Breedsmic–syntonic equivalence continuum: Difference between revisions

The '''breedsmic–syntonic equivalence continuum''' is a [[equivalence continuum|continuum]] of 7-limit temperament families which equate a number of [[2401/2400|breedsmas (2401/2400)]] with a [[81/80|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit temperament families supported by [[Meantone family#Squares|squares]] temperament. In addition, 81/80 and 2401/2400 are the smallest 5-limit and 7-limit [[superparticular]] intervals to be tempered out by [[31edo]].

|-

| −4

|  

|-

| −3

|  

|-

| −2

| 51883209/51200000

|-

| −1

| [[Squalentine]]

| [[64827/64000]]

|-

| 0

| [[81/80]]

|-

| 1

| [[2430/2401]]

|-

| 2

| 5832000/5764801

|-

| 3

| 13996800000/13841287201

|-

| 4

|  

|-

| 5

|  

|-

| 6

|  

|-

| 7

|  

|-

| 8

|  

|-

| …

|-

| 30

|  

|-

| …

| [[Breedsmic temperaments|Breedsmic]]

| [[2401/2400]]

|}

Examples of temperaments with fractional values of ''n'':

* [[Subgroup temperaments#Skwares 3|Skwares]] ({{nowrap|''n'' {{=}} {{frac|1|2}} {{=}} 0.5}})