Magic extensions: Difference between revisions

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+intuition (also an important extension)
Line 3: Line 3:
* '''Tridecimal magic''' (19 & 22f) – tempering out 100/99, 105/104, 144/143, and 196/195;  
* '''Tridecimal magic''' (19 & 22f) – tempering out 100/99, 105/104, 144/143, and 196/195;  
* '''Necromancy''' (19f & 22) – tempering out 100/99, 225/224, 245/243, and 275/273;  
* '''Necromancy''' (19f & 22) – tempering out 100/99, 225/224, 245/243, and 275/273;  
* '''Witchcraft''' (19e & 22ef) – tempering out 105/104, 196/195, 245/243, and 275/273;
* '''Sorcery''' (19 & 22) – tempering out 65/64, 78/77, 91/90, and 100/99;  
* '''Sorcery''' (19 & 22) – tempering out 65/64, 78/77, 91/90, and 100/99;  
* '''Witchcraft''' (19e & 22ef) – tempering out 105/104, 196/195, 245/243, and 275/273;  
* '''Intuition''' (19e & 22f) – tempering out 55/54, 66/65, 99/98, and 105/104;  
* '''Telepathy''' (19e & 22) – tempering out 55/54, 65/64, 91/90, and 99/98.  
* '''Telepathy''' (19e & 22) – tempering out 55/54, 65/64, 91/90, and 99/98.  


The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11.  
The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11.  


Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Telepathy adopts less complex and less accurate mapping for both primes 11 and 13.  
Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Likewise, intuitive uses a less complex and less accurate mapping for prime 11. Finally, telepathy adopts the changes of both sorcery and intuition, resulting in a very low-accuracy temperament.  


