Pianotech

Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Cents

C	0.00
C#	91.45
D	193.16
D#	294.87
E	386.31
F	498.29
F#	589.74
G	696.58
G#	793.16
A	889.74
A#	996.58
B	1088.02
C	1200.00

Offsets in Cents from Pure Octave Equal Temperament

C	0.00
C#	−8.55
D	−6.84
D#	−5.13
E	−13.69
F	−1.71
F#	−10.26
G	−3.42
G#	−6.84
A	−10.26
A#	−3.42
B	−11.98
C	0.00

Frequencies in Hz

A0	27.50
A#0	29.25
B0	30.84
C1	32.90
C#1	34.68
D1	36.78
D#1	39.01
E1	41.12
F1	43.87
F#1	46.25
G1	49.19
G#1	52.02
A1	55.00
A#1	58.50
B1	61.67
C2	65.80
C#2	69.36
D2	73.56
D#2	78.01
E2	82.24
F2	87.74
F#2	92.50
G2	98.39
G#2	104.03
A2	110.00
A#2	117.00
B2	123.35
C3	131.59
C#3	138.73
D3	147.12
D#3	156.03
E3	164.49
F3	175.48
F#3	185.00
G3	196.77
G#3	208.06
A3	220.00
A#3	234.01
B3	246.70
C4	263.18
C#4	277.46
D4	294.25
D#4	312.05
E4	328.98
F4	350.96
F#4	369.99
G4	393.55
G#4	416.13
A4	440.00
A#4	468.01
B4	493.40
C5	526.36
C#5	554.91
D5	588.49
D#5	624.10
E5	657.95
F5	701.92
F#5	739.99
G5	787.10
G#5	832.25
A5	880.00
A#5	936.02
B5	986.79
C6	1052.73
C#6	1109.83
D6	1176.98
D#6	1248.20
E6	1315.91
F6	1403.83
F#6	1479.98
G6	1574.19
G#6	1664.51
A6	1760.00
A#6	1872.04
B6	1973.58
C7	2105.45
C#7	2219.65
D7	2353.97
D#7	2496.41
E7	2631.81
F7	2807.66
F#7	2959.96
G7	3148.38
G#7	3329.01
A7	3520.00
A#7	3744.08
B7	3947.16
C8	4210.90

Features and Modifications

Pure Major Third: C-E.

Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.

Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.


The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya
------------------------------

Thanks, I'll compare this to Anthony Willey's offsets on Piano Meter.....
I may have to adjust some due to inharmonicity, depending on the piano.

I'm not sure how strict David Winnegar is when he render's his tuning.
I do believe he's using an electric tuner to set temperment, but not
sure if his device allows for pure octaves in the central 3 octaves.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------

Original Message:
Sent: 09-13-2019 12:25
From: Roshan Kakiya
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Cents

