User:Eliora/5ed100: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Eliora (talk | contribs)
autopatrolled
3,351 edits
No edit summary
Moremajorthanmajor (talk | contribs)
autopatrolled
3,126 edits
No edit summary
Line 2: Line 2:


== 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.  
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.


===Scale tree===
{| class="wikitable"
|-
! colspan="3" |Generator
! |<span style="display: block; text-align: center;">'''Generator size (cents) '''</span>
!<span style="display: block; text-align: center;">'''Generator size (ed4\3)'''</span>
! |Pentachord steps
! |Comments
|-
| |4\35
| |
| |
| |<u>911.157…</u>
|''914.285…''
| |<nowiki>1 1|1 0</nowiki>
| |
|-
|25\220
|
|
|<u>905.980…</u>
|''909.{{Overline|09}}''
|<nowiki>6 6|6 1</nowiki>
|
|-
|
|71\625
|
|<u>905.690…</u>
|''908.8''
|<nowiki>17 17|17 3</nowiki>
|
|-
|
|46\405
|
|<u>905.532…</u>
|''908.641…''
|<nowiki>11 11|11 2</nowiki>
|
|-
|
|67\590
|
|<u>905.366…</u>
|''908.474…''
|<nowiki>16 16|16 3</nowiki>
|
|-
| |21\185
| |
| |
| |<u>905.000…</u>
|''908.{{Overline|108}}''
| |<nowiki>5 5|5 1</nowiki>
| |
|-
|
|80\705
|
|<u>904.695…</u>
|''907.801…''
|<nowiki>19 19|19 4</nowiki>
|
|-
|
|59\520
|
|<u>904.586…</u>
|''907.692…''
|<nowiki>14 14|14 3</nowiki>
|
|-
|
|38\335
|
|<u>904.357…</u>
|''907.462…''
|<nowiki>9 9|9 2</nowiki>
|
|-
|
|55\485
|
|<u>904.112…</u>
|''907.216…''
|<nowiki>13 13|13 3</nowiki>
|
|-
|
|72\635
|
|<u>903.982…</u>
|''907.086…''
|<nowiki>17 17|17 4</nowiki>
|
|-
|
|89\785
|
|<u>903.902…</u>
|''907.006…''
|<nowiki>21 21|21 5</nowiki>
|
|-
| |17\30
| |
| |
| |<u>903.564…</u>
|''906.{{Overline|6}}''
| |<nowiki>4 4|4 1</nowiki>
| |L/s = 4
|-
|
|115\1015
|
|<u>903.302…</u>
|''906.403…''
|<nowiki>27 27|27 7</nowiki>
|
|-
|
|98\865
|
|<u>903.257…</u>
|''906.358…''
|<nowiki>23 23|23 6</nowiki>
|
|-
|
|81\715
|
|<u>903.192…</u>
|''906.293…''
|<nowiki>19 19|19 5</nowiki>
|
|-
|
|64\565
|
|<u>903.094…</u>
|''906.194…''
|<nowiki>15 15|15 4</nowiki>
|
|-
|
|47\415
|
|<u>902.924…</u>
|''906.024…''
|<nowiki>11 11|11 3</nowiki>
|
|-
| |
| |30\265
| |
| |<u>902.561…</u>
|''905.660…''
| |<nowiki>7 7|7 2</nowiki>
| |
|-
|
|
|73\645
|<u>902.328…</u>
|''905.426…''
|<nowiki>17 17|17 5</nowiki>
|
|-
| |
| |43\380
| |
| |<u>902.165…</u>
|''905.263…''
| |<nowiki>10 10|10 3</nowiki>
| |
|-
| |
| |56\495
| |
| |<u>901.953…</u>
|''905.{{Overline|05}}''
| |<nowiki>13 13|13 4</nowiki>
| |
|-
| |
| |69\610
| |
| |<u>901.921…</u>
|''904.918…''
| |<nowiki>16 16|16 5</nowiki>
| |
|-
| |
| |82\725
| |
| |<u>901.731…</u>
