meantone was never widely used. The absolutely pure major thirds and the excessively wide semitones are not suitable for most baroque music; moreover, the sevenths are dissonant. Instead, in the 18th century, sixth comma meantone was used. Sixth comma meantone was the standard intonation of the 18th century (NOT quarter comma), and several contemporary sources show this, such as Telemann, Quantz, Leopold Mozart, and so do sources on temperaments such as Neidhardt, Sorge, Young and Vallotti. Concerning meantone, there is a video on TH-cam by early music sources, called tuning and temperaments in the renaissance, that debunks the myth that meantone automatically means quarter comma meantone.
Quarter comma meantone is the only true meantone because there the whole step is the geometric mean between the 2 sizes of whole tones you get in ptolemaic tuning ((9/8)*(10/9))^(1/2). While the other equally-narrowed fifths systems often get called meantones, that's really a misnomer because in those other systems the whole tone isn't the mean of anything
@padaneis Thank you for your posting! The choice of tuning is of course a choice of taste, yet I am conmpletely with you concerning your preference for just intonation in this piece (I mean, just intonation gives the parallel thirds a completely new touch). P.S.: You don't happen to have the time and possibility of posting the Gigue, or do you?
I'm so sad that I can't hear the difference!!!! I'm a musician of three instruments and have been since I was 8 and I thought I had a good ear. Clearly not :(
Sorry about that :( Maybe this is due to the fact the piece is long... please try this comparison (2-5-1 cadence) instead: th-cam.com/video/D9tpzF0eChQ/w-d-xo.html
@@prw6430 A contact form will soon be available, through my blog (which will be linked at my TH-cam channel). Unfortunately, the general today situation has slowed down many projects.
@@ClaudiMeneghin Hi, I have not seen any link to a blog at your TH-cam channel. I think it will be easier for us to just contact you through a business email, as it is a one-time thing.
Well this is quite fascinating listening. I really like the brightness of just intonation, then meantone sounds kind of "dull" afterwards but actually turns out to be the most beautiful to listen to, and then after that, 12-equal sounds horribly off to my ears... though they adjust to it again fairly quickly. It's weird though, once you hear it, you can't un-hear it. 12-equal is horribly off... actually all of the time... erk!
@fryBASS Honestly, the idea has been running around in my brain for over a decade. I need to learn more about programming sound before I could hope to do this idea justice, unfortunately.
The just intonation you use here is the pythagorean just? (I mean pythagorean with perfect octaves and the wolf left for a chosen non (most) used interval). Thanks.
Golden meantone is defined by making the relation between the whole tone and diatonic semitone intervals be the Golden Ratio
φ=(1/2)(√5+1)≈1.6180339887… This makes the Golden fifth is exactly (8−φ)/11 times the octave, or (9600−1200φ)/11 cents, i.e., approximately 696.214 cents :)
Well, not necessarily... the change rather resides in the tuning table i.e. in the exact meaning of notes and accidentals, which is different according to each tuning :)
Thank you for your interest 😀 ! Yes, I use just intonation via software: I use the following free programs: 1) Huygens Fokker Scala to tune files (see below which ones); 2) SynthFont (in combination with soundfonts) to play the files tuned by Scala; The files in 1) are text files essentially representing pitches and durations. I set them up by means of an electronic spreadsheet :) Here's a link to Huygens Fokker Scala: www.huygens-fokker.org/scala/ The underlying logic is definitely an "abc" one, rather than WYSIWYG. You could be interested in Csound as well: csound.com/ 🙂 Happy new year ! 😊
THANK YOU, CLAUDI! This video has been needed for many, many years! Finally, we can actually LISTEN to the three principal tuning systems of the past millenium, applied, rather than simply reading about their theoretical differences! It must have been a most challenging task, but so worthwhile! I arrived at a tuning system based on the relative frequencies of the visible spectrum of light, and it turned out to be virtually identical to Just Intonation, simply by transposing the frequencies of the 12 primary, secondary and tertiary colours of the spectrum downward by exact octaves! You can hear the results at th-cam.com/video/9ssRLX1G2z0/w-d-xo.html. Although light waves and sound waves are quite different, I'm not surprised by the parallel... everything in the universe is made of waves, and all waves have certain common properties. The discovery of the resonance resulting from the interaction of PHOTONS and PHONONS is a testimony to the Harmonicity of the Universe! THANK YOU, AGAIN!
