Koepf's Editions - Alle 351 Skalen im Tonumfang einer Oktav, ohne Umkehrungen

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Koepf's Editions – Writings – Die Skalen im Tonumfang einer Oktav – Alle 351 Skalen im Tonumfang einer Oktav, ohne Umkehrungen

Die Skalen im Tonumfang einer Oktav

Siegfried Koepf, März 2009

[N]	Intervallfolge	Symmetrien	Ausgeschlossene Intervalle	Name
Alle 351 Skalen im Tonumfang einer Oktav ohne Umkehrungen
[1]	12	s2	1 2 3 4 5 6 7 8 9 10 11	Ton
[2]	1 11	s2	. 2 3 4 5 6 7 8 9 10 .	Kleine Sekund
[3]	2 10	s2	1 . 3 4 5 6 7 8 9 . 11	Große Sekund
[4]	3 9	s2	1 2 . 4 5 6 7 8 . 10 11	Kleine Terz
[5]	4 8	s2	1 2 3 . 5 6 7 . 9 10 11	Große Terz
[6]	5 7	s2	1 2 3 4 . 6 . 8 9 10 11	Reine Quart
[7]	6 6	t2 s4	1 2 3 4 5 . 7 8 9 10 11	Tritonus
[8]	1 1 10	s2	. . 3 4 5 6 7 8 9 . .
[9]	1 2 9		. . . 4 5 6 7 8 . . .
[10]	1 3 8		. 2 . . 5 6 7 . . 10 .
[11]	1 4 7		. 2 3 . . 6 . . 9 10 .
[12]	1 5 6		. 2 3 4 . . . 8 9 10 .
[13]	1 6 5		. 2 3 4 . . . 8 9 10 .
[14]	1 7 4		. 2 3 . . 6 . . 9 10 .
[15]	1 8 3		. 2 . . 5 6 7 . . 10 .
[16]	1 9 2		. . . 4 5 6 7 8 . . .
[17]	2 2 8	s2	1 . 3 . 5 6 7 . 9 . 11
[18]	2 3 7		1 . . 4 . 6 . 8 . . 11
[19]	2 4 6		1 . 3 . 5 . 7 . 9 . 11
[20]	2 5 5	s2	1 . 3 4 . 6 . 8 9 . 11
[21]	2 6 4		1 . 3 . 5 . 7 . 9 . 11	Hartverminderter Dreiklang 1. U.
[22]	2 7 3		1 . . 4 . 6 . 8 . . 11
[23]	3 3 6	s2	1 2 . 4 5 . 7 8 . 10 11	Verminderter Dreiklang
[24]	3 4 5		1 2 . . . 6 . . . 10 11	Moll-Dreiklang
[25]	3 5 4		1 2 . . . 6 . . . 10 11	Dur-Dreiklang 1. U.
[26]	4 4 4	t3 s6	1 2 3 . 5 6 7 . 9 10 11	Übermäßiger Dreiklang
[27]	1 1 1 9	s2	. . . 4 5 6 7 8 . . .
[28]	1 1 2 8		. . . . 5 6 7 . . . .
[29]	1 1 3 7		. . . . . 6 . . . . .
[30]	1 1 4 6		. . 3 . . . . . 9 . .
[31]	1 1 5 5	s2	. . 3 4 . . . 8 9 . .
[32]	1 1 6 4		. . 3 . . . . . 9 . .
[33]	1 1 7 3		. . . . . 6 . . . . .
[34]	1 1 8 2		. . . . 5 6 7 . . . .
[35]	1 2 1 8	s2	. . . . 5 6 7 . . . .
[36]	1 2 2 7		. . . . . 6 . . . . .
[37]	1 2 3 6		. . . 4 . . . 8 . . .
[38]	1 2 4 5
[39]	1 2 5 4		. . . . . 6 . . . . .
[40]	1 2 6 3		. . . . 5 . 7 . . . .
[41]	1 2 7 2	s2	. . . 4 . 6 . 8 . . .
[42]	1 3 1 7	s2	. 2 . . . 6 . . . 10 .
[43]	1 3 2 6
[44]	1 3 3 5		. 2 . . . . . . . 10 .
