Marvel temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
→Decic: remove breed in subtitle to facilitate linking; remove 10edo as it's trivial; apply new template for wedgie
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
Tags: Mobile edit Mobile web edit
Line 1,658: Line 1,658:


[[Mapping]]: [{{val| 10 0 39 28 }}, {{val| 0 1 -1 0 }}]
[[Mapping]]: [{{val| 10 0 39 28 }}, {{val| 0 1 -1 0 }}]
Mapping generators: ~15/14, ~3


{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
[[Tuning ranges]]:
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* nice range: ~3/2 = [693.686, 701.955]
* strict range: ~3/2 = [696.000, 700.000]


{{Val list|legend=1| 10, 50, 60, 110d }}
{{Val list|legend=1| 10, 50, 60, 110d }}
Line 1,686: Line 1,693:


Mapping: [{{val| 10 0 39 28 3 }}, {{val| 0 1 -1 0 2 }}]
Mapping: [{{val| 10 0 39 28 3 }}, {{val| 0 1 -1 0 2 }}]
Mapping generators: ~15/14, ~3
Tuning ranges:
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* nice range: ~3/2 = [693.686, 701.955]
* strict range: ~3/2 = [696.000, 700.000]


{{Val list|legend=1| 10, 50, 60 }}
{{Val list|legend=1| 10, 50, 60 }}
Line 1,711: Line 1,725:


Mapping: [{{val| 10 0 39 28 3 37 }}, {{val| 0 1 -1 0 2 0 }}]
Mapping: [{{val| 10 0 39 28 3 37 }}, {{val| 0 1 -1 0 2 0 }}]
Mapping generators: ~14/13, ~3
Tuning ranges:
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* nice range: ~3/2 = [693.686, 701.955]
* strict range: ~3/2 = [696.000, 700.000]


{{Val list|legend=1| 10, 50, 60 }}
{{Val list|legend=1| 10, 50, 60 }}
Line 1,736: Line 1,757:


Mapping: [{{val| 10 0 39 28 3 37 25 }}, {{val| 0 1 -1 0 2 0 1 }}]
Mapping: [{{val| 10 0 39 28 3 37 25 }}, {{val| 0 1 -1 0 2 0 1 }}]
Mapping generators: ~14/13, ~3
Tuning ranges:
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* nice range: ~3/2 = [693.686, 701.955]
* strict range: ~3/2 = [696.000, 700.000]


{{Val list|legend=1| 10, 50, 60 }}
{{Val list|legend=1| 10, 50, 60 }}

Revision as of 13:49, 23 March 2021

This page discusses some of the temperaments tempering out [-5 2 2 -1⟩ = 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.

Since (5/4)2 = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.

Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)

Negri

Main article: Negri

Negri tempers out the negri comma in the 5-limit, 49/48 and 225/224 in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 to the comma list; this will be discussed below under the title of negra.

5-limit

Period: 1\1

Optimal (POTE) generator: ~16/15 = 125.7549

EDO generators: 1\9, 1\10, 2\19

Scales (Scala files):

Technical data

Subgroup: 2.3.5

Comma list: 16875/16384

Mapping: [⟨1 2 2], ⟨0 -4 3]]

Wedgie: ⟨⟨4 -3 -14]]

Template:Val list

7-limit

Period: 1\1

Optimal (POTE) generator: ~15/14 = 125.608

EDO generators: 1\9, 1\10, 2\19

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 49/48, 225/224

Mapping: [⟨1 2 2 3], ⟨0 -4 3 -2]]

Wedgie: ⟨⟨4 -3 2 -14 -8 13]]

Template:Val list

Negra

This is the 2.3.5.7.13 extension of negri.