0:01 - Just Intonation
3:55 - Meantone
7:50 - 12-Equal
Thank you
Please, give this comment a pin
At the risk of getting into a youtube argument, Bach's Well
Tempered Clavier wasn't written for equal temperament; it was written for well temperament. Some writers have suggested that Bach's treatment of dissonace etc varies depending on the character each key would have had in such a temperament.
Then there's WTC I, #8: the prelude is in d-flat minor and the fugue in d-sharp minor.
The circle of fifth is closed, there are no wolf in a well-tempered temperament, so there can harmonics and a same key can have more than one name. No need for equal temperament
And why would he have written in all keys if they all sounded the same, kind of meaningless
Just intonation: Sounds perfect
Meantone: Sounds fancy
12-Equal: Sounds normal
Pretty much!
the just intonation sounds a little too perfect to me, with a mechanical edge. It'd fit well into some abrasive Aphex Twin type music, something like this works better without it.
@@DixieDee Woah, woah, easy there! I'm just saying this particular piece in JI sounds perfect, not JI is perfect. I also don't understand why you involve Christianity.
@@DixieDee God has given everyone Liberty to choose any tuning we want. As a consequence, though technically these are all equal temperaments, the Arabs chose 24edo, and the Turks chose 53edo. I suggest you to listen to some xenharmonic pieces. For example, Gleam (22edo), Desert Island Rain (313edo), and Droplets (53edo) by Sevish.
ET is neither nature's standard nor any deity's. All of ET's iterations are equally wrong, except the octave.
Those unequal stretches in meantone really brings out the emotion of pure major thirds lovely. It's sad that people only know that alright equal temperament.
Absolutely true!
Absolutely Golden
With the ear accustomized after the first two, that high F# sounds truly awful in equal temperament.
pure major thirds dont have an emotion.
When tuning an ensemble with experienced musicians, generally I find that just intonation falls into place naturally without consideration. Unfortunately, equal tempered instruments are hard to blend into those ensembles.
Rameau recommended that other instrumentalists attempt to imitate the temperament of the harpsichord in small ensembles. In fact, he thought that violinists who tuned pure fifths were lazy and that they should be narrowed to emulate keyboard tuning and improve the thirds.
I just love how flat those C naturals are in just intonation. Those 31 cents go a long way, and add a surprising spice to the ending of the piece that I find very exciting😂
Loving the 7/4 for C, really gives a new spin on the piece. My fave intonation for this piece is meantone - you can't beat the classics eh!
misotanni
Pythagorean tuning suxks
yikes its hard to hear that C in equal after the meantone, huh
of course you are here
In the meantone example, the higher voices to me seem "flatter". As in tuned flatter. More mellow. The thirds seems much more harmonious.
I prefer it over the other two. I went to music school, and I don't have perfect pitch. So, while no, I probably wouldn't be able to tell tuning systems if you blinded me, it's interesting to hear the differences in tuning relationships side by side.
That's because the thirds are pure. If one were to tune all of the fifths in the circle as pure 3/2 ratios (except for one, of course, which would need to be narrowed to get all 12 pitches to fit into an octave), the thirds that would be produced would end up much wider than their pure 5/4 state- almost bordering on the line of dissonance. Therefore, in meantone, all of the fifths are slightly narrowed by just the right amount to get 8 of the (most commonly used) major thirds pure. However, one of the fifths, called the "wolf", (which is actually a diminished sixth) must be left conspicuously wide in order to get the fifths to "fit" the octave. Traditionally it is placed between G# and Eb. Any chord or key signature requiring that fifth is therefore sacrificed, more or less eradicating the idea of enharmonics. Try to use that accidental between D and E and it's a perfect Eb- more perfect than one would ever hear in equal temperament. But try to use it as a D# and it sounds hideous. So, meantone temperament sounds more in-tune than equal temperament, but only in key signatures that it allows for. If the wolf is between G# and Eb you have all key signatures not exceeding 3 sharps or 2 flats at your disposal: C, F, G, D, A, and Bb major, along with A minor, D minor, and G minor. If you really wanted to you could use F# minor, B minor, or E minor, but you would have no access to a raised leading-tone. Of course, one could easily duck this issue by a. moving the wolf around (which would just change which keys with which one would encounter problems) or b. not requiring that 12 pitches fit into an octave and instead use split sharps (on the keyboard) and get not a CIRCLE of fifths, but rather a SPIRAL so to say.
