Equal 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.
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Download Scala-File Maria Renold I
Download Scala-File Maria Renold II
Maria Renold Frequencies
Maria Renold I
Piano Key Number | Note | Frequency (Hz) |
---|---|---|
-9 | C0 | 16 |
-8 | C#0/Db0 | 16,97 |
-7 | D0 | 18 |
-6 | D#0/Eb0 | 19.09 |
-5 | E0 | 20.25 |
-4 | F0 | 21.33 |
-3 | F#0/Gb0 | 22.63 |
-2 | G0 | 24 |
-1 | G#0/Ab0 | 25.46 |
01 | A0 | 27 |
02 | A#0/Bb0 | 28.64 |
03 | B0 | 30.38 |
04 | C1 | 32 |
05 | C#1/Db1 | 33.94 |
06 | D1 | 36 |
07 | D#1/Eb1 | 38.18 |
08 | E1 | 40.5 |
09 | F1 | 42.67 |
10 | F#1/Gb1 | 45.25 |
11 | G1 | 48 |
12 | G#1/Ab1 | 50.91 |
13 | A1 | 54 |
14 | A#1/Bb1 | 57.28 |
15 | B1 | 60.75 |
16 | C2 | 64 |
17 | C#2/Db2 | 67.89 |
18 | D2 | 72 |
19 | D#2/Eb2 | 72.37 |
20 | E2 | 81 |
21 | F2 | 85.33 |
22 | F#2/Gb2 | 90.51 |
23 | G2 | 96 |
34 | G#2/Ab2 | 101.82 |
25 | A2 | 108 |
26 | A#2/Bb2 | 114.55 |
27 | B2 | 121.5 |
28 | C3 | 128 |
29 | C#3/Db3 | 135.76 |
30 | D3 | 144 |
31 | D#3/Eb3 | 152.73 |
32 | E3 | 162 |
33 | F3 | 170.67 |
34 | F#3/Gb3 | 181.02 |
35 | G3 | 192 |
36 | G#3/Ab3 | 203.65 |
37 | A3 | 216 |
38 | A#3/Bb3 | 229.10 |
39 | B3 | 243 |
40 | C4 | 256 |
41 | C#4/Db4 | 271.53 |
42 | D4 | 288 |
43 | D#4/Eb4 | 305.47 |
44 | E4 | 324 |
45 | F4 | 341.33 |
46 | F#4/Gb4 | 362.04 |
47 | G4 | 384 |
48 | G#4/Ab4 | 407.29 |
49 | A4 | 432 |
50 | A#4/Bb4 | 458.21 |
51 | B4 | 486 |
52 | C5 | 512 |
53 | C#5/Db5 | 543.06 |
54 | D5 | 576 |
55 | D#5/Eb5 | 610.94 |
56 | E5 | 648 |
57 | F5 | 682.67 |
58 | F#5/Gb5 | 724.08 |
59 | G5 | 768 |
60 | G#5/Ab5 | 814.59 |
61 | A5 | 864 |
62 | A#5/Bb5 | 916.41 |
63 | B5 | 972 |
46 | C6 | 1024 |
65 | C#6/Db6 | 1086.12 |
66 | D6 | 1152 |
67 | D#6/Eb6 | 1221.88 |
68 | E6 | 1296 |
69 | F6 | 1365.33 |
70 | F#6/Gb6 | 1458.16 |
71 | G6 | 1536 |
72 | G#6/Ab6 | 1629.18 |
73 | A6 | 1728 |
74 | A#6/Bb6 | 1832.82 |
75 | B6 | 1944 |
76 | C7 | 2048 |
77 | C#7/Db7 | 2172.23 |
78 | D7 | 2304 |
79 | D#7/Eb7 | 2443.76 |
80 | E7 | 2592 |
81 | F7 | 2730.66 |
82 | F#7/Gb7 | 2896.31 |
83 | G7 | 3072 |
84 | G#7/Ab7 | 3258.35 |
85 | A7 | 3456 |
86 | A#7/Bb7 | 3665.64 |
87 | B7 | 3888 |
88 | C8 | 4096 |
89 | C#8/Db8 | 4344.46 |
90 | D8 | 4608 |
91 | D#8/Eb8 | 4887.52 |
92 | E8 | 5184 |
93 | F8 | 5461.33 |
94 | F#8/Gb8 | 5792.62 |
95 | G8 | 6144 |
96 | G#8/Ab8 | 6516.70 |
97 | A8 | 6912 |
98 | A#8/Bb8 | 7331.28 |
