Physics-first music theory

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Pitch Reference Table

The canonical mapping between PhizMusic step-numbers, Dodeka syllables, Western note names, MIDI numbers, and frequencies in hertz.

Reference Frequency Convention

The choice of Do = C and f₀ = 261.63 Hz for octave 4 is arbitrary but conventional. All PhizMusic formulas use a reference frequency variable. 261.63 Hz is the default.

The standard tuning anchor is La4 (A4) = 440 Hz = MIDI note 69.

Frequency Formula

MIDI note number:  n = (octave + 1) × 12 + step
Frequency (Hz):    f = 440 × 2^((n - 69) / 12)

Equivalently, from a reference pitch:

f = f₀ × 2^(step / 12)

where f₀ is the frequency of step-0 (Do) in the given octave.

Compact Table — One Octave

The 12 chromatic steps within a single octave, showing the ratio from step-0:

Step Syllable Western Ratio from Step-0 Cents
0 Do C 1.0000 0
1 Ka C♯/D♭ 1.0595 100
2 Re D 1.1225 200
3 Xo D♯/E♭ 1.1892 300
4 Mi E 1.2599 400
5 Fa F 1.3348 500
6 Hu F♯/G♭ 1.4142 600
7 So G 1.4983 700
8 Bi G♯/A♭ 1.5874 800
9 La A 1.6818 900
10 Ve A♯/B♭ 1.7818 1000
11 Si B 1.8877 1100

Each ratio = 2^(step/12). Each step adds exactly 100 cents in 12-TET.

Full Table — All Octaves

Frequencies computed using f = 440 × 2^((n - 69) / 12) and rounded to 2 decimal places.

The commonly used range for most instruments and music spans roughly octaves 2 through 7 (MIDI 36-107, ~65 Hz to ~3951 Hz).

Octave 0

Oct.Step Syllable Western MIDI Hz
0.0 Do0 C0 12 16.35
0.1 Ka0 C♯0 13 17.32
0.2 Re0 D0 14 18.35
0.3 Xo0 D♯0 15 19.45
0.4 Mi0 E0 16 20.60
0.5 Fa0 F0 17 21.83
0.6 Hu0 F♯0 18 23.12
0.7 So0 G0 19 24.50
0.8 Bi0 G♯0 20 25.96
0.9 La0 A0 21 27.50
0.10 Ve0 A♯0 22 29.14
0.11 Si0 B0 23 30.87

Octave 1

Oct.Step Syllable Western MIDI Hz
1.0 Do1 C1 24 32.70
1.1 Ka1 C♯1 25 34.65
1.2 Re1 D1 26 36.71
1.3 Xo1 D♯1 27 38.89
1.4 Mi1 E1 28 41.20
1.5 Fa1 F1 29 43.65
1.6 Hu1 F♯1 30 46.25
1.7 So1 G1 31 49.00
1.8 Bi1 G♯1 32 51.91
1.9 La1 A1 33 55.00
1.10 Ve1 A♯1 34 58.27
1.11 Si1 B1 35 61.74

Octave 2

Oct.Step Syllable Western MIDI Hz
2.0 Do2 C2 36 65.41
2.1 Ka2 C♯2 37 69.30
2.2 Re2 D2 38 73.42
2.3 Xo2 D♯2 39 77.78
2.4 Mi2 E2 40 82.41
2.5 Fa2 F2 41 87.31
2.6 Hu2 F♯2 42 92.50
2.7 So2 G2 43 98.00
2.8 Bi2 G♯2 44 103.83
2.9 La2 A2 45 110.00
2.10 Ve2 A♯2 46 116.54
2.11 Si2 B2 47 123.47

