Comma pump examples: Difference between revisions

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Ih7 = w1 - y3 - w5 - z7 = 1/1-5/4-3/2-7/4
yVIs7 = w1 - y3 - ry4 - y6 = 1/1-5/4-10/7-5/3
rIIh7 = w1 - r2 - ry4 - r6 = 1/1-8/7-10/7-12/7
ryVIIs7 = ry7 - r2 - ry4 - rry5 = 20/21-8/7-10/7-80/49
rrIIIh7 = rr7 - r2 - rr3 - rry5 = 48/49-8/7-64/49-80/49
zIVs7 = rrIIIs7 = rr7 - r<sup>3</sup>1 - rr3 - rrg5 = 48/49-384/343-64/49-384/245
Vh7 = r<sup>3</sup>IVh7 = r<sup>3</sup>1 - rr3 - r<sup>3</sup>4 - r<sup>3</sup>y6 = 384/343-64/49-512/343-640/343
zVIIs7 = rrVIs7 = rrg1 - rr3 - r<sup>3</sup>4 - rr6 = 256/245-64/49-512/343-256/147
Ih7 = sr<sup>3</sup>VIIh7 = sr<sup>3</sup>7 - r<sup>3</sup>y2 - r<sup>3</sup>4 - rr6 = 1024/1029-1280/1029-512/343-256/147
Ih7 = 1/1-5/4-3/2-7/4
rIIh7 = 1/1-8/7-10/7-12/7
rIIIh7 = 48/49-8/7-64/49-80/49
Vh7 = r<sup>3</sup>IVh7 = 384/343-64/49-512/343-640/343
Ih7 = sr<sup>3</sup>VIIh7 = 1024/1029-1280/1029-512/343-256/147
==1728/1715 (orwellismic or triple-ru gu)==
==1728/1715 (orwellismic or triple-ru gu)==
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/pumps/1728.mp3 pump1728]''  Ch7 -- zEbs7 -- zEbh7 -- [zzGb=rgF]s7 - rgFh7 -- gAbs7 -- gAbh7 -- Cs7 -- Ch7 -- zEbh7 -- [zzGb=rgF]h7 -- gAbh7 -- Ch7
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/pumps/1728.mp3 pump1728]''  Ch7 -- zEbs7 -- zEbh7 -- [zzGb=rgF]s7 - rgFh7 -- gAbs7 -- gAbh7 -- Cs7 -- Ch7 -- zEbh7 -- [zzGb=rgF]h7 -- gAbh7 -- Ch7
Line 713: Line 641:
Ih7 = z<sup>3</sup>yIIh7 = 1715/1728-8575/6912-1715/1152-12005/6912
Ih7 = z<sup>3</sup>yIIh7 = 1715/1728-8575/6912-1715/1152-12005/6912


==2401/2400 (breed or quadzo gugu)==
==2401/2400 (breed or quadzoagugu)==
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/pumps/2401.mp3 pump2401]''  chords: Ch7 -- zBbs7 -- zgGbh7 -- zzDbs7 -- [zzgFb=rryD#]h7 -- ryC#s7 -- rAh7 -- yEs7 -- Gh7 -- zBbs7 -- Ch7 -- zgGbh7 -- [zzgFb=rryD#]h7 -- rAh7 -- Gh7 -- Ch7  
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/pumps/2401.mp3 pump2401]''  chords: Ch7 -- zBbs7 -- zgGbh7 -- zzDbs7 -- [zzgFb=rryD#]h7 -- ryC#s7 -- rAh7 -- yEs7 -- Gh7 -- zBbs7 -- Ch7 -- zgGbh7 -- [zzgFb=rryD#]h7 -- rAh7 -- Gh7 -- Ch7  


Line 1,146: Line 1,074:
4000/3969-5000/3969-2000/1323-1000/567
4000/3969-5000/3969-2000/1323-1000/567


==4375/4374 (ragismic or zo quadyo)==
==4375/4374 (ragismic or zoquadyo)==
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/pumps/4375.mp3 pump4375]''
''[http://clones.soonlabel.com/public/micro/gene_ward_smith/pumps/4375.mp3 pump4375]''


Revision as of 01:41, 19 December 2018


Chord names are explained here: Color notation chord names

3-limit examples

256/243 (blackwood)

battaglia-blackwood [dead link]

5-limit examples

81/80 (meantone)

These are very familiar from classical and popular music. See Meantone comma pump examples.

