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'''5ed100''', or '''the stellar magnitude tuning''', is an equal-step tuning with each pitch being about 2.512 times larger than the other, the number known as the Pogson's ratio.
{{Editable user page}}
{{Novelty}}
{{Infobox ET|debug=1}}
'''5ed100''', '''the stellar magnitude tuning''' or '''5 equal divisions [[Ed100|of the double decave]]''', is an equal-step tuning with each pitch being about 2.512 times larger than the other, the number known as the Pogson's ratio.
== Theory ==
== Theory ==
The tuning is pretty meaningless as far as pitches go, since there's only 7-8 steps of it in the entire human hearing range, but it has a real life equivalence to astronomy - each step of it is known as the Pogson's ratio and it has an application of being the factor which sets two stars being 1 magnitude apart. This means subdividing it makes a meaningful major tenth of 1594.525 cents.
The tuning is pretty meaningless as far as pitches go, since there's only 7-8 steps of it in the entire human hearing range, but it has a real life equivalence to astronomy - each step of it is known as the Pogson's ratio and it has an application of being the factor which sets two stars being 1 magnitude apart. This means subdividing it makes a meaningful major tenth of 1594.525 cents.
| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
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|<u>896.676…</u>
|''899.755…''
|<nowiki>51 51|51 26</nowiki>
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|<u>896.667…</u>
|''899.745…''
|<nowiki>49 49|49 25</nowiki>
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|<u>896.656…</u>
|''899.734…''
|<nowiki>47 47|47 24</nowiki>
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|<u>896.644…</u>
|''899.722…''
|<nowiki>45 45|45 23</nowiki>
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|<u>896.631…</u>
|''899.710…''
|<nowiki>43 43|43 22</nowiki>
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|<u>896.617…</u>
|''899.696…''
|<nowiki>41 41|41 21</nowiki>
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|<u>896.602…</u>
|''899.680…''
|<nowiki>39 39|39 20</nowiki>
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|<u>896.585…</u>
|''899.663…''
|<nowiki>37 37|37 19</nowiki>
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|<u>896.565…</u>
|''899.644…''
|<nowiki>35 35|35 18</nowiki>
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|<u>896.544…</u>
|''899.622…''
|<nowiki>33 33|33 17</nowiki>
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|<u>896.520…</u>
|''899.598…''
|<nowiki>31 31|31 16</nowiki>
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|<u>896.492…</u>
|''899.570…''
|<nowiki>29 29|29 15</nowiki>
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|<u>896.461…</u>
|''899.539…''
|<nowiki>27 27|27 14</nowiki>
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|<u>896.424…</u>
|''899.502…''
|<nowiki>25 25|25 13</nowiki>
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|<u>896.381…</u>
|''899.459…''
|<nowiki>23 23|23 12</nowiki>
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|''899.408…''
|<nowiki>21 21|21 11</nowiki>
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|<u>896.269…</u>
|''899.346…''
|<nowiki>19 19|19 10</nowiki>
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|<u>896.193…</u>
|''899.270…''
|<nowiki>17 17|17 9</nowiki>
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|<u>896.096…</u>
|''899.173…''
|<nowiki>15 15|15 8</nowiki>
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| |59\525
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| |<u>895.971…</u>
|''899.047…''
| |<nowiki>13 13|13 7</nowiki>
| |Terra Rubra 1/13-tone
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| |
| |50\445
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| |<u>895.800…</u>
|''898.876…''
| |<nowiki>11 11|11 6</nowiki>
| |Terra Rubra 1/11-tone
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| |41\365
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| |<u>895.555…</u>
|''898.630…''
| |<nowiki>9 9|9 5</nowiki>
| |Terra Rubra 1/9-tone
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| |32\285
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| |<u>895.172…</u>
|''898.245…''
| |<nowiki>7 7|7 4</nowiki>
| |Terra Rubra 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b')</span>
Astronomers might sometimes round 2.512 to 2.5, which leads to confusion with the other 2.5 - that is the logarithm multiplier required for base-10 logarithm conversion, with the formula being involved 2.5 log10(m1 - m2). The factor of 2.5 is simply coincidentally close enough to the 5th root of 100.
Astronomers might sometimes round 2.512 to 2.5, which leads to confusion with the other 2.5 - that is the logarithm multiplier required for base-10 logarithm conversion, with the formula being involved 2.5 log10(m1 - m2). The factor of 2.5 is simply coincidentally close enough to the 5th root of 100.
If this is taken as a comma to be tempered, it results in 100 / 97.65625 = 1.024 = [[128/125]], the lesser diesis.
If this is taken as a comma to be tempered, it results in 100 / 97.65625 = 1.024 = [[128/125]], the lesser diesis.
== References ==
== References ==
* Wikipedia Contributors, [[Wikipedia:Magnitude (astronomy)|Magnitude (astronomy)]].
* Wikipedia Contributors, [[Wikipedia:Magnitude (astronomy)|Magnitude (astronomy)]].
[[Category:Extreme]]
[[Category:Real-life sonifications]]
[[Category:Sonifications]]
Latest revision as of 14:43, 1 August 2025
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5ed100, the stellar magnitude tuning or 5 equal divisions of the double decave, is an equal-step tuning with each pitch being about 2.512 times larger than the other, the number known as the Pogson's ratio.
Theory
The tuning is pretty meaningless as far as pitches go, since there's only 7-8 steps of it in the entire human hearing range, but it has a real life equivalence to astronomy - each step of it is known as the Pogson's ratio and it has an application of being the factor which sets two stars being 1 magnitude apart. This means subdividing it makes a meaningful major tenth of 1594.525 cents.
Tempered commas
Astronomers might sometimes round 2.512 to 2.5, which leads to confusion with the other 2.5 - that is the logarithm multiplier required for base-10 logarithm conversion, with the formula being involved 2.5 log10(m1 - m2). The factor of 2.5 is simply coincidentally close enough to the 5th root of 100.
If this is taken as a comma to be tempered, it results in 100 / 97.65625 = 1.024 = 128/125, the lesser diesis.
