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I stopped watching after the death of Bach, because I didn't notice Andreas Werckmeister who as far as I know invented the "well tempering". Am I wrong? Or did I just miss it? Sorry, he really goes too fast for my English.
I stopped watching after the death of Bach, because I didn't notice Andreas Werckmeister who as far as I know invented the "well tempering". Am I wrong? Or did I just miss it? Sorry, he really goes too fast for my English.
He covers the concept at 3:37…equal temp was something Bach and others were pushing towards. It wasn’t until Cher and Britney Spears that Autotune finally got it right.
ORIGINAL: mecmachin So which is the official standard tempering of a concert piano nowadays?
Officially equal temperament (BTW Bach's well-tempered clavier wasn't equally-temprered but that's a different issue).
However, in order for intervals/chords to sound good, the practical tuning of the piano has to compensate for the inharmonicity of real strings (partials are at slightly higher than multiples of base frequency because the restoring force gets an extra kick from the strings not being perfectly elastic (i.e. being a bit stiff); the shorter the string the larger the effect; the thicker the string the larger the effect; the higher the partial the larger the effect.
So to tune a piano properly, tuners tune according to something called the Railsback curve- resulting in lower notes being lower than equal temperament and higher notes being higher:
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Interesting most singing occurs within the 4th octave range and it is right on zero.
BTW Bach's well-tempered clavier wasn't equally-temprered but that's a different issue
I would really have to dig for it, but some famous musician wrote about his experience with Bach, and described that he was very particular about his personal tuning of instruments, and that in general all his thirds were very sharp. Sounds suspiciously like equal temperament to me…as in he did what had to be done so he could play in every key without any particular one sounding different than the other.
In Bach's time organs with more than 12 keys per octave were still quite common. For example, there would be split black keys for A-flat and G-sharp, and other pairs that are enharmonic in the guitar's equal temperament. Various tunings in unequal temperament were used to provide pure thirds, fourths and fifths. Still, not all keys were equally feasible on a keyboard with 18 notes.
While Bach retained many of the older musical forms such as chaconne, fugue, and dance suites, he composed in the "modern" major-minor modes and modulated freely among keys. In his earlier career Bach kept to the 15 keys feasible in just temperament, never going beyond four sharps or four flats.
With Das Wohl Temperirt Klavier Bach demonstrated a tuning which made all twenty-four major and minor keys playable. Bach didn't use equal temperament, nor did he invent the "well-temperament" he exemplified in Das Wohltemperirt Klavier, but he was certainly a "modernizing" influence. He was hired several times to oversee major organ building projects, or to perform acceptance testing for new instruments, so his practical influence was wide spread.
"Johann Sebastian Bach: The Learned Musician" by Christoph Wolff (2000) is an authoritative artistic biography, and a good read if you're a Bach fan.
Konstantin's explanation of the "stretching" of piano tuning calls attention to the inharmonicity of strings. The string's resistance to bending leads to the higher partials going sharp.
D'Addario came out with a composite third string. They may still sell it. It was/is a drab greenish color, and sounded terrible on Romanillos #407. It was/is denser and stiffer than the clear nylon 3rd of the EJ-45 set. Though it was somewhat louder, its tone grated on my ear.
To the player, Romanillos #407's third string sounds very slightly quieter, though not as much as some guitars. The player quickly adjusts, as he does to any great instrument.
The second half of 2000 I lived in a condo in Honolulu. The living/dining room was 18 feet long, and had a glass wall and sliding door to the balcony at one end. Sitting 12 or 14 feet away from the glass wall, the reflected sound of the third string sounded perfectly in balance with the rest, when played with the same touch. Guitars usually sound somewhat different to the player than to the listener.
My spruce/Brazilian Abel Garcia has the best 2nd and 3rd strings, relative to the rest, of any guitar I have ever owned. I don't own a guitar with a "bad" third string, but I have played quite a few. All of Abel's guitars I have played have had great 2nd and 3rd strings.
Abel took Romanillos' course, and twice served as his assistant, so he is quite familiar with Romanillos' methods. He also studied with Felix Manzanero and other Spanish luthiers when they visited Paracho. Abel's guitars have his own unique fan bracing. Instead of angling the stout strut below the sound hole, Abel puts it straight across, but includes a much lighter "treble cutoff," angled like the heavy strut in many Santos Hernandez, Ramirez, etc.