Of course, in theory, a series of meantone fifths can extend infinitely the same as Pythagorean fifths can, or any other size of fifths not found in ET.
Ekvitarius, thank you - as a non-musician, I find this fascinating.
PS. How would that "split sharps" keyboard look like? Are there any attempts to actually construct one (presumably electronic midi would be easier)? Or any mockups, to help visualise?
In the realm of electronic instruments, I'm only aware of continuously-variable temperament, which uses an algorithm to automatically (in real-time) achieve the "cleanest" frequency ratios. Of course, that works with any midi keyboard. I don't remember the name it was marketed under.
Search for studio31 or Johannes Keller on youtube. They have several split sharp instruments there.
That was fun. In my opinion, the melody comes out most clearly and strongly in meantone. The only exception is the first few measures where you can hear the comma. But after that, it's much stronger than either of the other two temperaments.
Wow! So interesting to hear those C naturals that I always thought were such a terrible note choice all my 12EDO life. It sounds perfectly lovely in Just or Meantone, how it was presumably written.
All three are lovely in different ways
I think midi is emotionless and thus why it's one good way to demonstrate the temperament.
So was Baroque to that extent. It just required intense discipline to not stand out.
You hit the nail on the head..true/just intonation emits/releases true emotion
Very Nice!
No. This was either badly programmed in, or played and rendered using notation software therefore there is zero variation in tempo or dynamics. That’s why it sounds emotionless. MIDI is just a way of recording and playing back music data. The human has to put that emotion in themselves - the computer is not going to help you with that (although Noteperformer is making great strides to help in this area).
If this were recorded acoustically, the results would sound much different due to the ways sound waves work. The overtones produced by each pitch would line up with the other various notes in a way that MIDI cannot produce. But great video nonetheless!
yes, in favor of just tuning.
@Pavel Cimbál listen to any barbershop music or good acapella groups like the Pentatonix
I mean the sound as it is has harmonics, they’re not sine waves. Maybe not as rich as pipes but one gets the idea
You’re wrong about that. And honestly, your comment sounds like you know very little of what you’re talking about (“the way sound waves work”... do you mean interference?), neither about physics/acoustics nor what MIDI is. MIDI is a standard for representing music, not a particular technology for generating audio from it. There are more and there are less sophisticated ways to do the latter. In the simplest case, sine wave signals in the respective overtone mix are added(!). The interference happens there just as well. The only thing it will not capture is anharmonicity effects.
there would be emphasis of different frequencies, due to the self interference with the sound reflected by the environment, but that should be fairly static for a stationary sound; and it wouldn't invalidate the core effect of just intonation, which is that the *ratios* between frequencies are small and therefore produce short interference patterns - ones that don't have phasing effects from chromatic being slightly off.
I think I liked meantone the best, because it sounded warmer, darker, and fuller, which I guess helped the synths sound more like the real instruments :P
It has always bugged me, those dissonant notes at the end, especially in just intonation where their dissonance is highlighted because of the perfectly consonant tones surrounding it. Meantone almost made that section sound almost bluesy though, I liked it. Equal temperament is, as with any situation, the middle ground :P
Interesting... I actually think the dissonant suspensions are more enjoyable in just intonation than in meantone temperament. The easier recognition of the dissonance I think is a virtue, because it makes things really expressive!
Enharmonic drift is the reason why just intonation can never be anything more than a novelty.
Chicken and egg, ladies and gentlemen.
Music written in the past few centuries for 12TET is -- of course -- going to be best suited for performance in an ET musical framework. I should hope that makes sense to everyone. Why would anyone expect anything else?
There is, however, music written for Just intonation that -- for those attuned to the sometimes piquant harmonic dissonance as well as pure and sweet consonances produced by true, mathematically correct intervals -- is balm to ears jarred by endless spew of out-of-tune ET intervals.
