If temperament wasn't described as "clearly out of tune." then I could actually use this for teaching purposes. temperament is not out of tune, it is just a different form of tuning, and depending on the type of temperament, it many times "sounds" more in tune.
They fail to mention that pure harmony makes the whole piano out of tune from one end to the other end of the keyboard. The only reason an instrument is tempered is because the octaves don't match up in pure harmony. By the way, string instruments use perfect harmony.
@aaaaaaaaaaaaaaaa9219 SAY WHAAAT???? No, the octaves DEFINITELY match up in pure harmony. 2:1 ratio, bro. root 1 wavelength, octave 2 waves. The octave is the ONLY interval that "matches up" on the piano. The convenience of equal temp is that it eliminates problem of syntonic comma, so you can play any mode, play in any key on the same instrument and you'll be more or less alright.
The Well-Tempered Clavier, according to recent scholarship, was more likely to have been an exploration of the various key characters available in well temperament, not a celebration of equal's growing popularity and convenient stability. Tension and release had a uniquely sophisticated intercourse in well temperament, and Bach mastered that.
But wow, wow WOW what an amazingly perfect video and demonstration! Bravo and thank you! It's a new permanent favorite, and a fantastic advertisement.
I dunno, I find that I couldn't listen to the sounds with the narrator... the explanation could have been shown on the screen with the visuals, and that would have allowed me to focus on watching closely for the difference between the tunings.
Bach did not intend Prelude No.1 in C Major for pure temperament he intended it for WELL temperament thats why its called WELL TEMPERED clavier. Although pure temperament has its benefits, it is not superior to equal temperament. Lots of the music composed in the last 150 years is heavily chromatic and lacks tonality, pure temperament only works with tonal music. Pure temperament favors the key its tuned to and the father you go from that key, the more out of tune it sounds.
I don't like this video. It is assuming one way of tuning is superior to another. The fact is they are both different with different attributes. One aspect this film doesn't touch is what happens when you modulate to distant keys; the chords get super wobbly. The farther you go, the harsher the sound.
If you like that clean harmonic sound, then use just intonation; if you want to modulate to distant keys while retaining "cleaner chords" use 12 tone equal temperament.
Yeah, this is great and all, but just try playing I-ii-V-I in just intonation. Temperament isn't a comprise, it allows us new musical possibilities not possible in just intonation.
@kratanuva725 Temperament is too a compromise. It gives up pure just intonation tunings in order to get something else, particularly the ability to do certain progressions acceptably enough without microtonal pitch shifts.. I-ii-V-I is completely possible in just intonation, as is any other progression, we just need more than 12 notes per octave. JI is NOT a fixed 12-note tuning. JI can utilize an infinite number of pitches.
@nphony First off, this assumes that the beatlessness of pure chords is always more desirable. This has not been historically true, and is not true today. And secondly, I flubbed on the reference to chord progressions not possible in JI. I meant that I-IV-ii-V isn't possible (assuming major triads with 1/1 5/4 3/2 and minor triads with 1/1 6/5 3/2) without moving by a wolf, or causing comma drift of 81/80. (continued)...
@kratanuva725 I did NOT assume beatlessness is always desirable. Temperament gives up certain possibilities in favor of others. That is inherently a compromise, unless you think everything temperament gives up is always undesirable. I think we're just arguing semantics about the word "compromise".
Anyway, I knew what you meant. There's nothing wrong with a comma drift of 81/80. Many listeners barely notice it if the timbre is complex and pitches glide smoothly.
@kratanuva725 There is no reason to assume that an 81/80 drift or an 81/80 SHIFT (quite different) is inherently unacceptable. The only valid point is to say that JI causes this situation and temperament avoids it. Depending on musical goals, these are the issues we can choose from. Comma shifts are barely perceptible in real-world complex context, but then, the same goes for some of the differences between JI and tempered tuning!
@nphony Probably. My point was that the sound of a pure 5/4 and a slightly sharp 5/4 both have their place, so moving either from the 5-limit to 12-tet or from 12-tet to the 5-limit could be described as a compromise, but I really don't think that terminology is useful, because calling something a compromise implies superiority.
Anyway, thanks for taking the time to reply. I enjoyed the discussion.
@kratanuva725 Sorry for definitely playing with semantics here... "Compromise" does not imply superiority/inferiority. There are times when compromise is the arguably superior choice because non-compromise means you get one feature at the total expense of another. Compromise is only inferior when there exists a way to get everything you want without compromise. If getting everything is impossible, then compromise may be as good as any other imperfect option.
@elgaed69 Ok, but if you insist on the physics definition of the word "harmony" (which is NOT the same as the musical definition), then it is analogous to my point before about a perfect circle. The physical concept of a circle is like the physical concept of harmony. Most real-world tokens of either are imperfect. And once we move to aesthetics, then our subjective experience of either is all that matters.
@kratanuva725 The real point is that the EXTERNAL world of physics in music is irrelevant unless it has significance to the INTERNAL world of subjective perception.
My experience is that strict JI or strict temperament are dogmatic positions that are usually inapplicable to real music. In most cases, there is vibrato and chorusing and slightly inharmonic timbres and gliding portamento... comma shifts are FINE, but insisting on absolute JI is unnecessary anyway.
@nphony ...(continued) You give up the bright sound of the 400 cent major third in 12-tet by switching to 5-limit just intonation. By the way, when speaking of 'temperament' you are not talking about one tuning, you are talking about the theoretically infinite number of tuning systems not encompassing just intonation. Also, you can approximate temperaments using rational intonation just as you can approximate just intonation using a temperament.
@nphony Of course, you probably already knew this, but the tuning of your tonal plexus is not just intonation, but a approximation of it using 205 tone equal temperament.
@kratanuva725 Nope, you're wrong about that. My videos with the Tonal Plexus actually utilize a C-based extended JI tuning that I created as a variant of the 205 ET. But most of the time it is indistinguishable when using complex timbres as 205ET has a maximum error of 3 cents — but I notice it for harmonies like 4:7 and sometimes prefer actual JI, especially with pure timbres.
@nphony I recommend that you read 'Harmonic Experience' by W.A. Mathieu. It's an invaluable book on the differences between just intonation and temperament. (It only specifically applies to 12-tet, but the principles laid out in the book can be applied to any tuning) The book also covers what progressions will and will not work in JI without a comma shift or wolf intervals.
@kratanuva725 Thanks for all the replies. I'll try to address them briefly. I have read Harmonic Experience — it is a remarkable book. It is also seriously flawed in its attempts to limit the theory to 5-limit harmony and it's assumption of keeping tunings always connected to a tonic even when out a long way. I still think highly of the book overall. You should read the great review by Norman Carey in Music Theory Spectrum Spring 2002, vol. 24, no. 1, p. 121-134
Oh, I guess I wasn't clear. Read that review because it does a great job of bringing up some criticisms of Harmonic Experience that you should consider.
@nphony And if you prefer the sound of just intonation, that's fine, I have no qualms with that. Even I prefer just intonation, just not all the time. I use just intonation when the mood of the piece I'm working on is suited for it.
@kratanuva725 I agree completely that just intonation is good sometimes and not always preferred. The end point is that it is largely a subjective experience.
@elliedwa they used a galvanometer with a laser pointer, probably they used the mere audio input conected to the galvanometer as well, a galvanometer is a kind of oscilator actioned by coils, such oscilations can be controled with accuracy and proporcionaly to a given electrical signal drawing an X-Y pattern that shows shapes and fluctuations of waves
@elliedwa A simple way to build a similar device is this: get a speaker, a common one of a home stereo, stick a mirror in the cone well fitted in order to not detach or fall (With superglue or stuff) get a laser pointer and aim it to the mirror, you'll see the point of light in a clear wall (that will be your screen), so play the sound you want to sample and make it go to the speaker and.... Voilà.! That's the same principle used when compact disc was designed
The only problem with using a computer to tune automatically is that you might modulate from G# to A-flat! There is a difference. Also Bach, I am sure, wanted to have compensations otherwise it becomes boring to hear mainly consonance, It is playing his Well-Tempered clavier in Werckmeister, When it wanders from C the tension grows. Also each key has a really good flavor. Also that jazz progression (Or what ever it is) does not sound very good to my ears because there are sharped 1sts!
@Bachlives2 How is there a difference between G# and Ab on any keyboard instrument? Those keys include the same notes. Additionally, G# major is a key that no one really plays in, as the key signature has 8 sharps and remembering to play F-double-sharp all the time gets tedious.
Also, while it does become boring when you only have consonance, it is dissonant INTERVALS, not intonation, that brings interest, in my opinion.
@elliedwa You get differences between G# and Ab if you get a keyboard with two different keys, or play them differently on a fretless instrument, or treat them differently with software. I own a keyboard that has about 20 keys just between each half-step, made by H-Pi instruments, called the Tonal Plexus keyboard. Check out my videos if you want to see it.
that was great. i'm working in pd right now on the mathematics of emotions. math that sounds good, resonates with hearts. makes me wish i hadn't GIVEN AWAY my dual-trace oscilloscope. this music can materialize matter using energy. to create an orange in spacetime, you need the right chord progression.
Well, you can't say false tuning.. It's just different. I prefer natural though, it seems much more logic to me to use it. Why was tempered even developed?
@WhynotMiha because in equal temperament every interval has the same quality and every triad sound the same in every key signature. Bach chose his tuning on what he thought sounded the best to him which apparently makes every key signature usable but also each key signature maintaining a distinct character.