C	0.00
C#	91.45
D	193.16
D#	294.87
E	386.31
F	498.29
F#	589.74
G	696.58
G#	793.16
A	889.74
A#	996.58
B	1088.02
C	1200.00

Offsets in Cents from Pure Octave Equal Temperament

C	0.00
C#	−8.55
D	−6.84
D#	−5.13
E	−13.69
F	−1.71
F#	−10.26
G	−3.42
G#	−6.84
A	−10.26
A#	−3.42
B	−11.98
C	0.00

Frequencies in Hz

A0	27.50
A#0	29.25
B0	30.84
C1	32.90
C#1	34.68
D1	36.78
D#1	39.01
E1	41.12
F1	43.87
F#1	46.25
G1	49.19
G#1	52.02
A1	55.00
A#1	58.50
B1	61.67
C2	65.80
C#2	69.36
D2	73.56
D#2	78.01
E2	82.24
F2	87.74
F#2	92.50
G2	98.39
G#2	104.03
A2	110.00
A#2	117.00
B2	123.35
C3	131.59
C#3	138.73
D3	147.12
D#3	156.03
E3	164.49
F3	175.48
F#3	185.00
G3	196.77
G#3	208.06
A3	220.00
A#3	234.01
B3	246.70
C4	263.18
C#4	277.46
D4	294.25
D#4	312.05
E4	328.98
F4	350.96
F#4	369.99
G4	393.55
G#4	416.13
A4	440.00
A#4	468.01
B4	493.40
C5	526.36
C#5	554.91
D5	588.49
D#5	624.10
E5	657.95
F5	701.92
F#5	739.99
G5	787.10
G#5	832.25
A5	880.00
A#5	936.02
B5	986.79
C6	1052.73
C#6	1109.83
D6	1176.98
D#6	1248.20
E6	1315.91
F6	1403.83
F#6	1479.98
G6	1574.19
G#6	1664.51
A6	1760.00
A#6	1872.04
B6	1973.58
C7	2105.45
C#7	2219.65
D7	2353.97
D#7	2496.41
E7	2631.81
F7	2807.66
F#7	2959.96
G7	3148.38
G#7	3329.01
A7	3520.00
A#7	3744.08
B7	3947.16
C8	4210.90

Features and Modifications

Pure Major Third: C-E.

Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.

Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.


The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each Fifth is a Pure Fifth reduced by 1/4 Syntonic comma. C-E is a Pure Major Third in this Modified Kirnberger III and in Kirnberger III.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each Fifth is a Pure Fifth reduced by 1/8 Schisma.

------------------------------
Roshan Kakiya
------------------------------

David, please excuse the typo (just woke up)... that should have read David Pinnegar!...sorry....

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------

Original Message:
Sent: 09-13-2019 13:04
From: Richard Adkins
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Thanks, I'll compare this to Anthony Willey's offsets on Piano Meter.....
I may have to adjust some due to inharmonicity, depending on the piano.

I'm not sure how strict David Winnegar is when he render's his tuning.
I do believe he's using an electric tuner to set temperment, but not
sure if his device allows for pure octaves in the central 3 octaves.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA

Original Message:
Sent: 09-13-2019 12:25
From: Roshan Kakiya
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Cents

C	0.00
C#	91.45
D	193.16
D#	294.87
E	386.31
F	498.29
F#	589.74
G	696.58
G#	793.16
A	889.74
A#	996.58
B	1088.02
C	1200.00

Offsets in Cents from Pure Octave Equal Temperament

C	0.00
C#	−8.55
D	−6.84
D#	−5.13
E	−13.69
F	−1.71
F#	−10.26
G	−3.42
G#	−6.84
A	−10.26
A#	−3.42
B	−11.98
C	0.00

Frequencies in Hz

A0	27.50
A#0	29.25
B0	30.84
C1	32.90
C#1	34.68
D1	36.78
D#1	39.01
E1	41.12
F1	43.87
F#1	46.25
G1	49.19
G#1	52.02
A1	55.00
A#1	58.50
B1	61.67
C2	65.80
C#2	69.36
D2	73.56
D#2	78.01
E2	82.24
F2	87.74
F#2	92.50
G2	98.39
G#2	104.03
A2	110.00
A#2	117.00
B2	123.35
C3	131.59
C#3	138.73
D3	147.12
D#3	156.03
E3	164.49
F3	175.48
F#3	185.00
G3	196.77
G#3	208.06
A3	220.00
A#3	234.01
B3	246.70
C4	263.18
C#4	277.46
D4	294.25
D#4	312.05
E4	328.98
F4	350.96
F#4	369.99
G4	393.55
G#4	416.13
A4	440.00
A#4	468.01
B4	493.40
C5	526.36
C#5	554.91
D5	588.49
D#5	624.10
E5	657.95
F5	701.92
F#5	739.99
G5	787.10
G#5	832.25
A5	880.00
A#5	936.02
B5	986.79
C6	1052.73
C#6	1109.83
D6	1176.98
D#6	1248.20
E6	1315.91
F6	1403.83
F#6	1479.98
G6	1574.19
G#6	1664.51
A6	1760.00
A#6	1872.04
B6	1973.58
C7	2105.45
C#7	2219.65
D7	2353.97
D#7	2496.41
E7	2631.81
F7	2807.66
F#7	2959.96
G7	3148.38
G#7	3329.01
A7	3520.00
A#7	3744.08
B7	3947.16
C8	4210.90

Features and Modifications

Pure Major Third: C-E.

Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.

Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.


The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each Fifth is a Pure Fifth reduced by 1/4 Syntonic comma. C-E is a Pure Major Third in this Modified Kirnberger III and in Kirnberger III.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each Fifth is a Pure Fifth reduced by 1/8 Schisma.

------------------------------
Roshan Kakiya
------------------------------

Original Message------

Thanks, I'll compare this to Anthony Willey's offsets on Piano Meter.....
I may have to adjust some due to inharmonicity, depending on the piano.

I'm not sure how strict David Winnegar is when he render's his tuning.
I do believe he's using an electric tuner to set temperment, but not
sure if his device allows for pure octaves in the central 3 octaves.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------

David,

"By the way Roshan - what's the point of your modification?"

My modification achieves equal division of the Syntonic comma and equal division of the Schisma.

The benefits of this approach are as follows:

The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 09-13-2019 13:21
From: David Pinnegar
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Yes - if tuning Kirnberger III pure octaves in the central section is vital. Chopin's Raindrop Prelude is the acid test as to whether it's too strong.

Kirnberger III is ideally suited for Mozart in particular. I have used it for Beethoven and other things but in particular on an 1859 Broadwood with a particular harmonic structure that favours the 3rd harmonic with virtually no 5th harmonic in the sound at all. You'll probably find recordings on YouTube if you look up 1859 Broadwood.

I tuned a 1905 Baby Grand Broadwood to it as an experiment for a concert with standard stretch - it was fine but au point. No stretch in the temperament octaves would have been better.

By the way Roshan - what's the point of your modification? 

Really with the way in which pianos go out of tune in time tuning isn't as precise a science as decimal points might indicate. The importance of Kirnberger or Kellner are the very pleasant smooth thirds in F C and G and their contrast in modulation which gives a feeling of movement in the music. This effect is achieved even if tuning has degraded so whilst it's nice to be spot on, obsessive attention to detail isn't musically vital at all.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Thanks, I'll compare this to Anthony Willey's offsets on Piano Meter.....
I may have to adjust some due to inharmonicity, depending on the piano.

I'm not sure how strict David Winnegar is when he render's his tuning.
I do believe he's using an electric tuner to set temperment, but not
sure if his device allows for pure octaves in the central 3 octaves.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------

Original Message------

David,

"By the way Roshan - what's the point of your modification?"

My modification achieves equal division of the Syntonic comma and equal division of the Schisma.

The benefits of this approach are as follows:

The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 09-13-2019 13:21
From: David Pinnegar
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Yes - if tuning Kirnberger III pure octaves in the central section is vital. Chopin's Raindrop Prelude is the acid test as to whether it's too strong.

Kirnberger III is ideally suited for Mozart in particular. I have used it for Beethoven and other things but in particular on an 1859 Broadwood with a particular harmonic structure that favours the 3rd harmonic with virtually no 5th harmonic in the sound at all. You'll probably find recordings on YouTube if you look up 1859 Broadwood.

I tuned a 1905 Baby Grand Broadwood to it as an experiment for a concert with standard stretch - it was fine but au point. No stretch in the temperament octaves would have been better.

By the way Roshan - what's the point of your modification? 

Really with the way in which pianos go out of tune in time tuning isn't as precise a science as decimal points might indicate. The importance of Kirnberger or Kellner are the very pleasant smooth thirds in F C and G and their contrast in modulation which gives a feeling of movement in the music. This effect is achieved even if tuning has degraded so whilst it's nice to be spot on, obsessive attention to detail isn't musically vital at all.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Thanks, I'll compare this to Anthony Willey's offsets on Piano Meter.....
I may have to adjust some due to inharmonicity, depending on the piano.

