Xenharmonic Wiki

Kleismic family: Difference between revisions

← Older edit
VisualWikitext
m Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"
Tags: Mobile edit Mobile web edit
Jerdle (talk | contribs)
autopatrolled, emailconfirmed
227 edits
→Marfifths: The major tenth is a compound major third, 10/3 is a compound major sixth.
 
(5 intermediate revisions by 3 users not shown)
Line 6: Line 6:
}}
}}
{{Technical data page}}
{{Technical data page}}
The [[5-limit]] parent comma for the '''kleismic family''' is [[15625/15552]], the kleisma. The [[generator]] is a [[6/5|classical minor third (6/5)]], and to get to the interval class of [[5/4|major thirds]] requires five of these, and so to get to [[3/2|fifths]] requires six. In fact, (6/5)<sup>5</sup> = 5/2 × 15625/15552. This 5-limit temperament (virtually a [[microtemperament]]) is sometimes called '''hanson''', and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
The [[5-limit]] parent comma for the '''kleismic family''' is [[15625/15552]], the kleisma. The [[generator]] is a [[6/5|classical minor third (6/5)]], and to get to the interval class of [[5/4|major thirds]] requires five of these, and so to get to [[3/2|fifths]] requires six. In fact, (6/5)<sup>5</sup> = 5/2 × 15625/15552. This 5-limit temperament (virtually a [[microtemperament]]) is sometimes called ''hanson'', and 14\53 is about perfect as a generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].


The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. [[875/864]], the keemic comma, gives keemun. [[4375/4374]], the ragisma, gives catakleismic. [[5120/5103]], hemifamity, gives countercata. [[6144/6125]], the porwell comma, gives hemikleismic. [[245/243]], sensamagic, gives clyde. [[1029/1024]], the gamelisma, gives tritikleismic. [[2401/2400]] the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3-octave period with minor third generator, and quadritikleismic a 1/4-octave period with the minor third generator.
The second comma of the [[normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. [[875/864]], the keemic comma, gives keemun. [[4375/4374]], the ragisma, gives catakleismic. [[5120/5103]], hemifamity, gives countercata. [[6144/6125]], the porwell comma, gives hemikleismic. [[245/243]], sensamagic, gives clyde. [[1029/1024]], the gamelisma, gives tritikleismic. [[2401/2400]] the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3-octave period with minor third generator, and quadritikleismic a 1/4-octave period with the minor third generator.


== Hanson ==
== Kleismic a.k.a. hanson ==
{{Main| Hanson and cata }}
{{Main| Kleismic }}


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 33: Line 33:
[[Badness]]: 0.013234
[[Badness]]: 0.013234


=== Cata ===
=== 2.3.5.13 subgroup (cata) ===
Hanson lends itself nicely to this extension in the 2.3.5.13 subgroup, as the hemitwelfth, reached by three generator steps, can be interpreted as [[26/15]]. Notice 15625/15552 = ([[325/324]])([[625/624]]) and 325/324 = (625/624)([[676/675]]). The [[S-expression]]-based comma list of the temperament is {[[325/324|S10/S12 = S25*S26]], ([[625/624|S25]],) [[676/675|S13/S15 = S26]]}. For the high-limit version of cata with a 1\5 period, see [[thunderclysmic]].
Hanson lends itself nicely to this extension in the 2.3.5.13 subgroup, as the hemitwelfth, reached by three generator steps, can be interpreted as [[26/15]]. Notice 15625/15552 = ([[325/324]])([[625/624]]) and 325/324 = (625/624)([[676/675]]). The [[S-expression]]-based comma list of the temperament is {[[325/324|S10/S12 = S25*S26]], ([[625/624|S25]],) [[676/675|S13/S15 = S26]]}. For the high-limit version of cata with a 1\5 period, see [[thunderclysmic]].