@WhynotMiha Because you can transpose a melody by just starting from another note. An organ would have to be re-tuned every time a key signature change would be made (e. g. in a church the pastor would have to retune the organ for the regular sermon with adults, and to accompany children during the school the pastor would have to retune the organ to suit the children's higher voice. Today with computers it is possible to re-tune on the fly, but during middle age the organ builders had no chance
the reason equal temperament was chosen as a standard is because it was so close to having perfect intervals while having those equal interval's character the same at any transposition, and because the major or minor keys remained the same at any level in equal temperament is was yet another practical reason to make it standard. plus equal temperaments slightly "out of tune" intervals (especailly triads) in my opinion have a richer character while still being fairly faithful to it's structure.
@wewillprosper I'm not sure that's the point. Maybe it is, but as the video says, modern musicians are expanding the palate of sounds available to them. The question should not be "which has more character" but "which character is better for the music I want to create?" Equal temperament might be better for Bebop but worse for a lullaby. Or imagine a work that plays the same notes, once in equal temperament, once in just intonation; the contrast between the two could be important.
@wewillprosper : Yes, but the art is in the _designed_ modulation of harmonic intervals, rather than _imposed_ uneven tempering. Would you rather have freedom of choice, or a neat-o "jail cell". think about it.
So since cellos and violins, etc. are fretless, does that mean you can get "just" intonations with them, it there any thing holding that instrument back like the guitar?
@gamergeek3000 Most string players will not play ET notes, as it's an act of listening to adjust the note correctly ET thirds really out of tune, as do the 7ths.
Even on guitar it's adjustable by pulling or slacking the string, bending...
I once was veering down the path of this ridiculous JI-fundamentalism, but I learned better. The suggestion of this video is comparable to suggesting that all art be made with perfect circles. It is true that approximate-circles aren't pure-perfect circles but that doesn't mean one choice is the right artistic one. Most of the meaning in the music is not in this level of tuning detail. Strict adherence to either tempered or JI tuning is a mistake. Timbre is major too. Read Bill Sethares' book!
@elgaed69 Thanks, bro, for the comment that utterly fails to further the discussion or provide any evidence or logical claim or anything. If you want to show that I'm wrong or my analogy is bad, logically you have to indicate why. In case you are just being emotionally defensive, know that I myself prefer the sound of JI and am NOT trying to defend temperament. The fact remains: it is more complex than this. I assume you haven't read Bill Sethares' Tuning Timbre Spectrum Scale.
@nphony An imperfect circle is an imperfect representation. Harmony is not representative, but productive. You actually make, or fail to make, a harmony, rather than simply representing it well or poorly. An representation of harmony would be, e.g., sheet-music or a graph. A poor production of harmony is a disharmony, as e.g. results from equal temperament.
@elgaed69 Wrong. Sorry. Harmony is represented in your brain subjectively. There is no such thing as harmony as a physical production. It's a psychological representation correlated to sensory input. If the sensory inputs triggers you to have a sense of blended harmony, then you have it. If the real world, many timbres are inharmonic, pitches go by quickly, there is vibrato and tons of complexity. There can be close-enough approximations to JI that are imperceptible from exact JI.
@elgaed69 Not that you have any logical argument or evidence why my point is nonsense... I'm sorry, but music doesn't exist as a physical phenomenon in the world. Sound waves, pressure waves exist. Music is only in our minds. Likewise, words don't exist in the physical world either. There are acoustic sounds and patterns of light or pigment, but these physical things are not words. Acoustic interference exists physically, but that's not harmony.
@freezazoid These are Lissajous figures, sine waves at right-angles. You put two inputs together, one controlling the horizontal (X) axis and the other controlling the vertical (Y) axis. If you get regular shapes, it means that, for example C and G, 3 wavelengths of a G-note take exactly the same time as 2 wavelengths of a C-note. The frequency relationship of G to C is a frequency of 1.5 times (3/2) in a just intonation. Equal-tempered has modified this, but the LIssajous is now all jagged.
@googlefrump No, there are only 2 sine-waves at a time. You can HEAR them as 2 separate tones. One of these sine-waves controls the X or left-right motion of an oscilloscope. If there were one tone it would produce a line, the vibration too fast for you to see. The other sine-wave controls the Y or up-down motion. Also too fast to see. HOWEVER, in just intonation these waves have a ratio relation to each other, so you see a fixed 2D pattern. With equal tempered you see a mess.
@googlefrump What you are seeing are not the sine-waves themselves, but the "beat" patterns of two sine-waves oscillating at right-angles to each other. There are only ever two sine-waves at a time, and you can HEAR the 2 tones. If the frequencies of the sine-waves have a relation in terms of simple ratios, what you see in the patterns are those ratios. E.g. if they play C and a just G, ratio of frequencies is 2:3. So you see a pattern of 2 waves of C matching 3 of the G.
@Dracopol : The tempered major at 55 secs has 3 tones (sine waves), not 2. The pure major at 1:05 has 4 tones (sine waves), not 2, giving a unique curve shape. Please first watch, listen, and then please explain why these are still only 2 sine waves.
@googlefrump Well I don't know what they are doing for 3 or 4 tones together. Maybe they are running the 3rd and 4th sine-wave oscillating at a 45-degree angle to the first two, to try to represent the overlaid pattern with those increasingly complex shapes. But the amplitude of each sine-wave seems to be different too. Please ask the maker of the video, not me.
This is all well and good when you only use it on one specific triad, but people should know that when you adopt this tuning you HAVE to retune to a new set of pitches when changing key, there are various huge clashes between non-diatonic intervals, meaning you also have to remain fairly tonal. Tuning shouldn't really influence composition in that way. If you are looking for this 'precisely tuned sound', i point you towards hermode tuning, which adapts to what the user (via midi) is playing.
It's definitely a biased account of Just Intonation, as it shows many of the positives, such as brilliant and bright harmony, but ignores many of the negatives, such as transposition and wolf fifths. Oh, if there was a solution! Unfortunately, I appreciate the advantages of equal tempermant to pure musical harmony. Just Intonation isn't a perfect solution for harmony, it's just one solution.
@evinism I disagree. As long as the key is selected right, Tonality will tune the chords to each other, the notes to the chords, and the notes to each other. It allows you to play in just intonation without any wolf fifths!
@evinism I agree overall. But be aware that extended JI, meaning JI played on fretless instruments or voices or keyboards with far more notes (like the Tonal Plexus) or programmed to allow all sorts of possible pitches... THAT JI can handle all transpositions without wolf fifths, if we allow comma shifts or comma drifts (which really can be nearly imperceptible, or at least perfectly acceptable, when hidden in a complex context)
What do the curves represent? The waves of the overtones interacting?
Ignorance really is bliss. I can't hear the difference so it's ALL good to me. But I am getting there. I used to be pretty bad with not being able to tell if things were slightly out of tune but not I can tell so I guess as I get better I'll be able to hear the slight difference in these temperaments.
@abrightcoldday Good point. It's nice to be able to play a composition for 5 voices on a keyboard before giving it to the choir. Why sacrifice while doing it?
Only in the Renaissance they began to show interest for "better" thirds (like those of meantone family of temperaments), becase they began to use thirds in "stable" chords.
We have still to decide whether the tool (temperament) is designed for the goal (music), or if the music is bound to stay inside the limits defined by the tool (because, indeed, a "stable" chord (for instance at the final cadence) under Pythagore *would* sound weird).
Plus, it's not correct to discuss temperament without considering musical style.
For instance, under the so called "Pythagorician" temperament used till about 1500,
the major thirds were even "worse" than the ET ones ; *but* there were mostly used as transitions toward a fifth (and "too narrow" minor thirds were going to the unison).
First of all, there is no reason to move away from dissonant intonations. There is nothing wrong with it. It's not exactly in tune, but it sounds great regardless. Consonance isn't always better. Personally, I find they suit different pieces - there is a place for both.
Also, no, music will not just become digital if people get used to Just Intonation. Digital music cannot reproduce many of the qualities that real instruments can.
@Prometheus4096 Certainly not. With digital technology, you don't have to tune - but then there is the vast array of non-digital music, which will never go. As such, equal temperament will never be obsolete.
yes, but unfortunately, if it wasn't for equal temperament, you would have to retune your instrument everytime you wanted to play something in a different key =(
I can notice a difference straight away, Justonic sounds richer, deeper and sweeter where the Tempered version conflicts with its self and sounds muddy, Justonic delivers more sustain and is more accurate, the notes stand out more and sound more punchy, the compositions are still valid as they are I think they would have a greater impact with better tuned instruments.
@sephiroth3782 I did not know that you can fiddle with intervals to fatten or narrow digrees that will give certain characteristics (like bach tuning), so the normal tunning is an all rounder then and the equal temperment is just one option.
The video confuses Tempered with Equal temperament. Bach was NOT an advocate of neither just nor equal temperament, but WELL Temperament. He was well aware of both, and in order to reconcile the pythagorean ratios with the harmonic of other scales, he came up with his own version of Well temperament to enable playing in all scales. Bach did not use the Werkmeister tuning, but the other way around. Werkmeister's well temperament is believed to be close to Bach's. Too much misinformation...
@Rendereason Did Bach oppose Equal Temperament? I thought he didn't even know what ET sounded like due to the difficulty (not well known) method of tuning to ET. Or did Bach compose the WTC simply to demonstrate a possible (not better) alternative to other temperament such as ET?
@NimbleTurtle13, ET did exist but not popular. But Bach also played the violin so his ears probably would not have liked the fact that every interval (besides the octave) in equal temperament is slightly out of tune.
@NimbleTurtle13 Like you said, Equal temperament is not something they could tune in their time. In fact, it was natural to compose for a certain key, as each key had different feelings and sounded different. Equal temperament is a relatively new intonation, possible only in modern times. In equal temperament, it doesn't matter what key you play in, as it all sounds the same, only the pitch changes. There is no different "feeling" also called "affekt".