== Interval chain ==
== Interval chain ==
Line 17: Line 18:
! rowspan="3" | #
! rowspan="3" | #
! rowspan="3" | Cents*
! rowspan="3" | Cents*
! colspan="6" | Approximate ratios
! colspan="7" | Approximate ratios
|-
|-
! rowspan="2" | 7-limit
! rowspan="2" | 7-limit
! colspan="5" | 13-limit extensions
! colspan="6" | 13-limit extensions
|-
|-
! Magic
! Magic
! Necromancy
! Necromancy
! Witchcraft
! Sorcery
! Sorcery
! Witchcraft
! Intuition
! Telepathy
! Telepathy
|-
|-
Line 31: Line 33:
| 0.0
| 0.0
| '''1/1'''
| '''1/1'''
|
|  
|  
|  
|  
Line 41: Line 44:
| '''5/4'''
| '''5/4'''
| 26/21
| 26/21
|
|  
|  
| '''16/13'''
| '''16/13'''
Line 49: Line 53:
| 760.9
| 760.9
| 14/9
| 14/9
|
|  
|  
|  
|  
| 20/13
| 20/13
|  
| 11/7
| 11/7, 20/13
| 11/7, 20/13
|-
|-
Line 60: Line 65:
| 52/27, 64/33
| 52/27, 64/33
| 64/33
| 64/33
| 52/27
| 64/33
| 64/33
| 52/27
| 21/11, 52/27
| 88/45
| 21/11
|-
|-
| 4
| 4
Line 69: Line 75:
| 40/33
| 40/33
| 40/33
| 40/33
|
| 40/33
| 40/33
|  
| 11/9, 13/11
| 11/9
| 11/9
|-
|-
Line 76: Line 83:
| 702.3
| 702.3
| '''3/2'''
| '''3/2'''
|
|  
|  
|  
|  
Line 87: Line 95:
| 13/7
| 13/7
|  
|  
| 13/7
| 24/13
| 24/13
| 13/7
| 13/7
Line 94: Line 103:
| 263.2
| 263.2
| 7/6
| 7/6
|
|  
|  
|  
|  
Line 105: Line 115:
| 13/9, '''16/11'''
| 13/9, '''16/11'''
| '''16/11'''
| '''16/11'''
| 13/9
| '''16/11'''
| '''16/11'''
| 13/9
| 13/9, 22/15
| 22/15
| 22/15
|-
|-
Line 114: Line 125:
| 20/11
| 20/11
| 20/11
| 20/11
|
| 20/11
| 20/11
|  
| 11/6
| 11/6
| 11/6
|-
|-
Line 121: Line 133:
| 204.6
| 204.6
| '''9/8'''
| '''9/8'''
|
|  
|  
|  
|  
Line 130: Line 143:
| 585.0
| 585.0
| 7/5
| 7/5
|
|  
|  
|  
|  
Line 141: Line 155:
| 26/15
| 26/15
|  
|  
| 26/15
|  
|  
| 26/15
| 26/15
Line 150: Line 165:
| 12/11, 13/12
| 12/11, 13/12
| 12/11
| 12/11
| 13/12
| 12/11, 14/13
| 12/11, 14/13
| 13/12
| 11/10, 13/12
| 11/10, 14/13
| 11/10, 14/13
|-
|-
Line 159: Line 175:
| 15/11
| 15/11
| 15/11
| 15/11
|
| 15/11
| 15/11
|  
| '''11/8'''
| '''11/8'''
| '''11/8'''
|-
|-
Line 167: Line 184:
| 27/16, 42/25
| 27/16, 42/25
|  
|  
| 22/13
| 22/13
| 22/13
|
|  
|  
| 22/13
| 22/13
Line 176: Line 195:
|  
|  
|  
|  
| 22/21
| 27/26
| 27/26
| 22/21
|  
| 27/26
| 27/26
|-
|-
Line 186: Line 206:
|  
|  
|  
|  
| 13/10
| 13/10
| 13/10
|  
|  
Line 194: Line 215:
| '''13/8''', 18/11
| '''13/8''', 18/11
| 18/11
| 18/11
| '''13/8'''
| 18/11, 21/13
| 18/11, 21/13
| '''13/8'''
| '''13/8'''
Line 203: Line 225:
| 45/44
| 45/44
| 45/44
| 45/44
|
| 45/44
| 45/44
|  
| 33/32
| 33/32
| 33/32
|-
|-
Line 212: Line 235:
| 14/11
| 14/11
| 14/11
| 14/11
|
| 14/11
| 14/11
|  
|  
Line 220: Line 244:
| 63/40
| 63/40
|  
|  
|
| 11/7
|  
|  
|  
|  
| 11/7
|  
|  
|-
|-
Line 228: Line 253:
| 1170.1
| 1170.1
| 49/25, 63/32
| 49/25, 63/32
| 39/20
|
| 39/20
| 39/20
|  
|  
|  
|  
| 39/20
|  
|  
|}
|}
Line 603: Line 629:
| 381.818
| 381.818
|  
|  
|-
|
| 9/7
| 382.458
|
|-
|
| 5/4
| 386.314
|
|}
=== Witchcraft ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Generator (¢)
! Comments
|-
|
| 13/7
| 378.617
|
|-
|
| 5/3
| 378.910
|
|-
| 6\19
|
| 378.947
| 19e val
|-
|
| 15/13
| 379.355
|
|-
|
| 13/9
| 379.577
|
|-
|
| 13/10
| 379.660
|
|-
|
| 9/5
| 379.733
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|
| 13/12
| 379.890
|
|-
| 19\60
|
| 380.000
| 60e val
|-
|
| 13/8
| 380.029
|
|-
|
| 15/14
| 380.093
|
|-
|
| 15/11
| 380.113
| 15-odd-limit minimax
|-
|
| 11/7
| 380.119
| 13-odd-limit minimax
|-
|
| 11/10
| 380.156
|
|-
|
| {{monzo| 0 -106 -111 11 179 59 }}
| 380.193
| 15-odd-limit least squares
|-
| 32\101
|
| 380.198
| 101cdf val
|-
|
| {{monzo| 0 -67 -72 5 152 47 }}
| 380.218
| 13-odd-limit least squares
|-
|
| 7/5
| 380.228
|
|-
|
| {{monzo| 0 -38 -55 11 137 }}
| 380.278
| 11-odd-limit least squares
|-
|
| 11/9
| 380.322
|
|-
|
| 11/6
| 380.334
|
|-
|
| 11/8
| 380.343
| 11-odd-limit minimax
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| 3/2
| 380.391
| 5-, 7- and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| 13/11
| 380.719
|
|-
|
| 7/4
| 380.735
|
|-
| 33\104
|
| 380.769
| 104eeff val
|-
| 20\63
|
| 380.952
| 63eef val
|-
|
| 7/6
| 380.982
|
|-
|
| 15/8
| 381.378
|
|-
| 7\22
|
| 381.818
| 22ef val
|-
|-
|  
|  
Line 804: Line 1,014:
|}
|}