Bach didn't use equal temperament, not did he invent the "well-temperament" he exemplified in Das Wohltempiert Klavier, but he was certainly a "modernizing" influence. He was hired several times to oversee major organ building projects, or to perform acceptance testing for new instruments, so his practical influence was wide spread.
It might be one of the oldest arguments that continues, but the evidence points to EQ was what he actually used IMO:
“…let no man tell me about this or that musician or amateur who approved a third which was altered in the ratio 81:80…Mr. Kirnberger himself has more than once told me as well as others about how the famous Joh. Seb. Bach, during the time when the former was enjoying musical instruction at his hands, confided to him that he tune ALL the major thirds sharp. In a temperament in which all the major thirds are somewhat sharp, i.e, in which they all are to beat by reason of being too large, a pure major third cannot occur, and once no pure major third can occur, no major third enlarged by 81:80 is possible either…” Frederick Wilhelm Marpurg, 1776.
“In the tuning of harpsichords he achieved so correct and pure a temperament that all the tonalities sounded pure and agreeable. He knew of no tonalities which, because of impure intonation, one must avoid.” Agricola, Bach’s Obituary.
“The exact tuning of his instruments as well as of the whole orchestra had his greatest attention. No one could tune and quill his instruments to please him. He did everything himself.” CPE Bach, 1774
“Silbermann would not tolerate EQ temperament in his organs”- Adlung. (Bach on the other hand probably was in favor of reasonably equal temperament on the organ as well as the Clavier-footnote 60 The Bach Reader, edit by HT David, A. Mendel. )
(Bach speaking to Silbermann) “You tune the organ in the manner YOU please, and I will play the organ in the key I please”, thereupon used to strike off a Fantasia in Ab major…ending in Silbermann’s retiring to avoid his own “wolf”.- E.J. Hopkins. [If you can’t tell, Bach was making fun of the poor guy’s organ cuz it was freaking out of tune in Ab for the sake of a sweetened C major zone. Such a joke is not possible with equal temperament].
(Regarding Silbermann organs)”…The 4 bad triads are of a rough, wild, or as Capellmeister Bach in Leipzig says, barbaric nature intolerable to a good ear.”- GA Sorge, 1748
“If the composers previously mentioned had not made a PURE temperament, necessary enough, then the Leipzig Bach with his…passages into hitherto wholly unused keys, made it quite indispensable…the best keyboard instruments were unusable on account of their impure tuning…even the organs by Silbermann”- JS Petri, 1782
“He also tuned both his harpsichord and his clavichord himself, and was so practiced in the operation that it never cost him above a quarter of an hour.”- JN Forkel, 1802. [how could anyone tune a harpsichord with some specific odd mixture vs simply an EQ temp. Across the board in 15 minutes or less? ]
“If Bach played in tune, then call me Cher!”- Justin Bieber, 2022.
“I came in like a well-tempered wrecking ball!”-Miley Cirus, 2018.
“Autotune is out of tune”- Rick Beato’s son Dylan, 2015.
Yes, its a weird song. Actually reading about the fun Bach had messing with peoples keyboards in Ab major reminded me that this fugue seems as adventurous as the chromatic fantasy…maybe he conceived it just for this tuning purpose? Around 2 minute mark is especially crazy…anything but equal temp would sound like hell IMO:
ORIGINAL: Richard Bach didn't use equal temperament, not did he invent the "well-temperament" he exemplified in Das Wohltempiert Klavier, but he was certainly a "modernizing" influence. He was hired several times to oversee major organ building projects, or to perform acceptance testing for new instruments, so his practical influence was wide spread.
It might be one of the oldest arguments that continues, but the evidence points to EQ was what he actually used IMO: [..]
The evidence you quote is all indirect and accommodates an alternative explanation to Bach using equal temperament. More recent research (last 15-20 years or so) shows that what Richard summarized is essentially the current understanding. So what did Bach use - if not equal temperament - such that he could play well-sounding music in all keys?
