### Magrathean diacritics

Posted:

**Wed Dec 26, 2018 9:29 pm**I received the following query by email:

The main reason we have never before published it, is that it is kind of embarrassing that it even exists. Some people already complain that Sagittal has too many symbols, often failing to appreciate that 99% of what anyone ever wants to do microtonally can be notated with the Spartan subset of 8 symbols.

But since we are dealing here with symbols (specifically diacritical marks or accents) having a resolution of a half-tina or 0.07 cents (completely inaudible except in very special circumstances), we needed a name for some beings that were more powerful than the Olympian gods, and yet were ridiculous. The Magratheans of Douglas Adams' comedy sci-fi

To ensure that the symbols were as distinct as possible given their necessarily-small size, George and I used the discipline of forcing ourselves to represent them in as few pixels as possible. You can see the final result here, at two different resolutions, one with 6 pixels between staff-line centres, and one with 8. The 3 and 6 tina symbols are identical to the 1 and 2 mina symbols described in the previous post, and the 9 tina symbol can also be used for 3 minas. To these we add 1 and 2 tina symbols and a dot to represent a half-tina. The intention is that, in a proper outline font, the 1, 2 and 3 tina symbols should be something like miniature versions of the following symbols without their shafts , and the half-tina dot should be circular.

George came up with the following definitions, with the help of a comma list produced by Gene Ward Smith. The ratios below have had their powers of 2 and 3 removed. These can be found if necessary, since we know the approximate size in cents. The trailing "n" is the symbol for "schismi

0.5 tina: 49:9765625n

1 tina: 121:1225n

1.5 tinas: 121:5359375n

2 tinas: 13:6655n

2.5 tinas: 343:15625n

3 tinas, 1 mina: 455n (~4375n)

3.5 tinas: 11:47n

4 tinas: 7:3025n

4.5 tinas: (no definition)

5 tinas: 25:2401n (~343:14641n)

5.5 tinas: (no definition)

6 tinas, 2 minas: 65:77n (~13:125n)

6.5 tinas: 13:37n

7 tinas: 143:1715n

7.5 tinas: 3125:5929n

8 tinas: 420175n

8.5 tinas: (no definition)

9 tinas: 539n

9.5 tinas: (no definition)

I had difficulty finding what George and I had agreed on, about 5 years ago. So I thought I should put the answer here, so the work is not lost.... I noticed SMuFL had a range for Magrathean Sagittal. Just wondering about the current state of the project, and what it would be like.

The main reason we have never before published it, is that it is kind of embarrassing that it even exists. Some people already complain that Sagittal has too many symbols, often failing to appreciate that 99% of what anyone ever wants to do microtonally can be notated with the Spartan subset of 8 symbols.

But since we are dealing here with symbols (specifically diacritical marks or accents) having a resolution of a half-tina or 0.07 cents (completely inaudible except in very special circumstances), we needed a name for some beings that were more powerful than the Olympian gods, and yet were ridiculous. The Magratheans of Douglas Adams' comedy sci-fi

*The Hitchhikers Guide to the Galaxy*were ideal for this.To ensure that the symbols were as distinct as possible given their necessarily-small size, George and I used the discipline of forcing ourselves to represent them in as few pixels as possible. You can see the final result here, at two different resolutions, one with 6 pixels between staff-line centres, and one with 8. The 3 and 6 tina symbols are identical to the 1 and 2 mina symbols described in the previous post, and the 9 tina symbol can also be used for 3 minas. To these we add 1 and 2 tina symbols and a dot to represent a half-tina. The intention is that, in a proper outline font, the 1, 2 and 3 tina symbols should be something like miniature versions of the following symbols without their shafts , and the half-tina dot should be circular.

George came up with the following definitions, with the help of a comma list produced by Gene Ward Smith. The ratios below have had their powers of 2 and 3 removed. These can be found if necessary, since we know the approximate size in cents. The trailing "n" is the symbol for "schismi

**n**a" (our name for commas smaller than 1.8075 cents).0.5 tina: 49:9765625n

1 tina: 121:1225n

1.5 tinas: 121:5359375n

2 tinas: 13:6655n

2.5 tinas: 343:15625n

3 tinas, 1 mina: 455n (~4375n)

3.5 tinas: 11:47n

4 tinas: 7:3025n

4.5 tinas: (no definition)

5 tinas: 25:2401n (~343:14641n)

5.5 tinas: (no definition)

6 tinas, 2 minas: 65:77n (~13:125n)

6.5 tinas: 13:37n

7 tinas: 143:1715n

7.5 tinas: 3125:5929n

8 tinas: 420175n

8.5 tinas: (no definition)

9 tinas: 539n

9.5 tinas: (no definition)