Meantone family: Difference between revisions

The [[7/4]] in septimal meantone is the augmented sixth (C-A♯), and other septimal intervals are [[7/6]], the augmented second (C-D♯), [[7/5]], the augmented fourth (C-F♯), and [[21/16]], the augmented third (C-E♯). Septimal meantone tempers out the common 7-limit commas [[126/125]] and [[225/224]] and in fact can be defined as the 7-limit temperament that tempers out any two of 81/80, 126/125 and 225/224.

Undecimal meantone maps the [[11/8]] to the double augmented third (C-Ex), and tridecimal meantone maps the [[13/8]] to the double augmented fifth (C-Gx). Note 13/11 is conflated with 6/5, represented by the minor third. Note also 11/10~13/12 is the double augmented unison; 12/11, double diminished third; and 14/13, minor second.  

Dubbed ''meantoid'' here, this extension maps 17/16~19/18 to the augmented unison (C-C♯) and 19/16 to the augmented second (C-D♯). For any tuning flatter than 12edo, the sizes of 17/16 (augmented unison) and 18/17 (minor second) are inverse, so genuine septendecimal and undevicesimal harmony cannot be expected.  

Meridetone maps the 13/8 to the quadruple augmented fourth (C-Fxx).