Xenharmonic Wiki

Comma pump examples

Revision as of 19:37, 19 December 2018 by TallKite (talk | contribs) (more of the same)


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 trigu)

See 12edo comma pump examples.

250/243 (porcupine or triyo)

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

Ch7 Ih7 1/1 5/4 3/2 7/4 ~ 125/126 625/504 125/84 125/72
zBbs7 zVIIs7 21/20 21/16 3/2 7/4 ~ 25/24 125/96 125/84 125/72
gEbh7 gIIIh7 21/20 6/5 3/2 9/5 ~ 25/24 25/21 125/84 25/14
gEbs7 gIIIs7 36/35 6/5 36/25 9/5 ~ 50/49 25/21 10/7 25/14
[ggGb=ryF#]h7 [ggV=ryIV]h7 27/25 63/50 36/25 9/5 ~ 15/14 5/4 10/7 25/14
Ch7 Ih7 126/125 63/50 189/125 441/250 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4 ~ 125/126 625/504 125/84 125/72
gEbs7 gIIIh7 21/20 6/5 3/2 9/5 ~ 25/24 25/21 125/84 25/14
[ggGb=ryF#]h7 [ggV=ryIV]h7 27/25 63/50 36/25 9/5 ~ 15/14 5/4 10/7 25/14
Ch7 Ih7 126/125 63/50 189/125 441/250 ~ 1/1 5/4 3/2 7/4

225/224 (marvel or ruyoyo)

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

Ch7 Ih7 1/1 5/4 3/2 7/4 ~ 225/224 1125/896 675/448 225/128
zEbs7 zIIIs7 1/1 7/6 7/5 7/4 ~ 225/224 75/64 45/32 225/128
zgCbh7 zgIh7 14/15 7/6 7/5 49/30 ~ 15/16 75/64 45/32 105/64
[zAb=yyG#]s7 [zVI=yyV]s7 14/15 7/6 4/3 14/9 ~ 15/16 75/64 75/56 25/16
yEh7 yIIIh7 14/15 49/45 56/45 14/9 ~ 15/16 35/32 5/4 25/16
yEs7 yIIIs7 14/15 16/15 56/45 112/75 ~ 15/16 15/14 5/4 3/2
Ch7 Ih7 224/225 56/45 112/75 392/225 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4 ~ 225/224 1125/896 675/448 225/128
zEbs7 zIIIs7 1/1 7/6 7/5 7/4 ~ 225/224 75/64 45/32 225/128
[zAb=yyG#]s7 [zVI=yyV]s7 14/15 7/6 4/3 14/9 ~ 15/16 75/64 75/56 25/16
yEs7 yIIIs7 14/15 16/15 56/45 112/75 ~ 15/16 15/14 5/4 3/2
Ch7 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

Ch7 Ih7 1/1 5/4 3/2 7/4 ~ 245/243 1225/972 245/162 1715/972
rAh7 rVIh7 15/14 9/7 3/2 12/7 ~ 175/162 35/27 245/162 140/81
[rE=zyF]h7 [rIII=zyIV]h7 27/28 9/8 9/7 45/28 ~ 35/36 245/216 35/27 175/108
yDh7 yIIh7 27/28 54/49 135/98 81/49 ~ 35/36 10/9 25/18 5/3
yAh7 yVIh7 405/392 243/196 81/56 81/49 ~ 25/24 5/4 35/24 5/3
Ch7 Ih7 243/245 243/196 729/490 243/140 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4 ~ 245/243 1225/972 245/162 1715/972
[rE=zyF]h7 [rIII=zyIV]h7 27/28 9/8 9/7 45/28 ~ 35/36 245/216 35/27 175/108
yAh7 yVIh7 405/392 243/196 81/56 81/49 ~ 25/24 5/4 35/24 5/3
Ch7 Ih7 243/245 243/196 729/490 243/140 ~ 1/1 5/4 3/2 7/4