[45]	1 3 4 4		. 2 . . . 6 . . . 10 .	Großer Moll-Septakkord 3. U.
[46]	1 3 5 3	s2	. 2 . . . 6 . . . 10 .
[47]	1 3 6 2		. . . . 5 . 7 . . . .
[48]	1 4 1 6	s2	. 2 3 . . . . . 9 10 .
[49]	1 4 2 5		. . 3 . . . . . 9 . .
[50]	1 4 3 4	s2	. 2 . . . 6 . . . 10 .	Großer Dur-Septakkord 3. U.
[51]	1 4 4 3		. 2 . . . 6 . . . 10 .	Großer übermäßiger Septakkord 3. U.
[52]	1 4 5 2		. . . . . 6 . . . . .
[53]	1 5 1 5	t2 s4	. 2 3 4 . . . 8 9 10 .
[54]	1 5 2 4		. . 3 . . . . . 9 . .
[55]	1 5 3 3		. 2 . . . . . . . 10 .
[56]	1 5 4 2
[57]	1 6 2 3
[58]	1 6 3 2		. . . 4 . . . 8 . . .
[59]	1 7 2 2		. . . . . 6 . . . . .
[60]	2 2 2 6	s2	1 . 3 . 5 . 7 . 9 . 11
[61]	2 2 3 5		1 . . . . 6 . . . . 11
[62]	2 2 4 4	s2	1 . 3 . 5 . 7 . 9 . 11
[63]	2 2 5 3		1 . . . . 6 . . . . 11
[64]	2 3 2 5	s2	1 . . 4 . 6 . 8 . . 11
[65]	2 3 3 4		1 . . . . . . . . . 11	Halbverminderter Septakkord 3. U.
[66]	2 3 4 3	s2	1 . . . . 6 . . . . 11	Kleiner Moll-Septakkord 3. U.
[67]	2 4 2 4	t2 s4	1 . 3 . 5 . 7 . 9 . 11
[68]	2 4 3 3		1 . . . . . . . . . 11	Kleiner Dur-Septakkord 3. U.
[69]	3 3 3 3	t4 s8	1 2 . 4 5 . 7 8 . 10 11	Verminderter Septakkord
[70]	1 1 1 1 8	s2	. . . . 5 6 7 . . . .
[71]	1 1 1 2 7		. . . . . 6 . . . . .
[72]	1 1 1 3 6
[73]	1 1 1 4 5
[74]	1 1 1 5 4
[75]	1 1 1 6 3
[76]	1 1 1 7 2		. . . . . 6 . . . . .
[77]	1 1 2 1 7		. . . . . 6 . . . . .
[78]	1 1 2 2 6
[79]	1 1 2 3 5
[80]	1 1 2 4 4
[81]	1 1 2 5 3		. . . . . 6 . . . . .
[82]	1 1 2 6 2	s2	. . . . 5 . 7 . . . .
[83]	1 1 3 1 6
[84]	1 1 3 2 5
[85]	1 1 3 3 4
[86]	1 1 3 4 3	s2	. . . . . 6 . . . . .
[87]	1 1 3 5 2		. . . . . 6 . . . . .
[88]	1 1 4 1 5		. . 3 . . . . . 9 . .
[89]	1 1 4 2 4	s2	. . 3 . . . . . 9 . .
[90]	1 1 4 3 3
[91]	1 1 4 4 2
[92]	1 1 5 1 4		. . 3 . . . . . 9 . .
[93]	1 1 5 2 3
[94]	1 1 5 3 2
[95]	1 1 6 1 3
[96]	1 1 6 2 2
[97]	1 1 7 1 2		. . . . . 6 . . . . .
[98]	1 2 1 2 6
[99]	1 2 1 3 5
[100]	1 2 1 4 4	s2	. . . . . 6 . . . . .
[101]	1 2 1 5 3
[102]	1 2 1 6 2
[103]	1 2 2 1 6	s2
[104]	1 2 2 2 5
[105]	1 2 2 3 4		. . . . . 6 . . . . .
[106]	1 2 2 4 3
[107]	1 2 2 5 2		. . . . . 6 . . . . .
