Good question about a circular diagram, showing comma fractions. There is one on my web site (larips): click on the small version of it, or on the word "diagram", to bring up a page with those details and a bigger copy of that diagram.
For the regular 1/6 comma layout used in the first half of this video, it's -1/6 all the way around the diagram...except for the leftover Eb-G# wolf, which is much wider than a pure 5th.
For the modified version in the second half, the B-F#, F#-C#, and C#-G# all change to 0. All of Ab-Eb, Eb-Bb, and Bb-F are also close to 0, but one or two of those are the slightest touch wide, to taste. It's done by listening experience, not by mathematical calculations.
Can you please elucidate what you mean by "stays out of tune" in that comment? It's carefully IN tune here, in an unequal temperament that offers different advantages! Most notably, there is stronger resonance in the most commonly used major/minor triads and 7th-chords. Equal doesn't do that....
Dr; Would you please clarify this in terms of a circle of 5ths. Fractions of a comma or something. I find that tuning lines are difficult. Please take into account that I am a novice. The circle is easier for me to understand. Your Bach tuning, when circled, makes sense to me.
Brad Lehman here goes a small part of the way from equal temperament towards meantone, but nowhere near far enough to make much difference. Already, in the first steps of the tuning, you can hear he makes the thirds more out of tune than the other intervals. (Actually, most 17th century tuning instructions say to make the thirds as pure as possible.) And the final steps in the tuning bring it even closer to equal, further washing out any contrasts between different intervals and keys.
Lindley's article "Temperaments" in New Grove asserts that the most common 17th century tuning manner was probably closer to 1/5 comma (i.e. with somewhat sharp thirds) than to 1/4. If you'd like to disagree with that, build a case. It's a basis of approximately 1/5 comma naturals being demonstrated here.
It's also important to spend several months, each, playing in regular 1/5 and 1/6 comma...and not only 1/4 comma. All have different advantages, musically. I spent more than 15 years playing in 1/4 most of the time (whether modified or not), but now I prefer a 1/6 or 1/5 basis for 17th century rep. The pure tritones of 1/6 are especially alluring.
Dr; What are your thoughts about 1/3 comma well on a piano. I believe Owen referred to it as a Salinas. It seems very symmetric to me as a whole. The common keys are stark and the others are vibrant. It is easy to set up and plays the crowd excellent on pieces they normally hear.
So far as you can hear the instrument (I won't say more about the audio quality), this sounds okay.
But it could, and should, sound much better - purer, more sonorous, much more full of colour and contrast.
The point is the difference between modern equal temperament (regular piano tuning) where all the thirds are very impure; - and historical meantone-based tuning, where most of the thirds in use were purely tuned, or very nearly so. This was used in England until the early 19th century.
It does sound "much better" live, with this harpsichord and others, than any cheap videocam (and free production software, and zero video budget) can convey. "The point" is: this is free DIY instruction for open-eared musicians to learn how to do this by ear on acoustic instruments, and to spend weeks/months playing real music in it to get the feel of its operation.
Dude, Man! This is borrrrrrrrrrring! You need to get some KUSH! yeahhhhhh!
InTootingBec 3 years ago
Good question about a circular diagram, showing comma fractions. There is one on my web site (larips): click on the small version of it, or on the word "diagram", to bring up a page with those details and a bigger copy of that diagram.
thebpl 3 years ago
For the regular 1/6 comma layout used in the first half of this video, it's -1/6 all the way around the diagram...except for the leftover Eb-G# wolf, which is much wider than a pure 5th.
For the modified version in the second half, the B-F#, F#-C#, and C#-G# all change to 0. All of Ab-Eb, Eb-Bb, and Bb-F are also close to 0, but one or two of those are the slightest touch wide, to taste. It's done by listening experience, not by mathematical calculations.
thebpl 3 years ago
Ω, τοιουτος 'ηβρις!
dolofonos 3 years ago
Very interesting. Thanks for posting it.
alkanista 4 years ago
no...
greeentaxi 4 years ago
The only problem you have is your instrument stays out of tune,.
AlsatianCousin 4 years ago
Can you please elucidate what you mean by "stays out of tune" in that comment? It's carefully IN tune here, in an unequal temperament that offers different advantages! Most notably, there is stronger resonance in the most commonly used major/minor triads and 7th-chords. Equal doesn't do that....
thebpl 4 years ago
Dr; Would you please clarify this in terms of a circle of 5ths. Fractions of a comma or something. I find that tuning lines are difficult. Please take into account that I am a novice. The circle is easier for me to understand. Your Bach tuning, when circled, makes sense to me.
chewreece 3 years ago
Brad Lehman here goes a small part of the way from equal temperament towards meantone, but nowhere near far enough to make much difference. Already, in the first steps of the tuning, you can hear he makes the thirds more out of tune than the other intervals. (Actually, most 17th century tuning instructions say to make the thirds as pure as possible.) And the final steps in the tuning bring it even closer to equal, further washing out any contrasts between different intervals and keys.
stringph 4 years ago
Lindley's article "Temperaments" in New Grove asserts that the most common 17th century tuning manner was probably closer to 1/5 comma (i.e. with somewhat sharp thirds) than to 1/4. If you'd like to disagree with that, build a case. It's a basis of approximately 1/5 comma naturals being demonstrated here.
thebpl 4 years ago
It's also important to spend several months, each, playing in regular 1/5 and 1/6 comma...and not only 1/4 comma. All have different advantages, musically. I spent more than 15 years playing in 1/4 most of the time (whether modified or not), but now I prefer a 1/6 or 1/5 basis for 17th century rep. The pure tritones of 1/6 are especially alluring.
thebpl 4 years ago
Dr; What are your thoughts about 1/3 comma well on a piano. I believe Owen referred to it as a Salinas. It seems very symmetric to me as a whole. The common keys are stark and the others are vibrant. It is easy to set up and plays the crowd excellent on pieces they normally hear.
chewreece 3 years ago
So far as you can hear the instrument (I won't say more about the audio quality), this sounds okay.
But it could, and should, sound much better - purer, more sonorous, much more full of colour and contrast.
The point is the difference between modern equal temperament (regular piano tuning) where all the thirds are very impure; - and historical meantone-based tuning, where most of the thirds in use were purely tuned, or very nearly so. This was used in England until the early 19th century.
stringph 4 years ago
It does sound "much better" live, with this harpsichord and others, than any cheap videocam (and free production software, and zero video budget) can convey. "The point" is: this is free DIY instruction for open-eared musicians to learn how to do this by ear on acoustic instruments, and to spend weeks/months playing real music in it to get the feel of its operation.
thebpl 4 years ago