|''904.827…''
| |<nowiki>19 19|19 6</nowiki>
| |
|-
| |
| |95\840
| |
| |<u>901.666…</u>
|''904.761…''
| |<nowiki>22 22|22 7</nowiki>
| |
|-
| |
| |
| |
| |<u>901.662…</u>
|''904.758…''
| |<nowiki>π π|π 1</nowiki>
| |L/s = π
|-
| |
| |108\955
| |
| |<u>901.616…</u>
|''904.712…''
| |<nowiki>25 25|25 8</nowiki>
| |
|-
| |
| |121\1070
| |
| |<u>901.577…</u>
|''904.672…''
| |<nowiki>28 28|28 9</nowiki>
| |28;9 Superdiatonic 1/28-tone
|-
| |
| |134\1185
| |
| |<u>901.546…</u>
|''904.642…''
| |<nowiki>31 31|31 10</nowiki>
| |
|-
| |13\115
| |
| |
| |<u>901.235…</u>
|''904.347…''
| |<nowiki>3 3|3 1</nowiki>
| |Terra Rubra 1/3-tone
|-
| |
| |126\1115
| |
| |<u>900.942…</u>
|''904.035…''
| |<nowiki>29 29|29 10</nowiki>
| |Terra Rubra <span style="font-size: 12.8000001907349px;"><big>1/29-tone</big></span>
|-
| |
| |113\1000
| |
| |<u>900.906…</u>
|''904''
| |<nowiki>26 26|26 9</nowiki>
| |Terra Rubra <span style="font-size: 12.8000001907349px;"><big>1/26-tone</big></span>
|-
| |
| |100\885
| |
| |<u>900.861…</u>
|''903.954…''
| |<nowiki>23 23|23 8</nowiki>
| |
|-
| |
| |87\770
| |
| |<u>900.803…</u>
|''903.896…''
| |<nowiki>20 20|20 7</nowiki>
| |
|-
| |
| |74\655
| |
| |<u>900.724…</u>
|''903.816…''
| |<nowiki>17 17|17 6</nowiki>
| |Terra Rubra 1/17-tone
|-
| |
| |61\840
| |
| |<u>915</u>
|''900.611…''
| |<nowiki>14 14|14 5</nowiki>
| |Terra Rubra 1/14-tone
|-
| |
| |
| |109\965
| |<u>914.685…</u>
|''900.535…''
| |<nowiki>25 25|25 9</nowiki>
| |Terra Rubra 1/25-tone
|-
| |
| |48\425
| |
| |<u>900.437…</u>
|''903.529…''
| |<nowiki>11 11|11 4</nowiki>
| |Terra Rubra 1/11-tone
|-
| |
| |
| |
| |<u>900.324…</u>
|''903.415…''
| |<nowiki>e e|e 1</nowiki>
| |L/s = e
|-
| |
| |35\310
| |
| |<u>900.135…</u>
|''903.225…''
| |<nowiki>8 8|8 3</nowiki>
| |Terra Rubra 1/8-tone
|-
| |
| |
| |92\815
| |<u>899.977…</u>
|''903.067…''
| |<nowiki>21 21|21 8</nowiki>
| |21;8 Superdiatonic 1/21-tone
|-
| |
| |
| |
| |<u>899.950…</u>
|''903.040…''
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"><nowiki>φ+1 φ+1|φ+1 1</nowiki></span>
| |Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)
|-
| |
| |
| |57\505
| |<u>899.880…</u>
|''902.970…''
| |<nowiki>13 13|13 5</nowiki>
| |13;5 Superdiatonic 1/13-tone
|-
|
|
|79\700
|<u>899.767…</u>
|''902.857…''
|<nowiki>18 18|18 7</nowiki>
|
|-
| |
| |22\195
| |
| |<u>899.475…</u>
|''902.564…''
| |<nowiki>5 5|5 2</nowiki>
| |Terra Rubra 1/5-tone
|-
| |
| |
| |75\665
| |<u>899.168…</u>
|''902.255…''
| |<nowiki>17 17|17 7</nowiki>
| |17;7 Superdiatonic 1/17-tone
|-
| |
| |
| |53\470
