Comma pump examples: Difference between revisions
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Chord names are explained here: [[Color notation#Chord names|Color notation chord names]] | Chord names are explained here: [[Color notation#Chord names|Color notation chord names]] | ||
== 3-limit examples== | == 3-limit examples == | ||
=== 256/243 (blackwood) === | === 256/243 (blackwood) === | ||
[http://snd.sc/iZLLpY battaglia-blackwood] {{dead link}} | [http://snd.sc/iZLLpY battaglia-blackwood] {{dead link}} | ||
== 5-limit examples== | == 5-limit examples == | ||
=== 81/80 (meantone) === | === 81/80 (meantone) === | ||
| Line 17: | Line 16: | ||
See [[12edo comma pump examples]]. | See [[12edo comma pump examples]]. | ||
=== 250/243 (porcupine or triyo) === | === 250/243 (porcupine or triyo) === | ||
* [https://web.archive.org/web/20201127013712/http://micro.soonlabel.com/petr_parizek/pp_pump_examples/pump_2.ogg Pařízek's porcupine comma pump] | |||
[https://www.youtube.com/watch?v=XSfnyr1MhXE Mike Battaglia Porcupine pump] | * [https://www.youtube.com/watch?v=XSfnyr1MhXE Mike Battaglia Porcupine pump] | ||
[[file:PorcupineCommaPump22edo.mp3]] | [[file:PorcupineCommaPump22edo.mp3]] | ||
From „Mizarian Ouverture“ by Herman Miller | From „Mizarian Ouverture“ by Herman Miller | ||
=== 2048/2025 (diaschismic or sagugu) === | === 2048/2025 (diaschismic or sagugu) === | ||
Pařízek's diaschisma pump [https://web.archive.org/web/20201127014513/http://micro.soonlabel.com/petr_parizek/pp_pump_examples/pump_1.ogg play] | [https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A90)_%7Br220hz%7D%0A%23_This_is_a_transcription_of_Pa%C5%99%C3%ADzek's_diaschisma_comma_pump.png%0A%23_Just_intonation%2C_with_pitch_drifting.%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%0A%23_We_are_now_4_diaschismas_from_where_we_started.%0A...%0A2%3A3%3A5-_%7Br220hz%7D_2%3A3%3A5-%0A..%0A%23_12edo%2C_the_comma_is_tempered_out_therefore_there_is_no_pitch_drifting.%0A%0A%7B12edo%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%0A%23The_root_hasn't_changed_from_where_we_started. xenpaper] | |||
[https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A90)_%7Br220hz%7D%0A% | |||
Also see [[12edo comma pump examples]]. | Also see [[12edo comma pump examples]]. | ||
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=== 16875/16384 (negri or laquadyo) === | === 16875/16384 (negri or laquadyo) === | ||
* [https://web.archive.org/web/20201127013814/http://micro.soonlabel.com/petr_parizek/pp_pump_examples/pump_3.ogg Pařízek's negri comma pump] | |||
* [https://www.youtube.com/watch?v=bCLZChG6U6c Mike Battaglia negri pump] | |||
=== 20000/19683 (tetracot or saquadyo) === | |||
* [https://web.archive.org/web/20201127012628/http://micro.soonlabel.com/petr_parizek/pp_pump_examples/pump_7.ogg Pařízek's tetracot comma pump] | |||