I'm not sure how strict David Winnegar is when he render's his tuning.
I do believe he's using an electric tuner to set temperment, but not
sure if his device allows for pure octaves in the central 3 octaves.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------

David,

"Hmmm... I thought in Kirnberger C-E was a pure major third in the first place?"

I have preserved C-E, the Pure Major Third, in the modified version of Kirnberger III. I have only altered the way in which the Schisma is distributed.


"With due respect I do wonder if you're spending a lot of effort in splitting hairs".

Practical temperaments are constructed by distributing commas ('splitting hairs'). This process is an essential part of the production of practical temperaments. Practical temperaments are temperaments that do not contain severely out of tune wolf intervals.

The ways in which commas could be distributed should be considered because there are many ways in which commas could be distributed.


"Young might well be the Passanda."

Young's temperament is beautiful:

http://rollingball.com/images/Young.gif

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 09-13-2019 17:04
From: David Pinnegar
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Hmmm... I thought in Kirnberger C-E was a pure major third in the first place?

With due respect I do wonder if you're spending a lot of effort in splitting hairs which in practice are inaudible or untunable and, if you make any more thirds purer you'll start to exaggerate the wider ones.

Kirnberger III is on the edge of the precipice of general usability. It's a Vindaloo rather than a Jalfresi or a Balti. Young might well be the Passanda.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

David,

"By the way Roshan - what's the point of your modification?"

My modification achieves equal division of the Syntonic comma and equal division of the Schisma.

The benefits of this approach are as follows:

The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya

Original Message:
Sent: 09-13-2019 13:21
From: David Pinnegar
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Yes - if tuning Kirnberger III pure octaves in the central section is vital. Chopin's Raindrop Prelude is the acid test as to whether it's too strong.

Kirnberger III is ideally suited for Mozart in particular. I have used it for Beethoven and other things but in particular on an 1859 Broadwood with a particular harmonic structure that favours the 3rd harmonic with virtually no 5th harmonic in the sound at all. You'll probably find recordings on YouTube if you look up 1859 Broadwood.

I tuned a 1905 Baby Grand Broadwood to it as an experiment for a concert with standard stretch - it was fine but au point. No stretch in the temperament octaves would have been better.

By the way Roshan - what's the point of your modification? 

Really with the way in which pianos go out of tune in time tuning isn't as precise a science as decimal points might indicate. The importance of Kirnberger or Kellner are the very pleasant smooth thirds in F C and G and their contrast in modulation which gives a feeling of movement in the music. This effect is achieved even if tuning has degraded so whilst it's nice to be spot on, obsessive attention to detail isn't musically vital at all.

Best wishes

David P

--

- - - - - - - - - - - - - - - - - - - - - - - -
David Pinnegar, B.Sc., A.R.C.S.
- - - - - - - - - - - - - - - - - - - - - - - -
+44 1342 850594

Original Message------

Thanks, I'll compare this to Anthony Willey's offsets on Piano Meter.....
I may have to adjust some due to inharmonicity, depending on the piano.

I'm not sure how strict David Winnegar is when he render's his tuning.
I do believe he's using an electric tuner to set temperment, but not
sure if his device allows for pure octaves in the central 3 octaves.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561
------------------------------

Original Message:
Sent: 09-13-2019 12:25
From: Roshan Kakiya
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Cents

