Monkey: Difference between revisions

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Line 12:

| Odd limit 2 = 13-limit 21 | Mistuning 2 = 12.8 | Complexity 2 = 34

}}

The '''monkey''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (~~15625~~/~~15552~~), and is naturally a full [[13-limit]] temperament.

The '''monkey''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.

In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.

In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.11.13 subgroup|2.3.5.11.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.

Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -12 generator steps.

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In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.

{| class="wikitable ~~right~~-1 right-2"

{| class="wikitable center-1 right-2"

|-

! #

Line 201:

| 11/10

| 165.004

|

|-

| 1\7

|

| 171.429

|

|-

Line 312:

Line 317:

| 176.905

|

|-

| 4\27

|

| 177.778

| 27de val

|-

|

Line 322:

Line 332:

| 179.736

|

|-

| 3\20

|

| 180.000

| 20cdde val

|-

|

@@ Line 12: / Line 12: @@
 | Odd limit 2 = 13-limit 21 | Mistuning 2 = 12.8 | Complexity 2 = 34
 }}
-The '''monkey''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (15625/15552), and is naturally a full [[13-limit]] temperament.
+The '''monkey''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.
-In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.
+In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.11.13 subgroup|2.3.5.11.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.
 Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -12 generator steps.
@@ Line 23: / Line 23: @@
 In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.
-{| class="wikitable right-1 right-2"
+{| class="wikitable center-1 right-2"
 |-
 ! #
@@ Line 201: / Line 201: @@
 | 11/10
 | 165.004
+|
+|-
+| 1\7
+|
+| 171.429
 |
 |-
@@ Line 312: / Line 317: @@
 | 176.905
 |
+|-
+| 4\27
+|
+| 177.778
+| 27de val
 |-
 |
@@ Line 322: / Line 332: @@
 | 179.736
 |
+|-
+| 3\20
+|
+| 180.000
+| 20cdde val
 |-
 |