We still don't know for certain, however in the mid-2000s scholar Bradley Lehman published a series of articles in the journal 'Early Music' (and an accompanying website - http://www.larips.com/ - which is the word "spiral" backwards) presenting an exciting theory - that the 'recipe' for the unequal temperament Bach preferred is encoded as simple tuning instructions in the title page of the manuscript of the 1722 Well-Tempered Clavier.
The original title page of the manuscript looks like this (notice the top line of squiggles above the title):
and the idea is that when you turn the page upside-down you get a set of instructions for tuning by the number of squiggles/little loops inside the big loops.
The upside-down image looks like this (with notation by Lehman providing additional detail):
One gets the sequence 2-2-2-2-2-0-0-0-1-1-1 which tells a tuner by how many twelfths of a Pythagorean comma(*) to make the eleven fifths narrower from a perfect fifth as you go around the spiral of fifths.
"Naturals F-C-G-D-A-E as normal" means that the fifths are tempered by 2/12 of a Pythagorean comma (PC), i.e. 1/6 PC; "Pure" means perfect fifths, i.e. no tempering, for the next three fifths E-B-F#-C#; and 'flattened' for the last three fifths C#-G#-D#-A# means tempered by 1/12 PC (half the "normal" amount). The remaining fifth A#-F is then by residual 1/12 PC wider than a perfect fifth.
By doing this we have followed the instructions 2-2-2-2-2-0-0-0-1-1-1 and bent the spiral of fifths into a circle with a particular unequal temperament which happens to work well in all keys and, unlike equal temperament, preserves different keys having a different character, thus avoiding the major compromise of equal tempering.
Presented within a circle of fifths, the tuning looks like this:
The sound is [claimed to be] very pleasing and rich, with different keys having different impressions without sounding out of tune, and in comparison the equal temperament is dull-sounding. You can hear how it sounds from here: http://www-personal.umich.edu/~bpl/larips/samples.html which contains direct links to YouTube recordings in this tuning by Lehman.
ORIGINAL: Ricardo “He also tuned both his harpsichord and his clavichord himself, and was so practiced in the operation that it never cost him above a quarter of an hour.”- JN Forkel, 1802. [how could anyone tune a harpsichord with some specific odd mixture vs simply an EQ temp. Across the board in 15 minutes or less?]
Here’s Lehman tuning a harpsichord to this unequal temperament in under 8 minutes (establishing all the notes), with another 5 or so minutes for copying by octaves for the rest of the instrument; he says he can do the complete tuning in as little as 10 minutes:
(*) A Pythagorean Comma (PC) is 531441/524288. It is the ratio of an interval of 12 perfect fifths versus an interval of 7 octaves, and is the amount by which an octave is overshot after going twelve perfect fifths around a circle of fifths, compared to seven octaves. A cycle of tuning twelve consecutive perfect fifths must remove a total of one PC to avoid overshooting the seven octaves. The result of removing a total of 1 PC is a closed loop - the spiral of fifths becomes the circle of fifths.
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Original Kitarist: The sound is [claimed to be] very pleasing and rich, with different keys having different impressions without sounding out of tune,
"Werckmeister's term 'well-tempered' ( wohl temperirt ) indicates his preference for a slightly modified system of tuning with 'all the thirds sharp' enabling him to play in all twenty-four keys without losing the character of individual keys--a loss that occurs if the octave is divided into absolutely equal semitones. What was to become a new standard would have been regarded as a serious drawback." Wolff, op. cit. pp. 228-229
Well, look you guys. Werkmeister (cool name) divides 1/12…essentially Equal temp. To argue it keeps some loony tune character of individual keys is nonsense (accepting his altered versions designed to sweeten certain keys over others). What “character” could that be other than out of freakin tuneness???? The point was when you (meaning BAch and any others with an ear) have good relative pitch, transposing a piece from one key to another (Bach did this all the time, with no special avoid tones) is intended to preserve all the character of the original. WTC2 I have on hand, in the appendix, the same chords sketched out in C major for the C# prelude. There can be no argument that one key has special intervals that the other doesn’t and vice versa. That of course WILL be the case if you do any of these wacky tuning methods.