=== 20000/19683 (tetracot or saquadyo) === | * [https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A60)_%7Br220hz%7D%0A%23_Just_intonation%2C_with_pitch_drifting.%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D_%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D%0A8%3A10%3A12---%0A%23_We_are_now_4_tetracot_commas_from_where_we_started.%0A8%3A10%3A12-%7Br220hz%7D8%3A10%3A12-%0A..%0A%0A%23_34edo%2C_the_comma_is_tempered_therefore_there_is_no_pitch_drifting.%0A%7B34edo%7D%0A%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C9%2C20%5D-_%7Br%6014%7D_%5B0%2C9%2C20%5D_%7Br5%7D_%5B0%2C9%2C20%5D_%7Br5%7D%0A%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C9%2C20%5D-_%7Br%6014%7D_%5B0%2C9%2C20%5D_%7Br5%7D_%5B0%2C9%2C20%5D_%7Br5%7D%0A%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C9%2C20%5D-_%7Br%6014%7D_%5B0%2C9%2C20%5D_%7Br5%7D_%5B0%2C9%2C20%5D_%7Br5%7D%0A%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C11%2C20%5D-_%7Br5%7D_%5B0%2C9%2C20%5D-_%7Br%6014%7D_%5B0%2C9%2C20%5D_%7Br5%7D_%5B0%2C9%2C20%5D_%7Br5%7D%5B0%2C11%2C20%5D---%0A%23_The_root_hasn't_changed_from_where_we_started.%0A%0A JI and 34edo tetracot pump] | ||
[https://luphoria.com/xenpaper/#(osc%3Asawtooth8)(bpm%3A60)_%7Br220hz%7D%0A%23_Just_intonation%2C_with_pitch_drifting.%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D_%0A8%3A10%3A12-_%7Br10%2F9%7D_8%3A10%3A12-_%7Br10%2F9%7D10%3A12%3A15-_%7Br2%2F3%7D_10%3A12%3A15_%7Br10%2F9%7D_10%3A12%3A15_%7Br10%2F9%7D%0A8%3A10%3A12---%0A% | |||
=== 78732/78125 (sensi or sepgu) === | === 78732/78125 (sensi or sepgu) === | ||
Revision as of 13:36, 11 May 2025
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)
From „Mizarian Ouverture“ by Herman Miller
2048/2025 (diaschismic or sagugu)
Pařízek's diaschisma pump play | xenpaper
(bpm%3A90)_%7Br220hz%7D%0A%23_This_is_a_transcription_of_Pa%C5%99%C3%ADzek's_diaschisma_comma_pump.png%0A%23_Just_intonation%2C_with_pitch_drifting.%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%7Br5%2F4%7D_2%3A3%3A4-_%7Br%603%2F2%7D_2%3A3%3A5_%7Br%603%2F2%7D_2%3A5%3A6--_%7Br5%2F4%7D_2%3A3%3A5-_%7Br%603%2F2%7D_2%3A5%3A6_%7Br3%2F2%7D_%0A2%3A3%3A5--%0A%23_We_are_now_4_diaschismas_from_where_we_started.%0A...%0A2%3A3%3A5-_%7Br220hz%7D_2%3A3%3A5-%0A..%0A%23_12edo%2C_the_comma_is_tempered_out_therefore_there_is_no_pitch_drifting.%0A%0A%7B12edo%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%7Br4%7D_%5B0%2C7%2C12%5D-_%7Br%607%7D_%5B0%2C7%2C16%5D_%7Br%607%7D_%5B0%2C16%2C19%5D--_%7Br4%7D_%5B0%2C7%2C16%5D-_%7Br%607%7D_%5B0%2C16%2C19%5D_%7Br7%7D%0A%5B0%2C7%2C16%5D--_%0A%23The_root_hasn't_changed_from_where_we_started.){kind=link}
Also see 12edo comma pump examples.
3125/3072 (magic or laquinyo)
15625/15552 (hanson or tribiyo)
16875/16384 (negri or laquadyo)
20000/19683 (tetracot or saquadyo)
78732/78125 (sensi or sepgu)
1600000/1594323 (amity or saquinyo)
2109375/2097152 (semicomma, 5-limit orwell or lasepyo)
7-limit examples
Every s6 chord can also be thought of as a s7 chord, e.g. zBbs6 could be Gs7.