Period: 1\1

Optimal (POTE) generator: ~14/13 = 125.567

EDO generators: 1\9, 1\10, 2\19

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.13

Comma list: 49/48, 65/64, 91/90

Mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -3]]

Gencom map: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3]]

Gencom: [2 14/13; 49/48 65/64 91/90]

Template:Val list

11-limit

Period: 1\1

Optimal (POTE) generator: ~15/14 = 126.474

EDO generators: 1\9, 1\10, 2\19

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 45/44, 49/48, 56/55

Mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -5]]

Template:Val list

Badness: 0.0262

13-limit

Period: 1\1

Optimal (POTE) generator: ~14/13 = 126.431

EDO generators: 1\9, 1\10, 2\19

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 49/48, 56/55, 78/77

POTE generator: ~14/13 = 126.431

Mapping: [⟨1 2 2 3 4 4], ⟨0 -4 3 -2 -5 -3]]

Template:Val list

Negril

Period: 1\1

Optimal (POTE) generator: ~15/14 = 124.767

EDO generators: 2\19, 3\29

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 225/224

Mapping: [⟨1 2 2 3 2], ⟨0 -4 3 -2 14]]

Template:Val list

Badness: 0.0387

13-limit

Period: 1\1

Optimal (POTE) generator: ~14/13 = 124.716

EDO generators: 2\19, 3\29

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 875/858

Mapping: [⟨1 2 2 3 2 4], ⟨0 -4 3 -2 14 -3]]

Template:Val list

Badness: 0.0244

Negric

Period: 1\1

Optimal (POTE) generator: ~15/14 = 127.039

EDO generators: 1\9, 2\19

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 33/32, 49/48, 77/75

Mapping: [⟨1 2 2 3 3], ⟨0 -4 3 -2 4]]

Template:Val list

Badness: 0.0306

13-limit

Period: 1\1

Optimal (POTE) generator: ~14/13 = 127.039

EDO generators: 1\9, 2\19

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 33/32, 49/48, 65/64, 91/90

Mapping: [⟨1 2 2 3 3 4], ⟨0 -4 3 -2 4 -3]]

Template:Val list

Badness: 0.0202

Negroni

Period: 1\1

Optimal (POTE) generator: ~15/14 = 124.539

EDO generators: 1\10, 2\19, 3\29

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 225/224

Mapping: [⟨1 2 2 3 5], ⟨0 -4 3 -2 -15]]

Template:Val list

Badness: 0.0353

13-limit

Period: 1\1

Optimal (POTE) generator: ~14/13 = 124.545

EDO generators: 1\10, 2\19, 3\29

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 65/64, 91/90

Mapping: [⟨1 2 2 3 5 4], ⟨0 -4 3 -2 -15 -3]]

Template:Val list

Badness: 0.0216

Wilsec

Period: 1\1

Optimal (POTE) generator: ~11/8 = 537.186

EDO generators: 13\29, 17\38

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 225/224

Mapping: [⟨1 6 -1 5 4], ⟨0 -8 6 -4 -1]]

Template:Val list

Badness: 0.0419

13-limit

Period: 1\1

Optimal (POTE) generator: ~11/8 = 537.208

EDO generators: 13\29, 17\38

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 121/120

Mapping: [⟨1 6 -1 5 4 7], ⟨0 -8 6 -4 -1 -6]]

Template:Val list

Badness: 0.0252

17-limit

Period: 1\1

Optimal (POTE) generator: ~11/8 = 537.230

EDO generators: 13\29, 17\38

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 65/64, 91/90, 121/120, 154/153

Mapping: [⟨1 6 -1 5 4 7 -2], ⟨0 -8 6 -4 -1 -6 11]]

Template:Val list

Badness: 0.0218

19-limit

Period: 1\1

Optimal (POTE) generator: ~11/8 = 537.214

EDO generators: 13\29, 17\38

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153

Mapping: [⟨1 6 -1 5 4 7 -2 7], ⟨0 -8 6 -4 -1 -6 11 -5]]

Template:Val list

Badness: 0.0168

Passive

See also: Archytas clan § Passion

Period: 1\1

Optimal (POTE) generator: ~16/15 = 98.809

EDO generators: 1\12, 1\13

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 256/245

Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]

Template:Val list

Badness: 0.0751

Wizard

For the 5-limit version of this temperament, see High badness temperaments #Wizard.