I mean, take a 'perfectly' tuned 12TET digital keyboard and play a major third... and then listen to those beat tones... ugh.
@@jellosapiens7261
You are full of ignorance with this opinion
The septimal C sounded funny at first, but it turned out to be a brilliant choice!
the same point but
1:31 JustIntonation
5:24 MeanTone
9:19 12TET
The intervals are so much more clear and characteristic in just intonation.
WOW the difference between the passage with the C naturals is stunning. They sound so rich in meantone and so grating in 12edo.
I have a hard time hearing them apart, but I liked the meantone best, surprisingly.
Thank you so much for sharing. I've been curious about the difference for years. Finally my curiosity is satisfied. I loved the just tuning!
Just all the way 3:00 to 3:50 tells exactly why JUST tuning reveals exactly where everynote is through all that overlaying very dense and the most densely you can construct tastefully.
It's fucking incredible if you think about it ... how music was derived from mere sound. Now we've made it so easy to dive straight into the realm of harmony. To understand what I mean, imagine you awake in the middle of a forest with nothing. How do you make music that is in any way complex?
you sing & hit things with your hands or sticks, allowing you to create intricate melodic and rhythmic complexity
I really couldn't tell the difference - the most significant change for me was the C natural in the last page. Interesting!
Thank you so much for uploading this fascinating video. I can't believe how awful this piece sounds with equal temperament. The thing is, where would we be without Debussy and he needed equal temperament to get those unique harmonies.
Just Intonation is calmest, most beautiful, it just feels right for me ;)
After JI and meantone... ET sounds like an outatune circus organ....
agreed
Wtf, yeah lol
Dat enharmonic drift doe
3:00 started to sound like sniffing glue at a carnival.
I am thinking perhaps I prefer the sound of equal temperament best because my ears are most used to it?
I remember reading a while ago that younger people -- which I guess now includes people in their mid-20's or even 30's -- prefer the sound of music in MP3 format rather than the raw audio, even though MP3 is lossy and technically "not as good."
You really can tell the difference with MP3s -- drum hits, for example, noticeably dull the rest of the music when they occur. There are better lossy formats out there, like Vorbis.
mightyNosewings Thats definitely not true, flac or wav sound so much better. That said listening on most earbuds, crappy laptop speakers etc. you probably can't tell the difference
starofcctv94
I meant that if you must store music in a lossy format, Vorbis is better than MP3.
mightyNosewings I was saying that young people prefer mp3 isnt true
starofcctv94
You're wrong. You may personally think that it sounds better, but the majority of younger people don't agree.
How about this NEW 12-equal temperament in comparison with others? Please comment!
app.box.com/s/u10xz4rgoiakuu4bqsces3esl2w0dm0e
7:50 OK so here's what it sounds like in our Modern 12 Tone Equal Temperament.
I love how crunchy feels all the music till 12edo
😉
Thanks for the post! All three very interesting and have different emotional impact for sure
So much easier for my ears to hear the music in just intonation
No, it's not.
Dantré Dogborsa, it actually is. There’s less “beating” because of the perfect ratios. There also seems to be less dissonance due to frequencies lining up to the harmonic series, or simply overtones of a note.
@@dantredogborsa7048 Why would it not be? Also, scientifically, it is easier to hear. The beating created by complex ratios is volume fluctuations. So in just intonation, everything is as close to being the same volume as possible.
@@dantredogborsa7048 now that's what I call edgy
I like just, always thought it sounds more in tune than 12 equal. Still, big sigh of relief when good old 12 equal came back at the end 😅
😉
@@ClaudiMeneghin I love you
A interesting fact, my hear phone speaker "broked" the sound much easier with 12-equal then the other 2 temperament. There is a actually a great dissonance between the "harmonics". But anyway, i prefer how the imperfection of 12-equal fill more the sound.
He might be talking about the distortion and clipping that comes from amplifying sounds too much and playing them out of a shitty speaker
"Not interested in technical details about tuning? See (link)... for Pachelbel's canon with mountain views from Switzerland" I couldn't stop laughing! Also, great video, and thanks for the technical details! I recently have been searching for those "lost" sonorities of music and training my ear to them :]
Thanks for uploading this. Quite a comparison.
