Comma pump examples

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

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 = 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 - r³1 - rr3 - rrg5 = 48/49-384/343-64/49-384/245

Vh7 = r³IVh7 = r³1 - rr3 - r³4 - r³y6 = 384/343-64/49-512/343-640/343

zVIIs7 = rrVIs7 = rrg1 - rr3 - r³4 - rr6 = 256/245-64/49-512/343-256/147

Ih7 = sr³VIIh7 = sr³7 - r³y2 - r³4 - 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 = r³IVh7 = 384/343-64/49-512/343-640/343

Ih7 = sr³VIIh7 = 1024/1029-1280/1029-512/343-256/147

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 quadzo gugu)

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 zo quadyo)

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