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.256

EDO generators: 7\22, 16\50, 23\72, 30\94

Scales (Scala files): wizard22

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 118098/117649

Mapping: [⟨2 1 5 2], ⟨0 6 -1 10]]

Mapping generators: ~1225/864, ~245/216

Wedgie: ⟨⟨12 -2 20 -31 -2 52]]

Template:Val list

Badness: 0.0408

11-limit

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.232

EDO generators: 7\22, 16\50, 23\72, 30\94

Scales (Scala files): wizard22

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 4000/3993

Mapping: [⟨2 1 5 2 8], ⟨0 6 -1 10 -3]]

Mapping generators: ~99/70, ~25/22

Template:Val list

Badness: 0.0185

Lizard

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.389

EDO generators: 16\50, 23\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 351/350, 364/363, 385/384

Mapping: [⟨2 1 5 2 8 11], ⟨0 6 -1 10 -3 -10]]

Mapping generators: ~99/70, ~25/22

Template:Val list

Badness: 0.0218

17-limit

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.381

EDO generators: 16\50, 23\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 273/272, 289/288, 351/350, 375/374

Mapping: [⟨2 1 5 2 8 11 6], ⟨0 6 -1 10 -3 -10 6]]

Mapping generators: ~17/12, ~17/15

Template:Val list

Badness: 0.0145

19-limit

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.477

EDO generators: 16\50, 23\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342

Mapping: [⟨2 1 5 2 8 11 6 2], ⟨0 6 -1 10 -3 -10 6 18]]

Mapping generators: ~17/12, ~17/15

Template:Val list

Badness: 0.0157

Gizzard

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.170

EDO generators: 23\72, 30\94

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 325/324, 385/384, 1573/1568

Mapping: [⟨2 1 5 2 8 -2], ⟨0 6 -1 10 -3 26]]

Mapping generators: ~99/70, ~25/22

Template:Val list

Badness: 0.0203

17-limit

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.175

EDO generators: 23\72, 30\94

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 289/288, 325/324, 375/374, 385/384

Mapping: [⟨2 1 5 2 8 -2 6], ⟨0 6 -1 10 -3 26 6]]

Mapping generators: ~17/12, ~17/15

Template:Val list

Badness: 0.0136

19-limit

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.138

EDO generators: 23\72, 30\94

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594

Mapping: [⟨2 1 5 2 8 -2 6 15], ⟨0 6 -1 10 -3 26 6 -18]]

Mapping generators: ~17/12, ~17/15

Template:Val list

Badness: 0.0148

Mage

Period: 1\2

Optimal (POTE) generator: ~5/4 = 383.124

EDO generators: 7\22, 16\50, 23\72, 30\94

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1331/1296

Mapping: [⟨2 1 5 2 4], ⟨0 6 -1 10 8]]

Mapping generators: ~77/54, ~55/48

Template:Val list

Badness: 0.0578

Triton

For the 5-limit version of this temperament, see High badness temperaments #Stump.

Period: 1\1

Optimal (POTE) generator: ~7/5 = 568.865

EDO generators: 9\19, 10\21

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 1029/1000

Mapping: [⟨1 0 6 7], ⟨0 3 -7 -8]]

Wedgie: ⟨⟨3 -7 -8 -18 -21 1]]

Template:Val list

Badness: 0.0592

11-limit

Period: 1\1

Optimal (POTE) generator: ~7/5 = 569.144

EDO generators: 9\19, 10\21

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 45/44, 56/55, 1029/1000

Mapping: [⟨1 0 6 7 4], ⟨0 3 -7 -8 -1]]

Template:Val list

Badness: 0.0457

Tritonic

For the 5-limit version of this temperament, see High badness temperaments #Tritonic.

Period: 1\1

Optimal (POTE) generator: ~7/5 = 580.286

EDO generators: 14\29, 15\31, 29\60

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 50421/50000

Mapping: [⟨1 4 -3 -3], ⟨0 -5 11 12]]

Wedgie: ⟨⟨5 -11 -12 -29 -33 3]]

Template:Val list

11-limit

Period: 1\1

Optimal (POTE) generator: ~7/5 = 580.267

EDO generators: 14\29, 15\31, 29\60

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 441/440

Mapping: [⟨1 4 -3 -3 2], ⟨0 -5 11 12 3]]

Template:Val list

Badness: 0.0237

13-limit

Period: 1\1

Optimal (POTE) generator: ~7/5 = 580.108

EDO generators: 14\29, 15\31, 29\60

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 121/120, 196/195, 275/273

Mapping: [⟨1 4 -3 -3 2 -5], ⟨0 -5 11 12 3 18]]

Template:Val list

Badness: 0.0230

Tritoni

Period: 1\1

Optimal (POTE) generator: ~7/5 = 580.389

EDO generators: 15\31, 44\91, 59\122

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 27783/27500

Mapping: [⟨1 4 -3 -3 17], ⟨0 -5 11 12 -28]]

Template:Val list

Badness: 0.0455

Merman

For the 5-limit version of this temperament, see High badness temperaments #Merman.