Bach didn’t have a digital tuner, nor Werckmeister, but it is or would be exactly what they wanted EVERYBODY ELSE to freakin use. Just like my method of tuning is 2 cents off….a longer beat than a freakin note can sustain on the guitar!!! As much as how I tune guitars is “not Equal tempered” these keyboards might have been. But the point is the thinking is the same. Arguing cents is splitting hairs. I am certain if Bach was a modern day producer he would be auto tuning everybody that had no talent. Just like he tuned all the orchestra instruments himself as his son noted. It is the ONLY thing that makes sense. This character of different keys just reveals the see-saw game of the ignorant…it is give and take, until everything is literally (or conceptually) EQUAL.
I don’t need a scientific analysis of Lehman to know it is no way in hell what BAch wanted. I only need to hear him trying to tune by ear his harpsichord then play something in E major or B major….sounds like dog sh1t. But, not surprisingly people have been able to shoot down the crazy idea a doodle sketch might be a tuning system.
Anyway, i look on line and watch guys play with different tuning methods and the comments are hilarious. “I love A, even though that one chords sounds bad…it actually sounds cool it resolves”….”I don’t know what it is but version B is the best, it sparkles’…”for me version C is bland and has not character”…..etc etc. All nonsense subjective tone deafness. Thank god for Autotune after all I guess
Listen at 4:05 left is Twerkmeister and right is equal temp in unison:
What “character” could that be other than out of freakin tuneness
As you know equal temperament made all keys out of tune - by the same amount thus erasing differences between the keys (what is referred to as "character" or "mood" and is not to do with being out of tune) and this was considered a major drawback until people got used to it for the convenience of transposition without retuning.
Blurb: "What if Bach and Mozart heard richer, more dramatic chords than we hear in music today? What sonorities and moods have we lost in playing music in "equal temperament"—the equal division of the octave into twelve notes that has become our standard tuning method? Thanks to How Equal Temperament Ruined Harmony, "we may soon be able to hear for ourselves what Beethoven really meant when he called B minor 'black'" (Wall Street Journal).In this "comprehensive plea for more variety in tuning methods" (Kirkus Reviews), Ross W. Duffin presents "a serious and well-argued case" (Goldberg Magazine) that "should make any contemporary musician think differently about tuning" (Saturday Guardian). "
The tempering of perfect intervals did NOT have to be equal everywhere to achieve the goal of being able to play in all keys without retuning. There are many unequal temperaments that are distributed enough across the circle of fifths and are mild enough so that they achieve the same goal yet let keys be different i.e. keep different characters.
Lehman's one is one of them. The "refutation" (catchy title) you link to just says doodles could be just doodles on that manuscript title page (or it could after all be exactly what Lehman proposed they mean; as I said at the beginning of my post on this, we are not certain what Bach preferred and Lehman has not claimed otherwise), but it does not refute the fact that the temperament allows playing in all keys without retuning.
I totally disagree. Of course you can play in all keys with sh1t tuning, it doesn’t stop you. It allows you to instead develop a bias against certain intervals relative to others. This idea that EQ Temp ruined music, is a weird bias modern people have and then they want old music on some ****ty tuning just “because its not EQ temp”. The quote of BAch himself says it all (making fun of Silberman instruments)…you simply can’t play a single piece that moves into other keys without the “other key” being sour, unless you have it basically “equal” in someway. Splitting hairs about 5ths or 3rds etc, is simply deluding oneself that some key is meant to be “different” than another. I often talk about modal vs tonal. It is very simple….modal music sounds sweet because the tuning is mathematical (natural or Pythagorean) and not equal split by 12. Arguing about character of a key vs another is exactly that. The sweeter intervals that are closer to natures modality. Tonality (Bach Ab fugue) shows how it doesn’t work if you want modulations. All we are really arguing about other than that is how was Bach’s ear vs a computer? Did he lean more modal sweet or more computer perfectly non modal mathematically precisely out of tune everywhere? Where on that scale or spectrum he was and wanted to be. To me the anecdotes make it darn obvious he leans AWAY from the sweet modality, and this imposition of modern minds that somehow Bach would have leaned the other way makes no MUSICAL sense. I mean that “Beethoven Bminor sound black” subjective nonsense is pure subjectivity (and probably has more to do with the part of the brain where color association operates…to me A minor is blue, F#m gold etc). Then people that are anti Equal temp claim “why would Bach use different keys if they all sound the same”. Right there shows the ignorance. And the doodle pic….why his kids and students copied it “wrong” and dad never told them about it? It is really silly pseudo science.
