9 ms·
Well vs. Equal Temperament (2000)
- xpda 11y agoThere is some debate as to whether Bach intended equal-temperament or well-temperament. These terms were not well-defined in his day. https://books.google.com/books?id=yZ95L8Xohs0C&pg=PA4 https://books.google.com/books?id=yZ95L8Xohs0C&pg=PA4
- plaguuuuuu 11y agoThere's one guy on youtube who claims Bach's squiggles underneath each piece title in the original WTC manuscript actually represents an ideal tuning system for that piece. I thought that was a crackpot theory, but then he played some pieces in their respective individual tuning systems on a harpsichord, and they sounded absolutely amazing, better than well tempered (or equal obviously). So who knows!
- lamby 11y agoBach seems to attract all sorts of bizarre numerology, alas.
- plaguuuuuu 11y agoI agree, but when it actually works.... shrug
- lamby 11y agoWell, The Bible Code "works" too.
- codezero 11y agoDoes anyone have links to audio samples where these differences are prominent? In addition to comments, this video has a decent comparison using sawtooth tones: https://www.youtube.com/watch?v=VRlp-OH0OEA https://www.youtube.com/watch?v=VRlp-OH0OEA
- CarVac 11y agoI went looking. https://www.youtube.com/watch?v=TBt6APk21tU https://www.youtube.com/watch?v=TBt6APk21tU
- EarthLaunch 11y agoThank you. That is astounding. I wonder if there is any way to find music performed using original tunings. It sounds SO much better to me.
- CarVac 11y agoI know, it's amazing. Each example had my mouth agape. For me, the closest analogy would be watching Japanese movies and TV shows being able to understand their original language as opposed to relying on subtitles or dubs; there's a whole dimension of nuance I was missing before I learned the language.
- EarthLaunch 11y agoYes. In return, while learning about this I found this great explanation: http://contentspiano.blogspot.com/2006/02/pythagorean-equal-meantone-and-well.html http://contentspiano.blogspot.com/2006/02/pythagorean-equal-...
- baddox 11y agoYou can listen to barbershop music if you want to hear justly tuned chords. Just don't get too obsessed with it unless you want equal-tempered music (i.e. almost all recorded music) to sound just a bit wrong. YouTube videos are hard to come by, but I posted two examples in this thread: https://news.ycombinator.com/item?id=10145785 https://news.ycombinator.com/item?id=10145785 And another clip I uploaded of using pitch-detecting software on a studio recording (notice it detects a lot more than 4 simultaneous notes, because it's "hearing" overtones): http://youtu.be/v7kHnEaGIfg http://youtu.be/v7kHnEaGIfg
- Omnus 11y ago
- Cshelton 11y agoSo this is interesting, I know a piano tuner who has tuned for countless famous artist. He was working on a project to record songs, like Beethoven, as someone would have heard it in his time.
- c3534l 11y agoI actually found it a little odd that Beethoven was mentioned, since it he was a big fan of equal temperment. His 5th symphony was largely written to explore the idea. In well tempered tunings, you have to play around a central "root note" in order to get a harmonic melody. But in equal temperment, the dissonance is equally spread out across the notes. His 5th symphony was able to take advantage of that in two ways: by being an unusually dissonant symphony to begin with and by jumping all over the place, going from very high to very low, playing the same note repeatedly and yet having it sound the same no matter what key he went to. We're so used to it, however, I doubt most people could really hear the difference.
- shadgregory 11y agoI had no idea that Beethoven used equal temperament. Do you have a source for that?
- c3534l 11y agoNah, just from learning about music years ago. Not everything he wrote was equal temperment, though.
- stevetjoa 11y agoSlightly off-topic, but because I love this topic so much: there is a wonderful documentary called Pianomania about a piano tuner ("piano technician", if you will) to the stars. The story centers around a good-natured piano tuner and his seemingly impossible task of translating the pianists' vaguely expressed desires into a well-tuned piano. As the movie illustrates, piano tuning is just as much about timbre as it is about pitch -- perhaps even more so! As I discovered just now, the whole thing is available on YouTube [https://www.youtube.com/watch?v=TxEcifeMf08 https://www.youtube.com/watch?v=TxEcifeMf08, only 1.5 hours, not 3 hours as the video incorrectly suggests].
- analog31 11y agoIn addition to the sonic characteristics of the earlier tunings, an important practical factor was that the tuning procedure could be carried out successfully by the keyboardist prior to every performance, since instruments went out of tune quickly before the modern piano.
- haberman 11y agoAside from temperament, I had my piano tuner claim to me that tuning pianos is actually more complicated than that. He said that the high end of the piano had to be tuned different from the low end, with some explanation like how the hammer strike bends the pitch of low vs high strings (I wish I could remember the specifics of what he said, but this was many years ago). I couldn't decide at the time if what he was saying was legit or if he was just trying to convince me that I needed to hire him again instead of just buying an electronic tuner and a wrench.
- gtani 11y agolegit, she/he was talking inharmonicity and the resulting octave stretching that makes octaves sound truest. https://en.wikipedia.org/wiki/Inharmonicity https://en.wikipedia.org/wiki/Inharmonicity
- elihu 11y agohttps://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_curve https://en.wikipedia.org/wiki/Piano_acoustics#The_Railsback_...