Hello again.
I've been working on an programming project to explore musical tunings (and other departures from the everyday Western musical system). Have a look at some fun tunings here... :) Megruli Nana in different tunings
I love how when I play in just intonation for a while, I can't listen to equal temp the same way again
@fleebness i dunno, I get your point absolutely but I think that's a bit of an extreme :P. Equal temperament allows music to be whatever it wants to be with the full realization of a tonality that folds back into itself, and is thus equal on both sides (unlike just temperament, where music is VERY uneven on each side). There are tonal qualities of just temperament, but compositions in just temperament could never accomplish pieces from the 1700's(ish) on. It's more limiting than anything.
@BustTheNotes Hehheh... well, sometimes, it's fun to think of an extreme way to describe your point, just to add a little levity to the mix. I wonder, sometimes, with the advances we have made in digital instruments, etc. if we could perhaps create instruments that allowed you to specify the key in which to tune the instrument to a particular just/mean temperament, so as to allow for purer tones while having the flexibility of equal temperament.
12-TET is so dissonant, it’s a miracle that it has caught on
12-TET has good perfect fifths, fourths, major seconds and minor sevenths, and tends to sound good in minor keys and with complex chords. That's why it caught on.
Modulation is the reason ET exists.
boptillyouflop 12-EDO doesn't have true perfect fifths.
Yes, fifths are ok and semitones are good too. But tonal music doesn't need beautiful semitones.
For most uses Valoti is superior to equal temperament - it has a range of thirds with distinct colours that are a joy to discern and actually make modulation purposeful.
It's a compromise that allows modulation without the need to retune the instrument.
I quite enjoy the meantone one- Maybe cause I play the violin? It sounds the most natural to me.
Thank you, I think I'll check that out.
8:09 you can hear some third tones in there, too!
Must say I like just temperament the best, I think the dissonance sounds more interesting as well between 2:55 and 3:30. More interesting squeaky things going on
0:03 just
7:51: 12
And 3:55 meantone 😉
Gotta love that blue septimal C.
Hi Scott I am just learning about about all of this stuff I have played guitar for about 8 years now and music in general since I was 5, I found your comment interesting and I was wondering if you meant anything by it or if it was just a joke (which is totally cool, just wondering if you meant there was a certain quality to septimal C)
George Pr
Hey George, thanks for replying. Actually, I was quite serious: I love the sound of the sept, the pure harmonic seventh with the ratio of 7/4 to the fundamental. In the key of D that Pachelbel's Canon is in, the sept is flatter than an equal tempered C natural by quite a bit, and sounds strangely harmonious.
You can't really play it on a guitar except by bending a B natural up a bit more than halfway to C natural. But you hear this interval all the time in blues: it's the so-called "blue note".
cheers from cool Vienna, Scott
This is really interesting. The just intonation sounded the most "off" even though it is the purest, the meantone was most pleasing, even though I am obviously most used to equal temperament. How do figure that?
Adrian Bury
just intonation sounded off because you are used to equal temperament.
meantone was the most pleasing one because its not that far off from equal temperament, but still is better than equal temperament
You need to get better headphones
Dixie Lynn you can't tune a piano in JI. it's called *just* intonation for a reason. you always have to tune the next note in the melody relative to the previous.
@@toniokettner4821 That's not true, that's one of the million problems with JI. The melody is wonky because only the harmony is valued, resulting in extremely uneven steps. If the notes were tuned relative to the previous, it wouldn't be JI.
Yes but for string players where we are not limited by keys we always use Pythagorean and just intonation, never equal temperament
I have turned into a pure major third lover after learning about that temperament.
man, tuning is complicated
I wrote a Medium article explaining it @borisreitman
*Me reading about Reimann-Zeta function and tuning*
It sounds just fine in equal temperament.
This is, of course, an important subject to demonstrate (and discuss); however it is not quite effective due to the lack of the complex overtones produced by our traditional acoustical instruments. Thanks for the effort anyway.
@fleebness Yea definitely great point. I wonder how hard that would actually be... you should check out the fluid piano! I'm wondering if a similar system could be used for exactly what you're describing.
@fleebness I have been thinking of this recently, I think it's totally viable, and should be done soon!
