While I appreciate Dennis Johnson's attention to detail, I have to disagree with his statement "there is no way you will get anything close to the original temperament using numbers rounded off to the nearest whole cent." The differences a between the rounded numbers and those taken to two decimal points are in the range of 0.04¢ to 0.2¢. Next to nobody tunes to that degree of accuracy, and I would argue that absolutely nobody would be able to hear the difference. And the "original temperament" was, like ET, an aspiration accomplished by real, fallible humans using human methods.
Vallotti's temperament was set out originally as two sets of six 5ths each. One set, the rising fifths between F and B (FC, CG, GD, DA, AE, EB) were to be tuned narrow by 1/6 comma. The other set, those that include a sharp or flat, were all to be tuned just.
The M3s resulting from (contained within) the first set of fifths are FA, CE, and GB, all of which are as half as wide as ET M3s. Those resulting from the second set are BD#, F#A#, and C#F, and they are what is commonly called "Pythagorean 5ths," 1.5 times as wide as ET M3s. The remaining M3s consist of pairs between those two sizes, symmetrically arranged within the circle of 5ths. The sound is quite distinctive: play chromatic M3s or chords, and you instantly recognize the big difference between C and C#, F and F#, G and G#. The other differences are a good bit milder.
If you get into the weeds and go back to what Vallotti wrote, originally comma he was referring to was the "syntonic" one, the difference between and just M3 and a Pythagorean one, approximately 21.5¢. When Vallotti shared his pattern with a colleague, the colleague pointed out that the numbers didn't add up. He needed to be using the Pythagorean comma, which is about 23.5¢. Vallotti's response was to make one of the just fifths (I forget which one) narrow by about 2¢. (They related all this mathematical discussion in fractions/proportions, where the syntonic comma is 81/80).
All modern methods that I have heard about use 1/16 Pythagorean comma for the narrowed 5ths. 1/6 syntonic 5ths are 3.6¢ narrow, while 1/6 Pythagorean 5ths are 3.9¢ narrow.
Historically, tuning was done in a circle of 5ths. 1/6 syntonic comma meantone was a common tuning in Vallotti's Italy, so the sound of 5ths about that narrow would be commonly recognized, as would the sound of just 5ths. As to how precisely musicians tuned their 1/6 comma 5ths, one can only speculate since they had nothing concrete to use to test that precise degree of narrowing. One thing is crystal clear: they didn't use tables of beat rates. Although they had the math to calculate such things, pitch varied too much to make that calculation worthwhile. In particular, there were two standard pitches in most parts of Europe: "chorton" and "Kammerton," a major second apart. You needed to adapt to the pitch of the instruments you were playing with.
Just a wee bit of historical background for those who might be interested.
------------------------------
Fred Sturm
University of New Mexico
fssturm@unm.eduhttp://fredsturm.nethttp://www.artoftuning.com"We either make ourselves happy or miserable. The amount of work is the same." - Carlos Casteneda
------------------------------
Original Message:
Sent: 04-22-2023 21:09
From: Thomas Servinsky
Subject: Vallotti temperament
Well,I thoroughly understand the Vallotti temperament. I had to do 3 tunings throughout the day for this high level performance on a wonderful harpsichord . What a lovely way to spend the day. Now I have a new temperament to add to my bag of tricks.
Tom Servinsky
Registered Piano Technician
Concert Artist Piano Technician
Director/Conductor- Academy Orchestra
Assist. Conductor-Treasure Coast Youth Symphony
Clarinetist-Atlantic Classical Orchestra
772 221 1011 office
772 260 7110 cell
Original Message:
Sent: 4/22/2023 4:32:00 PM
From: Ed Sutton
Subject: RE: Vallotti temperament
Tom-
Tuning Vallotti at A415 indicates you are tuning a harpsichord.
Inharmonicity will not be an issue. Use the simple offsets and be happy.
Play around the circle of fifths from C around and back to C.
You will hear the pattern of thirds widening and narrowing.
That's it.
------------------------------
Ed Sutton
ed440@me.com
(980) 254-7413
Original Message:
Sent: 04-22-2023 09:26
From: Thomas Servinsky
Subject: Vallotti temperament
Thanks for that. I've been hired for a major concert today and the ensemble is requesting the Vallotti temperament at A415, so I'm just following their instructions. And no, I don't use a Cybertuner.
Tom Servinsky
Registered Piano Technician
Concert Artist Piano Technician
Director/Conductor- Academy Orchestra
Managing Conductor-Treasure Coast Youth Symphony
Keyboardist- Beatles Re-Imagined
Pianist with TLC Jazz Duo
tompiano@tomservinsky.com
772 221 1011 office
772 260 7110 cell
Original Message:
Sent: 4/22/2023 9:21:00 AM
From: Dennis Johnson
Subject: RE: Vallotti temperament
Tom-
If you use Cybertuner there are more accurate numbers for Vallotti in the Jorgenson library. I would probably recommend considering the Vallotti/Young as a bit milder, depending on the instrument, but there is no way you will get anything close to the original temperament using numbers rounded off to the nearest whole cent. That will not work and is one reason for so much confusion regarding the data gathered from Ellis' recordings of Broadwood tuners. I copied those numbers out to the nearest hundredth below. Hope that helps.
Best,
Dennis Johnson
A. 0.0
A#. 5.87
B. -3.91
C. 5.87
C#. 0.0
D. 1.96
D#. 3.91
E. -1.96
F. 7.82
F#. -1.96
G. 3.91
G#. 1.96
A. 0.0
Original Message:
Sent: 4/21/2023 8:41:00 PM
From: Thomas Servinsky
Subject: RE: Vallotti temperament
Dear List
Thanks to all that were Johnny on the spot in providing me with this temperament information.
What a great resource we have!
Tom Servinsky
Registered Piano Technician
Concert Artist Piano Technician
Director/Conductor- Academy Orchestra
Managing Conductor-Treasure Coast Youth Symphony
Keyboardist- Beatles Re-Imagined
Pianist with TLC Jazz Duo
tompiano@tomservinsky.com
772 221 1011 office
772 260 7110 cell
Original Message:
Sent: 4/21/2023 9:11:00 AM
From: Fred Sturm
Subject: RE: Vallotti temperament
Rounded numbers:
C: 6
C#: 0
D: 2
Eb: 4
E: -2
F: 8
F#: -2
G: 4
Ab: 2
A: 0
Bb: 6
B: -4
Original Message:
Sent: 4/21/2023 5:33:00 AM
From: Thomas Servinsky
Subject: Vallotti temperament
Dear List
Could someone provide me with the Vallotti temperament offsets ASAP. Thanks in advance.
Tom Servinsky
Registered Piano Technician
Concert Artist Piano Technician
Director/Conductor- Academy Orchestra
Managing Conductor-Treasure Coast Youth Symphony
Keyboardist- Beatles Re-Imagined
Pianist with TLC Jazz Duo
tompiano@tomservinsky.com
772 221 1011 office
772 260 7110 cell