- vfdfv 11y agoI am certainly no expert either, but maybe your piano tuner was referring to the practice of "stretching" an octave: The tuning described by the above beating plan provides a good approximation of equal temperament across the range of the temperament octave. If extended further, however, the actual tuning of the instrument becomes increasingly inaccurate because of inharmonicity, which causes harmonics to run slightly sharp, as increasingly higher tones in the harmonic series are reached. This problem is mitigated by "stretching" the octaves as one tunes above (and to an extent below) the temperament region. When octaves are stretched, they are tuned, not to the lowest coincidental overtone (second partial) of the note below, but to a higher one (often the 4th partial). This widens all intervals equally, thereby maintaining intervallic and tonal consistency. https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Piano_tuning#Stretch
- xpda 11y ago
- arntatis 11y agoCan this be applied to an electric piano to get a similar type of colour in the sound?
- archagon 11y agoYes! With the Scala file format: http://www.huygens-fokker.org/scala/ http://www.huygens-fokker.org/scala/ Might be a little tricky to set up, though, since only a few DAWs and plugins support it.
- mootothemax 11y ago>Can this be applied to an electric piano to get a similar type of colour in the sound? Every electronic "stage" piano I've owned has had an option to modify the tuning, at minimum allowing you to choose between equal, well, meantone, pythagorean. I remember one Yamaha I owned even had the option to customise the tuning yourself. Can't remember the model number, it cost a decent-ish chunk of change, around 800 GBP about 15 or so years ago.
- abannin 11y agoIt's all fun and games until you start trying to tune a guitar. Pianos have it easy.
- plaguuuuuu 11y agoRemove all frets and tune to 5ths :|
- Zuider 11y agoQ: What's the definition of a semitone? A: Two fret-less bass guitars playing in unison.
- plaguuuuuu 11y ago:D
- deleted 11y ago[deleted]
- Zuider 11y agoRelated link posted in a previous discussion: https://news.ycombinator.com/item?id=10120648 https://news.ycombinator.com/item?id=10120648 A web-demo of the Tune.js library which offers a small, but instructive selection of tunings and temperaments which can be controlled by the alphanumeric keyboard, or by pointing and clicking.
- JoachimS 11y agoThere is a company in Sweden that builds necks for guitars with true temperament frets: http://www.truetemperament.com/ http://www.truetemperament.com/ Looks weird, but is actually ok to play on. Steve Vai has an EVO with TT frets. http://www.truetemperament.com/videos/ http://www.truetemperament.com/videos/
- pierrec 11y agoI appreciate a good attack on 12-tone Equal Temperament from time to time (and more importantly a good defense of natural intervals), but this article really goes over the top in being extremely opinionated while forcibly trying to sound factual. His point is not helped by making false claims such as "Equal temperament actually did not come into use until the 20th century." More importantly, the idea that Bach's WTC was intended to "demostrate the varying key colors in well tempered tuning as one progresses around the circle of fifths" sounds pretty uncanny when you know some context. As an organist, Bach was used to being heavily restrained in which keys and intervals could be used while dodging the many obstacles that were dissonances in the instrument's tuning. The purpose of Well temperament, used on the harpsichord, was to get rid of those limitations and gain the ability to transpose everything freely while remaining consonant and in-tune. In this way, the Well temperament can be seen as an approximation of equal temperament in a time when the mathematical tools to achieve it were not really known. To me, it's pretty clear that the WTC is Bach gleefully exploring the freedom of transposition-invariance and free modulation. In other words: Bach would have loved the equal temperament, and this article would likely give him a hearty chuckle. I like natural intervals, but dividing the octave in 12 tones is a rather inappropriate way of using them. European classical music adopted this system early on, and therefore was doomed to end up on the equal temperament at some point. It's not the ultimate system nor the end of temperaments, but it's been really, really useful.
- Omnus 11y agoIn addition, the article puts forth a commonly held (but false) notion that equal temperament destroys any sense of key color or identity, apart from pitch. That would be true if every instrument or voice sounded exactly the same throughout its entire range, but that is never the case. Even in equal temperament a G minor chord sounds different than a D minor chord because they fall on different ranges of the instruments and the human auditory system. If you try transposing a piece in G minor to D minor, you'll notice a clear difference. You could either go up a 5th or down a 4th. If you choose to go up a 5th, things will sound quite a bit brighter. Conversely, going down a 4th could very well cause the piece to sound muddier, depending on the orchestration. At any rate, the other forms of tuning have other effects, of course, and are worthwhile to explore.
- graycat 11y agoThe OP and some of the links in this thread have a lot of terminology about tuning that is a bit short on precise definitions. Okay, since I made some progress with violin, I understand that the intervals of a minor third (three semi-tones), major third (four semi-tones), a fourth (five semi-tones), a fifth (seven semi-tones), a sixth (nine semi-tones), and an octave (12 semi-tones) consist of two frequencies that are ratios of small whole numbers and where the interval of a semi-tone is the ratio of two frequencies of approximately 2^(1/12). Commonly violinists call these intervals, especially the major third, fifth, and octave, perfect. And I understand that setting the frequency of the first A above middle C to 440 Hz and all the semi-tone frequency ratios to 2^(1/12) is tempered tuning. Ah, now I see in the OP: "Equal temperament, the modern and usually inappropriate system of tuning used in western music, is based on the twelfth root of 2. The ratio of frequencies for each semi tone is equal to the twelfth root of two." So, what I called tempered tuning the OP calls "equal temperament". Is that the same as well temperament? For all the other terminology about approaches to tuning, e.g., mean tuning, I have no clear definitions. E.g., it appears that the OP is still vague on just what equal tuning is. Is there a source with clear definitions?