| |<u>899.040…</u>
|''902.127…''
| |<nowiki>12 12|12 5</nowiki>
| |
|-
| |
| |31\275
| |
| |<u>898.732…</u>
|''901.{{Overline|81}}''
| |<nowiki>7 7|7 3</nowiki>
| |7;3 Superdiatonic 1/7-tone
|-
|
|
|71\630
|<u>898.502…</u>
|''901.587…''
|<nowiki>16 16|16 7</nowiki>
|
|-
| |
| |40\355
| |
| |<u>898.324…</u>
|''901.408…''
| |<nowiki>9 9|9 4</nowiki>
| |9;4 Superdiatonic 1/9-tone
|-
| |
| |49\435
| |
| |<u>898.066…</u>
|''901.149…''
| |<nowiki>11 11|11 5</nowiki>
| |11;5 Superdiatonic 1/11-tone
|-
| |
| |58\515
| |
| |<u>897.888…</u>
|''900.970…''
| |<nowiki>13 13|13 6</nowiki>
| |13;6 Superdiatonic 1/13-tone
|-
|
|67\595
|
|<u>897.758…</u>
|''900.840…''
|<nowiki>15 15|15 7</nowiki>
|
|-
|
|76\675
|
|<u>897.658…</u>
|''900.{{Overline|740}}''
|<nowiki>17 17|17 7</nowiki>
|
|-
|
|85\755
|
|<u>897.580…</u>
|''900.662…''
|<nowiki>19 19|19 9</nowiki>
|
|-
|
|94\835
|
|<u>897.517…</u>
|''900.598…''
|<nowiki>21 21|21 10</nowiki>
|
|-
|
|103\915
|
|<u>897.465…</u>
|''900.564…''
|<nowiki>23 23|23 11</nowiki>
|
|-
|
|112\995
|
|<u>897.421…</u>
|''900.502…''
|<nowiki>25 25|25 12</nowiki>
|
|-
|
|121\1075
|
|<u>897.384…</u>
|''900.465…''
|<nowiki>27 27|27 13</nowiki>
|
|-
| |9\80
| |
| |
| |<u>896.920…</u>
|''900''
| |<nowiki>2 2|2 1</nowiki>
| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
|-
|
|230\2045
|
|<u>896.676…</u>
|''899.755…''
|<nowiki>51 51|51 26</nowiki>
|
|-
|
|221\1965
|
|<u>896.667…</u>
|''899.745…''
|<nowiki>49 49|49 25</nowiki>
|
|-
|
|212\1885
|
|<u>896.656…</u>
|''899.734…''
|<nowiki>47 47|47 24</nowiki>
|
|-
|
|203\1805
|
|<u>896.644…</u>
|''899.722…''
|<nowiki>45 45|45 23</nowiki>
|
|-
|
|194\1725
|
|<u>896.631…</u>
|''899.710…''
|<nowiki>43 43|43 22</nowiki>
|
|-
|
|185\1645
|
|<u>896.617…</u>
|''899.696…''
|<nowiki>41 41|41 21</nowiki>
|
|-
|
|176\1565
|
|<u>896.602…</u>
|''899.680…''
|<nowiki>39 39|39 20</nowiki>
|
|-
|
|167\1485
|
|<u>896.585…</u>
|''899.663…''
|<nowiki>37 37|37 19</nowiki>
|
|-
|
|158\1405
|
|<u>896.565…</u>
|''899.644…''
|<nowiki>35 35|35 18</nowiki>
|
|-
|
|149\1325
|
|<u>896.544…</u>
|''899.622…''
|<nowiki>33 33|33 17</nowiki>
|
|-
|
|140\1245
|
|<u>896.520…</u>
|''899.598…''
|<nowiki>31 31|31 16</nowiki>
|
|-
|
|131\1165
|
|<u>896.492…</u>
|''899.570…''
|<nowiki>29 29|29 15</nowiki>
|
|-
|
|122\1085
|
|<u>896.461…</u>
|''899.539…''
|<nowiki>27 27|27 14</nowiki>
|
|-
|
|113\1005
|
|<u>896.424…</u>
|''899.502…''
|<nowiki>25 25|25 13</nowiki>
|
|-
|
|104\925
|
|<u>896.381…</u>
|''899.459…''
|<nowiki>23 23|23 12</nowiki>
|
|-
|
|95\845
|
|<u>896.330…</u>
|''899.408…''
