User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
m Added normalised bases
Line 86: Line 86:
TE Mistunings (cents)
TE Mistunings (cents)


⟨0.511, 1.196, 6.223, -13.002]
⟨0.511, 1.196, 6.223, -13.002]  
 
 
POTE Generator Tunings (cents)
 
⟨1200.0000, 350.9151]
 
 
POTE Step Tunings (cents)
 
⟨34.44279, 56.40591]
 
 
POTE Tuning Map (cents)
 
⟨1200.000, 3101.830, 7256.406, 7754.576]
 
 
POTE Mistunings (cents)
 
⟨0.000, -0.125, 3.133, -16.304]  


{| class="wikitable"
{| class="wikitable"
Line 132: Line 112:


=== Temperament data (normalised bases) ===
=== Temperament data (normalised bases) ===
{{todo|inline=yes|comment=fill out this section}}
 
 
Equal Temperament Mappings
{| class="wikitable"
!
!2
!3
!11
!89
!
|-
|[ ⟨
|7
|11
|24
|45
|]
|-
|⟨
|17
|27
|59
|110
|] ⟩
|}
 
 
Reduced Mapping
{| class="wikitable"
!
!2
!3
!11
!89
!
|-
|[ ⟨
|1
|1
|2
|5
|]
|-
|⟨
|0
|2
|5
|5
|] ⟩
|}
 
 
TE Generator Tunings (cents)
 
⟨1200.9365, 350.5869]
 
 
TE Step Tunings (cents)
 
⟨44.70571, 52.23509]
 
 
TE Tuning Map (cents)
 
⟨1200.936, 1902.110, 4154.807, 7757.617]
 
 
TE Mistunings (cents)
 
⟨0.936, 0.155, 3.489, -13.263]
 
{| class="wikitable"
|Complexity
|0.558811
|-
|Adjusted Error
|7.996249 cents
|-
|TE Error
|1.234802 cents/octave
|}
 
 
Unison Vectors
 
* [-3, 0, -1, 1⟩ (89:88)
* [-1, 5, -2, 0⟩ (243:242)
* [-2, -5, 1, 1⟩ (979:972)
* [-5, -5, 0, 2⟩ (7921:7776)


=== Example MOS scale: Floor[17] ===
=== Example MOS scale: Floor[17] ===
Line 242: Line 310:


⟨0.899, -7.060, 6.009, -1.999]
⟨0.899, -7.060, 6.009, -1.999]
POTE Generator Tunings (cents)
⟨1200.0000, 187.6886]
POTE Step Tunings (cents)
⟨73.86819, 39.95225]
POTE Tuning Map (cents)
⟨1200.000, 5175.377, 6938.443, 7763.066]
POTE Mistunings (cents)
⟨-0.000, -10.936, 0.812, -7.814]


{| class="wikitable"
{| class="wikitable"
Line 287: Line 335:


=== Temperament data (normalised bases) ===
=== Temperament data (normalised bases) ===
{{todo|inline=yes|comment=fill out this section}}
 
 
Equal Temperament Mappings
{| class="wikitable"
!
!2
!5
!11
!89
!
|-
|[ ⟨
|6
|14
|21
|39
|]
|-
|⟨
|7
|16
|24
|45
|] ⟩
|}
 
 
Reduced Mapping
{| class="wikitable"
!
!2
!5
!11
!89
!
|-
|[ ⟨
|1
|2
|3
|6
|]
|-
|⟨
|0
|2
|3
|3
|] ⟩
|}
 
 
TE Generator Tunings (cents)
 
⟨1200.2939, 188.3359]
 
 
TE Step Tunings (cents)
 
⟨118.05701, 70.27884]
 
 
TE Tuning Map (cents)
 
⟨1200.294, 2777.260, 4165.889, 7766.771]
 
 
TE Mistunings (cents)
 
⟨0.294, -9.054, 14.571, -4.109]
 
{| class="wikitable"
|Complexity
|0.356125
|-
|Adjusted Error
|18.722607 cents
|-
|TE Error
|2.891195 cents/octave
|}
 
 
Unison Vectors
 
* [-3, 0, -1, 1⟩ (89:88)
* [0, 3, -2, 0⟩ (125:121)
* [3, 3, -1, -1⟩ (1000:979)
* [6, 3, 0, -2⟩ (8000:7921)


=== Example MOS scale: Teefs[32] ===
=== Example MOS scale: Teefs[32] ===
Line 410: Line 546:


⟨0.853, -1.050, -5.200, 2.022]
⟨0.853, -1.050, -5.200, 2.022]
POTE Generator Tunings (cents)
⟨1200.0000, 567.3830]
POTE Step Tunings (cents)
⟨45.51082, 19.72320]
POTE Tuning Map (cents)
⟨1200.000, 4297.851, 7134.766, 7767.383]
POTE Mistunings (cents)
⟨0.000, -4.104, -10.270, -3.497]


{| class="wikitable"
{| class="wikitable"
Line 455: Line 571:


=== Temperament data (normalised bases) ===
=== Temperament data (normalised bases) ===
{{todo|inline=yes|comment=fill out this section}}
Equal Temperament Mappings
{| class="wikitable"
!
!2
!3
!31
!89
!
|-
|[ ⟨
|17
|27
|84
|110
|]
|-
|⟨
|19
|30
|94
|123
|] ⟩
|}
 
 
Reduced Mapping
{| class="wikitable"
!
!2
!3
!31
!89
!
|-
|[ ⟨
|1
|3
|4
|6
|]
|-
|⟨
|0
| -3
|2
|1
|] ⟩
|}
 
 
TE Generator Tunings (cents)
 
⟨1201.0755, 567.2153]
 
 
TE Step Tunings (cents)
 
⟨32.58899, 34.05593]
 
 
TE Tuning Map (cents)
 
⟨1201.075, 1901.581, 5938.732, 7773.668]
 
 
TE Mistunings (cents)
 
⟨1.075, -0.374, -6.303, 2.788]
 
{| class="wikitable"
|Complexity
|0.910794
|-
|Adjusted Error
|5.623550 cents
|-
|TE Error
|0.868404 cents/octave
|}
 
 
Unison Vectors
 
* [-5, 1, 2, -1⟩ (2883:2848)
* [8, 0, 1, -2⟩ (7936:7921)
* [-13, 1, 1, 1⟩ (8277:8192)
* [-18, 2, 3, 0⟩ (268119:262144)


=== Example MOS scale: Lylla[19] ===
=== Example MOS scale: Lylla[19] ===