Maria Renold Temperament

THE SCALE OF FIFTHS

The Maria Renold tuning was developed by Maria Renold (1917-2003), author of the book: “Of intervals, scales, tones and the concert pitch C = 128 Hz”. She spent her childhood in the USA, where her parents emigrated to establish eurythmy therapy in New York. She studied eurythmy and later violin and viola, touring with the Bush Chamber Orchestra and Bush String Quartet. One of Renold’s deeply felt questions concerned the proper chamber tone. When she heard of Rudolf Steiner’s suggestion of C = 128 Hz, she immediately put it into practice and experimented with it for many years in America and Europe. She discovered a new method of tuning the piano that is closer to the tuning of stringed instruments and achieves the concert pitch of A4 = 432 Hz. Her book was first published in German in 1985 and has become a modern classic of musical research.

This tuning makes it possible to play all major and minor scales and consists without exception of aurally true, non-tempered intervals.

Already in 1518 Heinrich Schreiber, who also called himself Henricus Grammateus, found this scale by geometrical division of a monochord.


Screenshot of the Maria Renold tuning in a Pianoteq digital instrument.
Here the tuning was loaded into the instrument with a Scala file.

Download der Scala-Datei Maria Renold I


Maria Renold 1

Piano Key NumberNoteFrequency (Hz)
-9C016
-8C#0/Db016,97
-7D018
-6D#0/Eb019.09
-5E020.25
-4F021.33
-3F#0/Gb022.63
-2G024
-1G#0/Ab025.46
01A027
02A#0/Bb028.64
03B030.38
04C132
05C#1/Db133.94
06D136
07D#1/Eb138.18
08E140.5
09F142.67
10F#1/Gb145.25
11G148
12G#1/Ab150.91
13A154
14A#1/Bb157.28
15B160.75
16C264
17C#2/Db267.89
18D272
19D#2/Eb272.37
20E281
21F285.33
22F#2/Gb290.51
23G296
34G#2/Ab2101.82
25A2108
26A#2/Bb2114.55
27B2121.5
28C3128
29C#3/Db3135.76
30D3144
31D#3/Eb3152.73
32E3162
33F3170.67
34F#3/Gb3181.02
35G3192
36G#3/Ab3203.65
37A3216
38A#3/Bb3229.10
39B3243
40C4256
41C#4/Db4271.53
42D4288
43D#4/Eb4305.47
44E4324
45F4341.33
46F#4/Gb4362.04
47G4384
48G#4/Ab4407.29
49A4432
50A#4/Bb4458.21
51B4486
52C5512
53C#5/Db5543.06
54D5576
55D#5/Eb5610.94
56E5648
57F5682.67
58F#5/Gb5724.08
59G5768
60G#5/Ab5814.59
61A5864
62A#5/Bb5916.41
63B5972
46C61024
65C#6/Db61086.12
66D61152
67D#6/Eb61221.88
68E61296
69F61365.33
70F#6/Gb61458.16
71G61536
72G#6/Ab61629.18
73A61728
74A#6/Bb61832.82
75B61944
76C72048
77C#7/Db72172.23
78D72304
79D#7/Eb72443.76
80E72592
81F72730.66
82F#7/Gb72896.31
83G73072
84G#7/Ab73258.35
85A73456
86A#7/Bb73665.64
87B73888
88C84096
89C#8/Db84344.46
90D84608
91D#8/Eb84887.52
92E85184
93F85461.33
94F#8/Gb85792.62
95G86144
96G#8/Ab86516.70
97A86912
98A#8/Bb87331.28
99B87776
100C98192

Maria Renold 2

Piano Key Number
Note
Frequency (Hz)
-9C0 15.88
-8 C#0/Db0  16.83
-7D0 17.85
-6 D#0/Eb0  18.93
-5E0 20.07
-4F0 21.96
-3 F#0/Gb0  22.47
-2G0 23.83
-1 G#0/Ab0  25.26
01A0 26.8
02 A#0/Bb0 28.41
03B030.12
04C1 31.81
05 C#1/Db1  33.73
06D135.77
07 D#1/Eb1  37.93
08E1 40.21
09F142.47
10 F#1/Gb1 45.04
11G147.75
12 G#1/Ab1 50.63
13A1 53.69
14 A#1/Bb1  56.93
15B160.35
16C263.75
17 C#2/Db2 67.60
18D271.68
19 D#2/Eb2  76
20E2 80.5
21F2 85.14
22 F#2/Gb2  90.25
23G295.7
34 G#2/Ab2 101.46
25A2107.58
26 A#2/Bb2 114.07
27B2120.95
28C3127.75
29 C#3/Db3  135.46
30D3143.63
31 D#3/Eb3 152.29
32E3161.48
33F3170.56
34 F#3/Gb3 180.85
35G3 191.75
36 G#3/Ab3  203.32
37A3215.58
38 A#3/Bb3  228.59
39B3242.38
40C4 256
41 C#4/Db4 271.44
42D4287.82
43 D#4/Eb4  305.17
44E4323.58
45F4341.77
46 F#4/Gb4 362.39
47G4384.25
48 G#4/Ab4  407.42
49A4 432
50 A#4/Bb4  458.06
51B4 485.68
52C5 512.99
53 C#5/Db5  543.93
54D5 576.75
55 D#5/Eb5  611.53
56E5648.41
57F5 684.87
58 F#5/Gb5 726.19
59G5 769.99
60 G#5/Ab5 816.42
61A5865.67
62 A#5/Bb5 917.89
63B5973.246
46C61027.97
65 C#6/Db6  1089.96
66D61155.74
67 D#6/Eb6  1225.43
68E61299.33
69F6 1372.40
70 F#6/Gb6 1455.19
71G61542.96
72 G#6/Ab6  1636.00
73A61734.70
74 A#6/Bb6 1839.35
75B61950.26
76C7 2059.92
77 C#7/Db7  2184.15
78D72315.96
79 D#7/Eb7  2455.60
80E7 2603.69
81F72750.12
82 F#7/Gb7  2916.014
83G7 3091.90
84 G#7/Ab7  3278.34
85A7 3476.12
86 A#7/Bb7 3685.82
87B73908.08
88C84127.83
89 C#8/Db8 4376.76
90D84640.89
91 D#8/Eb8 4920.72
92E85217.47
93F8 5510.88
94 F#8/Gb8  5843.32
95G8 6195.78
96 G#8/Ab8  6516.70
97A8 6965.71
98 A#8/Bb8  7385.91
99B8 7831.29
100C98271.64

Comparison: Maria Renold II Tuning and Just Intonation