|<nowiki>21 21|21 11</nowiki>
|
|-
|
|86\765
|
|<u>896.269…</u>
|''899.346…''
|<nowiki>19 19|19 10</nowiki>
|
|-
|
|77\685
|
|<u>896.193…</u>
|''899.270…''
|<nowiki>17 17|17 9</nowiki>
|
|-
|
|68\605
|
|<u>896.096…</u>
|''899.173…''
|<nowiki>15 15|15 8</nowiki>
|
|-
| |
| |59\525
| |
| |<u>895.971…</u>
|''899.047…''
| |<nowiki>13 13|13 7</nowiki>
| |Terra Rubra 1/13-tone
|-
| |
| |50\445
| |
| |<u>895.800…</u>
|''898.876…''
| |<nowiki>11 11|11 6</nowiki>
| |Terra Rubra 1/11-tone
|-
| |
| |41\365
| |
| |<u>895.555…</u>
|''898.630…''
| |<nowiki>9 9|9 5</nowiki>
| |Terra Rubra 1/9-tone
|-
| |
| |32\285
| |
| |<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>
|-
| |
| |
| |
| |<u>895.030…</u>
|''898.102…''
| |<span style="background-color: #ffffff;"><nowiki>√3 √3|√3 1</nowiki></span>
| |
|-
| |
| |
| |55\490
| |<u>894.886…</u>
|''897.959…''
| |<nowiki>12 12|12 7</nowiki>
| |
|-
| |
| |
| |78\695
| |<u>894.769…</u>
|''897.841…''
| |<nowiki>17 17|17 10</nowiki>
| |Terra Rubra 1/17-tone
|-
| |
| |23\205
| |
| |<u>894.489…</u>
|''897.560…''
| |<nowiki>5 5|5 3</nowiki>
| |5;3 Golden Terra Rubra 1/5-tone
|-
|
|
|83\740
|<u>894.227…</u>
|''897.{{Overline|297}}''
|<nowiki>18 18|18 11</nowiki>
|
|-
| |
| |
| |60\535
| |<u>894.126…</u>
|''897.196…''
| |<nowiki>13 13|13 8</nowiki>
| |13;8 Golden Terra Rubra 1/13-tone
|-
| |
| |
| |
| |<u>894.064…</u>
|''897.133…''
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"><nowiki>φ φ|φ 1</nowiki></span>
| |GOLDEN Terra Rubra (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
|-
| |
| |
| |97\865
| |<u>894.040…</u>
|''897.109…''
| |<nowiki>21 21|21 13</nowiki>
| |21;13 Golden Terra Rubra 1/21-tone
|-
| |
| |37\330
| |
| |<u>893.900…</u>
|''896.{{Overline|96}}''
| |<nowiki>8 8|8 5</nowiki>
| |8;5 Golden Terra Rubra 1/8-tone
|-
|
|
|88\785
|<u>893.746…</u>
|''896.815…''
|<nowiki>19 19|19 12</nowiki>
|
|-
| |
| |51\455
| |
| |<u>893.635…</u>
|''896.703…''
| |<nowiki>11 11|11 7</nowiki>
| |11;7 Superdiatonic 1/11-tone
|-
| |
| |
| |
| |<u>893.629…</u>
|''896.697…''
| |<nowiki>π π|π 2</nowiki>
| |
|-
| |
| |
| |116\1035
| |<u>893.550…</u>
|''896.618…''
| |<nowiki>25 25|25 16</nowiki>
| |25;16 Superdiatonic 1/25-tone
|-
| |
| |65\580
| |
| |<u>893.484…</u>
|''896.551…''
| |<nowiki>14 14|14 9</nowiki>
| |14;9 Superdiatonic 1/14-tone
|-
| |
| |79\705
| |
| |<u>893.386…</u>
|''896.453…''
| |<nowiki>17 17|17 11</nowiki>
| |17;11 Superdiatonic 1/17-tone
|-
| |
| |93\830
| |
| |<u>893.318…</u>
|''896.385…''
| |<nowiki>20 20|20 13</nowiki>
| |
|-
| |
| |107\955
| |
| |<u>893.268…</u>
