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Because the generator is so close to 1\3 of an octave, and the interval left over is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].  
Because the generator is so close to 1\3 of an octave, and the interval left over is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].  


* [[3L 4s]]: LsLsLss where L = 6/5
* [[3L 4s]]: LsLsLss where L represents 6/5
* [[3L 7s]]: LssLssLsss where L = 7/6
* [[3L 7s]]: LssLssLsss where L represents 7/6
* [[3L 10s]]: LsssLsssLssss where L = 9/8
* [[3L 10s]]: LsssLsssLssss where L represents 9/8
* [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family #Telepathy|telepathy]] temperament). In 22edo they are identical.
* [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family #Telepathy|telepathy]] temperament). In 22edo they are identical.


== Interval chain ==
== Interval chain ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
Line 60: Line 59:
| 15/8
| 15/8
| 7/6
| 7/6
| (16/11)
| (13/9~16/11)
| 9/5
| 9/5
| 9/8
| 9/8
| 7/5
| 7/5
| 7/4
| 7/4
| (12/11)
| (13/12~12/11)
|}
|}
<nowiki>*</nowiki> in 7-limit [[POTE tuning]]
<nowiki>*</nowiki> in 7-limit [[POTE tuning]]
Line 787: Line 786:
| 380.719
| 380.719
| 13- and 15-odd-limit minimax
| 13- and 15-odd-limit minimax
|-
|
| 8/7
| 380.735
|
|-
| 33\104
|
| 380.769
|
|-
| 20\63
|
| 380.952
|
|-
|
| 7/6
| 380.982
|
|-
|
| 16/15
| 381.378
|
|-
|
| <span style="font-size:0.75em">{{monzo| 0 19 -36 30 42 }}</span>
| 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
|
|-
|
| 12/11
| 383.263
|
|-
|
| 5/4
| 386.314
|
|-
|
| 11/9
| 386.852
|
|-
|
| 14/11
| 391.246
|
|}
=== Intuition ===
Gencom: [2 5/4; 55/54 66/65 99/98 105/104]
Gencom mapping: [{{map| 1 0 2 -1 -1 -2 }}, {{map| 0 5 1 12 14 18 }}]
{| class="wikitable center-all left-4"
|-
! ET<br>Generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]
! Generator<br>(¢)
! Comments
|-
|
| 13/11
| 372.302
|
|-
|
| 14/13
| 378.617
|
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|
| 378.947
|
|-
|
| 15/13
| 379.355
|
|-
|
| 18/13
| 379.577
|
|-
|
| 13/10
| 379.660
|
|-
|
| 10/9
| 379.733
|
|-
|
| 13/12
| 379.890
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
| 19\60
|
| 380.000
|
|-
|
| 16/13
| 380.029
| 13- and 15-odd-limit minimax
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
|
|-
|
| 7/5
| 380.228
|
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| 4/3
| 380.391
| 5-, 7- and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|-
|
|
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