126/125 (starling or zotrigu)
Monzo : [1 2 -3 1⟩
pump126 chords: Ch7 -- zBbs6 -- gEbh7 -- gEbs6 -- [ggGb=ryF#]h7 -- Ch7 -- gEbh7 -- [ggGg=ryF#]h7 -- Ch7
Ih7 -- zVIIs6 -- gIIIh7 -- gIIIs6 -- [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 |
| zBbs6 | zVIIs6 | 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 |
| gEbs6 | gIIIs6 | 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 |
| gEbs6 | 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)
Monzo: [5 2 2 -1⟩
pump225 chords: Ch7 -- zEbs6 -- zgCbh7 -- [zAb=yyG#]s6 -- yEh7 -- yEs6 -- Ch7 -- zEbs6 -- [zAb=yyG#]s6 -- yEs6 -- Ch7
Ih7 -- zIIIs6 -- zgIh7 -- [zVI=yyV]s6 -- yIIIh7 -- yIIIs6 -- Ih7 -- zIIIs6 -- [zVI=yyV]s6 -- yIIIs6 -- Ih7
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | ~ | 225/224 | 1125/896 | 675/448 | 225/128 |
| zEbs6 | zIIIs6 | 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#]s6 | [zVI=yyV]s6 | 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 |
| yEs6 | yIIIs6 | 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 |
| zEbs6 | zIIIs6 | 1/1 | 7/6 | 7/5 | 7/4 | ~ | 225/224 | 75/64 | 45/32 | 225/128 |
| [zAb=yyG#]s6 | [zVI=yyV]s6 | 14/15 | 7/6 | 4/3 | 14/9 | ~ | 15/16 | 75/64 | 75/56 | 25/16 |
| yEs6 | yIIIs6 | 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)
Monzo: [0 -5 1 2⟩
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 trizo-agugu)
Monzo: [1 -3 -2 3⟩
875/864 (keemic or zotriyo)
Monzo: [-5 -3 3 1⟩
1029/1024 (gamelismic or latrizo)
Monzo: [-10 1 0 3⟩
pump1029 chords: Ch7 -- yAs6 -- rDh7 -- ryBs6 -- [rrE=zF]h7 -- zFs6 -- Gh7 -- zBbs6 -- Ch7 -- rDh7 -- [rrE=zF]h7 -- Gh7 -- Ch7
Ih7 -- yVIs6 -- rIIh7 -- ryVIIs6 -- [rrIII=zIV]h7 -- zIVs6 -- Vh7 -- zVIIs6 -- Ih7 -- rIIh7 -- [rIII=zIV]h7 -- Vh7 -- Ih7
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| yAs6 | yVIs6 | 1/1 | 5/4 | 10/7 | 5/3 | |||||
| rDh7 | rIIh7 | 1/1 | 8/7 | 10/7 | 12/7 | |||||
| ryBs6 | ryVIIs6 | 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 |
| zFs6 | zIVs6 | 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 |
| zBbs6 | zVIIs6 | 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 triru-agu)
Monzo: [6 3 -1 -3⟩
pump1728 Ch7 -- zEbs6 -- zEbh7 -- [zzGb=rgF]s6 - rgFh7 -- gAbs6 -- gAbh7 -- Cs6 -- Ch7 -- zEbh7 -- [zzGb=rgF]h7 -- gAbh7 -- Ch7
Ih7 -- zIIIs6 -- zIIIh7 -- [zzV=rgIV]s6 -- rgIVh7 -- gVIs6 -- gVIh7 -- Is6 -- Ih7 -- zIIIh7 -- [zzV=rgIV]h7 -- gVIh7 -- Ih7
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| zEbs6 | zIIIs6 | 1/1 | 7/6 | 7/5 | 7/4 | |||||
| zEbh7 | zIIIh7 | 49/48 | 7/6 | 35/24 | 7/4 | |||||
| [zzGb=rgF]s6 | [zzV=rgIV]s6 | 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 |
| gAbs6 | gVIs6 | 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 |
| Cs6 | Is6 | 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 bizozogu)
Monzo: [-5 -1 -2 4⟩
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| zBbs6 | zVIIs6 | 21/20 | 21/16 | 3/2 | 7/4 | |||||
