Yes. It might balance this and that but what does it do to the experience of the music and then with and without stretching?
It's necessary to tune it and test it and do the experiments.
Writing or mathemetising about music is like dancing about architecture. It was probably someone here who quoted this and they are quite right.
Best wishes
David P
On Sunday, November 3, 2019, Roshan Kakiya via Piano Technicians Guild <
Mail@connectedcommunity.org> wrote:
David, Thomas Young's First Temperament (Young I) has symmetrical Major Thirds on either side of F# around the Circle of Fifths. This temperament...
Re: Circle of Fifths Conversion Formulas: P8fractions and P12fractions | | | David,
Thomas Young's First Temperament (Young I) has symmetrical Major Thirds on either side of F# around the Circle of Fifths. This temperament balances the tempering of the Major Thirds and the Fifths.
Pure 12th Equal Temperament causes the Fifth and the Octave to beat at the same rate. The Fifth and the Octave are tempered by the same amount in opposite directions. This temperament balances the tempering of the Fifths and the Octaves.
Roshan Kakiya's Stretched Young I completely preserves the symmetrical Major Thirds of Thomas Young's First Temperament and preserves to some extent the beat symmetry of the Fifth and the Octave in Pure 12th Equal Temperament. This temperament balances the tempering of the Major Thirds, the Fifths and the Octaves. This temperament combines the features of Thomas Young's First Temperament with the features of Pure 12th Equal Temperament.
------------------------------ Roshan Kakiya ------------------------------ | | Reply to Group Online View Thread Recommend Forward Mark as Inappropriate | ------------------------------
Original Message: Sent: 11-02-2019 20:30 | |
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Original Message------
Thomas Young's First Temperament has symmetrical Major Thirds on either side of F# around the Circle of Fifths. This temperament balances the tempering of the Major Thirds and the Fifths.
Pure 12th Equal Temperament causes the Fifth and the Octave to beat at the same rate. The Fifth and the Octave are tempered by the same amount in opposite directions. This temperament balances the tempering of the Fifths and the Octaves.
Roshan Kakiya's Stretched Young I preserves the symmetrical Major Thirds of Thomas Young's First Temperament and preserves the beat symmetry of the Fifth and the Octave in Pure 12th Equal Temperament. This temperament balances the tempering of the Major Thirds, the Fifths and the Octaves.
------------------------------
Roshan Kakiya
------------------------------
Original Message:
Sent: 11-02-2019 20:30
From: David Pinnegar
Subject: Circle of Fifths Conversion Formulas: P8fractions and P12fractions
: come through an exciting and exhausting week tuning for the Nice International Piano Competition. The Conservatoire wasn't available so we had to juggle between venues and this led me to different instruments, a Yamaha C7 for most of the week and today a Fazioli 280.
Whilst being with Roshan in the encouragement of exploration of unequal temperaments I'm less than enthusiastic about stretch and it was for that reason that I asked what musical consequence was the aim to which this mathematical work led.
Today's performers in Nice played concertos with full orchestra.
Not only did the piano sound different, more harmonious, and to the extent that a recording engineer heard the difference and wants me to tune for an upcoming disc, but time and time again the orchestra and the piano at both extremes came in and interwove at the same pitch. A viola player in particular noticed and bothered to ask me questions.
Last night I was asked to tune an upright outside of anything to do with the competition. To my chagri it hadn't been tuned for 20 years and was at 425. I took it up to 440 using a procedure based on Michael Gamble's techniques and think the result will be stable. It was four hours of battle and I charged double. The result was an instrument that sounded like a Steinway.
Effectively I'm tuning the piano as an organ. So the other day in the "Beginners'" class - although at the age of one winner 8 and an 11 year old, both achieving joint first award these children far outpassed anything I've heard before . . . an 8 year old lad played Bach. It was so superb, so musical that I knew he was up to the experiment. So I took him back in to shock the Jury.
In my opinion most fashionable playing of Bach on the piano is atrocious and unmusical. Because of the resonance my tuning achieves and because I'm reducing the total modes of vibration in which the whole instrument can work the sustaining pedal can be held down for lengths undreamed of in modern times, but as specified by both Chopin and by Beethoven. So I took the lad back in upon the stage and got him to play his Bach as if the instrument were the organ in a cathedral. The experiment had worked and had taught the Jury a bit about music, sound and composers. There had been some dispute on the Jury as to who to place in which position and my experiment with the lad affirmed those who had vouched for him in their deliberation. When all returned back into the room he performed and everyone was dumbfounded.
The result was a revelation. The President of the Jury on the day with the boy playing Bach hadn't voted for him, wanting another in his place but was outvoted. After the organ in the cathedral experiment, her face lit up and she came over and kissed me, as is the French manner.