This demonstration would be a lot more effective is the music was less diatonic, i.e. more harmonically interesting. Perhaps the E-flat minor prelude from the Well-Tempered, book 1?
Mean tone sounds best to me!
The last example doesn't sound like equal temperament to me.
That's because you'd just been listening to pure intervals.
Hi, I'm currently studying the emotional responses that an audience may have between Just Intonation and Equal Temperament, would you mind if I used small bits of audio from this comparison in an A/B survey? Many thanks!
Yes, please do :) I kindly ask you to send me an electronic copy of the survey when it's ready :)
Meantone have pure thirds but worser 5:ths and 4:th . In acoustic situations and with acoustic instruments it sound much more pleasant. I had fast listening now, but I'm not sure if the order is correct. (I'm piano tuner).. but nice intepration...
@elgaed69 Yeah, I'm of two minds about equal temperament. On the positive side, it has made it possible to write music for keyboards that changes to various keys quite easily without a tremendous amount of fuss. On the other hand, it has deprived generations of people of the opportunity to hear the beauty of pure intervals. In a way, showing people these nicer temperaments is like revealing that your ears have been raped for centuries.
I'm not so sure, if this piece is best explanation about temperaments, but there are so many musical styles etc..
I embrace equal temperament, because chromaticism is great.
As he did it quite impossible, as you'd need three hands and pedal, but you could, for example, leave out the tierce stop and play its melody line with the left hand together with the melody line of the larigot. or any combination of these. Anyhow, you need pedal for the principale 16'+8' because i've never seen an organ capable of coupling ("koppeln" i don't know to say it in english^^) the pedal pipes on manual.
Just Intonation all the way for this piece. It's mathematically perfect. Literally. Then meantone.
ji is too pure and sterile for me, less pure tunings such as equal temperaments provide the best sound, especially ones that don't approximate any simple ji intervals closely
@@cellularautomaton. it depends on the song don't you know that? Diatonic major scale music actually should be just temperament. Peices are written in the intonation it should be played in. Just Intonation only works when its a purely diatonic song like this one is except for like a note at the end?
The piece is not a very good choice for comparing the temperaments. In particular in meantone thirds are sweeter but it is really the chromatic scale that makes a difference compared to 12ET.
Thanks ! There are more comparisons of mine available 😉th-cam.com/video/AgB4TrV57AU/w-d-xo.html
This work is from more than 10 years ago 🙂
true, but you ca only play on two manuals at the same time...so either you take the same stop (register) for two of the three violins, or you take both stops for each one. Either way, you have to play at least two on the same manual...
thanks!
changing the pitch does not solve the non-harmonic ratios of 12-TET but it helps with vocal delivery as the 12-TET has some pretty sharp major notes (except the major second, Re) compared to the "pure" just intonation.
If Scheribler back in 1810s suggested the pitch A4 to be 439.5Hz with just intonation, you need to tune down the pitch at least 6.2 cents to be able to execute the vocal delivery. 6.3 cents down from 439.5Hz is 437.9Hz.
I am a singer and in my experince the A4 tuning with 440Hz/12-TET is too high for the voice.. Most singers are flat not sharp... 12-TET will always be a comprimise but with its "vibrant" sound it needs a lower pitch...
It is obivious if you listen to a large choir singing in 12-TET at 440Hz,, a lot will strain an naturally be a little flat of the required note.. My solution is that we lower the standard pitch in contemporary music where we use 12-TET that we tune our A4 to 437Hz (-11.84 cents).. Voices sound better and have less problems at the passaggios..
216Hz/432Hz is the relaxed natural resonance for A3/A4 for the human voice..but a bit calm for rock and pop music.. 437Hz will give you the lift but not out of reach (which 440Hz in 12-TET is)... Former European pitch with 12-TET (from ~ 1860 to late 1930s)was 435Hz,, a really good average pitch with 12-TET,, It was agreed upon by dozens of singers, composers, physicians back in France in 1859... 440Hz (12-TET) has no such agreements or argument for its installment.
If you're using equal temperament, why does the base frequency matter? It's not like A4 is the only note you'll be singing. Just write in a lower key if it's too high.
What was the 12-note scale used in Just Intonation?