| zgGgh7 | zgVh7 | 21/20 | 49/40 | 7/5 | 7/4 | |||||
| zzDbs6 | zzIIs6 | 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#s6 | ryIs6 | 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 |
| yEs6 | yIIIs6 | 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 |
| zBbs6 | zVIIs6 | 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 triru-aquinyo)
Monzo: [0 2 5 -3⟩
3136/3125 (hemimean or zozoquingu)
Monzo: [6 0 -5 2⟩
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| zEbs6 | zIIIs6 | 1/1 | 7/6 | 7/5 | 7/4 | |||||
| gAbh7 | gVIh7 | 1/1 | 6/5 | 7/5 | 8/5 | |||||
| zgCbs6 | zgIs6 | 14/15 | 28/25 | 7/5 | 8/5 | |||||
| zggEbbh7 | zggIIIh7 | 49/50 | 28/25 | 7/5 | 42/25 | |||||
| zggEbbs6 | zggIIIs6 | 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#s6 | yyVs6 | 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 |
| yEs6 | yIIIs6 | 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)
Monzo: [5 6 3 -2⟩
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| yEs6 | yIIIs6 | 1/1 | 5/4 | 10/7 | 5/3 | |||||
| ryF#h7 | ryIVh7 | 15/14 | 5/4 | 10/7 | 25/14 | |||||
| yEs6 | yIIIs6 | 1/1 | 5/4 | 10/7 | 5/3 | |||||
| ryBh7 | ryVIIh7 | 20/21 | 25/21 | 10/7 | 5/3 | |||||
| [ryyD#=zgEb]s6 | [ryyII=zgIII]s6 | 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 |
| wDs6 | wIIs6 | 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 |
| zFs6 | zIVs6 | 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 |
| zBbs6 | zVIIs6 | 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)
Monzo : [-1 -7 4 1⟩
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| yAs6 | yVIs6 | 1/1 | 5/4 | 10/7 | 5/3 | |||||
| yAh7 | yVIh7 | 25/24 | 5/4 | 35/24 | 5/3 | |||||
| zyCs6 | zyIs6 | 35/36 | 7/6 | 35/24 | 5/3 | |||||
| yDh7 | yIIh7 | 35/36 | 10/9 | 25/18 | 5/3 | |||||
| zyyAs6 | zyyVIs6 | 35/36 | 175/144 | 25/18 | 175/108 | |||||
| yyBh7 | yyVIIh7 | 25/27 | 125/108 | 25/18 | 175/108 | |||||
| [zyyD=ggDb]s6 | [zyyII=ggII]s6 | 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 |
| gBbs6 | gVIIs6 | 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 |
| Gs6 | Vs6 | 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 |
| Cs6 | Is6 | 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 saruyo)
Monzo : [9 -6 1 -1⟩
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| yEs6 | yIIIs6 | 35/32 | 5/4 | 35/24 | 7/4 | |||||
| yAh7 | yVIh7 | 25/24 | 5/4 | 35/24 | 5/3 | |||||
| yyIVs6 | yyF#s6 | 25/24 | 25/21 | 25/18 | 5/3 | |||||
| yDh7 | yIIh7 | 35/36 | 10/9 | 25/18 | 5/3 | |||||
| yDs6 | yIIs6 | 20/21 | 10/9 | 4/3 | 5/3 | |||||
| [ry=w]Eh7 | [ry=Lw]IIIh7 | 20/21 | 10/9 | 80/63 | 100/63 | ~ | 243/128 | 567/512 | 81/64 | 405/256 |
| yC#s6 | LyIs6 | 400/441 | 200/189 | 80/63 | 100/63 | ~ | 405/224 | 135/128 | 81/64 | 405/256 |
| Ah7 | wVIh7 | 200/189 | 80/63 | 40/27 | 320/189 | ~ | 135/128 | 81/64 | 189/128 | 27/16 |
| zCs6 | zIs6 | 80/81 | 32/27 | 40/27 | 320/189 | ~ | 63/64 | 189/160 | 189/128 | 27/16 |