=== Telepathy ===
=== Intuition ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|  
|
| 13/8
| 13/11
| 359.472
| 372.302
|  
|
|-
|
| 13/7
| 378.617
|
|-
|-
|  
|
| 13/10
| 5/3
| 372.893
| 378.910
|  
|  
|-
|-
|  
| 6\19
| 13/12
|
| 376.905
| 378.947
|  
|  
|-
|-
|  
|
| 15/13
| 15/13
| 378.249
| 379.355
|  
|
|-
|-
|  
|
| 13/9
| 13/9
| 378.489
| 379.577
|  
|
|-
|-
|
|
| 5/3
| 13/10
| 378.910
| 379.660
|
|
|-
| 6\19
|
| 378.947
| 19e val
|-
|  
| 13/7
| 379.100
|  
|-
|-
|  
|
| 9/5
| 9/5
| 379.733
| 379.733
|  
|
|-
|
| 13/12
| 379.890
|
|-
|-
|  
|
| 27/20
| 27/20
| 379.968
| 379.968
Line 863: Line 1,073:
|-
|-
| 19\60
| 19\60
|
| 380.000
|  
|  
| 380.000
| 60eeeff val
|-
|-
|  
|
| 13/8
| 380.029
| 13 and 15-odd-limit minimax
|-
|
| 15/14
| 15/14
| 380.093
| 380.093
Line 873: Line 1,088:
|-
|-
| 32\101
| 32\101
|
| 380.198
|  
|  
| 380.198
| 101cdeeeefff val
|-
|-
|  
|
| 7/5
| 7/5
| 380.228
| 380.228
|  
|  
|-
|-
|  
|
| {{monzo| 0 36 -23 32 }}
| {{monzo| 0 36 -23 32 }}
| 380.384
| 380.384
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
|-
|  
|
| 3/2
| 3/2
| 380.391
| 380.391
Line 893: Line 1,108:
|-
|-
| 13\41
| 13\41
|
| 380.488
|  
|  
| 380.488
| 41ef val
|-
|-
|  
|
| {{monzo| 0 1 -7 15 }}
| {{monzo| 0 1 -7 15 }}
| 380.506
| 380.506
| 7-odd-limit least squares
| 7-odd-limit least squares
|-
|-
|  
|
| {{monzo| 0 47 -34 43 57 -48 }}
| {{monzo| 0 -30 -73 30 46 78 }}
| 380.676
| 380.562
| 13-odd-limit least squares
|-
|
| {{monzo| 0 46 -35 49 65 -55 }}
| 380.691
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|  
|
| 13/11
| {{monzo| 0 -10 -53 24 38 66 }}
| 380.719
| 380.568
| 13- and 15-odd-limit minimax
| 13-odd-limit least squares
|-
|-
|  
|
| 7/4
| 7/4
| 380.735
| 380.735
Line 923: Line 1,133:
|-
|-
| 33\104
| 33\104
|
| 380.769
|  
|  
| 380.769
| 104eeefff val
|-
|-
| 20\63
| 20\63
|
| 380.952
|  
|  
| 380.952
| 63eff val
|-
|-
|  
|
| 7/6
| 7/6
| 380.982
| 380.982
|  
|  
|-
|-
|  
|
| 15/8
| 15/8
| 381.378
| 381.378
|  
|  
|-
|-
|  
|
| {{monzo| 0 19 -36 30 42 }}
| {{monzo| 0 19 -36 30 42 }}
| 381.380
| 381.380
Line 948: Line 1,158:
|-
|-
| 7\22
| 7\22
|  
|
| 381.818
| 381.818
|  
|  
|-
|-
|  
|
| 11/10
| 11/10
| 381.923
| 381.923
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
|  
|
| 11/8
| 11/8
| 382.237
| 382.237
|  
|  
|-
|-
|  
|
| 9/7
| 9/7
| 382.458
| 382.458
|  
|  
|-
|-
|  
|
| 15/11
| 15/11
| 382.881
| 382.881
|  
|  
|-
|-
|  
|
| 11/6
| 11/6
| 383.263
| 383.263
|  
|  
|-
|-
|  
|
| 5/4
| 5/4
| 386.314
| 386.314
|  
|  
|-
|-
|  
|
| 11/9
| 11/9
| 386.852
| 386.852
|  
|  
|-
|-
|  
|
| 11/7
| 11/7
| 391.246
| 391.246
Line 993: Line 1,203:
|}
|}