Octave 3

Oct.Step Syllable Western MIDI Hz
3.0 Do3 C3 48 130.81
3.1 Ka3 C♯3 49 138.59
3.2 Re3 D3 50 146.83
3.3 Xo3 D♯3 51 155.56
3.4 Mi3 E3 52 164.81
3.5 Fa3 F3 53 174.61
3.6 Hu3 F♯3 54 185.00
3.7 So3 G3 55 196.00
3.8 Bi3 G♯3 56 207.65
3.9 La3 A3 57 220.00
3.10 Ve3 A♯3 58 233.08
3.11 Si3 B3 59 246.94

Octave 4

Oct.Step Syllable Western MIDI Hz
4.0 Do4 C4 60 261.63
4.1 Ka4 C♯4 61 277.18
4.2 Re4 D4 62 293.66
4.3 Xo4 D♯4 63 311.13
4.4 Mi4 E4 64 329.63
4.5 Fa4 F4 65 349.23
4.6 Hu4 F♯4 66 369.99
4.7 So4 G4 67 392.00
4.8 Bi4 G♯4 68 415.30
4.9 La4 A4 69 440.00
4.10 Ve4 A♯4 70 466.16
4.11 Si4 B4 71 493.88

Octave 5

Oct.Step Syllable Western MIDI Hz
5.0 Do5 C5 72 523.25
5.1 Ka5 C♯5 73 554.37
5.2 Re5 D5 74 587.33
5.3 Xo5 D♯5 75 622.25
5.4 Mi5 E5 76 659.26
5.5 Fa5 F5 77 698.46
5.6 Hu5 F♯5 78 739.99
5.7 So5 G5 79 783.99
5.8 Bi5 G♯5 80 830.61
5.9 La5 A5 81 880.00
5.10 Ve5 A♯5 82 932.33
5.11 Si5 B5 83 987.77

Octave 6

Oct.Step Syllable Western MIDI Hz
6.0 Do6 C6 84 1046.50
6.1 Ka6 C♯6 85 1108.73
6.2 Re6 D6 86 1174.66
6.3 Xo6 D♯6 87 1244.51
6.4 Mi6 E6 88 1318.51
6.5 Fa6 F6 89 1396.91
6.6 Hu6 F♯6 90 1479.98
6.7 So6 G6 91 1567.98
6.8 Bi6 G♯6 92 1661.22
6.9 La6 A6 93 1760.00
6.10 Ve6 A♯6 94 1864.66
6.11 Si6 B6 95 1975.53

Octave 7

Oct.Step Syllable Western MIDI Hz
7.0 Do7 C7 96 2093.00
7.1 Ka7 C♯7 97 2217.46
7.2 Re7 D7 98 2349.32
7.3 Xo7 D♯7 99 2489.02
7.4 Mi7 E7 100 2637.02
7.5 Fa7 F7 101 2793.83
7.6 Hu7 F♯7 102 2959.96
7.7 So7 G7 103 3135.96
7.8 Bi7 G♯7 104 3322.44
7.9 La7 A7 105 3520.00
7.10 Ve7 A♯7 106 3729.31
7.11 Si7 B7 107 3951.07

Octave 8

Oct.Step Syllable Western MIDI Hz
8.0 Do8 C8 108 4186.01
8.1 Ka8 C♯8 109 4434.92
8.2 Re8 D8 110 4698.64
8.3 Xo8 D♯8 111 4978.03
8.4 Mi8 E8 112 5274.04
8.5 Fa8 F8 113 5587.65
8.6 Hu8 F♯8 114 5919.91
8.7 So8 G8 115 6271.93
8.8 Bi8 G♯8 116 6644.88
8.9 La8 A8 117 7040.00
8.10 Ve8 A♯8 118 7458.62
8.11 Si8 B8 119 7902.13

Key Reference Points

Note Oct.Step Syllable Western MIDI Hz Significance
— 0.9 La0 A0 21 27.50 Lowest piano key
— 4.0 Do4 C4 60 261.63 “Middle C,” reference pitch f₀
— 4.9 La4 A4 69 440.00 Standard tuning reference
— 8.0 Do8 C8 108 4186.01 Highest piano key

Connections