128/125 (augmented or triple gu)

See 12edo comma pump examples.

250/243 (porcupine or triple yo)

parizek2

2048/2025 (diaschismic or small gugu)

parizek1

Also see 12edo comma pump examples.

3125/3072 (magic or large quintyo)

parizek4

15625/15552 (hanson or sixfold yo)

parizek6

battaglia-hanson [dead link]

16875/16384 (negri or large quadyo)

parizek3

20000/19683 (tetracot or small quadyo)

parizek7

78732/78125 (sensi or sevenfold gu)

parizek5

pump78732

1600000/1594323 (amity or small quintyo)

amity

tetradic pump [dead link]

2109375/2097152 (semicomma, 5-limit orwell or large sevenfold yo)

semicomma

7-limit examples

Every s7 chord can also be thought of as a z7(zg5) chord, e.g. zVIIs7 could be Vz7(zg5).

126/125 (starling or zogugu)

pump126 chords: Ch7 -- zBbs7 -- gEbh7 -- gEbs7 -- [ggGb=ryF#]h7 -- Ch7 -- gEbh7 -- [ggGg=ryF#]h7 -- Ch7

Ih7 -- zVIIs7 -- gIIIh7 -- gIIIs7 -- [ggV=ryIV]h7 -- Ih7 -- gIIIh7 -- [ggV=ryIV]h7 -- Ih7

Ih7 1/1 5/4 3/2 7/4 ~ 125/126 625/504 125/84 125/72
zVIIs7 21/20 21/16 3/2 7/4 ~ 25/24 125/96 125/84 125/72
gIIIh7 21/20 6/5 3/2 9/5 ~ 25/24 25/21 125/84 25/14
gIIIs7 36/35 6/5 36/25 9/5 ~ 50/49 25/21 10/7 25/14
[ggV=ryIV]h7 27/25 63/50 36/25 9/5 ~ 15/14 5/4 10/7 25/14
Ih7 126/125 63/50 189/125 441/250 ~ 1/1 5/4 3/2 7/4
Ih7 1/1 5/4 3/2 7/4 ~ 125/126 625/504 125/84 125/72
gIIIh7 21/20 6/5 3/2 9/5 ~ 25/24 25/21 125/84 25/14
[ggV=ryIV]h7 27/25 63/50 36/25 9/5 ~ 15/14 5/4 10/7 25/14
Ih7 126/125 63/50 189/125 441/250 ~ 1/1 5/4 3/2 7/4

225/224 (marvel or ruruyo)

pump225 chords: Ch7 -- zEbs7 -- zgCbh7 -- [zAb=yyG#]s7 -- yEh7 -- yEs7 -- Ch7 -- zEbs7 -- [zAb=yyG#]s7 -- yEs7 -- Ch7

Ih7 -- zIIIs7 -- zgIh7 -- [zVI=yyV]s7 -- yIIIh7 -- yIIIs7 -- Ih7 -- zIIIs7 -- [zVI=yyV]s7 -- yIIIs7 -- Ih7