Also, which notes had to be compromised (wolf intervals) due to the 12-note scale?
Thanks!
Just 8 notes are used in Pachelbel's Canon: the Just Intonation scale, with respect to D, is:
D = 1
E = 9/8
F# = 5/4
G = 4/3
A = 3/2
B = 5/3
C = 7/4
C# = 15/8 🙂
@@grahamthomason8796 This would imply to use two different G's, which is undoubtedly legitimate. For some reasons, when I rendered this piece in 2011, I preferred to establish a 1-1 correspondence instead 😊
@@ClaudiMeneghin Chopin Prelude in E minor in Just Intonation:
th-cam.com/video/5QALGuZ7n9s/w-d-xo.html
@@ValkyRiver Thank you :) I made it in 19edo instead ;) th-cam.com/video/VyEKLxAtWm4/w-d-xo.html
renderend in a controversial baroquish way ;)
3:52 just intonation (reine stemming)
3:55 meantone (middentoonstemming)
7:50 12 equal temperament (gelijkzwevende stemming)
@elgaed69 My previous comment probably should have been directed to this. I'm wondering if you could elaborate your point?
The equal temperament is not what you think! It can be millions different types...All is in the volume of the half tone!!!
Indeed, early organum has a huge amount of dissonance, and Gesualdo's vocal music is full of crunchy harmonies!
Just intonation starts off nice, mellow...but becomes totally chaotic seeming at the end. The intervals totally stick out like a sore thumb at the end.
Mean doesn't have much personality but the dissonance seems much more controlled. All the intervals, even seconds, blend into the whole a lot better. It melts into one gooey mass.
Classical tuning really brings out the different voices the most with the least dissonance.
or maybe it's just me?
Which is the classical tuning?
You need to get better headphones
just intonation is best
I like meantone better as each key has a different mood. However, you can only play in a limited number of keys and modulations were limited to a small range of keys. Some keys would sound awful if used.
Am I crazy to like equal most?
That septimal second tho
I like it
How did you manage the ground base in JI without a pump?
I made this a bunch of years ago ;) if I recall correctly, I set up G-D-A-E Pythagorean, B-F#-C#-G# Pythagorean as well, with B-F#-C#-G# = 5* G-D-A-E, thus with a wolf between E and B, which is not used in the Canon as a fifth. Then I added C = 7*D.
Perfect funeral music for my aging robots in the basement
Meantone and just sound much richer than ET
0:11 4:05 7:59
It is often wrongly assumed that there is only one kind of meantone, but this is not true. The example here is obviously quarter comma meantone, but the historical evidence, and the musical evidence of our own ears, shows that quarter comma meantone was never widely used. The absolutely pure major thirds and the excessively wide semitones are not suitable for most baroque music; moreover, the sevenths are dissonant. Instead, in the 18th century, sixth comma meantone was used. Sixth comma meantone was the standard intonation of the 18th century (NOT quarter comma), and several contemporary sources show this, such as Telemann, Quantz, Leopold Mozart, and so do sources on temperaments such as Neidhardt, Sorge, Young and Vallotti. Concerning meantone, there is a video on TH-cam by early music sources, called tuning and temperaments in the renaissance, that debunks the myth that meantone automatically means quarter comma meantone.
Quarter comma meantone is the only true meantone because there the whole step is the geometric mean between the 2 sizes of whole tones you get in ptolemaic tuning ((9/8)*(10/9))^(1/2). While the other equally-narrowed fifths systems often get called meantones, that's really a misnomer because in those other systems the whole tone isn't the mean of anything
i think this music has a strage end in all versions...
@padaneis
Thank you for your posting!
The choice of tuning is of course a choice of taste, yet I am conmpletely with you concerning your preference for just intonation in this piece (I mean, just intonation gives the parallel thirds a completely new touch).
P.S.: You don't happen to have the time and possibility of posting the Gigue, or do you?
I'm so sad that I can't hear the difference!!!! I'm a musician of three instruments and have been since I was 8 and I thought I had a good ear. Clearly not :(
Sorry about that :( Maybe this is due to the fact the piece is long... please try this comparison (2-5-1 cadence) instead: th-cam.com/video/D9tpzF0eChQ/w-d-xo.html
@@ClaudiMeneghin Hi, is there an email that I can contact you for business/copyright inquiries?
