1547edo: Difference between revisions

{{ED intro}}

1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. As an equal temperament, it [[tempering out|tempers out]] [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma.

In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]].

In the 7-limit, it provides the [[optimal patent val]] for 7-limit [[brahmagupta]], the {{nowrap|441 & 1106}} temperament, and supports an alternative 11-limit extension to it. It also supports [[semidimi]], the {{nowrap|171 & 1376}} temperament.  

 

 

Since 1547 factors into 7 × 13 × 17, 1547edo has subset edos {{EDOs| 7, 13, 17, 91, 119, and 221 }}.

 

== Regular temperament properties ==

 

=== Rank-2 temperaments ===

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods<br />per 8ve

! Generator*

! Cents*

! Associated<br />ratio*

| 1

| 118\1547

| 91.532

| {{monzo| 9 -32 18 }}

| [[Gross]]

| 1

| 579\1547

| 449.127

| 35/27

| [[Semidimi]]

| 7

| 670\1547<br />(7\1547)

| 519.715<br />(5.429)

| 27/20<br />(325/324)

| [[Brahmagupta]] (7-limit)

| [[Chlorine]]

| 642\1547<br />(13\1547)

| 497.996<br />(10.084)

| 4/3<br />(176/175)

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

 

 

[[Category:Listen]]