Mersenne comma: Difference between revisions

Mersenne commas are a series of commas of the form <math>\frac{2^n}{2^n-1}</math>.

Since Mersenne prime commas effectively set their own prime limit, they are of no interest to EDO theory. Therefore, this time Mersenne composite numbers enter the stage - sequence [https://oeis.org/A135972 A135972] in OEIS.  

==Theory==

!Index

!Comma

!Prime

Subgroup

!Monzo

!Comments

|4

|[[16/15]]

|2.3.5

|[4 -1 -1⟩

|Classic diatonic semitone.

|6

|[[64/63]]

|2.3.7

|[6 -2 -1⟩

|Septimal comma.

|8

|[[256/255]]

|2.3.5.17

|[8 -1 -1 -1⟩

|Septendecimal kleisma.

|9

|[[512/511]]

|2.7.73

|[9 -1 -1⟩

|

|10

|[[1024/1023]]

|2.3.11.31

|[10 -1 -1 -1⟩

|

|11

|[[2048/2047]]

|2.23.89

|[11 -1 -1⟩

|12

|[[4096/4095]]

|2.3.5.7.13

|[12 -2 -1 -1 -1⟩

|Schismina.

[[Category:Octave-reduced subharmonics]]

[[Category:Rational intervals]]