Ih7 1/1 5/4 3/2 7/4 ~ 225/224 1125/896 675/448 225/128
zIIIs7 1/1 7/6 7/5 7/4 ~ 225/224 75/64 45/32 225/128
zgIh7 14/15 7/6 7/5 49/30 ~ 15/16 75/64 45/32 105/64
[zVI=yyV]s7 14/15 7/6 4/3 14/9 ~ 15/16 75/64 75/56 25/16
yIIIh7 14/15 49/45 56/45 14/9 ~ 15/16 35/32 5/4 25/16
yIIIs7 14/15 16/15 56/45 112/75 ~ 15/16 15/14 5/4 3/2
Ih7 224/225 56/45 112/75 392/225 ~ 1/1 5/4 3/2 7/4
Ih7 1/1 5/4 3/2 7/4 ~ 225/224 1125/896 675/448 225/128
zIIIs7 1/1 7/6 7/5 7/4 ~ 225/224 75/64 45/32 225/128
[zVI=yyV]s7 14/15 7/6 4/3 14/9 ~ 15/16 75/64 75/56 25/16
yIIIs7 14/15 16/15 56/45 112/75 ~ 15/16 15/14 5/4 3/2
Ih7 224/225 56/45 112/75 392/225 ~ 1/1 5/4 3/2 7/4

245/243 (sensamagic or zozoyo)

pump245 chords: Ch7 -- rAh7 -- [rE=zyF]h7 -- yDh7 -- yAh7 -- Ch7 -- [rE=zyF]h7 -- yAh7 -- Ch7

Ih7 -- rVIh7 -- [rIII=zyIV]h7 -- yIIh7 -- yVIh7 -- Ih7 -- [rIII=zyIV]h7 -- yVIh7 -- Ih7

Ih7 1/1 5/4 3/2 7/4 ~ 245/243 1225/972 245/162 1715/972
rVIh7 15/14 9/7 3/2 12/7 ~ 175/162 35/27 245/162 140/81
[rIII=zyIV]h7 27/28 9/8 9/7 45/28 ~ 35/36 245/216 35/27 175/108
yIIh7 27/28 54/49 135/98 81/49 ~ 35/36 10/9 25/18 5/3
yVIh7 405/392 243/196 81/56 81/49 ~ 25/24 5/4 35/24 5/3
Ih7 243/245 243/196 729/490 243/140 ~ 1/1 5/4 3/2 7/4
Ih7 1/1 5/4 3/2 7/4 ~ 245/243 1225/972 245/162 1715/972
[rIII=zyIV]h7 27/28 9/8 9/7 45/28 ~ 35/36 245/216 35/27 175/108
yVIh7 405/392 243/196 81/56 81/49 ~ 25/24 5/4 35/24 5/3
Ih7 243/245 243/196 729/490 243/140 ~ 1/1 5/4 3/2 7/4

686/675 (sengic or triple-zo gugu)

pump686

875/864 (keemic or zo triple-yo)

pump875

1029/1024 (gamelismic or large triple zo)

pump1029 chords: Ch7 -- yAs7 -- rDh7 -- ryBs7 -- [rrE=zF]h7 -- zFs7 -- Gh7 -- zBbs7 -- Ch7 -- rDh7 -- [rrE=zF]h7 -- Gh7 -- Ch7

Ih7 -- yVIs7 -- rIIh7 -- ryVIIs7 -- [rrIII=zIV]h7 -- zIVs7 -- Vh7 -- zVIIs7 -- Ih7 -- rIIh7 -- [rIII=zIV]h7 -- Vh7 -- Ih7

Ih7 1/1 5/4 3/2 7/4
yVIs7 1/1 5/4 10/7 5/3
rIIh7 1/1 8/7 10/7 12/7
ryVIIs7 20/21 8/7 10/7 80/49
[rrIII=zIV]h7 48/49 8/7 64/49 80/49 ~ 63/64 147/128 21/16 105/64
zIVs7 48/49 384/343 64/49 384/245 ~ 63/64 9/8 21/16 63/40
Vh7 384/343 64/49 512/343 640/343 ~ 9/8 21/16 3/2 15/8
zVIIs7 256/245 64/49 512/343 256/147 ~ 21/20 21/16 3/2 7/4
Ih7 1024/1029 1280/1029 512/343 256/147 ~ 1/1 5/4 3/2 7/4
Ih7 1/1 5/4 3/2 7/4
rIIh7 1/1 8/7 10/7 12/7
[rrIII=zIV]h7 48/49 8/7 64/49 80/49 ~ 63/64 147/128 21/16 105/64
Vh7 384/343 64/49 512/343 640/343 ~ 9/8 21/16 3/2 15/8
Ih7 1024/1029 1280/1029 512/343 256/147 ~ 1/1 5/4 3/2 7/4

