nulu
8 + x^11 = x^12

an extended secondary recurrent sequence ala Kraig Grady / Erv Wilson / Jacques Dudon

the MOS with cardinalty above 12 using converged generator small step sizes about 4.6852286724 cents between 259edo and 260edo.
So very small steps, the 12tone MOS is so close to 12edo its almost not indistinguishable , however the tones seem to fit together maybe a little bit better than in 12edo. I've recorded some in the 12,17,29,and 53 tone MOS. It's kinda what we are trying to get away from-12edo, but just enough of a difference to explore strange territory.

addendum:
have added some nulu ji recordings in scales made from using the recurrent sequence as pitch values.

nulu.12.ji, nulu.12.h.ji, nulu.29.ji, and nulu.41.ji scales from bottom of sequence.

nulu.12.b.ji and nulu.17.bji scales from higher in the sequence closer to convergence.

nulu.12.c.ji scale taken from sequence in between nulu.12.ji and nulu.12.b.ji.

ji scales available here
ia601405.us.archive.org/view_archive.php?archive=/27/items/envultured-servitude/nulu.zip
along with sequence list, program to generate sequence and ocrave reduce.


some MOS scales using converged generator below.


!MOS_nulu.2.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
2
!
499.6095642773
1200.0000000000


!MOS_nulu.3.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
3
!
499.6095642773
999.2191285546
1200.0000000000


!MOS_nulu.5.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
5
!
298.8286928319
499.6095642773
798.4382571092
999.2191285546
1200.0000000000


!MOS_nulu.7.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
7
!
98.0478213865
298.8286928319
499.6095642773
597.6573856638
798.4382571092
999.2191285546
1200.0000000000


!MOS_nulu.12.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
12
!
98.0478213865
196.0956427730
298.8286928319
396.8765142184
499.6095642773
597.6573856638
695.7052070503
798.4382571092
896.4860784957
999.2191285546
1097.2669499411
1200.0000000000


!MOS_nulu.17.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
17
!
98.0478213865
196.0956427730
294.1434641595
298.8286928319
396.8765142184
494.9243356049
499.6095642773
597.6573856638
695.7052070503
793.7530284368
798.4382571092
896.4860784957
994.5338998822
999.2191285546
1097.2669499411
1195.3147713276
1200.0000000000


!MOS_nulu.29.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
29
!
93.3625927141
98.0478213865
191.4104141006
196.0956427730
289.4582354871
294.1434641595
298.8286928319
392.1912855460
396.8765142184
490.2391069325
494.9243356049
499.6095642773
592.9721569914
597.6573856638
691.0199783779
695.7052070503
789.0677997644
793.7530284368
798.4382571092
891.8008498233
896.4860784957
989.8486712098
994.5338998822
999.2191285546
1092.5817212687
1097.2669499411
1190.6295426552
1195.3147713276
1200.0000000000


!MOS_nulu.41.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
41
!
88.6773640417
93.3625927141
98.0478213865
186.7251854282
191.4104141006
196.0956427730
284.7730068147
289.4582354871
294.1434641595
298.8286928319
387.5060568736
392.1912855460
396.8765142184
485.5538782601
490.2391069325
494.9243356049
499.6095642773
588.2869283190
592.9721569914
597.6573856638
686.3347497055
691.0199783779
695.7052070503
784.3825710920
789.0677997644
793.7530284368
798.4382571092
887.1156211509
891.8008498233
896.4860784957
985.1634425374
989.8486712098
994.5338998822
999.2191285546
1087.8964925963
1092.5817212687
1097.2669499411
1185.9443139828
1190.6295426552
1195.3147713276
1200.0000000000


!MOS_nulu.53.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
53
!
83.9921353693
88.6773640417
93.3625927141
98.0478213865
182.0399567558
186.7251854282
191.4104141006
196.0956427730
280.0877781423
284.7730068147
289.4582354871
294.1434641595
298.8286928319
382.8208282012
387.5060568736
392.1912855460
396.8765142184
480.8686495877
485.5538782601
490.2391069325
494.9243356049
499.6095642773
583.6016996466
588.2869283190
592.9721569914
597.6573856638
681.6495210331
686.3347497055
691.0199783779
695.7052070503
779.6973424196
784.3825710920
789.0677997644
793.7530284368
798.4382571092
882.4303924785
887.1156211509
891.8008498233
896.4860784957
980.4782138650
985.1634425374
989.8486712098
994.5338998822
999.2191285546
1083.2112639239
1087.8964925963
1092.5817212687
1097.2669499411
1181.2590853104
1185.9443139828
1190.6295426552
1195.3147713276
1200.0000000000


!MOS_nulu.65.scl
!
meru extended secondary sequence ,nulu H[n]=8H[n-12]+H[n-1] ,G=(8+G^11)^(1/12)=1.334538849 Log(2)=0.416341304 generator=499.6095642773 period=1200.0000000000
!
65
!
79.3069066969
83.9921353693
88.6773640417
93.3625927141
98.0478213865
177.3547280834
182.0399567558
186.7251854282
191.4104141006
196.0956427730
275.4025494699
280.0877781423
284.7730068147
289.4582354871
294.1434641595
298.8286928319
378.1355995288
382.8208282012
387.5060568736
392.1912855460
396.8765142184
476.1834209153
480.8686495877
485.5538782601
490.2391069325
494.9243356049
499.6095642773
578.9164709742
583.6016996466
588.2869283190
592.9721569914
597.6573856638
676.9642923607
681.6495210331
686.3347497055
691.0199783779
695.7052070503
775.0121137472
779.6973424196
784.3825710920
789.0677997644
793.7530284368
798.4382571092
877.7451638061
882.4303924785
887.1156211509
891.8008498233
896.4860784957
975.7929851926
980.4782138650
985.1634425374
989.8486712098
994.5338998822
999.2191285546
1078.5260352515
1083.2112639239
1087.8964925963
1092.5817212687
1097.2669499411
1176.5738566380
1181.2590853104
1185.9443139828
1190.6295426552
1195.3147713276
1200.0000000000