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Equal temperament was well-known but no-one had a way of achieving it like we do today with electronic tuners that can accurately divide the octave by mathematically equal fractions of the octave.
Hummel used to tune to a quasi-equal (truly equal was impossible) but most people did not like the sound and tempered tuning was the norm centuries after it was 'invented'
Bach wrote the well-tempered keyboard (instrument) because he was coming-out of an era where music was only in a few keys and you did not need to modulate chromatically..
he did modulate frequently in his own way, exploiting the different colors of the well temperament instead of fighting them.
as far as not getting your head around the concept.. it is quite easy to grasp, really..
tuning 101:
if you tune each key of the keyboard by perfect, beatless fifths, by the time you've covered all 12 tones you will be totally off..
ideally music, to be tuned perfectly, should always be in the same key, therefore you would not need any black keys.. no problems with tuning..
well-temperament is not a science but an artform subject to the musician's and tuner's sense of proportion and taste..
historically, there are dozens of examples to choose from, so that you can get nearer to what the composers used..
ET is a 20th century invention, based on equality... before 1900 equality did not exist anywhere.. everything was derived from heirarchy..
What really gets me is how so many publications seem to want to confuse Well Temperament with ET, essentially calling them synonymous when, in fact, the two are mutually exclusive.
It may well be that J. S. Bach's acceptance of a tuning system which permitted access to all 24 major and minor keys through the new idea at the time, Well Tempered Tuning (as I still prefer to call it), was a turning point in music history.
Sadly, however, so many books, even recent ones such as Stuart Isacoff's Temperament seem to deliberately choose to truncate the facts to make it appear as though keyboard tuning took a quantum leap after Bach's creation from 1/4 Meantone, directly to ET! It is simply NOT the truth!
Then, to take an untruth ever so much further, a video such as the one displayed on here, seeks to tell the general audience that all music after the WTC event was made possible and due entirely to ET!
Bill,
Howard Goodall made no such claim in the video. He said that the "well tempered keyboard" was here to stay after publication of the WTC. Then he went on to say that it took "another revolution altogether" over a century later, the industrial one, for the ET version to gain the ascendancy [e.g. Schiedmayer publishing a manual around 1830 saying his pianos should be tuned in ET - my comment].
Maybe Larry, as the OP, will say whether he found the video enlightening in any way.
Ian Russell Schiedmayer & Soehne, 1925 Model 14, 140cm Ibach, 1905 F-IV, 235cm
Equal temperament was well-known but no-one had a way of achieving it like we do today with electronic tuners that can accurately divide the octave by mathematically equal fractions of the octave.
...
ET is a 20th century invention, based on equality... before 1900 equality did not exist anywhere.. everything was derived from heirarchy..
One minor correction in an otherwise good post -"...some scale theories by Aristoxenus (c.300BC) were interpreted by some theorists as describing Equal Temperament...The earliest unequivocal and mathematically correct account of Equal Temperament was produced by Salinas (1577)." (di Veroli)
it's been an issue ever since people started tuning.
I would say that the music never needed it in truth until composers began to modulate more freely.
in the 1500's the music did not stray far from the main key so it was more or less a theoretical approach to harmony and I suspect a bit dangerous from a theologic point of view because of it's inherent lack of inner heirarchy.
The harmonic series is the purest, most natural tuning you can get and it is based on one main (fundamental) frequency from which all other frequencies are derived..
it's been an issue ever since people started tuning.
I would say that the music never needed it in truth until composers began to modulate more freely.
in the 1500's the music did not stray far from the main key so it was more or less a theoretical approach to harmony and I suspect a bit dangerous from a theologic point of view because of it's inherent lack of inner heirarchy.
The harmonic series is the purest, most natural tuning you can get and it is based on one main (fundamental) frequency from which all other frequencies are derived..
Interesting. In all the reading I have done about temperament over some 40+ years I do not remember encountering the idea that ET might be theologically heretical, but it is possible. Dividing the octave into 12 or more parts is not elegant.
Another thing which is worth mentioning is that Chopin wrote his 24 preludes in different keys, like Bach, and that he too exploited each key from a tempered point-of-view
Liszt, when he transcribed Shubert's Impromptu in Gb Major transposed the piece half a tone upwards..
Gb major in well temperaments is quite out-of-tune, so that would imply that Liszt corrected this and that perhaps, unless Shubert liked out-of-tune keys, the tuning system in Vienna was incorporating a close-to-equal temperament... or at least a temperament which made keys with more accidentals more in tune than the ones with naturals..
either way... the composers were 'well aware' of temperament.
Interesting. In all the reading I have done about temperament over some 40+ years I do not remember encountering the idea that ET might be theologically heretical, but it is possible. Dividing the octave into 12 or more parts is not elegant.
People were getting in trouble all the time for what is today considered normal.
The harmonic and geometric relationships which define harmony were considered to be sacred and they were also incorporated in high architecture etc.. they were in essence divine and not to be toyed with.
Our culture today gives emphasis to the democratic concept that everyone is equal and undefineable, in a way. This in the days before the late 1800's was considered heretical, against 'order' in general etc.. and to a great extent they were correct..
our concept of beauty today has been influenced by post-modern relativism which, at it's worst, aims to destroy the concept of natural beauty for political reasons.
but all we need to know is that the composers knew about unequal tempering, they used it regularly and were connoisseurs of how temperements influenced the sound of their music
whatsmore the older, pre-steinway, European pianos which had a wooden frame would resonate as a whole, or 'shake' as it were, with the right temperament and the right keys..
the metallic frame is yet another manifestation of this 'separation' of the notes, to make each one equal to the other.. with a wooden frame all the notes interact like a heirarchy.. some chords sound more resonant than others, some keys sound different than others and groups of notes sound different because the frame resonates with the total output of vibrations in a way..