|''896.335…''
| |<nowiki>23 23|23 15</nowiki>
| |
|-
| |
| |121\1080
| |
| |<u>893.229…</u>
|''896.{{Overline|296}}''
| |<nowiki>26 26|26 17</nowiki>
| |26;17 Superdiatonic 1/26-tone
|-
| |
| |135\1205
| |
| |<u>893.198…</u>
|''896.265…''
| |<nowiki>29 29|29 19</nowiki>
| |29;19 Superdiatonic 1/29-tone
|-
| |14\25
| |
| |
| |<u>892.934…</u>
|''896''
| |<nowiki>3 3|3 2</nowiki>
| |3;2 Golden Terra Rubra 1/3-tone
|-
| |
| |145\1295
| |
| |<u>892.688…</u>
|''895.752…''
| |<nowiki>31 31|31 21</nowiki>
| |31;21 Superdiatonic 1/31-tone
|-
| |
| |131\1170
| |
| |<u>892.661…</u>
|''895.726…''
| |<nowiki>28 28|28 19</nowiki>
| |28;19 Superdiatonic 1/28-tone
|-
| |
| |117\1045
| |
| |<u>892.629…</u>
|''895.693…''
| |<nowiki>25 25|25 17</nowiki>
| |
|-
| |
| |103\920
| |
| |<u>892.587…</u>
|''895.652…''
| |<nowiki>22 22|22 15</nowiki>
| |
|-
| |
| |89\795
| |
| |<u>892.533…</u>
|''895.579…''
| |<nowiki>19 19|19 13</nowiki>
| |
|-
| |
| |75\670
| |
| |<u>892.458…</u>
|''895.522…''
| |<nowiki>16 16|16 11</nowiki>
| |
|-
| |
| |61\545
| |
| |<u>892.349…</u>
|''895.412…''
| |<nowiki>13 13|13 9</nowiki>
| |
|-
| |
| |47\420
| |
| |<u>892.174…</u>
|''895.238…''
| |<nowiki>10 10|10 7</nowiki>
| |
|-
|
|
|80\715
|<u>892.042…</u>
|''895.104…''
|<nowiki>17 17|17 12</nowiki>
|
|-
| |
| |33\295
| |
| |<u>891.853…</u>
|''894.915…''
| |<nowiki>7 7|7 5</nowiki>
| |
|-
|
|
|85\760
|<u>891.675…</u>
|''894.736…''
|<nowiki>18 18|18 13</nowiki>
|
|-
|
|52\465
|
|<u>891.562…</u>
|''894.623…''
|<nowiki>11 11|11 8</nowiki>
|
|-
|
|71\635
|
|<u>891.427…</u>
|''894.488…''
|<nowiki>15 15|15 11</nowiki>
|
|-
| |19\170
| |
| |
| |<u>891.058…</u>
|''894.117…''
| |<nowiki>4 4|4 3</nowiki>
| |
|-
|
|62\555
|
|<u>890.635…</u>
|''893.{{Overline|693}}''
|<nowiki>13 13|13 10</nowiki>
|
|-
|
|43\385
|
|<u>890.449…</u>
|''893.506…''
|<nowiki>9 9|9 7</nowiki>
|
|-
|
|67\600
|
|<u>890.276…</u>
|''893.{{Overline|3}}''
|<nowiki>14 14|14 11</nowiki>
|
|-
|24\215
|
|
|<u>889.967…</u>
|''893.023…''
|<nowiki>5 5|5 4</nowiki>
|
|-
|
|53\475
|
|<u>889.577…</u>
|''892.631…''
|<nowiki>11 11|11 9</nowiki>
|
|-
|29\260
|
|
|<u>889.254…</u>
|''892.307…''
|<nowiki>6 6|6 5</nowiki>
|
|-
| |5\[[9edX|9]]
| |
| |
| |<u>885.847…</u>
|''888.{{Overline|8}}''
| |<nowiki>1 1|1 1</nowiki>
| |
|}
=== Tempered commas ===
=== 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.  
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.  

Revision as of 05:39, 7 July 2022

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.

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.