686/675 (sengic or trizoagugu)

pump686

875/864 (keemic or zotriyo)

pump875

1029/1024 (gamelismic or large trizo)

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

Ch7 Ih7 1/1 5/4 3/2 7/4
yAs7 yVIs7 1/1 5/4 10/7 5/3
rDh7 rIIh7 1/1 8/7 10/7 12/7
ryBs7 ryVIIs7 20/21 8/7 10/7 80/49
[rrE=zF]h7 [rrIII=zIV]h7 48/49 8/7 64/49 80/49 ~ 63/64 147/128 21/16 105/64
zFs7 zIVs7 48/49 384/343 64/49 384/245 ~ 63/64 9/8 21/16 63/40
Gh7 Vh7 384/343 64/49 512/343 640/343 ~ 9/8 21/16 3/2 15/8
zBbs7 zVIIs7 256/245 64/49 512/343 256/147 ~ 21/20 21/16 3/2 7/4
Ch7 Ih7 1024/1029 1280/1029 512/343 256/147 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4
rDh7 rIIh7 1/1 8/7 10/7 12/7
[rrE=zF]h7 [rrIII=zIV]h7 48/49 8/7 64/49 80/49 ~ 63/64 147/128 21/16 105/64
Gh7 Vh7 384/343 64/49 512/343 640/343 ~ 9/8 21/16 3/2 15/8
Ch7 Ih7 1024/1029 1280/1029 512/343 256/147 ~ 1/1 5/4 3/2 7/4

1728/1715 (orwellismic or triruagu)

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

Ch7 Ih7 1/1 5/4 3/2 7/4
zEbs7 zIIIs7 1/1 7/6 7/5 7/4
zEbh7 zIIIh7 49/48 7/6 35/24 7/4
[zzGb=rgF]s7 [zzV=rgIV]s7 49/48 7/6 49/36 49/30 ~ 36/35 288/245 48/35 288/175
rgFh7 rgIVh7 49/48 343/288 49/36 245/144 ~ 36/35 6/5 48/35 12/7
gAbs7 gVIs7 343/288 49/36 343/216 343/180 ~ 6/5 48/35 8/5 48/25
gAbh7 gVIh7 1715/1728 343/288 2401/1728 343/216 ~ 1/1 6/5 7/5 8/5
Cs7 Is7 1715/1728 343/288 1715/1152 245/144 ~ 1/1 6/5 3/2 12/7
Ch7 Ih7 1715/1728 8575/6912 1715/1152 12005/6912 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4
zEbh7 zIIIh7 49/48 7/6 35/24 7/4
[zzGb=rgF]h7 [zzV=rgIV]h7 49/48 343/288 49/36 245/144 ~ 36/35 6/5 48/35 12/7
gAbh7 gVIh7 1715/1728 343/288 2401/1728 343/216 ~ 1/1 6/5 7/5 8/5
Ch7 Ih7 1715/1728 8575/6912 1715/1152 12005/6912 ~ 1/1 5/4 3/2 7/4

2401/2400 (breed or quadzoagugu)