=== Witchcraft ===
=== Telepathy ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
Line 1,002: Line 1,212:
|-
|-
|  
|  
| 13/7
| 13/8
| 378.617
| 359.472
|  
|  
|-
|-
|  
|  
| 5/3
| 13/10
| 378.910
| 372.893
|  
|  
|-
|-
| 6\19
|  
|  
| 378.947
| 13/12
| 19e val
| 376.905
|  
|-
|-
|  
|  
| 15/13
| 15/13
| 379.355
| 378.249
|  
|  
|-
|-
|  
|  
| 13/9
| 13/9
| 379.577
| 378.489
|
|-
|
| 5/3
| 378.910
|  
|  
|-
|-
| 6\19
|  
|  
| 13/10
| 378.947
| 379.660
| 19e val
|-
|
| 13/7
| 379.100
|  
|  
|-
|-
Line 1,040: Line 1,260:
| 379.968
| 379.968
| 5-odd-limit least squares
| 5-odd-limit least squares
|-
|
| 13/12
| 379.890
|
|-
|-
| 19\60
| 19\60
|  
|  
| 380.000
| 380.000
| 60e val
| 60eeeff val
|-
|
| 13/8
| 380.029
|
|-
|-
|  
|  
Line 1,060: Line 1,270:
| 380.093
| 380.093
|  
|  
|-
|
| 15/11
| 380.113
| 15-odd-limit minimax
|-
|
| 11/7
| 380.119
| 13-odd-limit minimax
|-
|
| 11/10
| 380.156
|
|-
|
| {{monzo| 0 -106 -111 11 179 59 }}
| 380.193
| 15-odd-limit least squares
|-
|-
| 32\101
| 32\101
|  
|  
| 380.198
| 380.198
| 101cdf val
| 101cdeeeefff val
|-
|
| {{monzo| 0 -67 -72 5 152 47 }}
| 380.218
| 13-odd-limit least squares
|-
|-
|  
|  
Line 1,095: Line 1,280:
| 380.228
| 380.228
|  
|  
|-
|
| {{monzo| 0 -38 -55 11 137 }}
| 380.278
| 11-odd-limit least squares
|-
|
| 11/9
| 380.322
|
|-
|
| 11/6
| 380.334
|
|-
|
| 11/8
| 380.343
| 11-odd-limit minimax
|-
|-
|  
|  
Line 1,129: Line 1,294:
|  
|  
| 380.488
| 380.488
| 41ef val
|-
|  
|  
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|
| {{monzo| 0 47 -34 43 57 -48 }}
| 380.676
| 13-odd-limit least squares
|-
|
| {{monzo| 0 46 -35 49 65 -55 }}
| 380.691
| 15-odd-limit least squares
|-
|-
|  
|  
| 13/11
| 13/11
| 380.719
| 380.719
|  
| 13- and 15-odd-limit minimax
|-
|-
|  
|  
Line 1,144: Line 1,324:
|  
|  
| 380.769
| 380.769
| 104eeff val
| 104eeefff val
|-
|-
| 20\63
| 20\63
|  
|  
| 380.952
| 380.952
| 63eef val
| 63eff val
|-
|-
|  
|  
Line 1,160: Line 1,340:
| 381.378
| 381.378
|  
|  
|-
|
| {{monzo| 0 19 -36 30 42 }}
| 381.380
| 11-odd-limit least squares
|-
|-
| 7\22
| 7\22
|  
|  
| 381.818
| 381.818
| 22ef val
|  
|-
|
| 11/10
| 381.923
| 11-odd-limit minimax
|-
|
| 11/8
| 382.237
|
|-
|-
|  
|  
| 9/7
| 9/7
| 382.458
| 382.458
|
|-
|
| 15/11
| 382.881
|
|-
|
| 11/6
| 383.263
|  
|  
|-
|-
Line 1,174: Line 1,379:
| 5/4
| 5/4
| 386.314
| 386.314
|
|-
|
| 11/9
| 386.852
|
|-
|
| 11/7
| 391.246
|  
|  
|}
|}