Period: 1\1

Optimal (POTE) generator: ~7/5 = 585.585

EDO generators: 20\41, 21\43, 41\84

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 2500000/2470629

Mapping: [⟨1 5 -5 -5], ⟨0 -7 15 16]]

Wedgie: ⟨⟨7 -15 -16 -40 -45 5]]

Template:Val list

Badness: 0.0551

11-limit

Period: 1\1

Optimal (POTE) generator: ~7/5 = 585.606

EDO generators: 20\41, 21\43, 41\84

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 1344/1331

Mapping: [⟨1 5 -5 -5 2], ⟨0 -7 15 16 3]]

Template:Val list

Badness: 0.0364

13-limit

Period: 1\1

Optimal (POTE) generator: ~7/5 = 585.657

EDO generators: 20\41, 21\43, 41\84

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 225/224, 364/363, 441/440

Mapping: [⟨1 5 -5 -5 2 12], ⟨0 -7 15 16 3 -17]]

Template:Val list

Badness: 0.0275

Septimin

For the 5-limit version of this temperament, see High badness temperaments #Septimin.

Period: 1\1

Optimal (POTE) generator: ~7/6 = 263.632

EDO generators: 9\41, 11\50, 20\91

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 84035/82944

Mapping: [⟨1 4 1 5], ⟨0 -11 6 -10]]

Wedgie: ⟨⟨11 -6 10 -35 -15 40]]

Template:Val list

11-limit

Period: 1\1

Optimal (POTE) generator: ~7/6 = 263.634

EDO generators: 9\41, 11\50, 20\91

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 2401/2376

Mapping: [⟨1 4 1 5 5], ⟨0 -11 6 -10 -7]]

Template:Val list

13-limit

Period: 1\1

Optimal (POTE) generator: ~7/6 = 263.700

EDO generators: 9\41, 11\50, 20\91

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 245/242

Mapping: [⟨1 4 1 5 5 7], ⟨0 -11 6 -10 -7 -15]]

Template:Val list

Slender

Period: 1\1

Optimal (POTE) generator: ~49/48 = 38.413

EDO generators: 1\31, 1\32, 2\63, 3\94

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 589824/588245

Mapping: [⟨1 2 2 3], ⟨0 -13 10 -6]]

Wedgie: ⟨⟨13 -10 6 -46 -27 42]]

Template:Val list

Badness: 0.0569

11-limit

Period: 1\1

Optimal (POTE) generator: ~49/48 = 38.387

EDO generators: 1\31, 1\32, 2\63, 3\94

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 1331/1323

Mapping: [⟨1 2 2 3 4], ⟨0 -13 10 -6 -17]]

Template:Val list

Badness: 0.02534

13-limit

Period: 1\1

Optimal (POTE) generator: ~49/48 = 38.314

EDO generators: 1\31, 1\32, 2\63, 3\94

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 275/273, 385/384, 1331/1323

Mapping: [⟨1 2 2 3 4 3], ⟨0 -13 10 -6 -17 22]]

Template:Val list

Badness: 0.02591

Marvo

See also: Gravity family

Period: 1\1

Optimal (POTE) generator: ~27/20 = 516.694

EDO generators: 28\65, 31\72, 59\137

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 78125000/78121827

Mapping: [⟨1 5 12 29], ⟨0 -6 -17 -46]]

Wedgie: ⟨⟨6 17 46 13 56 59]]

Template:Val list

Badness: 0.0976

11-limit

Period: 1\1

Optimal (POTE) generator: ~27/20 = 516.699

EDO generators: 28\65, 31\72, 59\137

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 4000/3993

Mapping: [⟨1 5 12 29 12], ⟨0 -6 -17 -46 -15]]

