476edo: Difference between revisions

476edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1|3]] is about halfway its steps, while its [[5/1|5]] and [[7/1|7]] are both tuned flat. To start with, consider the 2.3.5.7 [[patent val]], as well as 2.9.15.21 and 2.9.5.7 [[subgroup]]s.

 

Using the patent val, the equal temperament [[tempering out|tempers out]] [[2401/2400]] and [[19683/19600]] in the 7-limit, [[support]]ing [[harry]]. The 11-limit 476e val tempers out [[3025/3024]] and [[41503/41472]], whereas the patent val tempers out [[243/242]], [[441/440]], [[540/539]], [[4000/3993]], [[8019/8000]], and [[9801/9800]], supporting 11-limit harry.  

476 factors into 2² × 7 × 17, with subset edos {{EDOs| 2, 4, 7, 14, 17, 28, 34, 68, 119, and 238 }}. [[952edo]], which doubles it, gives a good correction to the harmonic 3, but unfortunately it is inconsistent in the [[5-odd-limit]].

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

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

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

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

! colspan="2" | Tuning Error

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

| 2.9

| {{monzo| 1509 -476 }}

| {{mapping| 476 1509 }}

| 2.9.5

| {{monzo| 33 -17 9 }}, {{monzo| -65 0 28 }}

| {{mapping| 476 1509 1105 }}

| 2.9.5.7

| 703125/702464, 4802000/4782969, {{monzo| 25 3 -3 8 }}

| {{mapping| 476 1509 1105 1336 }}

! Generator*

! Cents*

| 1

| 205\476

| 516.81

| 27/20

| [[Larry]] (476)

| 2

| 205\476<br>(33\476)

| 516.81<br>(83.19)

| 27/20<br>(21/20)

| [[Harry]] (11-limit, 476)

| 28

| 197\476<br>(6\476)

| 496.64<br>(15.13)

| 4/3<br>(105/104)

| [[Oquatonic]] (5-limit)