[108]	1 2 3 1 5
[109]	1 2 3 2 4
[110]	1 2 3 3 3
[111]	1 2 3 4 2
[112]	1 2 4 1 4
[113]	1 2 4 2 3
[114]	1 2 4 3 2
[115]	1 2 5 1 3
[116]	1 2 5 2 2		. . . . . 6 . . . . .
[117]	1 3 1 3 4		. 2 . . . 6 . . . 10 .
[118]	1 3 1 4 3		. 2 . . . 6 . . . 10 .
[119]	1 3 1 5 2
[120]	1 3 2 1 5
[121]	1 3 2 2 4
[122]	1 3 2 3 3
[123]	1 3 2 4 2
[124]	1 3 3 1 4	s2	. 2 . . . . . . . 10 .
[125]	1 3 3 2 3
[126]	1 3 3 3 2
[127]	1 3 4 2 2
[128]	1 4 1 4 2
[129]	1 4 2 2 3
[130]	1 4 2 3 2
[131]	1 4 3 2 2		. . . . . 6 . . . . .
[132]	1 5 2 2 2
[133]	2 2 2 2 4	s2	1 . 3 . 5 . 7 . 9 . 11
[134]	2 2 2 3 3	s2	1 . . . . . . . . . 11
[135]	2 2 3 2 3	s2	1 . . . . 6 . . . . 11	Pentatonische Leiter
[136]	1 1 1 1 1 7	s2	. . . . . 6 . . . . .
[137]	1 1 1 1 2 6
[138]	1 1 1 1 3 5
[139]	1 1 1 1 4 4	s2
[140]	1 1 1 1 5 3
[141]	1 1 1 1 6 2
[142]	1 1 1 2 1 6
[143]	1 1 1 2 2 5
[144]	1 1 1 2 3 4
[145]	1 1 1 2 4 3
[146]	1 1 1 2 5 2	s2	. . . . . 6 . . . . .
[147]	1 1 1 3 1 5
[148]	1 1 1 3 2 4
[149]	1 1 1 3 3 3	s2
[150]	1 1 1 3 4 2
[151]	1 1 1 4 1 4	s2
[152]	1 1 1 4 2 3
[153]	1 1 1 4 3 2
[154]	1 1 1 5 1 3
[155]	1 1 1 5 2 2
[156]	1 1 1 6 1 2
[157]	1 1 2 1 1 6	s2
[158]	1 1 2 1 2 5
[159]	1 1 2 1 3 4
[160]	1 1 2 1 4 3		. . . . . 6 . . . . .
[161]	1 1 2 1 5 2
[162]	1 1 2 2 1 5
[163]	1 1 2 2 2 4
[164]	1 1 2 2 3 3
[165]	1 1 2 2 4 2
[166]	1 1 2 3 1 4
[167]	1 1 2 3 2 3
[168]	1 1 2 3 3 2	s2
[169]	1 1 2 4 1 3
[170]	1 1 2 4 2 2
[171]	1 1 2 5 1 2
[172]	1 1 3 1 1 5	s2
[173]	1 1 3 1 2 4
[174]	1 1 3 1 3 3
[175]	1 1 3 1 4 2
[176]	1 1 3 2 1 4
[177]	1 1 3 2 2 3	s2
[178]	1 1 3 2 3 2
[179]	1 1 3 3 1 3
[180]	1 1 3 3 2 2
[181]	1 1 3 4 1 2		. . . . . 6 . . . . .
[182]	1 1 4 1 1 4	t2 s4	. . 3 . . . . . 9 . .	Messiaens 5. Modus 2. U.
[183]	1 1 4 1 2 3
[184]	1 1 4 1 3 2
[185]	1 1 4 2 1 3
[186]	1 1 4 2 2 2
[187]	1 1 4 3 1 2
[188]	1 1 5 1 2 2
[189]	1 1 5 2 1 2
[190]	1 2 1 2 1 5	s2
[191]	1 2 1 2 2 4
[192]	1 2 1 2 3 3
[193]	1 2 1 2 4 2	s2
[194]	1 2 1 3 1 4
[195]	1 2 1 3 2 3	s2
[196]	1 2 1 3 3 2
[197]	1 2 1 4 1 3
[198]	1 2 1 4 2 2
[199]	1 2 2 1 2 4
[200]	1 2 2 1 3 3	s2
[201]	1 2 2 1 4 2
[202]	1 2 2 2 1 4	s2
[203]	1 2 2 2 2 3
[204]	1 2 2 2 3 2
[205]	1 2 2 3 1 3
[206]	1 2 2 3 2 2	s2	. . . . . 6 . . . . .
