Comma pump: Difference between revisions
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| Line 6: | Line 6: | ||
CEG | CEG | ||
-> ACEA (down by 6/5) | -> ACEA (C -> A: down by 6/5) | ||
-> DFA (up by 4/3) | -> DFA (A -> D: up by 4/3) | ||
-> GDGB (down by 3/2) | -> GDGB (D -> G: down by 3/2) | ||
-> CEGC (up by 4/3) | -> CEGC (G -> C: up by 4/3) | ||
In non-Meantone tunings, attempting this comma pump results in the end point flatter by 81/80 relative to the starting point. | In non-Meantone tunings, attempting this comma pump results in the end point flatter by 81/80 relative to the starting point. | ||
| Line 16: | Line 16: | ||
C Ev G | C Ev G | ||
-> Av C Ev Av (down 6/5) | -> Av C Ev Av (C -> Av: down 6/5) | ||
-> Dv F Av (up 4/3) | -> Dv F Av (Av -> Dv: up 4/3) | ||
-> Bb^ Db^^ F^ (down 6/5, Porcupine entails Dv = Db^^) | -> Bb^ Db^^ F^ (Dv -> Bvv = Bb^: down 6/5, Porcupine entails Dv = Db^^) | ||
-> G Bb^ D G (down 6/5) | -> G Bb^ D G (Bb^ -> G: down 6/5) | ||
-> C Ev G (up 4/3) | -> C Ev G (G -> C: up 4/3) | ||
There is some ambiguity in this term depending on whether the comma in question is tempered out (thus returning to the starting pitch) or not. If the comma is tempered out the chord progression could be called a '''comma cycle'''. | There is some ambiguity in this term depending on whether the comma in question is tempered out (thus returning to the starting pitch) or not. If the comma is tempered out the chord progression could be called a '''comma cycle'''. | ||
Given a comma, a comma pump may be constructed by stacking root movements by basic intervals in the JI group in question to that comma. Reordering movements of a comma pump creates another valid comma pump. | Given a comma, a comma pump may be constructed by stacking root movements by basic intervals in the JI group in question to that comma. Reordering movements of a comma pump creates another valid comma pump. | ||
Revision as of 22:39, 24 February 2026
A comma pump is a JI or tempered chord progression whose starting and ending points differ by a comma.
The I-vi-ii-V-I progression is a Meantone or 81/80 comma pump:
CEG -> ACEA (C -> A: down by 6/5) -> DFA (A -> D: up by 4/3) -> GDGB (D -> G: down by 3/2) -> CEGC (G -> C: up by 4/3)
In non-Meantone tunings, attempting this comma pump results in the end point flatter by 81/80 relative to the starting point.
Here's a Porcupine (250/243) pump, which only returns to the starting pitch in Porcupine tunings (^/v = 81/80 alteration):
C Ev G -> Av C Ev Av (C -> Av: down 6/5) -> Dv F Av (Av -> Dv: up 4/3) -> Bb^ Db^^ F^ (Dv -> Bvv = Bb^: down 6/5, Porcupine entails Dv = Db^^) -> G Bb^ D G (Bb^ -> G: down 6/5) -> C Ev G (G -> C: up 4/3)
There is some ambiguity in this term depending on whether the comma in question is tempered out (thus returning to the starting pitch) or not. If the comma is tempered out the chord progression could be called a comma cycle.
Given a comma, a comma pump may be constructed by stacking root movements by basic intervals in the JI group in question to that comma. Reordering movements of a comma pump creates another valid comma pump.