I will be putting recordings onto YouTube in due course, although with many hours recorded it will take some time.
So my objectives in my tunings are:
1. To restore differences in sound between keys, that we can actually hear, even measure, to increase the purity of home keys and not cause unpleasantness in wide thirds
2. To improve the sound of the instrument
- a. to bring it resonance, aweetness and
- b. to increase its dynamic power and therefore dynamic range.
3. to reduce available total numbers of modes of vibration
- a. to reduce confusion of sound
- b. to re-enable original specified pedalling by Chopin and Beethoven.
4. To enable greater compatibility with instrumentalists and even full orchestra
and the results of the Nice International Concours de Piano have found all four objectives to have been achieved.
So what objectives do you, and anyone else, expect to achieve with your chosen stretching of the octaves?
Best wishes
David P
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David Pinnegar, B.Sc., A.R.C.S.
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+44 1342 850594
Original Message------
The solution in cents is as follows:Stack of 7 Octaves = Stack of 12 Fifths.
Octave = Stack of 12 Fifths / 7.
The total value of a stack of 12 Fifths can be calculated by adding the value of each Fifth.
The total value of a stack of 12 Fifths must be divided by 7 to calculate the value of 1 Octave.
Roshan Kakiya's Stretched Young I:Pythagorean Comma = 23.460 cents.
Pure Fifth narrowed by 2/19 Pythagorean Comma = 699.486 cents.
Pure Fifth narrowed by 1/19 Pythagorean Comma = 700.720 cents.
Pure Fifth = 701.955 cents.
Stack of 12 Fifths = 4 × 699.486 cents + 4 × 700.720 cents + 4 × 701.955 cents = 8408.644 cents.Octave = Stack of 12 Fifths / 7 = 8408.644 cents / 7 = 1201.235 cents.Conclusion:
A Circle of 12 Fifths is all that is required to calculate the value of the Octave.------------------------------
Roshan Kakiya
Original Message:
Sent: 10-31-2019 22:08
From: Anthony Willey
Subject: Circle of Fifths Conversion Formulas: P8fractions and P12fractions
Re: "
Don't think in terms of one octave"
OK, I don't have a problem with widening the octave and narrowing all the fifths slightly less as you described. But I still don't see how the unequal temperament proposed above with 12 fifths narrowed by 1/19 or 2/19 P.C. would work. The Pythagorean Comma of 23.46 cents needs to fit somehow inside an octave of 12 notes, not 19 notes. If we want to define a new "octave" of 19 notes and divide a comma into an unequal temperament, then that comma would need to be bigger (37.15 cents?), because we're not going around the circle of fifths a whole number of times in the new "octave". I think. I don't know. It's confusing. ------------------------------
Anthony Willey, RPT
http://willeypianotuning.comhttp://pianometer.comOriginal Message:
Sent: 10-31-2019 16:58
From: Kent Swafford
Subject: Circle of Fifths Conversion Formulas: P8fractions and P12fractions
"I think I'm getting lost here. The Pythagorean Comma is 23.46 cents, and that has to be spread throughout the octave somehow. Yes?
Perfect 12th temperament is something like 1.24 cents wider than pure octave temperament, so there's a little less comma to spread around. (23.46 - 1.24 = 22.22 cents)"
Don't think in terms of "one octave".
It is as if the _difference_ between the "height" of a stack of 7 pure octaves and the "height" of 12 pure fifths is 23.46 cents, the Pythagorean comma.
To resolve the difference in "height" between the two stacks one traditionally shortens the stack of 12 fifths to match the "height" of the octave stack.
23.46 cents divided by 12 is 1.955 cents, the traditional contraction of the fifth in pure octave ET. Contract each 5th by 1.955 cents and the two stacks of intervals are equalized.
But there are other possible solutions. One could both shorten the stack of fifths _and_ make the octave stack higher. And it is entirely possible to contract each 5th and expand each octave by the same amount to accomplish this equalization of stacks.
There are 19 intervals in the two stacks, 7 octaves and 12 5ths.
23.48 cents / 19 = 1.2358 cents
So, if the stack of 7 octaves was made higher by expanding each octave 1.24 cents, and the stack of 12 5ths is made shorter by contracting each 5th by the same 1.24 cents, then the stacks are equalized. This is the solution used by pure 12th ET.
Unequal temperaments will have various "solutions", but in any event the two stacks must be equalized, one way or another.
Original Message------
The P8 example made twelve 5ths. P12 similarly makes nineteen 5ths. Two additional 5ths narrowed by 2/19 Pythagorean comma and three 5ths narrowed by 1/19 of the comma makes the difference. ( with two more "pure" 5ths)