# sagittal notation

[Dave Keenan, Yahoo tuning, message 47981]

The word "sagittal" (pronounced "SAJ-i-tl") means "arrow-like". Think of Sagittarius the archer.

The Sagittal notation system is a comprehensive system for notating musical pitch in all possible scales and tunings - a universal set of microtonal accidentals, equally suited to extended just intonation, equal divisions of whatever (including EDOs), and anything in between. It is called Sagittal because it uses various arrow-like symbols, pointing up or down to indicate raising or lowering of pitch.

Sagittal was developed by George Secor and Dave Keenan, with a major early contribution from Gene Ward Smith, and in cooperation with many others on the Yahoo Groups tuning and tuning-math.

. . . . . . . . .
[Dave Keenan, Yahoo tuning-math, message 10935 (Sat Jul 17, 2004 11:11 pm)]

[Note from Monzo: the table below shows the ASCII version of the sagittal accidentals, with the ratios they represent.]

```     ratio      [  2   3 , 5  7 11, 13 17 19, 23]-monzo  '|   )|   (|   /|   ~|   |~   |\   |)   |(   symbol    comma name

32768 / 32805  [ 15  -8, -1  0  0,  0  0  0,  0>         1    0    0    0    0    0    0    0    0    '|     5-schisma
512 / 513    [  9  -3,  0  0  0,  0  0 -1,  0>         0    1    0    0    0    0    0    0    0    )|     19-schisma
5103 / 5120   [-10   6, -1  1  0,  0  0  0,  0>         0    0    0    0    0    0    0    0    1    |(     5:7-kleisma
2176 / 2187   [  7  -7,  0  0  0,  0  1  0,  0>         0    0    0    0    1    0    0    0    0    ~|     17-kleisma
891 / 896    [ -7   4,  0 -1  1,  0  0  0,  0>         0    1    0    0    0    0    0    0    1    )|(    7:11-kleisma
4096 / 4131   [ 12  -5,  0  0  0,  0 -1  0,  0>         0    0    0    0    1    0    0    0    1    ~|(    17-comma
729 / 736    [ -5   6,  0  0  0,  0  0  0, -1>         0    0    0    0    0    1    0    0    0    |~     23-comma
2025 / 2048   [-11   4,  2  0  0,  0  0  0,  0>        -1    0    0    1    0    0    0    0    0    ./|    25-comma
19456 / 19683  [ 10  -9,  0  0  0,  0  0  1,  0>         0    1    0    0    0    1    0    0    0    )|~    19-comma
80 / 81     [ -4   4, -1  0  0,  0  0  0,  0>         0    0    0    1    0    0    0    0    0    /|     5-comma
524288 / 531441 [ 19 -12,  0  0  0,  0  0  0,  0>         1    0    0    1    0    0    0    0    0    '/|    3-comma
40960 / 41553  [ 13  -7,  1  0  0,  0  0 -1,  0>         0    1    0    1    0    0    0    0    0    )/|    5:19-comma
63 / 64     [ -6   2,  0  1  0,  0  0  0,  0>         0    0    0    0    0    0    0    1    0    |)     7-comma
54 / 55     [  1   3, -1  0 -1,  0  0  0,  0>         0    0    0    0    0    0    1    0    0    |\     55-comma
45056 / 45927  [ 12  -8,  0 -1  1,  0  0  0,  0>         0    0    1    0    0    0    0    0    0    (|     7:11-comma
44 / 45     [  2  -2, -1  0  1,  0  0  0,  0>         0    0    1    0    0    0    0    0    1    (|(    5:11-S-diesis
6400 / 6561   [  8  -8,  2  0  0,  0  0  0,  0>         0    0    0    2    0    0    0    0    0    //|    25-S-diesis
35 / 36     [ -2  -2,  1  1  0,  0  0  0,  0>         0    0    0    1    0    0    0    1    0    /|)    35-M-diesis
32 / 33     [  5  -1,  0  0 -1,  0  0  0,  0>         0    0    0    1    0    0    1    0    0    /|\    11-M-diesis
```
. . . . . . . . .

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