pump2401

Ch7 Ih7 1/1 5/4 3/2 7/4
zBbs7 zVIIs7 21/20 21/16 3/2 7/4
zgGgh7 zgVh7 21/20 49/40 7/5 7/4
zzDbs7 zzIIs7 49/48 49/40 49/32 7/4
[zzgFb=rryD#]h7 [zzgIV=rryII]h7 343/320 49/40 49/32 147/80 ~ 15/14 60/49 75/49 90/49
ryC#s7 ryIs7 343/320 1029/800 1029/640 147/80 ~ 15/14 9/7 45/28 90/49
rAh7 rVIh7 343/320 1029/800 2401/1600 343/200 ~ 15/14 9/7 3/2 12/7
yEs7 yIIIs7 343/320 2401/1920 2401/1600 2401/1280 ~ 15/14 5/4 3/2 15/8
Gh7 Vh7 7203/6400 16807/12800 2401/1600 2401/1280 ~ 9/8 21/16 3/2 15/8
zBbs7 zVIIs7 16807/16000 16807/12800 2401/1600 16807/9600 ~ 21/20 21/16 3/2 7/4
Ch7 Ih7 2401/2400 2401/1920 2401/1600 16807/9600 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4
zgGbh7 zgVh7 21/20 49/40 7/5 7/4
[zzgFb=rryD#]h7 [zzgIV=rryII]h7 343/320 49/40 49/32 147/80 ~ 15/14 60/49 75/49 90/49
rAh7 rVIh7 343/160 1029/400 2401/1600 343/200 ~ 15/7 18/7 3/2 12/7
Gh7 Vh7 7203/6400 16807/12800 2401/1600 2401/1280 ~ 9/8 21/16 3/2 15/8
Ch7 Ih7 2401/2400 2401/1920 2401/1600 16807/9600 ~ 1/1 5/4 3/2 7/4

3125/3087 (gariboh or triruaquintyo)

pump3125

3136/3125 (hemimean or zozoquintgu)

pump3136

Ch7 Ih7 1/1 5/4 3/2 7/4
zEbs7 zIIIs7 1/1 7/6 7/5 7/4
gAbh7 gVIh7 1/1 6/5 7/5 8/5
zgCbs7 zgIs7 14/15 28/25 7/5 8/5
zggEbbh7 zggIIIh7 49/50 28/25 7/5 42/25
zggEbbs7 zggIIIs7 24/25 28/25 168/125 42/25
[zg3Cbb=ryyA#]h7 [zg3I=ryyVI]h7 28/25 168/125 196/125 224/125 ~ 125/112 75/56 25/16 25/14
yyG#s7 yyVs7 147/125 168/125 196/125 1176/625 ~ 75/64 75/56 25/16 15/8
yEh7 yIIIh7 686/625 784/625 196/125 1176/625 ~ 35/32 5/4 25/16 15/8
yEs7 yIIIs7 672/625 784/625 4704/3125 1176/625 ~ 15/14 5/4 3/2 15/8
Ch7 Ih7 3136/3125 784/625 4704/3125 5488/3125 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4
gAbh7 gVIh7 1/1 6/5 7/5 8/5
zggEbbh7 zggIIIh7 28/25 7/5 42/25 49/25
[zg3Cbb=ryyA#]h7 [zg3I=ryyVI]h7 28/25 168/125 196/125 224/125 ~ 125/112 75/56 25/16 25/14
yEh7 yIIIh7 686/625 784/625 196/125 1176/625 ~ 35/32 5/4 25/16 15/8
Ch7 Ih7 3136/3125 784/625 4704/3125 5488/3125 ~ 1/1 5/4 3/2 7/4

4000/3969 (octagar or rurutriyo)