Scale tree

Generator Generator size (cents) Generator size (ed4\3) Pentachord steps Comments
4\35 911.157… 914.285… 1 1|1 0
25\220 905.980… 909.09 6 6|6 1
71\625 905.690… 908.8 17 17|17 3
46\405 905.532… 908.641… 11 11|11 2
67\590 905.366… 908.474… 16 16|16 3
21\185 905.000… 908.108 5 5|5 1
80\705 904.695… 907.801… 19 19|19 4
59\520 904.586… 907.692… 14 14|14 3
38\335 904.357… 907.462… 9 9|9 2
55\485 904.112… 907.216… 13 13|13 3
72\635 903.982… 907.086… 17 17|17 4
89\785 903.902… 907.006… 21 21|21 5
17\30 903.564… 906.6 4 4|4 1 L/s = 4
115\1015 903.302… 906.403… 27 27|27 7
98\865 903.257… 906.358… 23 23|23 6
81\715 903.192… 906.293… 19 19|19 5
64\565 903.094… 906.194… 15 15|15 4
47\415 902.924… 906.024… 11 11|11 3
30\265 902.561… 905.660… 7 7|7 2
73\645 902.328… 905.426… 17 17|17 5
43\380 902.165… 905.263… 10 10|10 3
56\495 901.953… 905.05 13 13|13 4
69\610 901.921… 904.918… 16 16|16 5
82\725 901.731… 904.827… 19 19|19 6
95\840 901.666… 904.761… 22 22|22 7
901.662… 904.758… π π|π 1 L/s = π
108\955 901.616… 904.712… 25 25|25 8
121\1070 901.577… 904.672… 28 28|28 9 28;9 Superdiatonic 1/28-tone
134\1185 901.546… 904.642… 31 31|31 10
13\115 901.235… 904.347… 3 3|3 1 Terra Rubra 1/3-tone
126\1115 900.942… 904.035… 29 29|29 10 Terra Rubra 1/29-tone
113\1000 900.906… 904 26 26|26 9 Terra Rubra 1/26-tone
100\885 900.861… 903.954… 23 23|23 8
87\770 900.803… 903.896… 20 20|20 7
74\655 900.724… 903.816… 17 17|17 6 Terra Rubra 1/17-tone
61\840 915 900.611… 14 14|14 5 Terra Rubra 1/14-tone
109\965 914.685… 900.535… 25 25|25 9 Terra Rubra 1/25-tone
48\425 900.437… 903.529… 11 11|11 4 Terra Rubra 1/11-tone
900.324… 903.415… e e|e 1 L/s = e
35\310 900.135… 903.225… 8 8|8 3 Terra Rubra 1/8-tone
92\815 899.977… 903.067… 21 21|21 8 21;8 Superdiatonic 1/21-tone
899.950… 903.040… φ+1 φ+1|φ+1 1 Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)
57\505 899.880… 902.970… 13 13|13 5 13;5 Superdiatonic 1/13-tone
79\700 899.767… 902.857… 18 18|18 7
22\195 899.475… 902.564… 5 5|5 2 Terra Rubra 1/5-tone
75\665 899.168… 902.255… 17 17|17 7 17;7 Superdiatonic 1/17-tone
53\470 899.040… 902.127… 12 12|12 5
31\275 898.732… 901.81 7 7|7 3 7;3 Superdiatonic 1/7-tone
71\630 898.502… 901.587… 16 16|16 7
40\355 898.324… 901.408… 9 9|9 4 9;4 Superdiatonic 1/9-tone
49\435 898.066… 901.149… 11 11|11 5 11;5 Superdiatonic 1/11-tone
58\515 897.888… 900.970… 13 13|13 6 13;6 Superdiatonic 1/13-tone
67\595 897.758… 900.840… 15 15|15 7
76\675 897.658… 900.740 17 17|17 7
85\755 897.580… 900.662… 19 19|19 9
94\835 897.517… 900.598… 21 21|21 10
103\915 897.465… 900.564… 23 23|23 11
112\995 897.421… 900.502… 25 25|25 12
121\1075 897.384… 900.465… 27 27|27 13
9\80 896.920… 900 2 2|2 1 [BOUNDARY OF PROPRIETY: smaller generators are strictly proper]
230\2045 896.676… 899.755… 51 51|51 26
221\1965 896.667… 899.745… 49 49|49 25
212\1885 896.656… 899.734… 47 47|47 24
203\1805 896.644… 899.722… 45 45|45 23