[207]	1 2 3 1 2 3	t2
[208]	1 2 3 1 3 2	s2
[209]	1 2 3 2 1 3	s2
[210]	1 2 3 2 2 2
[211]	1 3 1 3 1 3	t3 s6	. 2 . . . 6 . . . 10 .	Übermäßige Leiter 1. U.
[212]	1 3 1 3 2 2
[213]	1 3 2 1 3 2	t2
[214]	1 3 2 2 2 2
[215]	2 2 2 2 2 2	t6 s12	1 . 3 . 5 . 7 . 9 . 11	Ganzton-Leiter, Messiaens 1. Modus
[216]	1 1 1 1 1 1 6	s2
[217]	1 1 1 1 1 2 5
[218]	1 1 1 1 1 3 4
[219]	1 1 1 1 1 4 3
[220]	1 1 1 1 1 5 2
[221]	1 1 1 1 2 1 5
[222]	1 1 1 1 2 2 4
[223]	1 1 1 1 2 3 3
[224]	1 1 1 1 2 4 2	s2
[225]	1 1 1 1 3 1 4
[226]	1 1 1 1 3 2 3	s2
[227]	1 1 1 1 3 3 2
[228]	1 1 1 1 4 1 3
[229]	1 1 1 1 4 2 2
[230]	1 1 1 1 5 1 2
[231]	1 1 1 2 1 1 5
[232]	1 1 1 2 1 2 4
[233]	1 1 1 2 1 3 3
[234]	1 1 1 2 1 4 2
[235]	1 1 1 2 2 1 4
[236]	1 1 1 2 2 2 3
[237]	1 1 1 2 2 3 2
[238]	1 1 1 2 3 1 3
[239]	1 1 1 2 3 2 2
[240]	1 1 1 2 4 1 2
[241]	1 1 1 3 1 1 4
[242]	1 1 1 3 1 2 3
[243]	1 1 1 3 1 3 2
[244]	1 1 1 3 2 1 3
[245]	1 1 1 3 2 2 2
[246]	1 1 1 3 3 1 2
[247]	1 1 1 4 1 1 3
[248]	1 1 1 4 1 2 2
[249]	1 1 1 4 2 1 2
[250]	1 1 1 5 1 1 2
[251]	1 1 2 1 1 2 4
[252]	1 1 2 1 1 3 3	s2
[253]	1 1 2 1 1 4 2
[254]	1 1 2 1 2 1 4
[255]	1 1 2 1 2 2 3
[256]	1 1 2 1 2 3 2
[257]	1 1 2 1 3 1 3
[258]	1 1 2 1 3 2 2
[259]	1 1 2 1 4 1 2	s2
[260]	1 1 2 2 1 1 4	s2
[261]	1 1 2 2 1 2 3
[262]	1 1 2 2 1 3 2
[263]	1 1 2 2 2 1 3
[264]	1 1 2 2 2 2 2	s2
[265]	1 1 2 2 3 1 2
[266]	1 1 2 3 1 1 3
[267]	1 1 2 3 1 2 2
[268]	1 1 2 3 2 1 2
[269]	1 1 3 1 1 3 2
[270]	1 1 3 1 2 1 3	s2
[271]	1 1 3 1 2 2 2
[272]	1 1 3 1 3 1 2
[273]	1 1 3 2 1 2 2
[274]	1 1 3 2 2 1 2
[275]	1 1 4 1 2 1 2
[276]	1 2 1 2 1 2 3
[277]	1 2 1 2 1 3 2
[278]	1 2 1 2 2 1 3			Harmonisch-Moll-Leiter 6. U.
[279]	1 2 1 2 2 2 2	s2		Melodisch-Moll-Leiter 6. U.