A while ago I commented that most people can't discern the small differences between temperaments. Predictably I was accused of being tone deaf, etc. But I just tried a test of my pitch perception (at Tonometric), and found my pitch perception is better than average (at the 59th percentile), but not outstanding.
I love math, and I love the a priori of harmony with or without knowing the ratios. With just intonation, low whole-number rations have a particular consonance, and the math helps us to understand it, work with it, and maybe find more pleasure.
Boo! to musicians who disrespect the power of math because they feel threatened by it, AND to intellectuals who cling to the math and let it obscure the pleasure of music.
Math is a very useful tool in the pursuit of beauty.
I absolutely hear the difference, and I completely prefer the "wrong" tempered scale! most likely because I am used to it, but I also feel the inherent dissonance makes it interesting - the "pure" harmonies sound hollow and lifeless to me.
there you go...that should convince some of the mathematical nerds here that the physiological response to music is much deeper and complex than simple arithmetic. what is a "dissonance" to some is "interesting" to another. now who wants to argue about mathematical errors of less than 1%.
I'd prefer just temperament where possible because it would make modulations more pronounced and of course it would be more in tune. Anyways, does anybody know what they really did exactly with the graphical representation?
@parquar: I have no idea what they do in the case of triads, but with intervals
they apparently graph the first note (a pure sine curve, i.e., they don't have any overtones) on the y-axis and then the second note (again a pure sine curve, but now of a different frequency) on the x-axis. If the two note are the same
you get a circle or an ellipse, depending on the phase shift between the two notes, for an octave you get a figure 8 and more complicated pictures for more complicated ratios.
@c330user It really confuses me how it moves over time. I know it has to do with how frequency would just be how many periods the graph has across the x axis but I don't really understand the interactions and how they get the shapes they do. I don't know about most people, but I would seriously like an explanation of those shapes before I take too much meaning from them.
@parquar Take the fifth at 0:30 for example. A perfect fifth is the frequency ratio
3:2. In the example they take the notes A and E. If this were a pure fifth,
there would be 3 complete periods of the sine wave for the E during 2 periods for
the A. The dot on the oscilloscope that they show us goes up and down two times while it goes left to right and back 3 times. This creates the picture you see. Since the frequency ratio between A and E is not precisely 3:2
in equal temperament, the actual ratio is something else (actually an irrational number). So, while the dot moves up and down two times it moves left to right and back (and now I am making up a number since I don't know the correct ratio)
3.078 times, which means that the curve is not properly aligned as in the case of the pure fifth and therefore look somewhat messy. With minor and major thirds the difference more drastic since they more inaccurate in equal temperament than the fifth.
It's such bullshit to put a picture of a waveform right in front of you. Otherwise the difference would be imperceptible. Most of the people who go on about the "pureness" of just intonation probably couldn't pick it out of a line up without the help of stupid visual aids like this.
You're right, they're cheating. But some of the examples *are* clearly audible, even to an untrained ear. The fifth is only 1.886... cents off, an inaudible difference, but the major third is 14 cents off, a clearly audible difference. Intervals in equal temperament can reach almost 35 cents away from their JI counterpart, and make implying their function inconvenient.
Basically, the differences are very perceptible, though it's hard to be objective when you have pretty pictures in front of you.
Some comments here assume that everyone does, or should, have the same sensitivity of pitch hearing. This is demonstrably untrue (see any book of experimental psychology). I am willing to admit that some hyper-sensitive individuals may find equal temperament excruciatingly discordant, but most people obviously don't, or it wouldn't be so popular.
"most people obviously don't, or it wouldn't be so popular"
You are not taking into account the true motivations behind equal temperament, which are the conveniences of fitting it on a one dimensional interface like the piano, no matter the sacrifice in consonance. A few hundred years ago the average musical person, no hyper-sensitivity, would have cringed at the sound of our major third.
We are simply used to ET, and it is popular because it is easiest on a 1-D playing surface.
Unfortunately for your confident assertion, the traditional system of tuning was usually Pythagorean, in which the major third is even further away from the 'natural' third than the tempered third is. According to Carl Seashore (Psychology of Music p.223-4) unaccompanied violonists still (in the 1930s) tended to play Pythagorean thirds. So much for the theory!
Sorry. Their thirds were worse than ours. But that doesn't refute my point that the differences are clearly audible to the majority of the population, and so our equal temperament *does* sacrifice consonance. I just need to do my homework.
What is preferred in the ergonomics of playing an instrument generally doesn't correspond to the actual desired tonal effect, and even then, some things in ET *do* sound better, either because we're used to it or because it brings out certain colors.
Whether the differences are 'clearly audible to the majority of the population' is a matter for controlled blind tests. I'm no expert, but from the literature I have seen, the majority of untrained adults cannot distinguish between a tempered and natural fifth. They can usually distinguish between a tempered and a natural third, but only just. Which they prefer is another matter. In blind tests there is no consistent preference reported. If you disagree, cite the evidence.
interesting video, although there's something slightly misleading in the diagrams. i would also point to the tuning used by some of the most sublime music in the world, balinese gamelan. they deliberately tune their instruments somewhat off the exact ratios to create that shimmering quality. it is supposed to be a divine sound of sorts. that said, both just and equal temperament have their pros and cons. in reality both are present simultaneously in most music today, intentionally or not.
I have perfect pitch too! High 5! Do you not think Equal temperament sounds much purer though. I can still recognise what the pitches are despite whether it's ET or JI. There is not an awful lot of difference between them apart from that ET sounds purer really. Awh well! It's awesome that you have perfect pitch too though!
Side by side the tempered version really sucks. On the other side i really like beatings pulsations. I also enjoy badly tuned pianos and quarter tones. Also, harmony is not the "very foundation of the musical arts".
Instead of vulgar abuse, could some of the opponents of equal temperament answer my original question, and explain what the waves in the video represent? I suggest that they are just meaningless propaganda, with no scientific basis at all. If they have one, what is it?
PS: thousand of professional musicians have no problem with equal temperament. Are they all deaf, as CatSnot implies?
The figures there appear on an oscilloscope if you select the mode where you supply the X and Y signals. Something like this (I've played with this feature in college attracting the critique of the lab assistant who wanted something trivial displayed and measured).
Another point to note is that if you only speak of fundamentals, I don't know how the two temperaments compare.
Yes, those figures are called Lissajous-plots. But I don't understand either - the Lissajous plot shows the phase difference between 2 signals. But for, example, a chord is made from at least 3 different pitches/signals. So, I don't know exactly, what's on the vid :)
A just Intionation perfect fifth, for instance, is a 2 to 3 ratio of frequencies. So 200 Hz and 300 Hz, for instance. For every 2 cycles of one wave, the other wave cycles 3 times. The ratio is exactly 1.5. If you plot one wave on the X axis and one on the Y axis, you get a stationary figure like that. Equal temperament perfect fifth is 1.42857143, on the other hand, so the waves never line up correctly.
Ok, I'm an electronic engineer, so it's okay. I thought the vid is about a major chord, so I didn't understood it, bcos as you've mentioned a lissajous plot is made from 2 signals - and a chord is at least 3 different frequencies. It is kind of rational to use just intonation, these weird L.-plots are very strange to see :)) but I can barely hear the difference between ET and JI. sometimes I maybe made a "blind-test" with a friend, who plays a JI or ET chord, and I'll write down my answer.
But real string instruments do have overtones (harmonics) produced by the strings. If the overtones of C does not match E and G, dissonances arise. Also, yo u have to have a developed ear (or maybe it's something you're born with) to discern subtle nunces. This is, for those who don't know, a topic of nuances.
Intonation in music is a vast topic (and it's beyond my knowledge), all I know is that it is beyond the frequencies computed naively with the 12th root of 2.
Yes, the overtones make the dissonance even more obvious. :) Listen to piano chords in equal and just and you can hear the difference easily.
Actually the "harmonics" in a piano aren't really even harmonics. They get more sharp the higher you go. Using longer strings reduces this effect, which is why big pianos sound better than small uprights.
Thanks, that's very helpful. This video may well use Lissajous Curves. In which case I am right that this is a false representation of the difference between just and tempered intonation, because it means that someone has deliberately chosen a mathematical formula which exaggerates very small differences in ratios. It's like using an electron microscope to 'prove' that a razor blade is not sharp.
Somehow I cannot notice any difference, except when I look at the graphical representation. It seems the graphs are made to hypnotize people into buying the agenda of the tempered scale addicts! Does this mean that the thousands of amazing piano compositions of Beethoven Brahms and Mozart that have been enjoyed by millions is invalid? Please enlighten me if I am dead wrong. The ear doesnt do mathematics but feels. A just minor third and tempered minor third convey the same feeling etc.,.
jiggle: my point was about more or less math. but that the psycholgy of response to music doesnt care about math. It is too complex. If you are focused on the frequencies and ratios in schubert sonata you arent hearing the music but mathematics!
All art is an abstraction and approximation. If not why dont we just generate Fourier series and simply listen to the "pure" mathematical tones. Then you would'nt have the clarinet and the oboe. ya yay a I know they have different Fourier spectra but...
I'm pointing out that equal temperament is even more "mathematical", but it's math based on convenience, not based on physics.
Just Intonation sounds purer because it matches with the way our ears process sound. When you hear a pure chord, the neurons are firing simultaneously because the wave cycles line up with each other. That's what "3:2 ratio" means. For every 2 cycles of one wave, the other wave cycles exactly 3 times.
No, I dont think you see what I am saying. You keep explaining the math to me but I have read Helmholtz's classic text and understand why just intonation is more natural..due to Fourier series... But my point is that our perception of music is beyond the reach of mathematical precision. You can play a deeply moving piece of Schubert in ET piano and it will move the listener irrespective of the numbers. Unless the listener is a nerdy mathmetician who fails to listen with his right brain!