| Dh7 | wIIh7 | 80/81 | 640/567 | 800/567 | 320/189 | ~ | 63/64 | 9/8 | 45/32 | 27/16 |
| zDs6 | zIVs6 | 80/81 | 640/567 | 320/243 | 128/81 | ~ | 63/64 | 9/8 | 21/16 | 63/40 |
| Gh7 | Vh7 | 1600/1701 | 640/567 | 320/243 | 2560/1701 | ~ | 15/16 | 9/8 | 21/16 | 3/2 |
| zBbs6 | zVIIs6 | 256/243 | 320/243 | 2560/1701 | 1280/729 | ~ | 21/20 | 21/16 | 3/2 | 7/4 |
| Ch7 | Ih7 | 5120/5103 | 6400/5103 | 2560/1701 | 1280/729 | ~ | 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 | |||||
| [ry=w]Eh7 | [ry=Lw]IIIh7 | 20/21 | 10/9 | 80/63 | 100/63 | ~ | 243/128 | 567/512 | 81/64 | 405/256 |
| Ah7 | wVIh7 | 200/189 | 80/63 | 40/27 | 320/189 | ~ | 135/128 | 81/64 | 189/128 | 27/16 |
| Dh7 | wIIIh7 | 80/81 | 640/567 | 800/567 | 320/189 | ~ | 63/64 | 9/8 | 45/32 | 27/16 |
| Gh7 | Vh7 | 1600/1701 | 640/567 | 320/243 | 2560/1701 | ~ | 15/16 | 9/8 | 21/16 | 3/2 |
| zBbs6 | zVIIs6 | 256/243 | 320/243 | 2560/1701 | 1280/729 | ~ | 21/20 | 21/16 | 3/2 | 7/4 |
| Ch7 | Ih7 | 5120/5103 | 6400/5103 | 2560/1701 | 1280/729 | ~ | 1/1 | 5/4 | 3/2 | 7/4 |
6144/6125 (porwell or saruru-trigu)
Monzo : [11 1 -3 -2⟩
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| zyGs6 | zyVs6 | 35/32 | 5/4 | 35/24 | 7/4 | |||||
| yEh7 | yIIIh7 | 35/32 | 5/4 | 25/16 | 15/8 | |||||
| zyDs6 | zyIIs6 | 35/32 | 21/16 | 105/64 | 15/8 | |||||
| zyDh7 | zyIIh7 | 35/32 | 175/128 | 105/64 | 245/128 | |||||
| [zyyF#=rgF]s6 | [zyy=rg]IVs6 | 525/512 | 175/128 | 75/64 | 105/64 | ~ | 36/35 | 48/35 | 288/245 | 288/175 |
| rgFh7 | rgIVh7 | 525/512 | 1225/1024 | 175/128 | 875/512 | ~ | 36/35 | 6/5 | 48/35 | 12/7 |
| Cs6 | Is6 | 6125/6144 | 1225/1024 | 6125/4096 | 875/512 | ~ | 1/1 | 6/5 | 3/2 | 12/7 |
| gEbh7 | gIIIh7 | 8575/8192 | 1225/1024 | 6125/4096 | 3675/2048 | ~ | 21/20 | 6/5 | 3/2 | 9/5 |
| Gs6 | Vs6 | 18375/16384 | 2625/2048 | 6125/4096 | 3675/2048 | ~ | 9/8 | 9/7 | 3/2 | 9/5 |
| Gh7 | Vh7 | 18375/16384 | 42875/32768 | 6125/4096 | 30625/16384 | ~ | 9/8 | 21/16 | 3/2 | 15/8 |
| yEs6 | yIIIs6 | 4375/4096 | 30625/24576 | 6125/4096 | 30625/16384 | ~ | 15/14 | 5/4 | 3/2 | 15/8 |
| Ch7 | Ih7 | 6125/6144 | 30625/24576 | 6125/4096 | 42875/24576 | ~ | 1/1 | 5/4 | 3/2 | 7/4 |
| Ch7 | Ih7 | 1/1 | 5/4 | 3/2 | 7/4 | |||||
| yEh7 | yIIIh7 | 35/32 | 5/4 | 25/16 | 15/8 | |||||
| zyDh7 | zyIIh7 | 35/32 | 175/128 | 105/64 | 245/128 | |||||
| [zyyF#=rgF]h7 | [zyy=rg]IVh7 | 525/512 | 1225/1024 | 175/128 | 875/512 | ~ | 36/35 | 6/5 | 48/35 | 12/7 |
| gEbh7 | gIIIh7 | 8575/8192 | 1225/1024 | 6125/4096 | 3675/2048 | ~ | 21/20 | 6/5 | 3/2 | 9/5 |
| Gh7 | Vh7 | 18375/16384 | 42875/32768 | 6125/4096 | 30625/16384 | ~ | 9/8 | 21/16 | 3/2 | 15/8 |
| Ch7 | Ih7 | 6125/6144 | 30625/24576 | 6125/4096 | 42875/24576 | ~ | 1/1 | 5/4 | 3/2 | 7/4 |
10976/10935 (hemimage or satrizo-agu)
Monzo : [5 -7 -1 3⟩
64827/64000 (squalentine or laquadzo-atrigu)
Monzo : [-9 3 -3 4⟩
13-limit examples
676/675 (parizeksmic or bithogu)
Monzo : [2 -3 -2 0 0 2⟩