Why use duodecimal system for the notation of pitch? Because it is easy and compact!
The twelve tones are named 0,1,2,3,4,5,6,7,8,9,X,T.
c : 0 | c#/db : 1 | d : 2 | d#/eb : 3 | e : 4 | f : 5 | f#/gb : 6 | g : 7 | g#/ab : 8 | a : 9 | a#/bb : X | b : T |
Tones are fully denoted by two numbers.
The advantage over decimal MIDI numbers is that the first number denotes the octave and the second number denotes the semitone within the octave.
Following table illustrates the relation between different naming systems
| MIDI | Duodecimal MIDI | Frequency [Hz] | Note names | Note names (German) |
|---|---|---|---|---|
| 0 | 00 | 8.18 | ||
| 12 | 10 | 16.36 | C0 | C,, |
| 24 | 20 | 32.7 | C1 | C, |
| 36 | 30 | 65.41 | C2 | C |
| 48 | 40 | 130.81 | C3 | c |
| 49 | 41 | 139.59 | C#3/Db3 | cis/des |
| 50 | 42 | 146.83 | D3 | d |
| 51 | 43 | 155.56 | D#3/Eb3 | dis/es |
| 52 | 44 | 164.81 | E3 | e |
| 53 | 45 | 174.61 | F3 | f |
| 54 | 46 | 185.00 | F#3/Gb3 | fis/ges |
| 55 | 47 | 196.00 | G3 | g |
| 56 | 48 | 207.56 | G#3/Ab3 | gis/as |
| 57 | 49 | 220.00 | A3 | a |
| 58 | 4X | 233.08 | A#3/Bb3 | ais/b |
| 59 | 4T | 246.94 | B3 | h |
| 60 | 50 | 261.63 | C4 (middle C) | c' (Schloss-C) |
| 61 | 51 | 277.18 | C#4/Db4 | cis'/des' |
| 62 | 52 | 293.63 | D4 | d' |
| 63 | 53 | 311.13 | D#4/Eb4 | dis'/es' |
| 64 | 54 | 329.63 | E4 | e' |
| 65 | 55 | 349.23 | F4 | f' |
| 66 | 56 | 369.99 | F#4/Gb4 | fis'/ges' |
| 67 | 57 | 392.0 | G4 | g' |
| 68 | 58 | 415.3 | G#4/Ab4 | gis'/as' |
| 69 | 59 | 440 | A4 (concert pitch) | a' (Kammerton) |
| 70 | 5X | 466.16 | A#4/Bb4 | ais'/b' |
| 71 | 5T | 493.88 | B | h |
| 72 | 60 | 623.25 | C5 | c'' |
| ... | ||||
| 120 | X0 | 8387.02 | C9 | c'''''' |
| 127 | X7 | 12543.85 | G9 | g'''''' |
| one octave up | comment | ||
| MIDI | 48 52 55 60 | 60 64 67 72 | hard to learn the relation between number and tone |
| MIDI-XT | 40 44 47 50 | 50 54 57 60 | easy to learn the XT to note relation |
| Notes | C3 E3 G3 C4 | C4 E4 G4 C5 | well known; support enharmonic equivalent |
| Score |
| one octave up | comment | ||
| MIDI | 47 51 54 59 | 59 63 66 71 | hard to remember the tones |
| MIDI-XT | 3T 43 46 4T | 4T 53 56 5T | easy to shift octave up or down |
| Notes | B2 D#3 F#3 B3 | B3 D#4 F#4 B4 | Needs more characters, but may be compressed like (B3D#F#B). # and b may help but may also cause troubles. |
| Score |
Impressum: Music Synthesis Enterprise -- Bernhard Feiten -- bernhard.feiten@msye.com -- Am Triftpark 13, 13437 Berlin, Germany