Comma pump

An example of a comma pump: in 12edo, which tempers out 81/80, this progression returns to the starting note; in 15edo, which observes this comma, it does not.

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 (down by 6/5)
-> DFA (up by 4/3)
-> GDGB (down by 3/2)
-> CEGC (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 Porcupine (250/243) pump, which only returns to the startknv pitch in Porcupine tunings (^/v = 81/80 alteration):

C Ev G
-> Av C Ev Av (down 6/5)
-> Dv F Av (up 4/3)
-> Bb^ Db^^ F^ (down 6/5, Porcupine entails Dv = Db^^)
-> G Bb^ D G (down 6/5)
-> C Ev G (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.