List of superparticular intervals: Difference between revisions

[[Superparticular]] numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in [[just intonation]] and [[OverToneSeries|Harmonic Series]] music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio [[21/20]]. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common [[comma]]s are superparticular ratios.

| (2*13)/5²

| {{Monzo|1 0 -2 0 0 1}}

|-

| [[27/26]]

| 3³/(2*13)

| {{Monzo|-1 3 0 0 0 -1}}

|-

| [[40/39]]

| 19/(2*3²)

| {{Monzo|-1 -2 0 0 0 0 0 1}}

|-

| [[20/19]]

| (2²*19)/(3*5²)

| {{Monzo|2 -1 -2 0 0 0 0 1}}

|-

| [[77/76]]

| (7*11)/(2²*19)

| {{Monzo|-2 0 0 1 1 0 0 -1}}

|-

| [[96/95]]

| (3*23)/(2²*17)

|  

|-

| [[70/69]]

| (2*5*7)/(3*23)

|  

|-

| [[92/91]]

|-

| 161/160

| (7*23)/(2⁵*5)

|  

|-

| 208/207

|  

|  

|-

| 576/575

| (2⁶*3²)/(23*5²)

|  

| 19.786

| (2³*11)/(3*29)

|  

|