229edo: Difference between revisions

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== Theory ==

While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out 393216/390625 ([[würschmidt comma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, and using the [[patent val]], [[351/350]], [[2080/2079]], and [[4096/4095]] in the 13-limit, notably [[support|supporting]] [[hemiwürschmidt]], [[newt]], and [[trident]].

While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out 393216/390625 ([[würschmidt comma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, and using the [[patent val]], [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]] in the 13-limit, notably [[support|supporting]] [[hemiwürschmidt]], [[newt]], and [[trident]].

The 229b val supports a [[septimal meantone]] close to the [[CTE tuning]].

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=== Prime harmonics ===

== Regular temperament properties ==

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|-

| 2.3.5.7.11.13

| 351/350, 2080/2079~~, 3025/3024~~, 3136/3125, 4096/4095

| 351/350, 1573/1568, 2080/2079, 3136/3125, 4096/4095

| [{{val| 229 363 532 643 792 847 }}]

| -0.017

@@ Line 9: / Line 9: @@
 == Theory ==
-While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out 393216/390625 ([[würschmidt comma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, and using the [[patent val]], [[351/350]], [[2080/2079]], and [[4096/4095]] in the 13-limit, notably [[support|supporting]] [[hemiwürschmidt]], [[newt]], and [[trident]].
+While not highly accurate for its size, 229edo is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out 393216/390625 ([[würschmidt comma]]) and {{monzo| 39 -29 3 }} ([[tricot comma]]) in the 5-limit; [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[14348907/14336000]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[8019/8000]], [[14641/14580]] and 15488/15435 in the 11-limit, and using the [[patent val]], [[351/350]], [[1573/1568]], [[2080/2079]], and [[4096/4095]] in the 13-limit, notably [[support|supporting]] [[hemiwürschmidt]], [[newt]], and [[trident]].
 The 229b val supports a [[septimal meantone]] close to the [[CTE tuning]].
@@ Line 16: / Line 16: @@
 === Prime harmonics ===
-{{Primes in edo|229}}
+{{Harmonics in equal|229|columns=11}}
 == Regular temperament properties ==
@@ Line 58: / Line 58: @@
 |-
 | 2.3.5.7.11.13
-| 351/350, 2080/2079, 3025/3024, 3136/3125, 4096/4095
+| 351/350, 1573/1568, 2080/2079, 3136/3125, 4096/4095
 | [{{val| 229 363 532 643 792 847 }}]
 | -0.017