888music very good point. It is indeed interesting addition. I just take isse with osmeone saying one type of music is "wrong". Afterall what is wrong about dissonance?
Question: would the concept of modulation even be possible without ET. i.e., if you play an F chord in just intonation that wouldnt belong to a different key but it would in ET?
@nevertheless123 i think the dissonance is very obvious regardless of graphical representation. Bach definitely was a proponent of just intonation. Equal temperament was conceived in order to help musicians transpose keys without completely retuning their instruments which is logical, but I dont think every melody was meant to be heard in every key. If a song is written in a, id rather hear it just tuned to a. Its odd I feel songs sound more moving not equally tempered.
hmmm..I see. But I thought Bach was a major fan of ET? In fact he wrote the "well tempered clavier", 48 preludes an fugues, ie,. 2 x 2 for each of the 12 keys. This was the bread and butter for the greatest musicians of classical music like Beethoven and Mozart and even as late as Mahler. In other words, without the well tempered keyboard, most of classical music would not have come about.
Am I missing something ? or does a fractional mathematical error make most of these composers useless?
The confusion is over "well tempered". Well tempered does not equal Equal Tempered :) Well tempered referred to a specific temperament - something based on the just system but "tempered" slightly (not NEARLY as much as the equal tempered system). The truth is that Bach was somewhere in between. He wanted the flexibility of being able to write in all keys, but also wanted to maintain consonances and dissonances as close to the true intervals as possible. (continued....)
(... from last post)... Bach used the Werckmeister tuning (I believe) on the Well Tuned Klavier. Google around for it. Equal Temperament ("ET") was not only impossible to achieve on a keyboard instrument in Bach's time, but most people thought it sounded awful. A number of different temperaments were used during the Baroque, Classical, and even up until the Romantic period. True Equal Temperament did not become standardized until far later.
It's a modern misconception that Bach advocated equal temperament. Nobody used equal temperament in Bach's day, and that includes Bach himself. A well-tempered instrument can be used to play in any key, but at the same time, some keys are "sweeter" than others. This provides contrasting character as you change keys. Equal temperament is not a "well-temperament", because it destroys this contrast by making all keys equally sour.
@nevertheless123 Its really easy to hear the difference ... in a demonstration. I certainly dont need a graph to notice it. If you seriously cant hear it, thats ... just weird. But in actual music there is so much else going on that I would probably never notice the difference.
@nevertheless123 The chords of those composers have compromised tuning. That is because, for a just-tempered replacement, all of the keys would only be a fraction of those needed to produce all of the chords in just intonation. I myself can hear in this video how the equally tempered major third is sharp. As a brass player, I can tell you that wind ensembles' chords are balanced by ear to technically approximate just intonation.
@nevertheless123 -- see, hear, and feel the difference: the equal temperament is wobbly, not stable. The graphs are not hypnotizing people into buying into tempered scales - it's the opposite! to buy into just intonation - not equal temperament. This does not discredit bach and beethoven... many composers were aware of this problem, and were careful as to which keys they wrote in, as the piano was tuned to sound better in certain keys (Cmajor, Aminor, etc). and they didnt have software then.
@nevertheless123 I suspect the audio processing of the clip that takes place before the clip posted messes up the spectrum enough so that the difference in beat frequencies (for example) becomes hardly distinguishable between the two cases.
@nevertheless123 Actually, Beethoven and Mozart played on Claviers that were tuned closer to the examples shown in this video. The equal temperament scale slowly took over as the main piano tuning later on. I strongly disagree. If you want a better example, go to my website and click on the examples. It's a better tuning algorithm and doesn't try to hypnotize you with oscilloscope images.
I can't believe there are people associating tuning systems to socialism and psuedoscientific conspiracy theories. Both tuning systems are equally valid, and have their purposes. Just intonation is "perfect" in that it has an equal difference between steps. Equal temperament allows for simpler tuning of instruments because it makes all transpositions equal, and since instruments are often playing in different keys, having to retune every performance would be impractical.
Obviously you don't realize the whole key concept here. It doesn't matter if it's impractical; we should do whatever is necessary to bring life to Bach's music. Some people just can't stand Bach because it is so dry... pitch is just one of many problems. Metal strings are much more practical than gut strings but the sound of gut string has ALWAYS been preferred.
If temperament wasn't described as "clearly out of tune." then I could actually use this for teaching purposes. temperament is not out of tune, it is just a different form of tuning, and depending on the type of temperament, it many times "sounds" more in tune.
ShawnBoucke 2 weeks ago 3
Does anyone know where I can find the picture of the last slide that says 'stay tuned'? I'd love to print a copy for myself. Thanks!
fredrickgreen10 1 month ago
@fredrickgreen10 download screenhunter and grab it
renaissance27 1 month ago
They fail to mention that pure harmony makes the whole piano out of tune from one end to the other end of the keyboard. The only reason an instrument is tempered is because the octaves don't match up in pure harmony. By the way, string instruments use perfect harmony.
aaaaaaaaaaaaaaaa9219 2 months ago
@aaaaaaaaaaaaaaaa9219 SAY WHAAAT???? No, the octaves DEFINITELY match up in pure harmony. 2:1 ratio, bro. root 1 wavelength, octave 2 waves. The octave is the ONLY interval that "matches up" on the piano. The convenience of equal temp is that it eliminates problem of syntonic comma, so you can play any mode, play in any key on the same instrument and you'll be more or less alright.
untidaled 1 month ago
@untidaled He means that if you tune by either thirds or fifths you will end up past the octave by the Pythagorean Comma.
Look it up, that's how it's done.
Chucanelli 1 month ago
Bach-Lehman and Werckmeister are the two systems that sound the best imo.. Just intonation only works if you don't modulate to other keys
skrattkantarellen 2 months ago
The Well-Tempered Clavier, according to recent scholarship, was more likely to have been an exploration of the various key characters available in well temperament, not a celebration of equal's growing popularity and convenient stability. Tension and release had a uniquely sophisticated intercourse in well temperament, and Bach mastered that.
But wow, wow WOW what an amazingly perfect video and demonstration! Bravo and thank you! It's a new permanent favorite, and a fantastic advertisement.
Chucanelli 2 months ago in playlist senior project
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Chucanelli 2 months ago in playlist senior project
I dunno, I find that I couldn't listen to the sounds with the narrator... the explanation could have been shown on the screen with the visuals, and that would have allowed me to focus on watching closely for the difference between the tunings.
JayashriV 2 months ago
keyboards could have been tuned to just tuning, they...just didn't. because it sucks ass for intervals not against the tonic lol.
mattz1010 2 months ago
Bach did not intend Prelude No.1 in C Major for pure temperament he intended it for WELL temperament thats why its called WELL TEMPERED clavier. Although pure temperament has its benefits, it is not superior to equal temperament. Lots of the music composed in the last 150 years is heavily chromatic and lacks tonality, pure temperament only works with tonal music. Pure temperament favors the key its tuned to and the father you go from that key, the more out of tune it sounds.
MattDiazMusic 2 months ago
my ears are really used to tempered tuning.
some thimes just intonation sounds out of tune for me xD.
hjiuhfhrehui 3 months ago
I feel like I'm watching an informercial for just intonation...
dnvndvd 3 months ago
I don't like this video. It is assuming one way of tuning is superior to another. The fact is they are both different with different attributes. One aspect this film doesn't touch is what happens when you modulate to distant keys; the chords get super wobbly. The farther you go, the harsher the sound.
If you like that clean harmonic sound, then use just intonation; if you want to modulate to distant keys while retaining "cleaner chords" use 12 tone equal temperament.
zyxonian 3 months ago
This has been flagged as spam show
What those symbols that appear onscreen mean? Can someone answer this? (:
GuiFrnblx 4 months ago
Comment removed
GuiFrnblx 4 months ago
Yeah, this is great and all, but just try playing I-ii-V-I in just intonation. Temperament isn't a comprise, it allows us new musical possibilities not possible in just intonation.
kratanuva725 4 months ago
@kratanuva725 Temperament is too a compromise. It gives up pure just intonation tunings in order to get something else, particularly the ability to do certain progressions acceptably enough without microtonal pitch shifts.. I-ii-V-I is completely possible in just intonation, as is any other progression, we just need more than 12 notes per octave. JI is NOT a fixed 12-note tuning. JI can utilize an infinite number of pitches.
nphony 4 weeks ago
@nphony First off, this assumes that the beatlessness of pure chords is always more desirable. This has not been historically true, and is not true today. And secondly, I flubbed on the reference to chord progressions not possible in JI. I meant that I-IV-ii-V isn't possible (assuming major triads with 1/1 5/4 3/2 and minor triads with 1/1 6/5 3/2) without moving by a wolf, or causing comma drift of 81/80. (continued)...
kratanuva725 4 weeks ago
@kratanuva725 I did NOT assume beatlessness is always desirable. Temperament gives up certain possibilities in favor of others. That is inherently a compromise, unless you think everything temperament gives up is always undesirable. I think we're just arguing semantics about the word "compromise".
Anyway, I knew what you meant. There's nothing wrong with a comma drift of 81/80. Many listeners barely notice it if the timbre is complex and pitches glide smoothly.
nphony 4 weeks ago
@kratanuva725 There is no reason to assume that an 81/80 drift or an 81/80 SHIFT (quite different) is inherently unacceptable. The only valid point is to say that JI causes this situation and temperament avoids it. Depending on musical goals, these are the issues we can choose from. Comma shifts are barely perceptible in real-world complex context, but then, the same goes for some of the differences between JI and tempered tuning!
nphony 4 weeks ago
@nphony Probably. My point was that the sound of a pure 5/4 and a slightly sharp 5/4 both have their place, so moving either from the 5-limit to 12-tet or from 12-tet to the 5-limit could be described as a compromise, but I really don't think that terminology is useful, because calling something a compromise implies superiority.
