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. Called MIDI-XT notation.
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.
Why use X and T? X is the sign for Roman ten. T is somehow similar to 11. Just move the second 1 on top of the first one. Also these two letters are not used for the ABCDEFG notation. Using AB, TE or XE for ten and eleven might lead to confusion when mixing the duodecimal notation and ABC notation.
As example see a 12 tone melody from Webern written in ABC and in MIDI-XT notation:
B4 Bb4 D5 Eb4 G4 F#4 G#4 E4 F4 C5 C#5 A4
5T 5X 62 53 57 56 58 54 55 60 61 57
Both is equally grandiose.
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