This guy has it right IMO:
To summarize (it is long and he has an accent), he was part of the “lets play period music on period instruments with period tuning” crowd of recording nerds…a commercial movement by his account. Small niche. Along the way some Bach bothered him so he used ear to retune…gradually inching toward equal temp. Then he discovered what he did was Werkmeister. The direction thing here is obvious. Only thing is, I am thinking “duh”, but I learned this too thanks to my wrong neck I put on my electric …. I dealt with only playing in a few keys , and over compensate with fingers, with tears in the eyes until I gave in and got a new guitar . The reason people don’t understand is that Bach’s music was very advanced. I believed the myth too that “well tempered” did not mean equal. Thinking Bach’s Ab fugue was meant to be Ab because he chose special intervals that reinforce consonance over dissonance. Like the keyboard player in the video I realized after really looking deeper at Bach’s music, his reasons were the exact OPPOSITE concept…bring out all the sourness in order to force instrument makers to move toward equality. Develop an advanced music that forces the issue directly, head on. That was before I found the anecdotes that just make it way more obvious.
Unless you have absolute pitch, there is no difference between Am and F#m in equal temperament; in a proper blind experiment with electronically-generated sound where you are prevented from relying on temporary pitch memory, your colour assignment will be no better than chance.
In contrast, in the various unequal temperaments before equal temperament replaced them, people's historical references to colours or moods reflected real (objective) differences between keys - regardless of whether different people agreed on the same labels or not - the point is that different names did reflect real differences. So for Beethoven B minor was 'black' in whatever unequal temperament that was.
So yeah, people in general nowadays talking about different mood or colour or character for keys in equal temperament is silliness; not so for unequal temperament.
Nice discussion here, it really enlargens my horizon.
I haven't figured out how far this piece modulates, probably not too much.
To my ears it sounds "sweeter" in Werckmeister tuning, and in equal tuning somewhat dead, although the compositional idea is still transmitted. But how would it sound when transposed to other keys and played with the same Werckmeister tuning? Probably sweet might turn to sour.
Sorry for using so much non-contrapunctual adjectives, but they reflect some perceptive reality...
To my ears it sounds "sweeter" in Werckmeister tuning, and in equal tuning somewhat dead,
Right, I tried to address this earlier about the YouTube commenters. For me it is the exact opposite. You should Therefore think Katy Perry is “sweeter” without her Autotune. Me the opposite, she really needs it.
To Kitarist: You speak of my color association as if I don’t know what it is. I know exactly what it is and how it transfers too, pitch wise….it is something I developed as a kid learning GUITAR. When I use the capo the color association transfers. For example when I first heard Jucal by Nuñez, I heard it as “bronze” like open D tuning, exactly like Rondeña with drop D … only my ear recognized this jingling open strings up top like he dropped treble E to D as well…when I got my guitar and tried it (thinking Capo 2 exactly like Sanlucar’s buleria in Rondeña tuning), I quickly realized it was in E lydian standard tuning, and the whole “color” thing shifted in my brain to Black. Hilarious, but I am sure I am not alone in this thing.
But later in life (recently) I discovered a more realistic absolute sensation…the feeling of Vocal range. There is a thing humans have called “the break” and relative to this physical pitch zone, all pitches start to look absolute. I still think interms of a guitar and colors, however when I hear a computer generated pitch, I often check it with my voice and by the feeling of it, I instantly visualize the fretboard, string, and “color” and when I get a chance to check it I am really close or dead on in all cases. And after lots of practice I can come in singing a specific pitch by the feeling, without a reference. [try yourself, play a chord then sing a note in that chord…like throwing a dart, do you nail it? Or does your voice wander all over before settling on some pitch?] Of course this whole concept is about relative pitches and frequencies, I am no advocate for developing so called “perfect” pitch, and I dont’ even see the purpose (Dylan???!!!??).