C	0.00
C#	91.45
D	193.16
D#	294.87
E	386.31
F	498.29
F#	589.74
G	696.58
G#	793.16
A	889.74
A#	996.58
B	1088.02
C	1200.00

Offsets in Cents from Pure Octave Equal Temperament

C	0.00
C#	−8.55
D	−6.84
D#	−5.13
E	−13.69
F	−1.71
F#	−10.26
G	−3.42
G#	−6.84
A	−10.26
A#	−3.42
B	−11.98
C	0.00

Frequencies in Hz

A0	27.50
A#0	29.25
B0	30.84
C1	32.90
C#1	34.68
D1	36.78
D#1	39.01
E1	41.12
F1	43.87
F#1	46.25
G1	49.19
G#1	52.02
A1	55.00
A#1	58.50
B1	61.67
C2	65.80
C#2	69.36
D2	73.56
D#2	78.01
E2	82.24
F2	87.74
F#2	92.50
G2	98.39
G#2	104.03
A2	110.00
A#2	117.00
B2	123.35
C3	131.59
C#3	138.73
D3	147.12
D#3	156.03
E3	164.49
F3	175.48
F#3	185.00
G3	196.77
G#3	208.06
A3	220.00
A#3	234.01
B3	246.70
C4	263.18
C#4	277.46
D4	294.25
D#4	312.05
E4	328.98
F4	350.96
F#4	369.99
G4	393.55
G#4	416.13
A4	440.00
A#4	468.01
B4	493.40
C5	526.36
C#5	554.91
D5	588.49
D#5	624.10
E5	657.95
F5	701.92
F#5	739.99
G5	787.10
G#5	832.25
A5	880.00
A#5	936.02
B5	986.79
C6	1052.73
C#6	1109.83
D6	1176.98
D#6	1248.20
E6	1315.91
F6	1403.83
F#6	1479.98
G6	1574.19
G#6	1664.51
A6	1760.00
A#6	1872.04
B6	1973.58
C7	2105.45
C#7	2219.65
D7	2353.97
D#7	2496.41
E7	2631.81
F7	2807.66
F#7	2959.96
G7	3148.38
G#7	3329.01
A7	3520.00
A#7	3744.08
B7	3947.16
C8	4210.90

Features and Modifications

Pure Major Third: C-E.

Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.

Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.


The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya
------------------------------

So we could we say Roshan and Jorgensen are in agreement, even though they've never met
(obviously).

I have an 1864 Steinway concert
grand at hand and may try these tomorrow, but only on the center strings off 3 octaves to be tuned without stretch.
I have to put it back to ET for when the owners return Sunday....or I could leave it and see if they notice.

I could then put it back to ET next weekend.

See what happens. (They are friends, so it won't be a big deal.)

 I could then compare Anthony's Kirnberger III to Roshan's just
by changing out the various offsets (I hope)....

Thanks for this discussion. It's been stimulating.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA
------------------------------

Original Message:
Sent: 09-13-2019 18:09
From: Jason Kanter
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Here is the original (pure) Kirnberger 3, 1/4 syntonic comma and no manipulation of the schisma. Note that the CGAE fifths (blue) are significantly narrowed by 5.38 cents, having absorbed almost all of the offsets required to make the 2:1 octave. The remainder 1.95 cents is gathered in the B-F# fifth. 
Here is Jorgensen's "Idealized Kirnberger III" (2002), about which he told me: "This idealized temperament authentically represents Prinz, Kirnberger III, and Aron-Neidhardt... It completely restores the perfect harmonic balance for tonality that was intended in the beginning." Notice that the 1.95 cents has now been distributed equally among the other 8 fifths. (side note, ... as if anyone could do this aurally.)

And here is Roshan's modified Kirnberger III. I modified his offsets to have A at offset zero, which is the custom these days. Once I had done that I saw that the numbers (and the graph) are identical save for one 3.43 instead of 3.42.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561

Original Message:
Sent: 09-13-2019 12:25
From: Roshan Kakiya
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Cents