Anyway, thanks for taking the time to reply. I enjoyed the discussion.
kratanuva725 4 weeks ago
@kratanuva725 Sorry for definitely playing with semantics here... "Compromise" does not imply superiority/inferiority. There are times when compromise is the arguably superior choice because non-compromise means you get one feature at the total expense of another. Compromise is only inferior when there exists a way to get everything you want without compromise. If getting everything is impossible, then compromise may be as good as any other imperfect option.
nphony 4 weeks ago
@nphony Again you make the false analogy of representation = harmony. Harmony is a physical and mathematical phenomenon, not a mere figment.
elgaed69 4 weeks ago
@elgaed69 Ok, but if you insist on the physics definition of the word "harmony" (which is NOT the same as the musical definition), then it is analogous to my point before about a perfect circle. The physical concept of a circle is like the physical concept of harmony. Most real-world tokens of either are imperfect. And once we move to aesthetics, then our subjective experience of either is all that matters.
nphony 4 weeks ago
@kratanuva725 The real point is that the EXTERNAL world of physics in music is irrelevant unless it has significance to the INTERNAL world of subjective perception.
My experience is that strict JI or strict temperament are dogmatic positions that are usually inapplicable to real music. In most cases, there is vibrato and chorusing and slightly inharmonic timbres and gliding portamento... comma shifts are FINE, but insisting on absolute JI is unnecessary anyway.
nphony 4 weeks ago
@nphony ...(continued) You give up the bright sound of the 400 cent major third in 12-tet by switching to 5-limit just intonation. By the way, when speaking of 'temperament' you are not talking about one tuning, you are talking about the theoretically infinite number of tuning systems not encompassing just intonation. Also, you can approximate temperaments using rational intonation just as you can approximate just intonation using a temperament.
kratanuva725 4 weeks ago
@kratanuva725 Yup, I don't prefer the bright third usually. But it has its place. I know all about temperament theories, thanks though.
nphony 4 weeks ago
@nphony Of course, you probably already knew this, but the tuning of your tonal plexus is not just intonation, but a approximation of it using 205 tone equal temperament.
kratanuva725 4 weeks ago
@kratanuva725 Nope, you're wrong about that. My videos with the Tonal Plexus actually utilize a C-based extended JI tuning that I created as a variant of the 205 ET. But most of the time it is indistinguishable when using complex timbres as 205ET has a maximum error of 3 cents — but I notice it for harmonies like 4:7 and sometimes prefer actual JI, especially with pure timbres.
nphony 4 weeks ago
@nphony I recommend that you read 'Harmonic Experience' by W.A. Mathieu. It's an invaluable book on the differences between just intonation and temperament. (It only specifically applies to 12-tet, but the principles laid out in the book can be applied to any tuning) The book also covers what progressions will and will not work in JI without a comma shift or wolf intervals.
kratanuva725 4 weeks ago
@kratanuva725 Thanks for all the replies. I'll try to address them briefly. I have read Harmonic Experience — it is a remarkable book. It is also seriously flawed in its attempts to limit the theory to 5-limit harmony and it's assumption of keeping tunings always connected to a tonic even when out a long way. I still think highly of the book overall. You should read the great review by Norman Carey in Music Theory Spectrum Spring 2002, vol. 24, no. 1, p. 121-134
nphony 4 weeks ago
Oh, I guess I wasn't clear. Read that review because it does a great job of bringing up some criticisms of Harmonic Experience that you should consider.
nphony 4 weeks ago
@nphony And if you prefer the sound of just intonation, that's fine, I have no qualms with that. Even I prefer just intonation, just not all the time. I use just intonation when the mood of the piece I'm working on is suited for it.
kratanuva725 4 weeks ago
@kratanuva725 I agree completely that just intonation is good sometimes and not always preferred. The end point is that it is largely a subjective experience.
nphony 4 weeks ago
@nphony Sure, that's basically what I was getting at. :P
kratanuva725 4 weeks ago
Can anyone tell me what kind of oscilloscope or whatever was used to make the video?
elliedwa 4 months ago 2
@elliedwa they used a galvanometer with a laser pointer, probably they used the mere audio input conected to the galvanometer as well, a galvanometer is a kind of oscilator actioned by coils, such oscilations can be controled with accuracy and proporcionaly to a given electrical signal drawing an X-Y pattern that shows shapes and fluctuations of waves
noisedownloader 3 months ago
@elliedwa A simple way to build a similar device is this: get a speaker, a common one of a home stereo, stick a mirror in the cone well fitted in order to not detach or fall (With superglue or stuff) get a laser pointer and aim it to the mirror, you'll see the point of light in a clear wall (that will be your screen), so play the sound you want to sample and make it go to the speaker and.... Voilà.! That's the same principle used when compact disc was designed
noisedownloader 3 months ago
The only problem with using a computer to tune automatically is that you might modulate from G# to A-flat! There is a difference. Also Bach, I am sure, wanted to have compensations otherwise it becomes boring to hear mainly consonance, It is playing his Well-Tempered clavier in Werckmeister, When it wanders from C the tension grows. Also each key has a really good flavor. Also that jazz progression (Or what ever it is) does not sound very good to my ears because there are sharped 1sts!
Bachlives2 4 months ago
@Bachlives2 How is there a difference between G# and Ab on any keyboard instrument? Those keys include the same notes. Additionally, G# major is a key that no one really plays in, as the key signature has 8 sharps and remembering to play F-double-sharp all the time gets tedious.
Also, while it does become boring when you only have consonance, it is dissonant INTERVALS, not intonation, that brings interest, in my opinion.
elliedwa 4 months ago
@elliedwa I'll post a video when i have time explaining it with my harpsichord! There is a difference. Look up sub semitone, or archicembalo...
Bachlives2 4 months ago
@elliedwa You get differences between G# and Ab if you get a keyboard with two different keys, or play them differently on a fretless instrument, or treat them differently with software. I own a keyboard that has about 20 keys just between each half-step, made by H-Pi instruments, called the Tonal Plexus keyboard. Check out my videos if you want to see it.
nphony 4 weeks ago
@SatanCinque Makes so much sense! Thanks for the reply
StarsAreForStaring 6 months ago
The audio is so compressed with so many artifacts that you really don't get anywhere near the real effect here.
vibratingstring 7 months ago
that was great. i'm working in pd right now on the mathematics of emotions. math that sounds good, resonates with hearts. makes me wish i hadn't GIVEN AWAY my dual-trace oscilloscope. this music can materialize matter using energy. to create an orange in spacetime, you need the right chord progression.
andrespereyda 8 months ago
Music for Autistics
jimbob1969 8 months ago
Well, you can't say false tuning.. It's just different. I prefer natural though, it seems much more logic to me to use it. Why was tempered even developed?
WhynotMiha 10 months ago
@WhynotMiha because in equal temperament every interval has the same quality and every triad sound the same in every key signature. Bach chose his tuning on what he thought sounded the best to him which apparently makes every key signature usable but also each key signature maintaining a distinct character.
angryjalapeno 9 months ago
@WhynotMiha Because you can transpose a melody by just starting from another note. An organ would have to be re-tuned every time a key signature change would be made (e. g. in a church the pastor would have to retune the organ for the regular sermon with adults, and to accompany children during the school the pastor would have to retune the organ to suit the children's higher voice. Today with computers it is possible to re-tune on the fly, but during middle age the organ builders had no chance
PitchFeedback 9 months ago
@WhynotMiha so that you can play in more than one key on the same instrument? hello?
maximisatwat 6 months ago
@maximisatwat Yes, I learned a bit more after I posted that comment, and now it's clear to me.
WhynotMiha 5 months ago
the reason equal temperament was chosen as a standard is because it was so close to having perfect intervals while having those equal interval's character the same at any transposition, and because the major or minor keys remained the same at any level in equal temperament is was yet another practical reason to make it standard. plus equal temperaments slightly "out of tune" intervals (especailly triads) in my opinion have a richer character while still being fairly faithful to it's structure.
somnynightin78 10 months ago
What's the symbol at the end representing?
StarsAreForStaring 10 months ago
Wow!!! This is beautiful
StarsAreForStaring 10 months ago
i don't like this. uneven tempering has so much character. this is boring.
wewillprosper 1 year ago 5
@wewillprosper I'm not sure that's the point. Maybe it is, but as the video says, modern musicians are expanding the palate of sounds available to them. The question should not be "which has more character" but "which character is better for the music I want to create?" Equal temperament might be better for Bebop but worse for a lullaby. Or imagine a work that plays the same notes, once in equal temperament, once in just intonation; the contrast between the two could be important.
philosofool 2 months ago
@wewillprosper : Yes, but the art is in the _designed_ modulation of harmonic intervals, rather than _imposed_ uneven tempering. Would you rather have freedom of choice, or a neat-o "jail cell". think about it.
googlefrump 1 month ago
This has been flagged as spam show
Need to marry you **busizz4me.info**
mayakanthineela 1 year ago
Justonic "pure" harmony sounds like General MIDI to me.
DanielDavisMusic 1 year ago
So since cellos and violins, etc. are fretless, does that mean you can get "just" intonations with them, it there any thing holding that instrument back like the guitar?
gamergeek3000 1 year ago
@gamergeek3000 Most string players will not play ET notes, as it's an act of listening to adjust the note correctly ET thirds really out of tune, as do the 7ths.
Even on guitar it's adjustable by pulling or slacking the string, bending...
emixolydian 1 year ago
Just intonation sounds richer and warmer.
