User:FloraC/Sequence of equal temperaments by error/Supplement: Difference between revisions

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This just occurred to me when doing the temperament measures table for [[31edo]]. All GPVs (and only GPVs) are accounted. How I did it: [[Patent val/Properties]].  
For a method to iterate thru all GPVs, see [[Patent val/Properties]]. GPVs starting with a zero are excluded as they would meddle with the results. 


* 3-limit: {{EDOs| 1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867 }}…
The '''tier''' of an equal temperament is defined as the number of GPVs before it that is tuned more efficient than it.
* 5-limit: {{EDOs| 1, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296 }}…
* 7-limit: {{EDOs| 1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355 }}…
* 11-limit: {{EDOs| 1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691 }}…
* 13-limit: {{EDOs| 2cde, 2f, 3, 3de, 3def, 4ef, 5e, 7, 8d, 9, 12f, 19e, 19, 27e, 31, 41, 53, 58, 72, 224, 270, 494, 1506, 2190, 2684, 5585, 6079, 14618 }}…
* 17-limit: {{EDOs| 4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203 }}…
* 19-limit: {{EDOs| 7, 8d, 8dhh, 9g, 9, 12f, 19egh, 26, 27eg, 46, 72, 217, 270, 581, 742, 1178, 1578, 2000, 2460, 3395, 8269, 8539, 16808, 20203 }}…
* 23-limit: {{EDOs| 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808 }}…
* 29-limit: {{EDOs| 26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808 }}…
* 31-limit: {{EDOs| 46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808 }}…
* 37-limit: {{EDOs| 80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808 }}…


* sqrt (2).sqrt (3).5.7.11.13: {{EDOs| 10e, 10, 34d, 58, 72, 270, 2684, 13112 }}…
; 3-limit:
* sqrt (2).sqrt (3).5.7.11.13.17: {{EDOs| 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808 }}…
: {{EDOs| 1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867 }}…
 
; 5-limit:
: {{EDOs| 1, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296 }}…
 
; 7-limit:
: {{EDOs| 1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355 }}…
 
; 11-limit:
: {{EDOs| 1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691 }}…
 
; 13-limit:
: {{EDOs| 2cde, 2f, 3, 3de, 3def, 4ef, 5e, 7, 8d, 9, 12f, 19e, 19, 27e, 31, 41, 53, 58, 72, 224, 270, 494, 1506, 2190, 2684, 5585, 6079, 14618 }}…
 
; 17-limit:
: {{EDOs| 4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203 }}…
 
; 19-limit:
: {{EDOs| 7, 8d, 8dhh, 9g, 9, 12f, 19egh, 26, 27eg, 46, 72, 217, 270, 581, 742, 1178, 1578, 2000, 2460, 3395, 8269, 8539, 16808, 20203 }}…
 
; 23-limit:
: {{EDOs| 14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808 }}…
 
; 29-limit:
: {{EDOs| 26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808 }}…
 
; 31-limit:
: {{EDOs| 46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808 }}…
 
; 7-limit:
: {{EDOs| 80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808 }}…
 
; sqrt (2).sqrt (3).5.7.11.13 subgroup:
: {{EDOs| 10e, 10, 34d, 58, 72, 270, 2684, 13112 }}…
 
; sqrt (2).sqrt (3).5.7.11.13.17 subgroup:
: {{EDOs| 10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808 }}…

Revision as of 02:03, 9 June 2022

For a method to iterate thru all GPVs, see Patent val/Properties. GPVs starting with a zero are excluded as they would meddle with the results.

The tier of an equal temperament is defined as the number of GPVs before it that is tuned more efficient than it.

3-limit
1b, 1, 2, 5, 12, 41, 53, 306, 665, 15601, 31867
5-limit
1, 1c, 2c, 2, 3, 7, 12, 19, 34, 53, 118, 441, 559, 612, 1171, 1783, 2513, 4296
7-limit
1bd, 1c, 2cd, 3d, 4, 5, 10, 12, 19, 31, 72, 99, 171, 3125, 11664, 18355
11-limit
1ce, 2cde, 2, 3de, 5, 7, 8d, 9, 12, 22, 31, 72, 270, 342, 1848, 6079, 6691
13-limit
2cde, 2f, 3, 3de, 3def, 4ef, 5e, 7, 8d, 9, 12f, 19e, 19, 27e, 31, 41, 53, 58, 72, 224, 270, 494, 1506, 2190, 2684, 5585, 6079, 14618
17-limit
4ef, 5eg, 8d, 10, 19eg, 22, 26, 27eg, 31, 46, 72, 494, 1506, 3395, 7033, 16808, 20203
19-limit
7, 8d, 8dhh, 9g, 9, 12f, 19egh, 26, 27eg, 46, 72, 217, 270, 581, 742, 1178, 1578, 2000, 2460, 3395, 8269, 8539, 16808, 20203
23-limit
14cf, 15g, 26i, 29g, 46, 94, 190g, 193, 217, 270, 282, 311, 581, 1578, 2460, 8269, 11664, 16808
29-limit
26i, 46, 58hi, 80, 140, 159, 183, 243e, 311, 954hj, 1578, 16808
31-limit
46, 99efk, 103h, 183, 190g, 217, 311, 954hj, 4501, 16808
7-limit
80k, 99efk, 103hl, 270, 270i, 311, 1395, 1920, 4501, 16808
sqrt (2).sqrt (3).5.7.11.13 subgroup
10e, 10, 34d, 58, 72, 270, 2684, 13112
sqrt (2).sqrt (3).5.7.11.13.17 subgroup
10e, 10, 34d, 58, 72, 742, 954, 2000, 2684, 10356, 10427, 16808