[280]	1 2 1 3 1 2 2
[281]	1 2 2 1 2 2 2	s2		Dur-Tonleiter 6. U., Lokrisch
[282]	1 1 1 1 1 1 1 5	s2
[283]	1 1 1 1 1 1 2 4
[284]	1 1 1 1 1 1 3 3	s2
[285]	1 1 1 1 1 1 4 2
[286]	1 1 1 1 1 2 1 4
[287]	1 1 1 1 1 2 2 3
[288]	1 1 1 1 1 2 3 2	s2
[289]	1 1 1 1 1 3 1 3	s2
[290]	1 1 1 1 1 3 2 2
[291]	1 1 1 1 1 4 1 2
[292]	1 1 1 1 2 1 1 4
[293]	1 1 1 1 2 1 2 3
[294]	1 1 1 1 2 1 3 2
[295]	1 1 1 1 2 2 1 3
[296]	1 1 1 1 2 2 2 2	s2
[297]	1 1 1 1 2 3 1 2
[298]	1 1 1 1 3 1 1 3	s2
[299]	1 1 1 1 3 1 2 2
[300]	1 1 1 1 3 2 1 2
[301]	1 1 1 1 4 1 1 2
[302]	1 1 1 2 1 1 1 4	s2
[303]	1 1 1 2 1 1 2 3
[304]	1 1 1 2 1 1 3 2
[305]	1 1 1 2 1 2 1 3
[306]	1 1 1 2 1 2 2 2
[307]	1 1 1 2 1 3 1 2	s2
[308]	1 1 1 2 2 1 1 3
[309]	1 1 1 2 2 1 2 2	s2
[310]	1 1 1 2 2 2 1 2
[311]	1 1 1 2 3 1 1 2
[312]	1 1 1 3 1 1 1 3	t2 s4		Messiaens 4. Modus 3. U.
[313]	1 1 1 3 1 1 2 2
[314]	1 1 1 3 1 2 1 2
[315]	1 1 1 3 2 1 1 2
[316]	1 1 2 1 1 2 1 3
[317]	1 1 2 1 1 2 2 2	s2
[318]	1 1 2 1 1 3 1 2
[319]	1 1 2 1 2 1 1 3	s2
[320]	1 1 2 1 2 1 2 2
[321]	1 1 2 1 2 2 1 2	s2
[322]	1 1 2 2 1 1 2 2	t2 s4		Messiaens 6. Modus 2. U.
[323]	1 1 2 2 1 2 1 2
[324]	1 2 1 2 1 2 1 2	t4 s8		Halbton-Ganzton-Leiter, Messiaens 2. Modus
[325]	1 1 1 1 1 1 1 1 4	s2
[326]	1 1 1 1 1 1 1 2 3
[327]	1 1 1 1 1 1 1 3 2
[328]	1 1 1 1 1 1 2 1 3
[329]	1 1 1 1 1 1 2 2 2	s2
[330]	1 1 1 1 1 1 3 1 2
[331]	1 1 1 1 1 2 1 1 3
[332]	1 1 1 1 1 2 1 2 2
[333]	1 1 1 1 1 2 2 1 2
[334]	1 1 1 1 1 3 1 1 2
[335]	1 1 1 1 2 1 1 1 3
[336]	1 1 1 1 2 1 1 2 2
[337]	1 1 1 1 2 1 2 1 2	s2
[338]	1 1 1 1 2 2 1 1 2
[339]	1 1 1 1 3 1 1 1 2
[340]	1 1 1 2 1 1 1 2 2	s2
[341]	1 1 1 2 1 1 2 1 2
[342]	1 1 1 2 1 2 1 1 2
[343]	1 1 2 1 1 2 1 1 2	t3 s6		Messiaens 3. Modus 1. U.
[344]	1 1 1 1 1 1 1 1 1 3	s2
[345]	1 1 1 1 1 1 1 1 2 2	s2
[346]	1 1 1 1 1 1 1 2 1 2	s2
[347]	1 1 1 1 1 1 2 1 1 2	s2
[348]	1 1 1 1 1 2 1 1 1 2	s2
[349]	1 1 1 1 2 1 1 1 1 2	t2 s4		Messiaens 7. Modus 4. U.
[350]	1 1 1 1 1 1 1 1 1 1 2	s2
[351]	1 1 1 1 1 1 1 1 1 1 1 1	t12 s24		Chromatische Tonleiter

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