Revision as of 16:14, 29 December 2024

Magic has various competing extensions to the 11- and 13-limit. The following temperaments are discussed in this article:

  • Tridecimal magic (19 & 22f) – tempering out 100/99, 105/104, 144/143, and 196/195;
  • Necromancy (19f & 22) – tempering out 100/99, 225/224, 245/243, and 275/273;
  • Witchcraft (19e & 22ef) – tempering out 105/104, 196/195, 245/243, and 275/273;
  • Sorcery (19 & 22) – tempering out 65/64, 78/77, 91/90, and 100/99;
  • Intuition (19e & 22f) – tempering out 55/54, 66/65, 99/98, and 105/104;
  • Telepathy (19e & 22) – tempering out 55/54, 65/64, 91/90, and 99/98.

The most important of these is tridecimal magic, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 14/13 and 16/15 are tempered together. Necromancy takes the same mapping of 11 as magic, but swaps in a more complex mapping for 13, enabling the possibility of a higher-accuracy harmony. Similarly, witchcraft takes the same mapping of 13 as magic, but swaps in a more complex mapping for 11.

Sorcery swaps in a less complex and less accurate mapping for prime 13, as it finds ~16/13 where magic will find ~26/21, which is of course conflated with ~5/4. Likewise, intuitive uses a less complex and less accurate mapping for prime 11. Finally, telepathy adopts the changes of both sorcery and intuition, resulting in a very low-accuracy temperament.

Interval chain

In the following table, odd harmonics and subharmonics 1–13 are in bold.

# Cents* Approximate ratios
7-limit 13-limit extensions
Magic Necromancy Witchcraft Sorcery Intuition Telepathy
0 0.0 1/1
1 380.4 5/4 26/21 16/13 16/13
2 760.9 14/9 20/13 11/7 11/7, 20/13
3 1141.4 27/14 52/27, 64/33 64/33 52/27 64/33 21/11, 52/27 21/11
4 321.8 6/5 40/33 40/33 40/33 11/9, 13/11 11/9
5 702.3 3/2
6 1082.7 15/8, 28/15 13/7 13/7 24/13 13/7 24/13
7 263.2 7/6 13/11
8 643.7 35/24 13/9, 16/11 16/11 13/9 16/11 13/9, 22/15 22/15
9 1024.1 9/5 20/11 20/11 20/11 11/6 11/6
10 204.6 9/8
11 585.0 7/5 18/13 18/13
12 965.5 7/4 26/15 26/15 26/15
13 146.0 35/32 12/11, 13/12 12/11 13/12 12/11, 14/13 11/10, 13/12 11/10, 14/13
14 526.4 27/20 15/11 15/11 15/11 11/8 11/8
15 906.9 27/16, 42/25 22/13 22/13 22/13
16 87.3 21/20 22/21 27/26 27/26
17 467.8 21/16 13/10 13/10 13/10
18 848.2 49/30 13/8, 18/11 18/11 13/8 18/11, 21/13 13/8 21/13
19 28.7 49/48, 81/80, 126/125 45/44 45/44 45/44 33/32 33/32
20 409.2 63/50 14/11 14/11 14/11
21 789.6 63/40 11/7
22 1170.1 49/25, 63/32 39/20 39/20