999manman 1 year ago
I once was veering down the path of this ridiculous JI-fundamentalism, but I learned better. The suggestion of this video is comparable to suggesting that all art be made with perfect circles. It is true that approximate-circles aren't pure-perfect circles but that doesn't mean one choice is the right artistic one. Most of the meaning in the music is not in this level of tuning detail. Strict adherence to either tempered or JI tuning is a mistake. Timbre is major too. Read Bill Sethares' book!
nphony 1 year ago 2
@nphony You're totally wrong and making a false analogy.
elgaed69 1 month ago
@elgaed69 Thanks, bro, for the comment that utterly fails to further the discussion or provide any evidence or logical claim or anything. If you want to show that I'm wrong or my analogy is bad, logically you have to indicate why. In case you are just being emotionally defensive, know that I myself prefer the sound of JI and am NOT trying to defend temperament. The fact remains: it is more complex than this. I assume you haven't read Bill Sethares' Tuning Timbre Spectrum Scale.
nphony 4 weeks ago
@nphony An imperfect circle is an imperfect representation. Harmony is not representative, but productive. You actually make, or fail to make, a harmony, rather than simply representing it well or poorly. An representation of harmony would be, e.g., sheet-music or a graph. A poor production of harmony is a disharmony, as e.g. results from equal temperament.
elgaed69 4 weeks ago
@elgaed69 Wrong. Sorry. Harmony is represented in your brain subjectively. There is no such thing as harmony as a physical production. It's a psychological representation correlated to sensory input. If the sensory inputs triggers you to have a sense of blended harmony, then you have it. If the real world, many timbres are inharmonic, pitches go by quickly, there is vibrato and tons of complexity. There can be close-enough approximations to JI that are imperceptible from exact JI.
nphony 4 weeks ago
@nphony That's non-sense.
elgaed69 4 weeks ago
@elgaed69 Not that you have any logical argument or evidence why my point is nonsense... I'm sorry, but music doesn't exist as a physical phenomenon in the world. Sound waves, pressure waves exist. Music is only in our minds. Likewise, words don't exist in the physical world either. There are acoustic sounds and patterns of light or pigment, but these physical things are not words. Acoustic interference exists physically, but that's not harmony.
nphony 4 weeks ago
I don't get what the graph is doing? Why not just use a sign wave? I have no idea what the graph is trying to represent. It seems random.
freezazoid 1 year ago
@freezazoid These are Lissajous figures, sine waves at right-angles. You put two inputs together, one controlling the horizontal (X) axis and the other controlling the vertical (Y) axis. If you get regular shapes, it means that, for example C and G, 3 wavelengths of a G-note take exactly the same time as 2 wavelengths of a C-note. The frequency relationship of G to C is a frequency of 1.5 times (3/2) in a just intonation. Equal-tempered has modified this, but the LIssajous is now all jagged.
Dracopol 1 year ago 6
@Dracopol How do you make the lissajous curves add 3rd and 4th notes in a chord?
alreadytakenthe3rd 10 months ago
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googlefrump 1 month ago
@googlefrump No, there are only 2 sine-waves at a time. You can HEAR them as 2 separate tones. One of these sine-waves controls the X or left-right motion of an oscilloscope. If there were one tone it would produce a line, the vibration too fast for you to see. The other sine-wave controls the Y or up-down motion. Also too fast to see. HOWEVER, in just intonation these waves have a ratio relation to each other, so you see a fixed 2D pattern. With equal tempered you see a mess.
Dracopol 1 month ago
Comment removed
googlefrump 1 month ago
@googlefrump What you are seeing are not the sine-waves themselves, but the "beat" patterns of two sine-waves oscillating at right-angles to each other. There are only ever two sine-waves at a time, and you can HEAR the 2 tones. If the frequencies of the sine-waves have a relation in terms of simple ratios, what you see in the patterns are those ratios. E.g. if they play C and a just G, ratio of frequencies is 2:3. So you see a pattern of 2 waves of C matching 3 of the G.
Dracopol 4 weeks ago
@Dracopol : The tempered major at 55 secs has 3 tones (sine waves), not 2. The pure major at 1:05 has 4 tones (sine waves), not 2, giving a unique curve shape. Please first watch, listen, and then please explain why these are still only 2 sine waves.
googlefrump 4 weeks ago
@googlefrump Well I don't know what they are doing for 3 or 4 tones together. Maybe they are running the 3rd and 4th sine-wave oscillating at a 45-degree angle to the first two, to try to represent the overlaid pattern with those increasingly complex shapes. But the amplitude of each sine-wave seems to be different too. Please ask the maker of the video, not me.
Dracopol 4 weeks ago
This is all well and good when you only use it on one specific triad, but people should know that when you adopt this tuning you HAVE to retune to a new set of pitches when changing key, there are various huge clashes between non-diatonic intervals, meaning you also have to remain fairly tonal. Tuning shouldn't really influence composition in that way. If you are looking for this 'precisely tuned sound', i point you towards hermode tuning, which adapts to what the user (via midi) is playing.
thomasbalmforth 1 year ago
It's definitely a biased account of Just Intonation, as it shows many of the positives, such as brilliant and bright harmony, but ignores many of the negatives, such as transposition and wolf fifths. Oh, if there was a solution! Unfortunately, I appreciate the advantages of equal tempermant to pure musical harmony. Just Intonation isn't a perfect solution for harmony, it's just one solution.
evinism 1 year ago
@evinism I disagree. As long as the key is selected right, Tonality will tune the chords to each other, the notes to the chords, and the notes to each other. It allows you to play in just intonation without any wolf fifths!
intonationinc 1 year ago
@evinism I agree overall. But be aware that extended JI, meaning JI played on fretless instruments or voices or keyboards with far more notes (like the Tonal Plexus) or programmed to allow all sorts of possible pitches... THAT JI can handle all transpositions without wolf fifths, if we allow comma shifts or comma drifts (which really can be nearly imperceptible, or at least perfectly acceptable, when hidden in a complex context)
nphony 4 weeks ago
@sacktrack
The website appears to be abandoned.
If you click on "forums" at the bottom, you get an error message.
When I first went to the site, the forums were populated with questions from many years ago but with no responses.
I've never got a response from any of the many emails I sent.
Did you look at the products?
Did you notice the system requirements?
Windows XP or Mac OS 9. Those are old operating systems.
Would you buy something from this website?
888music 1 year ago
What do the curves represent? The waves of the overtones interacting?
Ignorance really is bliss. I can't hear the difference so it's ALL good to me. But I am getting there. I used to be pretty bad with not being able to tell if things were slightly out of tune but not I can tell so I guess as I get better I'll be able to hear the slight difference in these temperaments.
GuillermoSmyser 1 year ago
Why do people think this will lead to exclusively digital music? The human voice and fretless string instruments achieve this already.
abrightcoldday 1 year ago
@abrightcoldday Good point. It's nice to be able to play a composition for 5 voices on a keyboard before giving it to the choir. Why sacrifice while doing it?
intonationinc 1 year ago
"If anyone knows where I can get Justonic products, please let me know." erm try google search justonic and look at the first result?
leakeg 1 year ago 3
@leakeg
Did that. And all I got was an abandoned website with this video on it!
888music 1 year ago
@888music ahh ok, my bad... though there is a "buy" link at the bottom of the page...
leakeg 1 year ago
where sort of images are these?
leakeg 1 year ago
@leakeg found out they are Lissajous curves.
leakeg 1 year ago
Only in the Renaissance they began to show interest for "better" thirds (like those of meantone family of temperaments), becase they began to use thirds in "stable" chords.
We have still to decide whether the tool (temperament) is designed for the goal (music), or if the music is bound to stay inside the limits defined by the tool (because, indeed, a "stable" chord (for instance at the final cadence) under Pythagore *would* sound weird).
AlainNaigeon 1 year ago
Plus, it's not correct to discuss temperament without considering musical style.
For instance, under the so called "Pythagorician" temperament used till about 1500,
the major thirds were even "worse" than the ET ones ; *but* there were mostly used as transitions toward a fifth (and "too narrow" minor thirds were going to the unison).
AlainNaigeon 1 year ago
Things are not that simple, because if you play just chords :
- you'll have problems with horizontal lines ;
- you'll have problem with neighbouring keys (for instance D minor chord will sound weird).
Temperament must be a compromise in any case, just because 2 (octave), 3 (fifth), and 5(major third) have no common dividor (yes, that's the reason).
AlainNaigeon 1 year ago
This os BS. ! I am glad there is so much music in equal teperement and most of the world doesnt care about this crap. They simply enjoy music !
nevertheless123 1 year ago
First of all, there is no reason to move away from dissonant intonations. There is nothing wrong with it. It's not exactly in tune, but it sounds great regardless. Consonance isn't always better. Personally, I find they suit different pieces - there is a place for both.
Also, no, music will not just become digital if people get used to Just Intonation. Digital music cannot reproduce many of the qualities that real instruments can.
idshanks 1 year ago
@Prometheus4096 Certainly not. With digital technology, you don't have to tune - but then there is the vast array of non-digital music, which will never go. As such, equal temperament will never be obsolete.
idshanks 1 year ago
@Prometheus4096
yes, but unfortunately, if it wasn't for equal temperament, you would have to retune your instrument everytime you wanted to play something in a different key =(
So it does have it uses
sephiroth3782 1 year ago
I can notice a difference straight away, Justonic sounds richer, deeper and sweeter where the Tempered version conflicts with its self and sounds muddy, Justonic delivers more sustain and is more accurate, the notes stand out more and sound more punchy, the compositions are still valid as they are I think they would have a greater impact with better tuned instruments.