1728/1715 (orwellismic or triple-ru gu)

pump1728 Ch7 -- zEbs7 -- zEbh7 -- [zzGb=rgF]s7 - rgFh7 -- gAbs7 -- gAbh7 -- Cs7 -- Ch7 -- zEbh7 -- [zzGb=rgF]h7 -- gAbh7 -- Ch7

Ih7 -- zIIIs7 -- zIIIh7 -- [zzV=rgIV]s7 -- rgIVh7 -- gVIs7 -- gVIh7 -- Is7 -- Ih7 -- zIIIh7 -- [zzV=rgIV]h7 -- gVIh7 -- Ih7

Ih7 = w1 - y3 - w5 - z7 = 1/1-5/4-3/2-7/4

zIIIs7 = w1 - z3 - zg5 - z7 = 1/1-7/6-7/5-7/4

zIIIh7 = zz2 - z3 - zy5 - z7 = 49/48-7/6-35/24-7/4

zzVs7 = zz2 - z3 - zz5 - zzg7 = 49/48-7/6-49/36-49/30

rgIVh7 = zzVh7 = zz2 - z34 - zz5 - zzy7 = 49/48-343/288-49/36-245/144

gVIs7 = z3VIIs7 = z34 - zz5 - z37 - z3g9 = 343/288-49/36-343/216-343/180

gVIh7 = z3VIIh7 = z3y2 - z34 - z46 - zzz7 = 1715/1728-343/288-2401/1728-343/216

Is7 = z3yIIs7 = z3y2 - z34 - z3y6 - zzy7 = 1715/1728-343/288-1715/1152-245/144

Ih7 = z3yIIh7 = z3y2 - z3yy4 - z3y6 - z4y8 = 1715/1728-8575/6912-1715/1152-12005/6912

Ih7 = 1/1-5/4-3/2-7/4

zIIIh7 = 49/48-7/6-35/24-7/4

rgIVh7 = zzVh7 = 49/48-343/288-49/36-245/144

gVIh7 = z3VIIh7 = 1715/1728-343/288-2401/1728-343/216

Ih7 = z3yIIh7 = 1715/1728-8575/6912-1715/1152-12005/6912

2401/2400 (breed or quadzoagugu)

pump2401 chords: Ch7 -- zBbs7 -- zgGbh7 -- zzDbs7 -- [zzgFb=rryD#]h7 -- ryC#s7 -- rAh7 -- yEs7 -- Gh7 -- zBbs7 -- Ch7 -- zgGbh7 -- [zzgFb=rryD#]h7 -- rAh7 -- Gh7 -- Ch7

Ih7 -- zVIIs7 -- zgVh7 -- zzIIs7 -- [zzgIV=rryII]h7 -- ryIs7 -- rVIh7 -- yIIIs7 -- Vh7 -- zVIIs7 -- Ih7 -- zgVh7 -- [zzgIV=rryII]h7 -- rVIh7 -- Vh7 -- Ih7

Ih7 1/1 5/4 3/2 7/4
zVIIs7 21/20 21/16 3/2 7/4
zgVh7 21/20 49/40 7/5 7/4
zzIIs7 49/48 49/40 49/32 7/4
[zzgIV=rryII]h7 343/320 49/40 49/32 147/80 ~ 15/14 60/49 75/49 90/49
ryIs7 343/320 1029/800 1029/640 147/80 ~ 15/14 9/7 45/28 90/49
rVIh7 343/320 1029/800 2401/1600 343/200 ~ 15/14 9/7 3/2 12/7
yIIIs7 343/320 2401/1920 2401/1600 2401/1280 ~ 15/14 5/4 3/2 15/8
Vh7 7203/6400 16807/12800 2401/1600 2401/1280 ~ 9/8 21/16 3/2 15/8
zVIIs7 16807/16000 16807/12800 2401/1600 16807/9600 ~ 21/20 21/16 3/2 7/4
Ih7 2401/2400 2401/1920 2401/1600 16807/9600 ~ 1/1 5/4 3/2 7/4
Ih7 1/1 5/4 3/2 7/4
zgVh7 21/20 49/40 7/5 7/4
[zzgIV=rryII]h7 343/320 49/40 49/32 147/80 ~ 15/14 60/49 75/49 90/49
rVIh7 343/160 1029/400 2401/1600 343/200 ~ 15/7 18/7 3/2 12/7
Vh7 7203/6400 16807/12800 2401/1600 2401/1280 ~ 9/8 21/16 3/2 15/8
Ih7 2401/2400 2401/1920 2401/1600 16807/9600 ~ 1/1 5/4 3/2 7/4

