|
|
| Line 1: |
Line 1: |
| | THIS LIST IS SORTABLE, so you can sort by name or by pergen, and look up a specific temperament. Rules for choosing comma sets: prime limit strictly ascends, no torsion allowed, primes excluded because of downward inheritances are not allowed in other commas, and [[Odd limit|double-odd-limit]] is minimized. See: [[Color notation/Temperament Names|Color Notation/Temperament names]]. |
| | * Color name column: alternatives or objections are '''bolded''' |
| | * Pergen column: all double-splits are false doubles unless otherwise noted. |
| | * Commas column: ratios are grouped by prime limit with actual commas (","), and sorted within prime-limit by [[Odd limit|double odd limit]]. |
| | * Co = Complexity = corresponds roughly to the odd limit of the commas |
| | * Err = Error = corresponds roughly to the cents discrepancy from JI |
| | * Bad = Badness = a combination of complexity and error |
|
| |
|
| ya, za, ila and tha (1 comma)
| | == 1 comma == |
| | |
|
| |
|
| | === ya, za, ila and tha === |
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| |- | | |- |
| Line 421: |
Line 428: |
| |} | | |} |
|
| |
|
| | == 2 commas == |
|
| |
|
| yaza (2 commas) | | === yaza === |
| | |
|
| |
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| |- | | |- |
| Line 2,118: |
Line 2,124: |
| | style="font-size:0px;" | <<13 67 -6 76 -46 -202]] | | | style="font-size:0px;" | <<13 67 -6 76 -46 -202]] |
| |} | | |} |
|
| |
|
| |
|
| |
|
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| Line 2,344: |
Line 2,348: |
| |} | | |} |
|
| |
|
| | | === yala === |
| | | to do: remove za from the list |
| yazala (3 commas)
| |
|
| |
|
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| Line 3,857: |
Line 3,860: |
| | | 31.857 | | | | 31.857 |
| |} | | |} |
|
| |
|
| |
|
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| Line 4,120: |
Line 4,122: |
| |} | | |} |
|
| |
|
| | | === zala === |
| 3 commas
| | To do: remove ya from the list |
| | |
| yazala
| |
| | |
| | |
| (The original version of this page is here: [[Catalog of eleven-limit rank two temperaments]].)
| |
| | |
| Below is a '''complete''' listing of all 193 11-limit rank-two temperaments with TE complexity less than 16 and TE badness less than 1/30, obtained by the method discussed [[The_wedgie|here]]. The TE error is multiplied by 1200 so that it can be thought of as cents, and the badness is multiplied by 1000. Some "Junk" temperaments of very Low complexity are listed below the main list, which is ordered by increasing complexity.
| |
| | |
| =Temperament list= | |
| THIS LIST IS SORTABLE, so you can sort by name or by pergen, and look up a specific temperament. Rules for choosing comma sets: prime limit strictly ascends, no torsion allowed, primes excluded because of downward inheritances are not allowed in other commas, and [[Odd limit|double-odd-limit]] is minimized. See: [[Color notation/Temperament Names|Color Notation/Temperament names]].
| |
| * Color name column: alternatives or objections are '''bolded'''
| |
| * Pergen column: all double-splits are false doubles unless otherwise noted.
| |
| * Commas column: ratios are grouped by prime limit with actual commas (","), and sorted within prime-limit by [[Odd limit|double odd limit]].
| |
| * Co = Complexity = corresponds roughly to the odd limit of the commas
| |
| * Err = Error = corresponds roughly to the cents discrepancy from JI
| |
| * Bad = Badness = a combination of complexity and error
| |
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| |- | | |- |
| Line 5,647: |
Line 5,633: |
| | | 31.857 | | | | 31.857 |
| |} | | |} |
|
| |
|
| |
|
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| Line 5,910: |
Line 5,895: |
| |} | | |} |
|
| |
|
| | == 3 commas == |
|
| |
|
| | | === yazala === |
| | |
| | |
| | |
| | |
| (The original version of this page is here: [[Catalog of eleven-limit rank two temperaments]].)
| |
| | |
| Below is a '''complete''' listing of all 193 11-limit rank-two temperaments with TE complexity less than 16 and TE badness less than 1/30, obtained by the method discussed [[The_wedgie|here]]. The TE error is multiplied by 1200 so that it can be thought of as cents, and the badness is multiplied by 1000. Some "Junk" temperaments of very Low complexity are listed below the main list, which is ordered by increasing complexity.
| |
| | |
| =Temperament list= | |
| THIS LIST IS SORTABLE, so you can sort by name or by pergen, and look up a specific temperament. Rules for choosing comma sets: prime limit strictly ascends, no torsion allowed, primes excluded because of downward inheritances are not allowed in other commas, and [[Odd limit|double-odd-limit]] is minimized. See: [[Color notation/Temperament Names|Color Notation/Temperament names]].
| |
| * Color name column: alternatives or objections are '''bolded'''
| |
| * Pergen column: all double-splits are false doubles unless otherwise noted.
| |
| * Commas column: ratios are grouped by prime limit with actual commas (","), and sorted within prime-limit by [[Odd limit|double odd limit]].
| |
| * Co = Complexity = corresponds roughly to the odd limit of the commas
| |
| * Err = Error = corresponds roughly to the cents discrepancy from JI
| |
| * Bad = Badness = a combination of complexity and error
| |
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| |- | | |- |
| Line 7,438: |
Line 7,408: |
| |} | | |} |
|
| |
|
| =Junk temperaments=
| |
| Some of these contain the trivial commas 1-edo, Yobi, Rubi and Loquad, which set some prime to some number of octaves, and in effect remove the prime from the subgroup. These trivial commas can be omitted from the temperament name if desired.
| |
|
| |
| A fourth comma is included in the comma list if it has the same or smaller odd limit, and roughly the same or smaller size in cents. This comma isn't used in the temperament name, and is in parentheses.
| |
| {| class="wikitable sortable" | | {| class="wikitable sortable" |
| |- | | |- |