86Pow86 1 year ago
@86Pow86
at the beginning, when he compares the thirds, try humming a fifth
you can notice straight away, that with just intonation, your voice locks in to the chord
whereas in equal temperament, it doesn't really fit in as well
sephiroth3782 1 year ago
@sephiroth3782 I did not know that you can fiddle with intervals to fatten or narrow digrees that will give certain characteristics (like bach tuning), so the normal tunning is an all rounder then and the equal temperment is just one option.
86Pow86 1 year ago
I can really notice the difference in sound, sounds more smooth.
unchato 1 year ago
The video confuses Tempered with Equal temperament. Bach was NOT an advocate of neither just nor equal temperament, but WELL Temperament. He was well aware of both, and in order to reconcile the pythagorean ratios with the harmonic of other scales, he came up with his own version of Well temperament to enable playing in all scales. Bach did not use the Werkmeister tuning, but the other way around. Werkmeister's well temperament is believed to be close to Bach's. Too much misinformation...
Rendereason 1 year ago 21
@Rendereason I have been taught that equal temperament stemmed from the well temperament that Bach experimented with towards the end of his life.
intonationinc 1 year ago
@intonationinc Good for you.
Rendereason 1 year ago
@Rendereason Did Bach oppose Equal Temperament? I thought he didn't even know what ET sounded like due to the difficulty (not well known) method of tuning to ET. Or did Bach compose the WTC simply to demonstrate a possible (not better) alternative to other temperament such as ET?
NimbleTurtle13 1 year ago
@NimbleTurtle13, ET did exist but not popular. But Bach also played the violin so his ears probably would not have liked the fact that every interval (besides the octave) in equal temperament is slightly out of tune.
angryjalapeno 9 months ago
@NimbleTurtle13 Like you said, Equal temperament is not something they could tune in their time. In fact, it was natural to compose for a certain key, as each key had different feelings and sounded different. Equal temperament is a relatively new intonation, possible only in modern times. In equal temperament, it doesn't matter what key you play in, as it all sounds the same, only the pitch changes. There is no different "feeling" also called "affekt".
Rendereason 3 hours ago
A while ago I commented that most people can't discern the small differences between temperaments. Predictably I was accused of being tone deaf, etc. But I just tried a test of my pitch perception (at Tonometric), and found my pitch perception is better than average (at the 59th percentile), but not outstanding.
DavidB5501 2 years ago
(psst... those posts were @nevertheless123)
steveflato 2 years ago
I love math, and I love the a priori of harmony with or without knowing the ratios. With just intonation, low whole-number rations have a particular consonance, and the math helps us to understand it, work with it, and maybe find more pleasure.
Boo! to musicians who disrespect the power of math because they feel threatened by it, AND to intellectuals who cling to the math and let it obscure the pleasure of music.
Math is a very useful tool in the pursuit of beauty.
druidmechanics 2 years ago 3
I absolutely hear the difference, and I completely prefer the "wrong" tempered scale! most likely because I am used to it, but I also feel the inherent dissonance makes it interesting - the "pure" harmonies sound hollow and lifeless to me.
blueshifter 2 years ago
there you go...that should convince some of the mathematical nerds here that the physiological response to music is much deeper and complex than simple arithmetic. what is a "dissonance" to some is "interesting" to another. now who wants to argue about mathematical errors of less than 1%.
nevertheless123 2 years ago
I'd prefer just temperament where possible because it would make modulations more pronounced and of course it would be more in tune. Anyways, does anybody know what they really did exactly with the graphical representation?
parquar 1 year ago
@parquar: I have no idea what they do in the case of triads, but with intervals
they apparently graph the first note (a pure sine curve, i.e., they don't have any overtones) on the y-axis and then the second note (again a pure sine curve, but now of a different frequency) on the x-axis. If the two note are the same
you get a circle or an ellipse, depending on the phase shift between the two notes, for an octave you get a figure 8 and more complicated pictures for more complicated ratios.
c330user 1 year ago
@c330user It really confuses me how it moves over time. I know it has to do with how frequency would just be how many periods the graph has across the x axis but I don't really understand the interactions and how they get the shapes they do. I don't know about most people, but I would seriously like an explanation of those shapes before I take too much meaning from them.
parquar 1 year ago
@parquar Take the fifth at 0:30 for example. A perfect fifth is the frequency ratio
3:2. In the example they take the notes A and E. If this were a pure fifth,
there would be 3 complete periods of the sine wave for the E during 2 periods for
the A. The dot on the oscilloscope that they show us goes up and down two times while it goes left to right and back 3 times. This creates the picture you see. Since the frequency ratio between A and E is not precisely 3:2
(continued)
c330user 1 year ago
in equal temperament, the actual ratio is something else (actually an irrational number). So, while the dot moves up and down two times it moves left to right and back (and now I am making up a number since I don't know the correct ratio)
3.078 times, which means that the curve is not properly aligned as in the case of the pure fifth and therefore look somewhat messy. With minor and major thirds the difference more drastic since they more inaccurate in equal temperament than the fifth.
c330user 1 year ago
this is extreamly intresting, and the comments! great vid!
babtrombone 2 years ago
I want to know how they plotted three tones on a lissajous figure. Tone 1 on the X axis, tone 2 on the Y axis, and tone 3 on the ...... ???
jigglesnap 2 years ago
It's such bullshit to put a picture of a waveform right in front of you. Otherwise the difference would be imperceptible. Most of the people who go on about the "pureness" of just intonation probably couldn't pick it out of a line up without the help of stupid visual aids like this.
MyGreatestHeist 2 years ago
You're right, they're cheating. But some of the examples *are* clearly audible, even to an untrained ear. The fifth is only 1.886... cents off, an inaudible difference, but the major third is 14 cents off, a clearly audible difference. Intervals in equal temperament can reach almost 35 cents away from their JI counterpart, and make implying their function inconvenient.
Basically, the differences are very perceptible, though it's hard to be objective when you have pretty pictures in front of you.
JLMoriart 2 years ago
If the difference is imperceptible, why the debate? I believe I can hear a difference when listening to music in JI without a visual aid.
MatthewKaras 2 years ago 2
This is fantastic!!!! Thanks for posting this!
u10ajf 2 years ago
Some comments here assume that everyone does, or should, have the same sensitivity of pitch hearing. This is demonstrably untrue (see any book of experimental psychology). I am willing to admit that some hyper-sensitive individuals may find equal temperament excruciatingly discordant, but most people obviously don't, or it wouldn't be so popular.
DavidB5501 2 years ago
"most people obviously don't, or it wouldn't be so popular"
You are not taking into account the true motivations behind equal temperament, which are the conveniences of fitting it on a one dimensional interface like the piano, no matter the sacrifice in consonance. A few hundred years ago the average musical person, no hyper-sensitivity, would have cringed at the sound of our major third.
We are simply used to ET, and it is popular because it is easiest on a 1-D playing surface.
JLMoriart 2 years ago
Unfortunately for your confident assertion, the traditional system of tuning was usually Pythagorean, in which the major third is even further away from the 'natural' third than the tempered third is. According to Carl Seashore (Psychology of Music p.223-4) unaccompanied violonists still (in the 1930s) tended to play Pythagorean thirds. So much for the theory!
DavidB5501 2 years ago
Sorry. Their thirds were worse than ours. But that doesn't refute my point that the differences are clearly audible to the majority of the population, and so our equal temperament *does* sacrifice consonance. I just need to do my homework.
What is preferred in the ergonomics of playing an instrument generally doesn't correspond to the actual desired tonal effect, and even then, some things in ET *do* sound better, either because we're used to it or because it brings out certain colors.
JLMoriart 2 years ago
Whether the differences are 'clearly audible to the majority of the population' is a matter for controlled blind tests. I'm no expert, but from the literature I have seen, the majority of untrained adults cannot distinguish between a tempered and natural fifth. They can usually distinguish between a tempered and a natural third, but only just. Which they prefer is another matter. In blind tests there is no consistent preference reported. If you disagree, cite the evidence.
DavidB5501 2 years ago
Our auditory systems are tuned to the harmonics of the Overtone Series, which is, "Just Intonation".
KABRIS1 2 years ago 9
interesting video, although there's something slightly misleading in the diagrams. i would also point to the tuning used by some of the most sublime music in the world, balinese gamelan. they deliberately tune their instruments somewhat off the exact ratios to create that shimmering quality. it is supposed to be a divine sound of sorts. that said, both just and equal temperament have their pros and cons. in reality both are present simultaneously in most music today, intentionally or not.
goldenhelix 2 years ago
I have perfect pitch and almost on a daily basis I tend to struggle with Equal Temperament.
madderbass 2 years ago
I have perfect pitch too! High 5! Do you not think Equal temperament sounds much purer though. I can still recognise what the pitches are despite whether it's ET or JI. There is not an awful lot of difference between them apart from that ET sounds purer really. Awh well! It's awesome that you have perfect pitch too though!
freddiethebassist 2 years ago
the oscillocope images are lissajous figures. Used in electronics as well as music.
risvegliato 2 years ago 2
Side by side the tempered version really sucks. On the other side i really like beatings pulsations. I also enjoy badly tuned pianos and quarter tones. Also, harmony is not the "very foundation of the musical arts".
MLAOTNMCC 2 years ago
Instead of vulgar abuse, could some of the opponents of equal temperament answer my original question, and explain what the waves in the video represent? I suggest that they are just meaningless propaganda, with no scientific basis at all. If they have one, what is it?
PS: thousand of professional musicians have no problem with equal temperament. Are they all deaf, as CatSnot implies?
DavidB5501 2 years ago
The figures there appear on an oscilloscope if you select the mode where you supply the X and Y signals. Something like this (I've played with this feature in college attracting the critique of the lab assistant who wanted something trivial displayed and measured).