C	0.00
C#	91.45
D	193.16
D#	294.87
E	386.31
F	498.29
F#	589.74
G	696.58
G#	793.16
A	889.74
A#	996.58
B	1088.02
C	1200.00

Offsets in Cents from Pure Octave Equal Temperament

C	0.00
C#	−8.55
D	−6.84
D#	−5.13
E	−13.69
F	−1.71
F#	−10.26
G	−3.42
G#	−6.84
A	−10.26
A#	−3.42
B	−11.98
C	0.00

Frequencies in Hz

A0	27.50
A#0	29.25
B0	30.84
C1	32.90
C#1	34.68
D1	36.78
D#1	39.01
E1	41.12
F1	43.87
F#1	46.25
G1	49.19
G#1	52.02
A1	55.00
A#1	58.50
B1	61.67
C2	65.80
C#2	69.36
D2	73.56
D#2	78.01
E2	82.24
F2	87.74
F#2	92.50
G2	98.39
G#2	104.03
A2	110.00
A#2	117.00
B2	123.35
C3	131.59
C#3	138.73
D3	147.12
D#3	156.03
E3	164.49
F3	175.48
F#3	185.00
G3	196.77
G#3	208.06
A3	220.00
A#3	234.01
B3	246.70
C4	263.18
C#4	277.46
D4	294.25
D#4	312.05
E4	328.98
F4	350.96
F#4	369.99
G4	393.55
G#4	416.13
A4	440.00
A#4	468.01
B4	493.40
C5	526.36
C#5	554.91
D5	588.49
D#5	624.10
E5	657.95
F5	701.92
F#5	739.99
G5	787.10
G#5	832.25
A5	880.00
A#5	936.02
B5	986.79
C6	1052.73
C#6	1109.83
D6	1176.98
D#6	1248.20
E6	1315.91
F6	1403.83
F#6	1479.98
G6	1574.19
G#6	1664.51
A6	1760.00
A#6	1872.04
B6	1973.58
C7	2105.45
C#7	2219.65
D7	2353.97
D#7	2496.41
E7	2631.81
F7	2807.66
F#7	2959.96
G7	3148.38
G#7	3329.01
A7	3520.00
A#7	3744.08
B7	3947.16
C8	4210.90

Features and Modifications

Pure Major Third: C-E.

Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.

Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.


The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya
------------------------------

Offsets in Cents for Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma) if A = 0.00 Cents

C	+10.26
C#	+1.71
D	+3.42
D#	+5.13
E	−3.42
F	+8.55
F#	0.00
G	+6.84
G#	+3.42
A	0.00
A#	+6.84
B	−1.71
C	+10.26

I have used the Excel file on my original post to calculate these offsets.

------------------------------
Roshan Kakiya
------------------------------

Original Message:
Sent: 09-13-2019 18:31
From: Richard Adkins
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)


So we could we say Roshan and Jorgensen are in agreement, even though they've never met
(obviously).

I have an 1864 Steinway concert
grand at hand and may try these tomorrow, but only on the center strings off 3 octaves to be tuned without stretch.
I have to put it back to ET for when the owners return Sunday....or I could leave it and see if they notice.

I could then put it back to ET next weekend.

See what happens. (They are friends, so it won't be a big deal.)

 I could then compare Anthony's Kirnberger III to Roshan's just
by changing out the various offsets (I hope)....

Thanks for this discussion. It's been stimulating.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA

Original Message:
Sent: 09-13-2019 18:09
From: Jason Kanter
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Here is the original (pure) Kirnberger 3, 1/4 syntonic comma and no manipulation of the schisma. Note that the CGAE fifths (blue) are significantly narrowed by 5.38 cents, having absorbed almost all of the offsets required to make the 2:1 octave. The remainder 1.95 cents is gathered in the B-F# fifth. 
Here is Jorgensen's "Idealized Kirnberger III" (2002), about which he told me: "This idealized temperament authentically represents Prinz, Kirnberger III, and Aron-Neidhardt... It completely restores the perfect harmonic balance for tonality that was intended in the beginning." Notice that the 1.95 cents has now been distributed equally among the other 8 fifths. (side note, ... as if anyone could do this aurally.)