So, most of these temperament things, and compositional techniques and choices from the earliest times, are constructed around the Human voice. Again, the chart of the piano adjustments has the flat line right in the 4th octave, which is where both the male and female vocal breaks lie. This is no “coincidence” IMO. Another point is the historical evidence that points to something like a half step lower was the standard note A assignment actually makes sense to me (the idea that today’s A=440 was about a G# back then and they called it A), because up at the 5th octave we feel a change of technique required to hit the pitch. For me the feeling is between Bb and B in reality and it would make sense that in the old days that “feeling” or physical sensation was no different so they assigned the octave break there (B4-C5) to mentally deal with that situation. As vocal techniques of Bel canto and such improved tenor voices in males especially, I can imagine the pitch started pushing upward gradually. But even still, I have seen some opera examples where, for the sake of the tenor, an entire aria is pitched lower deliberately. In modern rock, since Hendrix, and later Van Halen, Yngwie, etc, many guitar players tune to Eb…and often the excuse is that the singers feel more comfortable. I see it as a natural progression and mostly these things revolve around the voice. Seeing Ramon Montoya doing similar things (de tuning the guitar) on early recordings is not surprising.
Anyway back to the Lehman, again he plays Eb major sounds fine, then E major sour. (Your recent thing, the Bmajor toward the end 2:14 to 2:29 is atrocious to me, later E major section 7:08 compare to 8:35, horrible). There is no way Bach would want that. I state again, the pieces on well temp clavier don’t stick to their prescribed tonality…they ALL freakin MODULATE!!!!!! If he was sticking to some tonality in order to demonstrate a special TUNING, then the modulations would all sound intentionally “weird”. The point in EQUAL TEMPERMANT of modulation, is to show the RELATIONSHIPS between keys that we see on the circle of 5ths. If you only play in one key, that is modality essentially, and like Indian sruti you choose the best intervals (sweet ones) that bring out the BEST of the key. But you NEVER MODULATE…it is in fact stupid to do that. The concept of modulation is an intellectual exercise, it is a much more advances concept. THAT is what Bach is going for in ALL his keyboard pieces, but especially those. He wanted to exploit the relationships between the keys, not point out the “sweet n sour” between them. The argument people make that THAT is what he was trying to do makes no musical logical sense. If you watched the German guy above I posted he also talks about playing TECHNIQUE….this was something I never thought about as a guitar player, but makes even more sense. I had no idea BAch was also introducing new fingering technique but there is yet another reason to discard this ridiculous idea that “keys should have different characters relative to one another”.
EDIT: by the way Lehman keyboard doesn’t sound perfectly Equal tempered to me anyway…he might have it deliberately off. Compare to a piano and good player, which sounds sweeter to me than both examples:
To Kitarist: You speak of my color association as if I don’t know what it is.
Sorry; I didn't mean it like that. I was only answering in the context that you mentioned it which was:
"I mean that “Beethoven Bminor sound black” subjective nonsense is pure subjectivity (and probably has more to do with the part of the brain where color association operates…to me A minor is blue, F#m gold etc). "
So to me it was a general, not personal, argument about key character/colour/mood associations in equal vs. unequal temperament; I intended my response to be seen in that context.
In your specific case, to me you definitely have some form of semi-absolute pitch and also chromesthesia; or at the very least pitch memory for a reference pitch (e.g. the pitch the passaggio is at) and able to work it out quickly from there.
Another point is the historical evidence that points to something like a half step lower was the standard note A assignment actually makes sense to me (the idea that today’s A=440 was about a G# back then and they called it A), because up at the 5th octave we feel a change of technique required to hit the pitch. For me the feeling is between Bb and B in reality and it would make sense that in the old days that “feeling” or physical sensation was no different so they assigned the octave break there (B4-C5) to mentally deal with that situation. As vocal techniques of Bel canto and such improved tenor voices in males especially, I can imagine the pitch started pushing upward gradually.
I wanted to comment on this as I'd looked into it relatively recently in detail. The causal link for the pitch drift was the opposite actually - the general rising of reference pitch (but it was all over as noted below) was to do with orchestras trying to sound more 'brilliant' and 'sparkling', and periodically the reference will get lowered again as the singers complained that it is getting too high and straining theirs singing.
I will paste what I wrote from another post in the foro from 2020 from page 3 of this thread : A-440 vs 432 Hz??