If you want to have some fun, feel the temperature rise as the tuners become ill-tempered whenever temperament is mentioned.
Yet so many of us sally forth weekly in fine fettle and well temperament to joust bravely at the windmills of making something untunable, ... well, ... tuned.
Thanks Chuck for your thoughts. There is something about a Good Temperament, particularly a gentle one like Bill's that can be very inspiring for a musician.
IMNSHO, whether we're striving for ET or a UT, we need to remember that the end result needs to be musical.
Is ET musical?
(duck & cover)
As a staunch supporter of GTs, I have to say, IMHO, that a really well tuned ET, done by someone who really listens to the piano as a whole, can be very musical.
That said, a really well tuned GT, done by someone who really listens to the piano as a whole, can be very musical.
Thanks for your contribution, Acotot. It is interesting to me that Thomas Salinas is mentioned, as I seen it before, since he was known for a temperament even more extreme than the 1/4 Meantone, the 1/3 Comma Meantone. I have tuned it before, just experimentally. It is my understanding that it was used primarily for funeral music. My impression of it was that the chords "dripped" from the piano as in one of Salvador Dali's paintings.
It was truly a bizarre sound but I can see how it could have invoked tears from people who heard it. And that leads me to recall very vividly what the entire purpose of Key Signature in Well Temperament really is: the emotion in music.
One earlier poster said something about scientific proof that beat speeds of Major (or minor) thirds definitely did invoke emotion and the PTG Journal editor challenged him to show that proof. I certainly don't have that proof, at least scientifically but I know it is true. Otherwise, what would someone say that when he heard music in the Vallotti temperament on the harpsichord, it "made his skin crawl"?
ET literally puts all music on Prozak. No highs, no lows, just all smooth sounds. No reason to be in any particular key. The video showed "Industrial mechanization" that supposedly made all instruments play in ET but when a choice of key signature based upon temperament is suggested, those who don't think key signature matters at all immediately point to Brass instruments having trouble with sharp keys and stringed instruments having trouble with flat keys. But they all "play in ET" don't they?
There supposedly is no distinction from one key signature to the next in ET (and there really is none) but there are many ET only advocates who still very strongly claim that they actually do hear a distinction! Yet if music is played in a Well Temperament, that distinction is too much! It jars the emotions and make the skin crawl! But an emotional response cannot be proved, so therefore it must not exist.
If you ask me, you have to return to what early 18th Century theorists suggested and that is that temperament should evolve to a point where all key signatures should be much more toned down in order that they be more accessible but not to the point where any and all distinction be erased. Hence, the "Victorian" style temperament. Several theorists advocated it. I have practiced it as my usual way to tune the piano for over twenty years.
I do not get any sense of emotional distinctions whatsoever from different keys in any temperament. I only get a sense or more or less sourness, but generally not enough to be bothered with unless the temperament is extreme. Changes in the level of sourness do not register with my musical appreciation senses. I don't have a problem with mild well temperaments, but I don't see the point in bothering about it.
Am it to be considered un-musical? Or, am I missing out on a higher plane of musical appreciation?
I do not get any sense of emotional distinctions whatsoever from different keys in any temperament. I only get a sense or more or less sourness, but generally not enough to be bothered with unless the temperament is extreme. Changes in the level of sourness do not register with my musical appreciation senses. I don't have a problem with mild well temperaments, but I don't see the point in bothering about it.
Am it to be considered un-musical? Or, am I missing out on a higher plane of musical appreciation?
Neither, I think.
What I enjoy about music is the struggle of tension and relaxation that occurs as a result of many factors, but primarily the harmonic changes. The tritone is tense, leading to a relaxed resolution. Another form of tension/relaxation occurs when the composer modulates from the tonic key to another key. The further around the circle of fifths the modulation occurs, the more tense the music becomes in a GT. This does occur in ET. The modulation back to the original key provides a relief from that tension.
I do not get any sense of emotional distinctions whatsoever from different keys in any temperament. I only get a sense or more or less sourness, but generally not enough to be bothered with unless the temperament is extreme. Changes in the level of sourness do not register with my musical appreciation senses. I don't have a problem with mild well temperaments, but I don't see the point in bothering about it.
Am it to be considered un-musical? Or, am I missing out on a higher plane of musical appreciation?
Neither, I think.
What I enjoy about music is the struggle of tension and relaxation that occurs as a result of many factors, but primarily the harmonic changes. The tritone is tense, leading to a relaxed resolution. Another form of tension/relaxation occurs when the composer modulates from the tonic key to another key. The further around the circle of fifths the modulation occurs, the more tense the music becomes in a GT. This does occur in ET. The modulation back to the original key provides a relief from that tension.
I enjoy the sense of tension an relaxation from harmonic changes as well, also from tense intervals resolving to calmer intervals. I also get a sense of pleasure from modulations resolving back or elsewhere. However, I also get this sense from listening to either piano ET, piano WT, or a string quartet or a choir etc etc. For me, a particular temperament is not the governing factor. There must be other intrinsic musical reasons why tension resolution occurs and that is what I pick up on.