And here is Roshan's modified Kirnberger III. I modified his offsets to have A at offset zero, which is the custom these days. Once I had done that I saw that the numbers (and the graph) are identical save for one 3.43 instead of 3.42.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561

Original Message:
Sent: 09-13-2019 12:25
From: Roshan Kakiya
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Cents

C	0.00
C#	91.45
D	193.16
D#	294.87
E	386.31
F	498.29
F#	589.74
G	696.58
G#	793.16
A	889.74
A#	996.58
B	1088.02
C	1200.00

Offsets in Cents from Pure Octave Equal Temperament

C	0.00
C#	−8.55
D	−6.84
D#	−5.13
E	−13.69
F	−1.71
F#	−10.26
G	−3.42
G#	−6.84
A	−10.26
A#	−3.42
B	−11.98
C	0.00

Frequencies in Hz

A0	27.50
A#0	29.25
B0	30.84
C1	32.90
C#1	34.68
D1	36.78
D#1	39.01
E1	41.12
F1	43.87
F#1	46.25
G1	49.19
G#1	52.02
A1	55.00
A#1	58.50
B1	61.67
C2	65.80
C#2	69.36
D2	73.56
D#2	78.01
E2	82.24
F2	87.74
F#2	92.50
G2	98.39
G#2	104.03
A2	110.00
A#2	117.00
B2	123.35
C3	131.59
C#3	138.73
D3	147.12
D#3	156.03
E3	164.49
F3	175.48
F#3	185.00
G3	196.77
G#3	208.06
A3	220.00
A#3	234.01
B3	246.70
C4	263.18
C#4	277.46
D4	294.25
D#4	312.05
E4	328.98
F4	350.96
F#4	369.99
G4	393.55
G#4	416.13
A4	440.00
A#4	468.01
B4	493.40
C5	526.36
C#5	554.91
D5	588.49
D#5	624.10
E5	657.95
F5	701.92
F#5	739.99
G5	787.10
G#5	832.25
A5	880.00
A#5	936.02
B5	986.79
C6	1052.73
C#6	1109.83
D6	1176.98
D#6	1248.20
E6	1315.91
F6	1403.83
F#6	1479.98
G6	1574.19
G#6	1664.51
A6	1760.00
A#6	1872.04
B6	1973.58
C7	2105.45
C#7	2219.65
D7	2353.97
D#7	2496.41
E7	2631.81
F7	2807.66
F#7	2959.96
G7	3148.38
G#7	3329.01
A7	3520.00
A#7	3744.08
B7	3947.16
C8	4210.90

Features and Modifications

Pure Major Third: C-E.

Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.

Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.


The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya
------------------------------

"I could then compare Anthony's Kirnberger III to Roshan's..."

It's not my Kirnberger. I got it from Unequal Temperaments: Theory, History and Practice by Claudio Di Veroli, page 135.

------------------------------
Anthony Willey, RPT
http://willeypianotuning.com
http://pianometer.com
------------------------------

Original Message:
Sent: 09-13-2019 18:31
From: Richard Adkins
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)


So we could we say Roshan and Jorgensen are in agreement, even though they've never met
(obviously).

I have an 1864 Steinway concert
grand at hand and may try these tomorrow, but only on the center strings off 3 octaves to be tuned without stretch.
I have to put it back to ET for when the owners return Sunday....or I could leave it and see if they notice.

I could then put it back to ET next weekend.

See what happens. (They are friends, so it won't be a big deal.)

 I could then compare Anthony's Kirnberger III to Roshan's just
by changing out the various offsets (I hope)....

Thanks for this discussion. It's been stimulating.

Richard

------------------------------
Richard Adkins
Piano Technician
Coe College
Cedar Rapids, IA

Original Message:
Sent: 09-13-2019 18:09
From: Jason Kanter
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Here is the original (pure) Kirnberger 3, 1/4 syntonic comma and no manipulation of the schisma. Note that the CGAE fifths (blue) are significantly narrowed by 5.38 cents, having absorbed almost all of the offsets required to make the 2:1 octave. The remainder 1.95 cents is gathered in the B-F# fifth. 
Here is Jorgensen's "Idealized Kirnberger III" (2002), about which he told me: "This idealized temperament authentically represents Prinz, Kirnberger III, and Aron-Neidhardt... It completely restores the perfect harmonic balance for tonality that was intended in the beginning." Notice that the 1.95 cents has now been distributed equally among the other 8 fifths. (side note, ... as if anyone could do this aurally.)