Template:Val list

Badness: 0.0317

13-limit

Period: 1\1

Optimal (POTE) generator: ~27/20 = 516.730

EDO generators: 28\65, 31\72, 59\137

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 351/350, 1625/1617

Mapping: [⟨1 5 12 29 12 39], ⟨0 -6 -17 -46 -15 -62]]

Template:Val list

Badness: 0.0269

Marvolo

Period: 1\1

Optimal (POTE) generator: ~21/20 = 83.348

EDO generators: 2\29, 3\43, 5\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 156250000/155649627

Mapping: [⟨1 2 1 1], ⟨0 -6 19 26]]

Wedgie: ⟨⟨6 -19 -26 -44 -58 -7]]

Template:Val list

Badness: 0.0833

11-limit

Period: 1\1

Optimal (POTE) generator: ~21/20 = 83.340

EDO generators: 2\29, 3\43, 5\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 4000/3993

Mapping: [⟨1 2 1 1 2], ⟨0 -6 19 26 21]]

Template:Val list

Badness: 0.0290

13-limit

Period: 1\1

Optimal (POTE) generator: ~21/20 = 83.330

EDO generators: 2\29, 3\43, 5\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 364/363, 441/440

Mapping: [⟨1 2 1 1 2 3], ⟨0 -6 19 26 21 10]]

Template:Val list

Badness: 0.0215

Amavil

5-limit (mabila)

Period: 1\1

Optimal (POTE) generator: ~512/375 = 529.6849

EDO generators: 15\34, 19\43, 34\77, 49\111

Scales (Scala files):

Technical data

Subgroup: 2.3.5

Comma list: 268435456/263671875

Mapping: [⟨1 6 1], ⟨0 -10 3]]

Template:Val list

Badness: 0.2325

7-limit

Period: 1\1

Optimal (POTE) generator: ~48/35 = 529.979

EDO generators: 15\34, 19\43

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 17496/16807

Mapping: [⟨1 6 1 9], ⟨0 -10 3 -14]]

Wedgie: ⟨⟨10 -3 14 -28 -6 41]]

Template:Val list

Badness: 0.1096

11-limit

Period: 1\1

Optimal (POTE) generator: ~15/11 = 529.974

EDO generators: 15\34, 19\43

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 864/847

Mapping: [⟨1 6 1 9 7], ⟨0 -10 3 -14 -8]]

Template:Val list

Badness: 0.0426

13-limit

Period: 1\1

Optimal (POTE) generator: ~15/11 = 529.951

EDO generators: 15\34, 19\43

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 144/143, 176/175

Mapping: [⟨1 6 1 9 7 9], ⟨0 -10 3 -14 -8 -12]]

Template:Val list

Badness: 0.0258

Enneaportent

Period: 1\9

Optimal (POTE) generator: ~5/4 = 383.165

EDO generators: 20\63, 23\72, 26\81

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 40353607/40310784

Mapping: [⟨9 0 28 11], ⟨0 2 -1 2]]

Wedgie: ⟨⟨18 -9 18 -56 -22 67]]

Template:Val list

Badness: 0.0937

11-limit

Period: 1\9

Optimal (POTE) generator: ~5/4 = 383.146

EDO generators: 20\63, 23\72, 26\81

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 12005/11979

Mapping: [⟨9 0 28 11 24], ⟨0 2 -1 2 1]]

Template:Val list

Badness: 0.0304

13-limit

Period: 1\9

Optimal (POTE) generator: ~5/4 = 383.047

EDO generators: 20\63, 23\72, 26\81

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 364/363, 1716/1715

Mapping: [⟨9 0 28 11 24 19], ⟨0 2 -1 2 1 2]]

Template:Val list

Badness: 0.0223

Submajor

5-limit

Period: 1\1

Optimal (POTE) generator: ~10125/8192 = 362.321

EDO generators: 13\43, 16\53, 19\63, 29\96, 35\116

Scales (Scala files):

Technical data

Subgroup: 2.3.5

Comma list: 69198046875/68719476736

Mapping: [⟨1 4 -1], ⟨0 -8 11]]