@@prw6430 A contact form will soon be available, through my blog (which will be linked at my TH-cam channel). Unfortunately,
the general today situation has slowed down many projects.
@@ClaudiMeneghin Hi, I have not seen any link to a blog at your TH-cam channel. I think it will be easier for us to just contact you through a business email, as it is a one-time thing.
None of these sound right to me. Is something wrong with my brain?
Of course there's nothing wrong :) Please try more tunings at Herman Miller's page: www.prismnet.com/~hmiller/music/warped-canon.html
What reference frequency and reference key did you use for meantone?
C = 261.6255653 Hz ; also, C has been used as reference key, but there are 31 fifths, so D major fits well within 😊
Well this is quite fascinating listening. I really like the brightness of just intonation, then meantone sounds kind of "dull" afterwards but actually turns out to be the most beautiful to listen to, and then after that, 12-equal sounds horribly off to my ears... though they adjust to it again fairly quickly. It's weird though, once you hear it, you can't un-hear it. 12-equal is horribly off... actually all of the time... erk!
@fryBASS Honestly, the idea has been running around in my brain for over a decade. I need to learn more about programming sound before I could hope to do this idea justice, unfortunately.
I meant Pachepel piece..
The just intonation you use here is the pythagorean just? (I mean pythagorean with perfect octaves and the wolf left for a chosen non (most) used interval).
Thanks.
No, if that were the case, the thirds would be dissonant.
I think it's in 7-limit tuning because it says "with septimal C" at the beginning.
MeanTone... Would that be Golden Mean?
Golden meantone is defined by making the relation between the whole tone and diatonic semitone intervals be the Golden Ratio
φ=(1/2)(√5+1)≈1.6180339887…
This makes the Golden fifth is exactly
(8−φ)/11
times the octave, or
(9600−1200φ)/11
cents, i.e., approximately 696.214 cents :)
@@ClaudiMeneghin very helpful
Thank you! #%^]
@@SolversSocietyHQ The video used quarter comma, though
Shouldn't the key change in just intonation?
Well, not necessarily... the change rather resides in the tuning table i.e. in the exact meaning of notes and accidentals, which is different according to each tuning :)
it would probably be easier to hear the difference if there were a few more overtones
Please try this other comparison :
th-cam.com/video/ARQgjVZlEck/w-d-xo.html
@@ClaudiMeneghin Much appreciated!
0:03
3:57
7:51
How do you use the just tempérament ? In software ?
Thank you for your interest 😀 !
Yes, I use just intonation via software:
I use the following free programs:
1) Huygens Fokker Scala to tune files (see below which ones);
2) SynthFont (in combination with soundfonts) to play the files tuned by Scala;
The files in 1) are text files essentially representing pitches and durations. I set them up by means of an electronic spreadsheet :)
Here's a link to Huygens Fokker Scala:
www.huygens-fokker.org/scala/
The underlying logic is definitely an "abc" one, rather than WYSIWYG.
You could be interested in Csound as well: csound.com/ 🙂
Happy new year ! 😊
THANK YOU, CLAUDI! This video has been needed for many, many years! Finally, we can actually LISTEN to the three principal tuning systems of the past millenium, applied, rather than simply reading about their theoretical differences! It must have been a most challenging task, but so worthwhile! I arrived at a tuning system based on the relative frequencies of the visible spectrum of light, and it turned out to be virtually identical to Just Intonation, simply by transposing the frequencies of the 12 primary, secondary and tertiary colours of the spectrum downward by exact octaves! You can hear the results at th-cam.com/video/9ssRLX1G2z0/w-d-xo.html. Although light waves and sound waves are quite different, I'm not surprised by the parallel... everything in the universe is made of waves, and all waves have certain common properties. The discovery of the resonance resulting from the interaction of PHOTONS and PHONONS is a testimony to the Harmonicity of the Universe! THANK YOU, AGAIN!
Thank you so much for your interest and appreciation 😀
What does meantone notation look like?
It's wetsern customary notation :) the difference with today 12edo practice is that fifths are tuned a little flatter, i.e. 696.578 cents.