And here is Roshan's modified Kirnberger III. I modified his offsets to have A at offset zero, which is the custom these days. Once I had done that I saw that the numbers (and the graph) are identical save for one 3.43 instead of 3.42.

------------------------------
Jason Kanter
Lynnwood WA
425-830-1561

Original Message:
Sent: 09-13-2019 12:25
From: Roshan Kakiya
Subject: Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Modified Kirnberger III (1/4 Syntonic Comma and 1/8 Schisma)

Cents

C	0.00
C#	91.45
D	193.16
D#	294.87
E	386.31
F	498.29
F#	589.74
G	696.58
G#	793.16
A	889.74
A#	996.58
B	1088.02
C	1200.00

Offsets in Cents from Pure Octave Equal Temperament

C	0.00
C#	−8.55
D	−6.84
D#	−5.13
E	−13.69
F	−1.71
F#	−10.26
G	−3.42
G#	−6.84
A	−10.26
A#	−3.42
B	−11.98
C	0.00

Frequencies in Hz

A0	27.50
A#0	29.25
B0	30.84
C1	32.90
C#1	34.68
D1	36.78
D#1	39.01
E1	41.12
F1	43.87
F#1	46.25
G1	49.19
G#1	52.02
A1	55.00
A#1	58.50
B1	61.67
C2	65.80
C#2	69.36
D2	73.56
D#2	78.01
E2	82.24
F2	87.74
F#2	92.50
G2	98.39
G#2	104.03
A2	110.00
A#2	117.00
B2	123.35
C3	131.59
C#3	138.73
D3	147.12
D#3	156.03
E3	164.49
F3	175.48
F#3	185.00
G3	196.77
G#3	208.06
A3	220.00
A#3	234.01
B3	246.70
C4	263.18
C#4	277.46
D4	294.25
D#4	312.05
E4	328.98
F4	350.96
F#4	369.99
G4	393.55
G#4	416.13
A4	440.00
A#4	468.01
B4	493.40
C5	526.36
C#5	554.91
D5	588.49
D#5	624.10
E5	657.95
F5	701.92
F#5	739.99
G5	787.10
G#5	832.25
A5	880.00
A#5	936.02
B5	986.79
C6	1052.73
C#6	1109.83
D6	1176.98
D#6	1248.20
E6	1315.91
F6	1403.83
F#6	1479.98
G6	1574.19
G#6	1664.51
A6	1760.00
A#6	1872.04
B6	1973.58
C7	2105.45
C#7	2219.65
D7	2353.97
D#7	2496.41
E7	2631.81
F7	2807.66
F#7	2959.96
G7	3148.38
G#7	3329.01
A7	3520.00
A#7	3744.08
B7	3947.16
C8	4210.90

Features and Modifications

Pure Major Third: C-E.

Pure Fifth reduced by 1/4 Syntonic comma: C-G, G-D, D-A and A-E.

Pure Fifth reduced by 1/8 Schisma: E-B, B-F#, F#-C#, C#-G#, G#-D#, D#-A#, A#-F and F-C.


The first 4 Fifths (C-G-D-A-E) are the same as those of Kirnberger III. Each of these Fifths is a Pure Fifth reduced by 1/4 Syntonic comma. This arrangement causes C-E to become a Pure Major Third.

The remaining 8 Fifths (E-B-F#-C#-G#-D#-A#-F-C) have been modified. Each of these Fifths is a Pure Fifth reduced by 1/8 Schisma. This arrangement causes each of these Fifths to become very nearly pure.

------------------------------
Roshan Kakiya
------------------------------