Another point to note is that if you only speak of fundamentals, I don't know how the two temperaments compare.
anonimuncartier 2 years ago
Yes, those figures are called Lissajous-plots. But I don't understand either - the Lissajous plot shows the phase difference between 2 signals. But for, example, a chord is made from at least 3 different pitches/signals. So, I don't know exactly, what's on the vid :)
od8086 2 years ago
A just Intionation perfect fifth, for instance, is a 2 to 3 ratio of frequencies. So 200 Hz and 300 Hz, for instance. For every 2 cycles of one wave, the other wave cycles 3 times. The ratio is exactly 1.5. If you plot one wave on the X axis and one on the Y axis, you get a stationary figure like that. Equal temperament perfect fifth is 1.42857143, on the other hand, so the waves never line up correctly.
jigglesnap 2 years ago
Ok, I'm an electronic engineer, so it's okay. I thought the vid is about a major chord, so I didn't understood it, bcos as you've mentioned a lissajous plot is made from 2 signals - and a chord is at least 3 different frequencies. It is kind of rational to use just intonation, these weird L.-plots are very strange to see :)) but I can barely hear the difference between ET and JI. sometimes I maybe made a "blind-test" with a friend, who plays a JI or ET chord, and I'll write down my answer.
od8086 2 years ago
But real string instruments do have overtones (harmonics) produced by the strings. If the overtones of C does not match E and G, dissonances arise. Also, yo u have to have a developed ear (or maybe it's something you're born with) to discern subtle nunces. This is, for those who don't know, a topic of nuances.
Intonation in music is a vast topic (and it's beyond my knowledge), all I know is that it is beyond the frequencies computed naively with the 12th root of 2.
anonimuncartier 2 years ago
Yes, the overtones make the dissonance even more obvious. :) Listen to piano chords in equal and just and you can hear the difference easily.
Actually the "harmonics" in a piano aren't really even harmonics. They get more sharp the higher you go. Using longer strings reduces this effect, which is why big pianos sound better than small uprights.
jigglesnap 2 years ago
DavidB5501, Search Wiki for "Lissajous curve".
kencc4791 2 years ago
Thanks, that's very helpful. This video may well use Lissajous Curves. In which case I am right that this is a false representation of the difference between just and tempered intonation, because it means that someone has deliberately chosen a mathematical formula which exaggerates very small differences in ratios. It's like using an electron microscope to 'prove' that a razor blade is not sharp.
DavidB5501 2 years ago
But you can hear the small differences in ratios, too, as beating. It's not somehow a lie or exaggeration to show it on a scope.
jigglesnap 2 years ago
Somehow I cannot notice any difference, except when I look at the graphical representation. It seems the graphs are made to hypnotize people into buying the agenda of the tempered scale addicts! Does this mean that the thousands of amazing piano compositions of Beethoven Brahms and Mozart that have been enjoyed by millions is invalid? Please enlighten me if I am dead wrong. The ear doesnt do mathematics but feels. A just minor third and tempered minor third convey the same feeling etc.,.
nevertheless123 2 years ago
A JI perfect fifth is a 3:2 ratio of frequencies.
An ET perfect fifth is a 2^(7/12):1 ratio of frequencies.
Which involves more mathematics?
jigglesnap 2 years ago
jiggle: my point was about more or less math. but that the psycholgy of response to music doesnt care about math. It is too complex. If you are focused on the frequencies and ratios in schubert sonata you arent hearing the music but mathematics!
All art is an abstraction and approximation. If not why dont we just generate Fourier series and simply listen to the "pure" mathematical tones. Then you would'nt have the clarinet and the oboe. ya yay a I know they have different Fourier spectra but...
nevertheless123 2 years ago
I'm pointing out that equal temperament is even more "mathematical", but it's math based on convenience, not based on physics.
Just Intonation sounds purer because it matches with the way our ears process sound. When you hear a pure chord, the neurons are firing simultaneously because the wave cycles line up with each other. That's what "3:2 ratio" means. For every 2 cycles of one wave, the other wave cycles exactly 3 times.
jigglesnap 2 years ago
No, I dont think you see what I am saying. You keep explaining the math to me but I have read Helmholtz's classic text and understand why just intonation is more natural..due to Fourier series... But my point is that our perception of music is beyond the reach of mathematical precision. You can play a deeply moving piece of Schubert in ET piano and it will move the listener irrespective of the numbers. Unless the listener is a nerdy mathmetician who fails to listen with his right brain!
nevertheless123 2 years ago
sorry in my previous post the first sentence should be "my point was NOT about more or less math..."
nevertheless123 2 years ago
I first heard this product via sound files and I really liked the sound of a C major chord. I could hear a big difference.
That does not mean I started disliking all other music.
I just thought it was another addition to the wonderful world of music.
This video is meant to sell their product so naturally they want you to believe that it is the best.
888music 2 years ago
888music very good point. It is indeed interesting addition. I just take isse with osmeone saying one type of music is "wrong". Afterall what is wrong about dissonance?
Question: would the concept of modulation even be possible without ET. i.e., if you play an F chord in just intonation that wouldnt belong to a different key but it would in ET?
nevertheless123 2 years ago
@nevertheless123 i think the dissonance is very obvious regardless of graphical representation. Bach definitely was a proponent of just intonation. Equal temperament was conceived in order to help musicians transpose keys without completely retuning their instruments which is logical, but I dont think every melody was meant to be heard in every key. If a song is written in a, id rather hear it just tuned to a. Its odd I feel songs sound more moving not equally tempered.
tawkinhedz 2 years ago
hmmm..I see. But I thought Bach was a major fan of ET? In fact he wrote the "well tempered clavier", 48 preludes an fugues, ie,. 2 x 2 for each of the 12 keys. This was the bread and butter for the greatest musicians of classical music like Beethoven and Mozart and even as late as Mahler. In other words, without the well tempered keyboard, most of classical music would not have come about.
Am I missing something ? or does a fractional mathematical error make most of these composers useless?
nevertheless123 2 years ago
The confusion is over "well tempered". Well tempered does not equal Equal Tempered :) Well tempered referred to a specific temperament - something based on the just system but "tempered" slightly (not NEARLY as much as the equal tempered system). The truth is that Bach was somewhere in between. He wanted the flexibility of being able to write in all keys, but also wanted to maintain consonances and dissonances as close to the true intervals as possible. (continued....)
steveflato 2 years ago
(... from last post)... Bach used the Werckmeister tuning (I believe) on the Well Tuned Klavier. Google around for it. Equal Temperament ("ET") was not only impossible to achieve on a keyboard instrument in Bach's time, but most people thought it sounded awful. A number of different temperaments were used during the Baroque, Classical, and even up until the Romantic period. True Equal Temperament did not become standardized until far later.
steveflato 2 years ago
@nevertheless123
It's a modern misconception that Bach advocated equal temperament. Nobody used equal temperament in Bach's day, and that includes Bach himself. A well-tempered instrument can be used to play in any key, but at the same time, some keys are "sweeter" than others. This provides contrasting character as you change keys. Equal temperament is not a "well-temperament", because it destroys this contrast by making all keys equally sour.
ccoraxfan 1 year ago
@nevertheless123 Its really easy to hear the difference ... in a demonstration. I certainly dont need a graph to notice it. If you seriously cant hear it, thats ... just weird. But in actual music there is so much else going on that I would probably never notice the difference.
panchamkauns 1 year ago
@nevertheless123 The chords of those composers have compromised tuning. That is because, for a just-tempered replacement, all of the keys would only be a fraction of those needed to produce all of the chords in just intonation. I myself can hear in this video how the equally tempered major third is sharp. As a brass player, I can tell you that wind ensembles' chords are balanced by ear to technically approximate just intonation.
parquar 1 year ago
@nevertheless123 -- see, hear, and feel the difference: the equal temperament is wobbly, not stable. The graphs are not hypnotizing people into buying into tempered scales - it's the opposite! to buy into just intonation - not equal temperament. This does not discredit bach and beethoven... many composers were aware of this problem, and were careful as to which keys they wrote in, as the piano was tuned to sound better in certain keys (Cmajor, Aminor, etc). and they didnt have software then.
untidaled 1 year ago
@untidaled so Bach Beethoven never composed in anything but Cmajor and Aminor? hahaha.
what about the well tempered clavier which was the daily bread for the greates composenrs. It is in ALL KEYS !
nevertheless123 1 year ago
@nevertheless123 most experts today think that Bach's "well tempered" scale was not our "modern" equally tempered scale.
AlainNaigeon 1 year ago
@nevertheless123 I suspect the audio processing of the clip that takes place before the clip posted messes up the spectrum enough so that the difference in beat frequencies (for example) becomes hardly distinguishable between the two cases.
JanPB 1 year ago
@nevertheless123 Actually, Beethoven and Mozart played on Claviers that were tuned closer to the examples shown in this video. The equal temperament scale slowly took over as the main piano tuning later on. I strongly disagree. If you want a better example, go to my website and click on the examples. It's a better tuning algorithm and doesn't try to hypnotize you with oscilloscope images.
intonationinc 1 year ago
I can't believe there are people associating tuning systems to socialism and psuedoscientific conspiracy theories. Both tuning systems are equally valid, and have their purposes. Just intonation is "perfect" in that it has an equal difference between steps. Equal temperament allows for simpler tuning of instruments because it makes all transpositions equal, and since instruments are often playing in different keys, having to retune every performance would be impractical.
TheRaven7 2 years ago 2
Obviously you don't realize the whole key concept here. It doesn't matter if it's impractical; we should do whatever is necessary to bring life to Bach's music. Some people just can't stand Bach because it is so dry... pitch is just one of many problems. Metal strings are much more practical than gut strings but the sound of gut string has ALWAYS been preferred.
Enix5548 2 years ago
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