"As a quick summary, A varied from 374 to 567 Hz (!!) over the 14th to 17th century. Then the range got narrower but still significant, 377-423, in the 18th century.
"Then, "During the nineteenth century the range was from about 424 to 494, a progressive rise being evident up to about 1887, reflecting no doubt, as always, a striving for increased brilliancy." And pitch generally got brought down occasionally because singers would complain that they cannot hit the notes anymore.
"In the late 19th century and early 20th century the reference pitch range narrowed again, to about 435-443 Hz. Finally the 1939 conference adopted 440 internationally as shown above.
"There are some papers from the 1880s that I am quoting from which contain long tables documenting tuning forks' actual pitches by year and location (which is where the numbers in the summary above are from) and a detailed discussion of factors that went into creating such a variability. "
(Your recent thing, the Bmajor toward the end 2:14 to 2:29 is atrocious to me, later E major section 7:08 compare to 8:35, horrible)
Interesting. The first one sounds fine to me ether way; the second one "E major section 7:08 compare to 8:35" it is the equal temp (8:35) that sounds really weird to me.
Here's another example (all in Lehman's temp.) which is an excerpt from "Ariadne musica" (1702/15) by JKF Fischer which is "20 preludes and fugues in 19 different keys, plus five ricercars based on chorales. As a whole, "Ariadne musica" calls for 19 different notes...and obviously the instrument is not to be retuned between these one-minute pieces!"
Also apparently " "Ariadne musica" itself was an inspiration for Bach to write his own books, going further to use all 24 keys. Bach also borrowed Fischer's F major fugue subject for his own similar F major subject in book 1, and Fischer's E major fugue subject for his own in book 2's E major."
The ending chord of the first piece in E major sounded very odd yesterday to me on first listen as that G# (I think) is noticeably higher than equal temp. But then today I gave it two more listens and it just sounded more uplifting but not sour anymore. I think there is some adjustment needed or happening when switching temperaments to make more stable judgments. However, for someone like you who is extremely sensitive to equal temperament, it would probably never lose its 'sourness'. Curious to hear how you perceive this (not just the first piece) in any case:
EDIT: by the way Lehman keyboard doesn’t sound perfectly Equal tempered to me anyway…he might have it deliberately off.
Yikes, deliberate manipulation would be very unethical and probably grounds for losing his job, so I doubt it. Maybe it's the harpsichord timbre which is kind of penetrating and harsher than that of a piano.
Curious to hear how you perceive this (not just the first piece) in any case:
The organ sustains with no vibrato, so any non-natural modal notes will beat noticeably and countably. I am sure, whoever tuned the thing actually wants those ridiculous countable beats. It is why those old organs had extra keys to avoid those clashes. Pianos and guitars don’t sustain those, but a singer will to vibrato anyway (always sharp of target, if they were trained). So with all that in mind, I went back through the examples and just stuck my snark contact tuner to my IPad. As you can imagine it jumped around a lot, however in Lehman “equal temp” some target notes were flat and some sharp. HIs Bach tuning had several flat, but most hitting the equal temp line and holding (which, based on his method, only C should do that, so his ear is fixing some intervals closer to Equal temp IMO, and conversely his ear might be “fixing” notes in Equal temp, when they should mostly hit the center line if he used a tuner like mine.). Gould was mostly on the line as I suspected but in general sharp (rarely flat of center line. Could be when attacked notes go sharp? Or overtones are affecting the snark as your piano tuning chart shows). The organ piece was mostly equal temp with some B’s coming in flat. (The Harpsichord, again had more flat notes registering.). Anyway a fun game you can try with your own tuner. Perhaps if I used a speaker system to check I get different results?
For fun I tuned my conde A26 (yes it is a bit compensated, 664 scale), after checking A open, to harmonics as prescribed (believed to be 2 cents off and additive) and all the strings hit the center line except G was flickering low. So I started playing and thinking the snark would behave similar to one of the above examples and ironically the thing stays put on the center line!!! . That means Conde is more equal tempered across the scale than any of those above keyboard! (In reality it is probably the overtones, which on a conde are almost non existent, as it is dry as a bone puro). Probably the clavichord, being so flat and dry, was Bach’s got to instrument for the same reason…it was like a conde.