194\1725 896.631… 899.710… 43 43|43 22
185\1645 896.617… 899.696… 41 41|41 21
176\1565 896.602… 899.680… 39 39|39 20
167\1485 896.585… 899.663… 37 37|37 19
158\1405 896.565… 899.644… 35 35|35 18
149\1325 896.544… 899.622… 33 33|33 17
140\1245 896.520… 899.598… 31 31|31 16
131\1165 896.492… 899.570… 29 29|29 15
122\1085 896.461… 899.539… 27 27|27 14
113\1005 896.424… 899.502… 25 25|25 13
104\925 896.381… 899.459… 23 23|23 12
95\845 896.330… 899.408… 21 21|21 11
86\765 896.269… 899.346… 19 19|19 10
77\685 896.193… 899.270… 17 17|17 9
68\605 896.096… 899.173… 15 15|15 8
59\525 895.971… 899.047… 13 13|13 7 Terra Rubra 1/13-tone
50\445 895.800… 898.876… 11 11|11 6 Terra Rubra 1/11-tone
41\365 895.555… 898.630… 9 9|9 5 Terra Rubra 1/9-tone
32\285 895.172… 898.245… 7 7|7 4 Terra Rubra 1/7-tone (the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b')
895.030… 898.102… √3 √3|√3 1
55\490 894.886… 897.959… 12 12|12 7
78\695 894.769… 897.841… 17 17|17 10 Terra Rubra 1/17-tone
23\205 894.489… 897.560… 5 5|5 3 5;3 Golden Terra Rubra 1/5-tone
83\740 894.227… 897.297 18 18|18 11
60\535 894.126… 897.196… 13 13|13 8 13;8 Golden Terra Rubra 1/13-tone
894.064… 897.133… φ φ|φ 1 GOLDEN Terra Rubra (L/s = φ)
97\865 894.040… 897.109… 21 21|21 13 21;13 Golden Terra Rubra 1/21-tone
37\330 893.900… 896.96 8 8|8 5 8;5 Golden Terra Rubra 1/8-tone
88\785 893.746… 896.815… 19 19|19 12
51\455 893.635… 896.703… 11 11|11 7 11;7 Superdiatonic 1/11-tone
893.629… 896.697… π π|π 2
116\1035 893.550… 896.618… 25 25|25 16 25;16 Superdiatonic 1/25-tone
65\580 893.484… 896.551… 14 14|14 9 14;9 Superdiatonic 1/14-tone
79\705 893.386… 896.453… 17 17|17 11 17;11 Superdiatonic 1/17-tone
93\830 893.318… 896.385… 20 20|20 13
107\955 893.268… 896.335… 23 23|23 15
121\1080 893.229… 896.296 26 26|26 17 26;17 Superdiatonic 1/26-tone
135\1205 893.198… 896.265… 29 29|29 19 29;19 Superdiatonic 1/29-tone
14\25 892.934… 896 3 3|3 2 3;2 Golden Terra Rubra 1/3-tone
145\1295 892.688… 895.752… 31 31|31 21 31;21 Superdiatonic 1/31-tone
131\1170 892.661… 895.726… 28 28|28 19 28;19 Superdiatonic 1/28-tone
117\1045 892.629… 895.693… 25 25|25 17
103\920 892.587… 895.652… 22 22|22 15
89\795 892.533… 895.579… 19 19|19 13
75\670 892.458… 895.522… 16 16|16 11
61\545 892.349… 895.412… 13 13|13 9
47\420 892.174… 895.238… 10 10|10 7
80\715 892.042… 895.104… 17 17|17 12
33\295 891.853… 894.915… 7 7|7 5
85\760 891.675… 894.736… 18 18|18 13
52\465 891.562… 894.623… 11 11|11 8
71\635 891.427… 894.488… 15 15|15 11
19\170 891.058… 894.117… 4 4|4 3
62\555 890.635… 893.693 13 13|13 10
43\385 890.449… 893.506… 9 9|9 7
67\600 890.276… 893.3 14 14|14 11
24\215 889.967… 893.023… 5 5|5 4
53\475 889.577… 892.631… 11 11|11 9
29\260 889.254… 892.307… 6 6|6 5
5\9 885.847… 888.8 1 1|1 1

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.

References

Retrieved from "https://en.xen.wiki/index.php?title=User:Eliora/5ed100&oldid=93327"