99 | B8 | 7776 |
100 | C9 | 8192 |
Maria Renold II
Piano Key Number | Note | Frequency (Hz) |
---|---|---|
-9 | C0 | 15.88 |
-8 | C#0/Db0 | 16.83 |
-7 | D0 | 17.85 |
-6 | D#0/Eb0 | 18.93 |
-5 | E0 | 20.07 |
-4 | F0 | 21.96 |
-3 | F#0/Gb0 | 22.47 |
-2 | G0 | 23.83 |
-1 | G#0/Ab0 | 25.26 |
01 | A0 | 26.8 |
02 | A#0/Bb0 | 28.41 |
03 | B0 | 30.12 |
04 | C1 | 31.81 |
05 | C#1/Db1 | 33.73 |
06 | D1 | 35.77 |
07 | D#1/Eb1 | 37.93 |
08 | E1 | 40.21 |
09 | F1 | 42.47 |
10 | F#1/Gb1 | 45.04 |
11 | G1 | 47.75 |
12 | G#1/Ab1 | 50.63 |
13 | A1 | 53.69 |
14 | A#1/Bb1 | 56.93 |
15 | B1 | 60.35 |
16 | C2 | 63.75 |
17 | C#2/Db2 | 67.60 |
18 | D2 | 71.68 |
19 | D#2/Eb2 | 76 |
20 | E2 | 80.5 |
21 | F2 | 85.14 |
22 | F#2/Gb2 | 90.25 |
23 | G2 | 95.7 |
34 | G#2/Ab2 | 101.46 |
25 | A2 | 107.58 |
26 | A#2/Bb2 | 114.07 |
27 | B2 | 120.95 |
28 | C3 | 127.75 |
29 | C#3/Db3 | 135.46 |
30 | D3 | 143.63 |
31 | D#3/Eb3 | 152.29 |
32 | E3 | 161.48 |
33 | F3 | 170.56 |
34 | F#3/Gb3 | 180.85 |
35 | G3 | 191.75 |
36 | G#3/Ab3 | 203.32 |
37 | A3 | 215.58 |
38 | A#3/Bb3 | 228.59 |
39 | B3 | 242.38 |
40 | C4 | 256 |
41 | C#4/Db4 | 271.44 |
42 | D4 | 287.82 |
43 | D#4/Eb4 | 305.17 |
44 | E4 | 323.58 |
45 | F4 | 341.77 |
46 | F#4/Gb4 | 362.39 |
47 | G4 | 384.25 |
48 | G#4/Ab4 | 407.42 |
49 | A4 | 432 |
50 | A#4/Bb4 | 458.06 |
51 | B4 | 485.68 |
52 | C5 | 512.99 |
53 | C#5/Db5 | 543.93 |
54 | D5 | 576.75 |
55 | D#5/Eb5 | 611.53 |
56 | E5 | 648.41 |
57 | F5 | 684.87 |
58 | F#5/Gb5 | 726.19 |
59 | G5 | 769.99 |
60 | G#5/Ab5 | 816.42 |
61 | A5 | 865.67 |
62 | A#5/Bb5 | 917.89 |
63 | B5 | 973.246 |
46 | C6 | 1027.97 |
65 | C#6/Db6 | 1089.96 |
66 | D6 | 1155.74 |
67 | D#6/Eb6 | 1225.43 |
68 | E6 | 1299.33 |
69 | F6 | 1372.40 |
70 | F#6/Gb6 | 1455.19 |
71 | G6 | 1542.96 |
72 | G#6/Ab6 | 1636.00 |
73 | A6 | 1734.70 |
74 | A#6/Bb6 | 1839.35 |
75 | B6 | 1950.26 |
76 | C7 | 2059.92 |
77 | C#7/Db7 | 2184.15 |
78 | D7 | 2315.96 |
79 | D#7/Eb7 | 2455.60 |
80 | E7 | 2603.69 |
81 | F7 | 2750.12 |
82 | F#7/Gb7 | 2916.014 |
83 | G7 | 3091.90 |
84 | G#7/Ab7 | 3278.34 |
85 | A7 | 3476.12 |
86 | A#7/Bb7 | 3685.82 |
87 | B7 | 3908.08 |
88 | C8 | 4127.83 |
89 | C#8/Db8 | 4376.76 |
90 | D8 | 4640.89 |
91 | D#8/Eb8 | 4920.72 |
92 | E8 | 5217.47 |
93 | F8 | 5510.88 |
94 | F#8/Gb8 | 5843.32 |
95 | G8 | 6195.78 |
96 | G#8/Ab8 | 6516.70 |
97 | A8 | 6965.71 |
98 | A#8/Bb8 | 7385.91 |
99 | B8 | 7831.29 |
100 | C9 | 8271.64 |