3125/3087 (gariboh or triple-ru quintyo)

pump3125

3136/3125 (hemimean or zozo quintgu)

pump3136 chords: Ch7 -- zEbs7 -- gAbh7 -- zgCbs7 -- zggEbbh7 -- zggEbbs7 -- [zg3Cbb=ryyA#]h7 -- yyG#s7 -- yEh7 -- yEs7 -- Ch7 -- -- Ch7 -- gAbh7 -- zggEbbh7 -- [zg3Cbb=ryyA#]h7 -- yEh7 -- Ch7

Ih7 -- zIIIs7 -- gVIh7 -- zgIs7 -- zggIIIh7 -- zggIIIs7 -- [zg3I=ryyVI]h7 -- yyVs7 -- yIIIh7 -- yIIIs7 -- Ih7 -- gVIh7 -- zggIIIh7 -- [zg3I=ryyVI]h7 -- -- yIIIh7 -- Ih7

Ih7 1/1 5/4 3/2 7/4
zIIIs7 1/1 7/6 7/5 7/4
gVIh7 1/1 6/5 7/5 8/5
zgIs7 14/15 28/25 7/5 8/5
zggIIIh7 49/50 28/25 7/5 42/25
zggIIIs7 24/25 28/25 168/125 42/25
[zg3I=ryyVI]h7 28/25 168/125 196/125 224/125 ~ 125/112 75/56 25/16 25/14
yyVs7 147/125 168/125 196/125 1176/625 ~ 75/64 75/56 25/16 15/8
yIIIh7 686/625 784/625 196/125 1176/625 ~ 35/32 5/4 25/16 15/8
yIIIs7 672/625 784/625 4704/3125 1176/625 ~ 15/14 5/4 3/2 15/8
Ih7 3136/3125 784/625 4704/3125 5488/3125 ~ 1/1 5/4 3/2 7/4
Ih7 1/1 5/4 3/2 7/4
gVIh7 1/1 6/5 7/5 8/5
zggIIIh7 28/25 7/5 42/25 49/25
[zg3I=ryyVI]h7 28/25 168/125 196/125 224/125 ~ 125/112 75/56 25/16 25/14
yIIIh7 686/625 784/625 196/125 1176/625 ~ 35/32 5/4 25/16 15/8
Ih7 3136/3125 784/625 4704/3125 5488/3125 ~ 1/1 5/4 3/2 7/4

4000/3969 (octagar or ruru triple-yo)

pump4000

1-5/4-3/2-7/4

1-5/4-10/7-5/3

15/14-5/4-10/7-25/14

1-5/4-10/7-5/3

20/21-25/21-10/7-5/3

50/49-25/21-10/7-25/14

50/49-25/21-200/147-250/147

1000/1029-500/441-200/147-250/147

500/441-200/147-100/63-800/441

125/126-500/441-250/189-100/63

500/441-250/189-2000/1323-2500/1323

200/189-250/189-2000/1323-1000/567

4000/3969-5000/3969-2000/1323-1000/567

1-5/4-3/2-7/4

15/14-5/4-10/7-25/14

20/21-25/21-10/7-5/3

50/49-25/21-200/147-250/147

500/441-200/147-100/63-800/441

500/441-250/189-2000/1323-2500/1323

4000/3969-5000/3969-2000/1323-1000/567

4375/4374 (ragismic or zoquadyo)