pump4000

Ch7 Ih7 1/1 5/4 3/2 7/4
yEs7 yIIIs7 1/1 5/4 10/7 5/3
ryF#h7 ryIVh7 15/14 5/4 10/7 25/14
yEs7 yIIIs7 1/1 5/4 10/7 5/3
ryBh7 ryVIIh7 20/21 25/21 10/7 5/3
[ryyD#=zgEb]s7 [ryyII=zgIII]s7 50/49 25/21 10/7 25/14 ~ 81/80 189/160 567/400 567/320
gFh7 gIVh7 50/49 25/21 200/147 250/147 ~ 81/80 189/160 27/20 27/16
wDs7 wIIs7 1000/1029 500/441 200/147 250/147 ~ 27/14 9/8 27/20 27/16
gBbh7 gVIIh7 500/441 200/147 100/63 800/441 ~ 9/8 27/20 63/40 9/5
zFs7 zIVs7 125/126 500/441 250/189 100/63 ~ 63/64 9/8 21/16 63/40
Gh7 Vh7 500/441 250/189 2000/1323 2500/1323 ~ 9/8 21/16 3/2 15/8
zBbs7 zVIIs7 200/189 250/189 2000/1323 1000/567 ~ 21/20 21/16 3/2 7/4
Ch7 Ih7 4000/3969 5000/3969 2000/1323 1000/567 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4
ryF#h7 ryIVh7 15/14 5/4 10/7 25/14
ryBh7 ryVIIh7 20/21 25/21 10/7 5/3
[rryyE#=gF]h7 [rryyIII=gIV]h7 50/49 25/21 200/147 250/147 ~ 81/80 189/160 27/20 27/16
gBbh7 gVIIh7 500/441 200/147 100/63 800/441 ~ 9/8 27/20 63/40 9/5
Gh7 Vh7 500/441 250/189 2000/1323 2500/1323 ~ 9/8 21/16 3/2 15/8
Ch7 Ih7 4000/3969 5000/3969 2000/1323 1000/567 ~ 1/1 5/4 3/2 7/4

4375/4374 (ragismic or zoquadyo)

pump4375

Ch7 Ih7 1/1 5/4 3/2 7/4
yAs7 yVIs7 1/1 5/4 10/7 5/3
yAh7 yVIh7 25/24 5/4 35/24 5/3
zyCs7 zyIs7 35/36 7/6 35/24 5/3
yDh7 yIIh7 35/36 10/9 25/18 5/3
zyyAs7 zyyVIs7 35/36 175/144 25/18 175/108
yyBh7 yyVIIh7 25/27 125/108 25/18 175/108
[zyyD=ggDb]s7 [zyyII=ggII]s7 25/27 175/162 35/27 175/108 ~ 324/350 27/25 162/125 81/50
ggDbh7 ggIIh7 175/162 875/648 175/108 1225/648 ~ 27/25 27/20 81/50 189/100
gBbs7 gVIIs7 175/162 875/648 125/81 875/486 ~ 27/25 27/20 54/35 9/5
gBbh7 gVIIh7 4375/3888 875/648 6125/3888 875/486 ~ 9/8 27/20 63/40 9/5
Gs7 Vs7 4375/3888 625/486 4375/2916 875/486 ~ 9/8 9/7 3/2 9/5
gEbh7 gIIIh7 6125/5832 875/729 4375/2916 875/486 ~ 21/20 6/5 3/2 9/5
Cs7 Is7 4375/4374 875/729 4375/2916 1250/729 ~ 1/1 6/5 3/2 12/7
Ch7 Ih7 4375/4374 21875/17496 4375/2916 30625/17496 ~ 1/1 5/4 3/2 7/4
Ch7 Ih7 1/1 5/4 3/2 7/4
yAh7 yVIh7 25/24 5/4 35/24 5/3
yDh7 yIIh7 35/36 10/9 25/18 5/3
yyBh7 yyVIIh7 25/27 125/108 25/18 175/108
[zyyD=ggDb]h7 [zyyII=ggII]h7 175/162 875/648 175/108 1225/648 ~ 27/25 27/20 81/50 189/100
gBbh7 gVIIh7 4375/3888 875/648 6125/3888 875/486 ~ 9/8 27/20 63/40 9/5
gEbh7 gIIIh7 6125/5832 875/729 4375/2916 875/486 ~ 21/20 6/5 3/2 9/5
Ch7 Ih7 4375/4374 21875/17496 4375/2916 30625/17496 ~ 1/1 5/4 3/2 7/4

5120/5103 (hemifamity or small ruyo)

pump5120

1/1 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
1/1 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

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 rurutrigu)

pump6144

1/1 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
1/1 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

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 trizoagu)

pump10976

64827/64000 (squalentine or large quadzoatrigu)

pump64827

13-limit examples

676/675 (parizeksmic or bithogu)

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

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