* In 7-limit CWE tuning

Tuning spectra

Magic

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
13/7 378.617
5/3 378.910
6\19 378.947 Lower bound of 9- to 15-odd-limit diamond monotone
15/13 379.355
13/9 379.577
13/10 379.660
9/5 379.733
13/12 379.890
27/20 379.968 5-odd-limit least squares
19\60 380.000
13/8 380.029
15/14 380.093
32\101 380.198 101cde val
7/5 380.228
13/11 380.354 13- and 15-odd-limit minimax
[0 56 -31 46 -94 88⟩ 380.377 13-odd-limit least squares
[0 36 -23 32⟩ 380.384 9-odd-limit least squares
[0 58 -29 52 -108 100⟩ 380.389 15-odd-limit least squares
3/2 380.391 5-, 7- and 9-odd-limit minimax
13\41 380.488
[0 1 -7 15⟩ 380.506 7-odd-limit least squares
11/9 380.700 11-odd-limit minimax
[0 85 -14 52 -68⟩ 380.714 11-odd-limit least squares
7/4 380.735
33\104 380.769 104ff val
11/6 380.818
11/7 380.875
20\63 380.952 63f val
7/6 380.982
11/8 381.085
15/11 381.211
15/88 381.378
11/10 381.666
7\22 381.818 22f val, upper bound of 9- to 15-odd-limit diamond monotone
9/7 382.458
5/4 386.314

Necromancy

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
5/3 378.910
6\19 378.947 19f val
9/5 379.733
27/20 379.968 5-odd-limit least squares
19\60 380.000 60f val
15/14 380.093
32\101 380.198 101cdeff val
7/5 380.228
[0 36 -23 32⟩ 380.384 9-odd-limit least squares
3/2 380.391 5-, 7- and 9-odd-limit minimax
13\41 380.488
[0 1 -7 15⟩ 380.506 7-odd-limit least squares
11/9 380.700 11-odd-limit minimax
13/9 380.709 13- and 15-odd-limit minimax
[0 85 -14 52 -68⟩ 380.714 11-odd-limit least squares
13/11 380.719
7/4 380.735
13/12 380.765
33\104 380.769
[0 -179 -10 -87 53 158⟩ 380.785 13-odd-limit least squares
13/7 380.809
[0 -222 -53 -93 67 187⟩ 380.817 15-odd-limit least squares
11/6 380.818
13/8 380.847
11/7 380.875
20\63 380.952
15/13 380.957
7/6 380.982
13/10 381.074
11/8 381.085
15/11 381.211
15/8 381.378
11/10 381.666
7\22 381.818
9/7 382.458
5/4 386.314

Witchcraft

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
13/7 378.617
5/3 378.910
6\19 378.947 19e val
15/13 379.355
13/9 379.577
13/10 379.660
9/5 379.733
27/20 379.968 5-odd-limit least squares
13/12 379.890
19\60 380.000 60e val
13/8 380.029
15/14 380.093
15/11 380.113 15-odd-limit minimax
11/7 380.119 13-odd-limit minimax
11/10 380.156
[0 -106 -111 11 179 59⟩ 380.193 15-odd-limit least squares
32\101 380.198 101cdf val
[0 -67 -72 5 152 47⟩ 380.218 13-odd-limit least squares
7/5 380.228
[0 -38 -55 11 137⟩ 380.278 11-odd-limit least squares
11/9 380.322
11/6 380.334
11/8 380.343 11-odd-limit minimax
[0 36 -23 32⟩ 380.384 9-odd-limit least squares
3/2 380.391 5-, 7- and 9-odd-limit minimax
13\41 380.488
13/11 380.719
7/4 380.735
33\104 380.769 104eeff val
20\63 380.952 63eef val
7/6 380.982
15/8 381.378
7\22 381.818 22ef val
9/7 382.458
5/4 386.314