Line 58: Line 58:


{{Mapping|legend=1| 1 0 1 2 | 0 6 5 3 }}
{{Mapping|legend=1| 1 0 1 2 | 0 6 5 3 }}
{{Multival|legend=1| 6 5 3 -6 -12 -7 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 316.473
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 316.473
Line 78: Line 76:


Mapping: {{mapping| 1 0 1 2 4 | 0 6 5 3 -2 }}
Mapping: {{mapping| 1 0 1 2 4 | 0 6 5 3 -2 }}
{{Multival|legend=1| 6 5 3 -2 -6 -12 -24 -7 -22 -16 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.576
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.576
Line 97: Line 93:


Mapping: {{mapping| 1 0 1 2 4 5 | 0 6 5 3 -2 -5 }}
Mapping: {{mapping| 1 0 1 2 4 5 | 0 6 5 3 -2 -5 }}
{{Multival|legend=1| 6 5 3 -2 -5 -6 -12 -24 -30 -7 -22 -30 -16 -25 -10 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.611
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.611
Line 199: Line 193:


{{Mapping|legend=1| 1 0 1 6 | 0 6 5 -12 }}
{{Mapping|legend=1| 1 0 1 6 | 0 6 5 -12 }}
{{Multival|legend=1| 6 5 -12 -6 -36 -42 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 318.267
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 318.267
Line 251: Line 243:


{{Mapping|legend=1| 1 0 1 -3 | 0 6 5 22 }}
{{Mapping|legend=1| 1 0 1 -3 | 0 6 5 22 }}
{{Multival|legend=1| 6 5 22 -6 18 37 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 316.732
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 316.732
Line 285: Line 275:


Mapping: {{mapping| 1 0 1 -3 9 | 0 6 5 22 -21 }}
Mapping: {{mapping| 1 0 1 -3 9 | 0 6 5 22 -21 }}
{{Multival|legend=1| 6 5 22 -21 -6 18 -54 37 -66 -135 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.719
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.719
Line 304: Line 292:


Mapping: {{mapping| 1 0 1 -3 9 0 | 0 6 5 22 -21 14 }}
Mapping: {{mapping| 1 0 1 -3 9 0 | 0 6 5 22 -21 14 }}
{{Multival|legend=1| 6 5 22 -21 14 -6 18 -54 0 37 -66 14 -135 -42 126 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.738
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.738
Line 455: Line 441:


{{Mapping|legend=1| 1 0 1 11 | 0 6 5 -31 }}
{{Mapping|legend=1| 1 0 1 11 | 0 6 5 -31 }}
{{Multival|legend=1| 6 5 -31 -6 -66 -86 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.121
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.121
Line 474: Line 458:


Mapping: {{mapping| 1 0 1 11 -5 | 0 6 5 -31 32 }}
Mapping: {{mapping| 1 0 1 11 -5 | 0 6 5 -31 32 }}
{{Multival|legend=1| 6 5 -31 32 -6 -66 30 -86 57 197 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.162
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.162
Line 493: Line 475:


Mapping: {{mapping| 1 0 1 11 -5 0 | 0 6 5 -31 32 14 }}
Mapping: {{mapping| 1 0 1 11 -5 0 | 0 6 5 -31 32 14 }}
{{Multival|legend=1| 6 5 -31 32 14 -6 -66 30 0 -86 57 14 197 154 -70 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.162
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.162
Line 513: Line 493:


{{Mapping|legend=1| 1 0 1 -12 | 0 6 5 56 }}
{{Mapping|legend=1| 1 0 1 -12 | 0 6 5 56 }}
{{Multival|legend=1| 6 5 56 -6 72 116 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.314
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 317.314
Line 528: Line 506:


Mapping: {{mapping| 1 0 1 -12 -5 | 0 6 5 56 32 }}
Mapping: {{mapping| 1 0 1 -12 -5 | 0 6 5 56 32 }}
{{Multival|legend=1| 6 5 56 32 -6 72 30 116 57 -104 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.311
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.311
Line 543: Line 519:


Mapping: {{mapping| 1 0 1 -12 -5 0 | 0 6 5 56 32 14 }}
Mapping: {{mapping| 1 0 1 -12 -5 0 | 0 6 5 56 32 14 }}
{{Multival|legend=1| 6 5 56 32 14 -6 72 30 0 116 57 14 -104 -168 -70 }}


Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.311
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 317.311
Line 558: Line 532:


{{Mapping|legend=1| 1 0 1 4 | 0 12 10 -9 }}
{{Mapping|legend=1| 1 0 1 4 | 0 12 10 -9 }}
{{Multival|legend=1| 12 10 -9 -12 -48 -49 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/32 = 158.649
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/32 = 158.649
Line 573: Line 545:


Mapping: {{mapping| 1 0 1 4 2 | 0 12 10 -9 11 }}
Mapping: {{mapping| 1 0 1 4 2 | 0 12 10 -9 11 }}
{{Multival|legend=1| 12 10 -9 11 -12 -48 -24 -49 -9 62 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 158.677
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 158.677
Line 588: Line 558:


Mapping: {{mapping| 1 0 1 4 2 0 | 0 12 10 -9 11 28 }}
Mapping: {{mapping| 1 0 1 4 2 0 | 0 12 10 -9 11 28 }}
{{Multival|legend=1| 12 10 -9 11 28 -12 -48 -24 0 -49 -9 28 62 112 56 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 158.655
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 158.655
Line 605: Line 573:


: mapping generators: ~2, ~9/7
: mapping generators: ~2, ~9/7
{{Multival|legend=1| 12 10 25 -12 6 30 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 441.335
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 441.335
Line 613: Line 579:
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~9/7 = {{monzo| 12/25 0 0 -1/25 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~9/7 = {{monzo| 12/25 0 0 -1/25 }}
: {{monzo list| 1 0 0 0 | 6/25 0 0 12/25 | 6/5 0 0 2/5 | 0 0 0 1 }}
: {{monzo list| 1 0 0 0 | 6/25 0 0 12/25 | 6/5 0 0 2/5 | 0 0 0 1 }}
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7


[[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges.
[[Algebraic generator]]: real root of 5''x''<sup>3</sup> - 6''x'' - 3, the Poussami generator. Approximately 441.309 [[cent]]s. Associated recurrence relationship quickly converges.
Line 627: Line 593:


Mapping: {{mapping| 1 6 6 12 -5 | 0 -12 -10 -25 23 }}
Mapping: {{mapping| 1 6 6 12 -5 | 0 -12 -10 -25 23 }}
{{Multival|legend=1| 12 10 25 -23 -12 6 -78 30 -88 -151 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 441.355
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 441.355
Line 642: Line 606:


Mapping: {{mapping| 1 6 6 12 -5 14 | 0 -12 -10 -25 23 -28 }}
Mapping: {{mapping| 1 6 6 12 -5 14 | 0 -12 -10 -25 23 -28 }}
{{Multival|legend=1| 12 10 25 -23 28 -12 6 -78 0 30 -88 28 -151 -14 182 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 441.363
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 441.363
Line 659: Line 621:


: mapping generators: ~63/50, ~6/5
: mapping generators: ~63/50, ~6/5
{{Multival|legend=1| 18 15 -6 -18 -60 -56 }}


[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~6/5 = 316.872 (~21/20 = 83.128)
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~6/5 = 316.872 (~21/20 = 83.128)
Line 667: Line 627:
* [[7-odd-limit]]: ~6/5 = {{monzo| 1/3 0 1/7 -1/7 }}
* [[7-odd-limit]]: ~6/5 = {{monzo| 1/3 0 1/7 -1/7 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5
* [[9-odd-limit]]: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
* [[9-odd-limit]]: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7


{{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }}
{{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }}
Line 685: Line 645:


Mapping: {{mapping| 3 0 3 10 8 | 0 6 5 -2 3 }}
Mapping: {{mapping| 3 0 3 10 8 | 0 6 5 -2 3 }}
{{Multival|legend=1| 18 15 -6 9 -18 -60 -48 -56 -31 46 }}


Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.881 (~21/20 = 83.119)
Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.881 (~21/20 = 83.119)
Line 693: Line 651:
* 11-odd-limit: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
* 11-odd-limit: ~6/5 = {{monzo| 5/21 1/7 0 -1/14 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
: eigenmonzo (unchanged-interval) basis: 2.9/7
: unchanged-interval (eigenmonzo) basis: 2.9/7


{{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }}
{{Optimal ET sequence|legend=1| 15, 42bc, 57, 72, 159, 231 }}
Line 705: Line 663:


Mapping: {{mapping| 3 0 3 10 8 0 | 0 6 5 -2 3 14 }}
Mapping: {{mapping| 3 0 3 10 8 0 | 0 6 5 -2 3 14 }}
{{Multival|legend=1| 18 15 -6 9 42 -18 -60 -48 0 -56 -31 42 46 140 112 }}


Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.9585 (~21/20 = 83.0415)
Optimal tuning (POTE): ~44/35 = 1\3, ~6/5 = 316.9585 (~21/20 = 83.0415)
Line 735: Line 691:


: mapping generators: ~25/21, ~6/5
: mapping generators: ~25/21, ~6/5
{{Multival|legend=1| 24 20 16 -24 -42 -19 }}


[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~6/5 = 316.9999 (~126/125 = 16.9999)
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~6/5 = 316.9999 (~126/125 = 16.9999)
Line 750: Line 704:


Mapping: {{mapping| 4 0 4 7 17 | 0 6 5 4 -3 }}
Mapping: {{mapping| 4 0 4 7 17 | 0 6 5 4 -3 }}
{{Multival|legend=1| 24 20 16 -12 -24 -42 -102 -19 -97 -89 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9247 (~100/99 = 16.9247)
Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9247 (~100/99 = 16.9247)
Line 765: Line 717:


Mapping: {{mapping| 4 0 4 7 17 0 | 0 6 5 4 -3 14 }}
Mapping: {{mapping| 4 0 4 7 17 0 | 0 6 5 4 -3 14 }}
{{Multival|legend=1| 24 20 16 -12 56 -24 -42 -102 0 -19 -97 56 -89 98 238 }}


Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9887 (~100/99 = 16.9887)
Optimal tuning (POTE): ~25/21 = 1\4, ~6/5 = 316.9887 (~100/99 = 16.9887)
Line 795: Line 745:


: mapping generators: ~2, ~25/21
: mapping generators: ~2, ~25/21
{{Multival|legend=1| 18 15 13 -18 -30 -12 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 294.303
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 294.303
Line 831: Line 779:


== Marfifths ==
== Marfifths ==
The ''marfifths'' temperament (19&amp;140) tempers out the [[hemimage comma]], 10976/10935. It splits the interval of major tenth (~10/3) into three marvelous fifth ([[112/75]]) intervals, and uses it for a generator.
The ''marfifths'' temperament (19&amp;140) tempers out the [[hemimage comma]], 10976/10935. It splits the interval of a major thirteenth (~10/3) into three marvelous fifth ([[112/75]]) intervals, and uses it for a generator.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 839: Line 787:
{{Mapping|legend=1| 1 -6 -4 -17 | 0 18 15 47 }}
{{Mapping|legend=1| 1 -6 -4 -17 | 0 18 15 47 }}


: mapping generators: ~2, ~75/56
: mapping generators: ~2, ~75/5
 
{{Multival|legend=1| 18 15 47 -18 24 67 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/56 = 505.705
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/56 = 505.705
Line 941: Line 887:


: mapping generators: ~2, ~56/45
: mapping generators: ~2, ~56/45
{{Multival|legend=1| 24 20 69 -24 42 104 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 379.252
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 379.252
Line 1,027: Line 971:


: mapping generators: ~2592/2401, ~6/5
: mapping generators: ~2592/2401, ~6/5
{{Multival|legend=1| 54 45 54 -54 -66 -1 }}


[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 1\9, ~6/5 = 317.005 (~36/35 = 50.338)
[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 1\9, ~6/5 = 317.005 (~36/35 = 50.338)
Line 1,074: Line 1,016:


: mapping generators: ~2, 125/98
: mapping generators: ~2, 125/98
{{Multival|legend=1| 30 25 38 -30 -24 18 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/98 = 416.603
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/98 = 416.603
Line 1,089: Line 1,029:


Mapping: {{mapping| 1 12 11 16 17 | 0 -30 -25 -38 -39 }}
Mapping: {{mapping| 1 12 11 16 17 | 0 -30 -25 -38 -39 }}
{{Multival|legend=1| 30 25 38 39 -30 -24 -42 18 4 -22 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.604
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.604
Line 1,104: Line 1,042:


Mapping: {{mapping| 1 12 11 16 17 28 | 0 -30 -25 -38 -39 -70 }}
Mapping: {{mapping| 1 12 11 16 17 28 | 0 -30 -25 -38 -39 -70 }}
{{Multival|legend=1| 30 25 38 39 70 -30 -24 -42 0 18 4 70 -22 56 98 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.585
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.585
Line 1,149: Line 1,085:


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Kleismic family| ]] <!-- main article -->
[[Category:Kleismic family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/Kleismic_family"