99edo: Difference between revisions

Line 12:

=== Prime harmonics ===

== Intervals ==

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | Subgroup

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~stretch~~ (¢)

! rowspan="2" | Optimal 8ve Stretch (¢)

! colspan="2" | Tuning ~~error~~

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

Line 49:

| 2.33

|-

| 2.3.5.7.11

| style="border-top: double;" | 2.3.5.7.11

| 243/242, 441/440, 896/891, 3136/3125

| style="border-top: double;" | 243/242, 441/440, 896/891, 3136/3125

| [{{val| 99 157 230 278 343 }}] (99e)

| style="border-top: double;" | [{{val| 99 157 230 278 343 }}] (99e)

| -0.694

| style="border-top: double;" | -0.694

| 0.612

| style="border-top: double;" | 0.612

| 5.05

| style="border-top: double;" | 5.05

|-

| 2.3.5.7.11

| style="border-top: double;" | 2.3.5.7.11

| 121/120, 176/175, 1375/1372, 2200/2187

| style="border-top: double;" | 121/120, 176/175, 1375/1372, 2200/2187

| [{{val| 99 157 230 278 342 }}] (99)

| style="border-top: double;" | [{{val| 99 157 230 278 342 }}] (99)

| +0.006

| style="border-top: double;" | +0.006

| 0.881

| style="border-top: double;" | 0.881

| 7.27

| style="border-top: double;" | 7.27

|}

* 99et is lower in relative error than any previous ~~ETs~~ in the 7-limit. Not until 171 do we find a better ET in terms of either absolute error or relative error.

* 99et is lower in relative error than any previous equal temperaments in the 7-limit. Not until 171 do we find a better equal temperament in terms of either absolute error or relative error.

=== Rank-2 temperaments ===

{| class="wikitable center-all right-3 left-5"

|+Table of rank-2 temperaments by generator

! Periods per ~~octave~~

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperament

|-

@@ Line 12: / Line 12: @@
 === Prime harmonics ===
-{{Primes in edo|99|columns=11}}
+{{Harmonics in equal|99|columns=11}}
 == Intervals ==
-{{main| Table of 99edo intervals }}
+{{Main| Table of 99edo intervals }}
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|Comma List]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
-! colspan="2" | Tuning error
+! colspan="2" | Tuning Error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 49: / Line 49: @@
 | 2.33
 |-
-| 2.3.5.7.11
+| style="border-top: double;" | 2.3.5.7.11
-| 243/242, 441/440, 896/891, 3136/3125
+| style="border-top: double;" | 243/242, 441/440, 896/891, 3136/3125
-| [{{val| 99 157 230 278 343 }}] (99e)
+| style="border-top: double;" | [{{val| 99 157 230 278 343 }}] (99e)
-| -0.694
+| style="border-top: double;" | -0.694
-| 0.612
+| style="border-top: double;" | 0.612
-| 5.05
+| style="border-top: double;" | 5.05
 |-
-| 2.3.5.7.11
+| style="border-top: double;" | 2.3.5.7.11
-| 121/120, 176/175, 1375/1372, 2200/2187
+| style="border-top: double;" | 121/120, 176/175, 1375/1372, 2200/2187
-| [{{val| 99 157 230 278 342 }}] (99)
+| style="border-top: double;" | [{{val| 99 157 230 278 342 }}] (99)
-| +0.006
+| style="border-top: double;" | +0.006
-| 0.881
+| style="border-top: double;" | 0.881
-| 7.27
+| style="border-top: double;" | 7.27
 |}
-* 99et is lower in relative error than any previous ETs in the 7-limit. Not until 171 do we find a better ET in terms of either absolute error or relative error.
+* 99et is lower in relative error than any previous equal temperaments in the 7-limit. Not until 171 do we find a better equal temperament in terms of either absolute error or relative error.
 === Rank-2 temperaments ===
 {| class="wikitable center-all right-3 left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperament
 |-