Sorcery

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
13/8 359.472
13/10 372.893
13/12 376.905
15/13 378.249
13/9 378.489
5/3 378.910
6\19 378.947
13/7 379.100
9/5 379.733
27/20 379.968 5-odd-limit least squares
19\60 380.000 60ff val
15/14 380.093
32\101 380.198 101cdefff val
7/5 380.228
[0 36 -23 32⟩ 380.384 9-odd-limit least squares
3/2 380.391 5-, 7- and 9-odd-limit minimax
[0 -113 12 -65 75 26⟩ 380.427 13-odd-limit least squares
[0 134 9 71 -89 -33⟩ 380.457 15-odd-limit least squares
13\41 380.488 41f val
[0 1 -7 15⟩ 380.506 7-odd-limit least squares
11/9 380.700 11-, 13- and 15-odd-limit minimax
[0 85 -14 52 -68⟩ 380.714 11-odd-limit least squares
7/4 380.735
33\104 380.769 104fff val
11/6 380.818
11/7 380.875
20\63 380.952 63ff val
7/6 380.982
11/8 381.085
15/11 381.211
15/8 381.378
11/10 381.666
7\22 381.818
9/7 382.458
13/11 384.173
5/4 386.314

Intuition

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
13/11 372.302
13/7 378.617
5/3 378.910
6\19 378.947
15/13 379.355
13/9 379.577
13/10 379.660
9/5 379.733
13/12 379.890
27/20 379.968 5-odd-limit least squares
19\60 380.000
13/8 380.029 13 and 15-odd-limit minimax
15/14 380.093
32\101 380.198
7/5 380.228
[0 36 -23 32⟩ 380.384 9-odd-limit least squares
3/2 380.391 5-, 7- and 9-odd-limit minimax
13\41 380.488
[0 1 -7 15⟩ 380.506 7-odd-limit least squares
[0 -30 -73 30 46 78⟩ 380.562 15-odd-limit least squares
[0 -10 -53 24 38 66⟩ 380.568 13-odd-limit least squares
7/4 380.735
33\104 380.769
20\63 380.952
7/6 380.982
15/8 381.378
[0 19 -36 30 42⟩ 381.380 11-odd-limit least squares
7\22 381.818
11/10 381.923 11-odd-limit minimax
11/8 382.237
9/7 382.458
15/11 382.881
11/6 383.263
5/4 386.314
11/9 386.852
11/7 391.246

Telepathy

Edo
generator 		Eigenmonzo
(unchanged-interval) 		Generator (¢) Comments
13/8 359.472
13/10 372.893
13/12 376.905
15/13 378.249
13/9 378.489
5/3 378.910
6\19 378.947 19e val
13/7 379.100
9/5 379.733
27/20 379.968 5-odd-limit least squares
19\60 380.000 60eeeff val
15/14 380.093
32\101 380.198 101cdeeeefff val
7/5 380.228
[0 36 -23 32⟩ 380.384 9-odd-limit least squares
3/2 380.391 5-, 7- and 9-odd-limit minimax
13\41 380.488 41ef val
[0 1 -7 15⟩ 380.506 7-odd-limit least squares
[0 47 -34 43 57 -48⟩ 380.676 13-odd-limit least squares
[0 46 -35 49 65 -55⟩ 380.691 15-odd-limit least squares
13/11 380.719 13- and 15-odd-limit minimax
7/4 380.735
33\104 380.769 104eeefff val
20\63 380.952 63eff val
7/6 380.982
15/8 381.378
[0 19 -36 30 42⟩ 381.380 11-odd-limit least squares
7\22 381.818
11/10 381.923 11-odd-limit minimax
11/8 382.237
9/7 382.458
15/11 382.881
11/6 383.263
5/4 386.314
11/9 386.852
11/7 391.246
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