pump4375

1-5/4-3/2-7/4

1-5/4-10/7-5/3

25/24-5/4-35/24-5/3

35/36-7/6-35/24-5/3

35/36-10/9-25/18-5/3

35/36-175/144-25/18-175/108

25/27-125/108-25/18-175/108

25/27-175/162-35/27-175/108

175/162-875/648-175/108-1225/648 ~ 27/25-27/20-81/50-189/100

175/162-875/648-125/81-875/486 ~ 27/25-27/20-54/35-9/5

4375/3888-875/648-6125/3888-875/486 ~ 9/8-27/20-63/40-9/5

4375/3888-625/486-4375/2916-875/486 ~ 9/8-9/7-3/2-9/5

6125/5832-875/729-4375/2916-875/486 ~ 21/20-6/5-3/2-9/5

4375/4374-875/729-4375/2916-1250/729 ~ 1-6/5-3/2-12/7

4375/4374-21875/17496-4375/2916-30625/17496 ~ 1-5/4-3/2-7/4

1-5/4-3/2-7/4

25/24-5/4-35/24-5/3

35/36-10/9-25/18-5/3

25/27-125/108-25/18-175/108

175/162-875/648-175/108-1225/648 ~ 27/25-27/20-81/50-189/100

4375/3888-875/648-6125/3888-875/486 ~ 9/8-27/20-63/40-9/5

6125/5832-875/729-4375/2916-875/486 ~ 21/20-6/5-3/2-9/5

4375/4374-21875/17496-4375/2916-30625/17496 ~ 1-5/4-3/2-7/4

5120/5103 (hemifamity or small ruyo)

pump5120

1-5/4-3/2-7/4

35/32-5/4-35/24-7/4

25/24-5/4-35/24-5/3

25/24-25/21-25/18-5/3

35/36-10/9-25/18-5/3

20/21-10/9-4/3-5/3

20/21-10/9-80/63-100/63

400/441-200/189-80/63-100/63

200/189-80/63-40/27-320/189

80/81-32/27-40/27-320/189

80/81-640/567-800/567-320/189

80/81-640/567-320/243-128/81

1600/1701-640/567-320/243-2560/1701

256/243-320/243-2560/1701-1280/729

5120/5103-6400/5103-2560/1701-1280/729

1-5/4-3/2-7/4

25/24-5/4-35/24-5/3

35/36-10/9-25/18-5/3

20/21-10/9-80/63-100/63

200/189-80/63-40/27-320/189

80/81-640/567-800/567-320/189

1600/1701-640/567-320/243-2560/1701

256/243-320/243-2560/1701-1280/729

5120/5103-6400/5103-2560/1701-1280/729

6144/6125 (porwell or small ruru triple-gu)

pump6144

1-5/4-3/2-7/4

35/32-5/4-35/24-7/4

35/32-5/4-25/16-15/8

35/32-21/16-105/64-15/8

35/32-175/128-105/64-245/128

525/512-175/128-75/64-105/64

525/512-1225/1024-175/128-875/512

6125/6144-1225/1024-6125/4096-875/512

8575/8192-1225/1024-6125/4096-3675/2048

18375/16384-2625/2048-6125/4096-3675/2048

18375/16384-42875/32768-6125/4096-30625/16384

4375/4096-30625/24576-6125/4096-30625/16384

6125/6144-30625/24576-6125/4096-42875/24576

1-5/4-3/2-7/4

35/32-5/4-25/16-15/8

35/32-175/128-105/64-245/128

525/512-1225/1024-175/128-875/512

8575/8192-1225/1024-6125/4096-3675/2048

18375/16384-42875/32768-6125/4096-30625/16384

6125/6144-30625/24576-6125/4096-42875/24576

10976/10935 (hemimage or small triple-zo gu)

pump10976

64827/64000 (squalentine or large quadzo triple-gu)

pump64827

13-limit examples

676/675 (parizeksmic or double thogu)

http://micro.soonlabel.com/petr_parizek/pp_pump_675.mp3

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