Benjamin,
I am not aware of a way to apply the tuning of the family of equal temperaments directly to the SAT.
However, we are a resourceful bunch, and perhaps someone will come up with a way of tuning the widths of ET with the SAT.
As to your question about cents, keep in mind that these numbers represent zero inharmonicity, and so the half-step numbers make no allowance for the half-steps of pianos that are enlarged by inharmonicity. The octave stretch numbers are more directly applicable, especially to the 4:2 octave.
Pure octave ET, 100 cents per half-step. Octaves tuned pure.
CHaS, (100.038 cents per half-step)
Octave expanded by 0.46 cents
Pure 26th ET, (100.046 cents per half-step)
Octave expanded by 0.55 cents
Pure 19th ET, (100.063 cents per half-step)
Octave expanded by 0.76 cents
Pure 12th ET, (100.103 cents per half-step)
Octave expanded by 1.23 cents
12-tone to the 2-cent-expanded octave, Rhodes factory stretch, (100.167 cents per half-step)
Octave expanded by 2 cents
Pure 5th ET, (100.279 cents per half-step)
Octave expanded by 3.35 cents
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Kent Swafford
Lenexa KS
913-631-8227
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Original Message:
Sent: 07-12-2017 13:28
From: Benjamin Sanchez
Subject: 21st Century Tuning Style
Hello Kent,
I read your article and liked the concept. But I had a few questions.
If I understand your arguments correctly, then the main difference between different styles of equal temperament are the amounts that each is stretched i.e. Using 1.05949 as opposed to 1.05953 as the increasing factor between half steps.
Am I correct in think that this is a difference in stretch amounts?
Second, in terms of cents, what is the difference between the different styles (traditional pure octaves vs. pure twelveths?). The reason I ask is, I use a SAT, and would like to try and duplicate this style, but to do so I must know what the difference is in terms of cents.
I look forward to your response.
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Benjamin Sanchez
Professional Piano Services
(805)315-8050
www.professional-piano-services.com
BenPianoPro@comcast.net
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Original Message:
Sent: 06-30-2017 09:01
From: Kent Swafford
Subject: 21st Century Tuning Style
If you receive the Piano Technicians Journal, then I hope you will note the first article in my "21st Century Tuning Style" series. If you can attend the upcoming PTG convention in St. Louis I hope you will consider my class, also entitled "21st Century Tuning Style". The subjects include pure 12th equal temperament and other widths of Equal Temperament tuned uniformly across a piano's scale; integrating stretch and temperament; and a "new" approach to dealing with inharmonicity while tuning. OnlyPure and RCT can both tune a great pure 12th equal temperament. And if you are a user of Verituner, we will discuss the style files I have shared to allow Verituner users to tune various widths of ET!
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Kent Swafford
Lenexa KS
913-631-8227
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