Template:Val list

Badness: 0.1302

7-limit

Period: 1\1

Optimal (POTE) generator: ~49/40 = 362.255

EDO generators: 13\43, 16\53, 19\63, 29\96, 35\116

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 51200/50421

Mapping: [⟨1 4 -1 1], ⟨0 -8 11 6]]

Wedgie: ⟨⟨8 -11 -6 -36 -32 17]]

Template:Val list

Badness: 0.0605

11-limit

Period: 1\1

Optimal (POTE) generator: ~27/22 = 362.101

EDO generators: 16\53, 19\63, 35\116

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 6655/6561

Mapping: [⟨1 4 -1 1 11], ⟨0 -8 11 6 -25]]

Template:Val list

Badness: 0.0506

13-limit

Period: 1\1

Optimal (POTE) generator: ~16/13 = 362.105

EDO generators: 16\53, 19\63, 35\116

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 275/273, 385/384

Mapping: [⟨1 4 -1 1 11 4], ⟨0 -8 11 6 -25 -1]]

Template:Val list

Badness: 0.0277

Interpental

Period: 1\1

Optimal (POTE) generator: ~49/40 = 362.418

EDO generators: 13\43, 16\53, 29\96

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 51200/50421

POTE generator: ~49/40 = 362.418

Mapping: [⟨1 4 -1 1 -5], ⟨0 -8 11 6 28]]

Template:Val list

Badness: 0.0518

13-limit

Period: 1\1

Optimal (POTE) generator: ~16/13 = 362.402

EDO generators: 13\43, 16\53, 29\96

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 169/168, 176/175, 640/637

POTE generator: ~16/13 = 362.402

Mapping: [⟨1 4 -1 1 -5 4], ⟨0 -8 11 6 28 -1]]

Template:Val list

Badness: 0.0297

Alphorn

Period: 1\1

Optimal (POTE) generator: ~48/35 = 556.221

EDO generators: 13\28, 19\41

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 5764801/5668704

Mapping: [⟨1 9 0 13], ⟨0 -16 5 -22]]

Wedgie: ⟨⟨16 -5 22 -45 -10 65]]

Template:Val list

Badness: 0.1293

11-limit

Period: 1\1

Optimal (POTE) generator: ~11/8 = 556.144

EDO generators: 13\28, 19\41

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 12250/11979

Mapping: [⟨1 9 0 13 3], ⟨0 -16 5 -22 1]]

Template:Val list

Badness: 0.0735

Decic

The decic temperament (10&50, named by Xenllium) tempers out the cloudy comma, 16807/16384 and the marvel comma, 225/224 in the 7-limit. It can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.

7-limit

Period: 1\10

Optimal (POTE) generator: ~3/2 = 698.696

EDO generators: 1\50, 1\60

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7

Comma list: 225/224, 16807/16384

Mapping: [⟨10 0 39 28], ⟨0 1 -1 0]]

Mapping generators: ~15/14, ~3

Wedgie: ⟨⟨ 10 -10 0 -39 -28 28 ]]

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [693.686, 701.955]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.089135

11-limit

Period: 1\10

Optimal (POTE) generator: ~3/2 = 696.791

EDO generators: 1\50, 1\60

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 3087/3025

Mapping: [⟨10 0 39 28 3], ⟨0 1 -1 0 2]]

Mapping generators: ~15/14, ~3

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [693.686, 701.955]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.063900

13-limit

Period: 1\10

Optimal (POTE) generator: ~3/2 = 696.993

EDO generators: 1\50, 1\60

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 2200/2197

Mapping: [⟨10 0 39 28 3 37], ⟨0 1 -1 0 2 0]]

Mapping generators: ~14/13, ~3

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [693.686, 701.955]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.036880

17-limit

Period: 1\10

Optimal (POTE) generator: ~3/2 = 697.085

EDO generators: 1\50, 1\60

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 144/143, 170/169, 196/195, 221/220

Mapping: [⟨10 0 39 28 3 37 25], ⟨0 1 -1 0 2 0 1]]

Mapping generators: ~14/13, ~3

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [693.686, 701.955]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.025064

Retrieved from "https://en.xen.wiki/index.php?title=Marvel_temperaments&oldid=63929"