Harpsichord tuning demonstration: in late 17th century style, useful into the early 18th century as well.
A regular system ("meantone") is set up first, with approximately 1/5th to 1/6th comma tem...
Harpsichord tuning demonstration: in late 17th century style, useful into the early 18th century as well.
A regular system ("meantone") is set up first, with approximately 1/5th to 1/6th comma tempering...i.e. with all the major 3rds slightly wider than pure, and all the 5ths slightly narrow. The whole line of notes is: Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#.
Then, to make the instrument more playable in keys of two or more sharps/flats, a simple modification is made to the several notes at each end of the sequence. The sharps are each raised in pitch, and the flats are each lowered, until they roughly meet one another (and can therefore be respelled as one another in music).
Two short pieces by Henry Purcell demonstrate the flexibility and color of this tuning: a Saraband in G minor, and a Hornpipe in D major.
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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.
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.
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.
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.
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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.