730edo: Difference between revisions

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The '''730 equal divisions of the octave''' ('''730edo'''), or the '''730(-tone) equal temperament''' ('''730tet''', '''730et''') divides the [[octave]] into 730 [[equal]] parts of 1.644 [[cent]]s each. It is a very strong five-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out the [[counterschisma]], {{~~monzo~~| ~~-69 45 -~~1 ~~}}, the minortone comma, {{monzo~~| ~~-16 35 -17 }}, the kwazy comma, {{monzo~~| ~~-53 10 16 }}, the whoosh comma, {{monzo| 37 25 -33 }}, and the pirate comma, {{monzo| -~~90 ~~-15 49 }}~~. ~~In the 7-limit it tempers out [[4375/4374]] and {{monzo~~| ~~-21 0 3 5~~ }}~~, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and~~ {{~~monzo~~| ~~4 -3 -6 4 1~~ }}~~, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.~~

{{Infobox ET

| Prime factorization = 2 × 5 × 73

| Step size = 1.64384¢

| Fifth = 427\730 (701.92¢)

| Semitones = 69:55 (113.42¢ : 90.41¢)

| Consistency = 15

}}

~~W. S. B. Woolhouse proposed~~ 730edo~~<ref name="summary">~~[~~http://www~~.~~webcitation~~.~~org~~/~~5zxZzQ3eS A summary of W. S. B. Woolhouse'~~s ~~Essay on musical intervals~~], ~~1999 by Joe Monzo</ref> as a~~ [[~~Interval size measure|logarithmic measure of interval size~~]], ~~sometimes called~~ the ~~'''Woolhouse unit'''~~. ~~While 730 is divisible by 2~~, ~~5, 10, 73, 146~~ and ~~365, it is not divisible by 12~~, ~~which can be regarded as either a good thing or a bad one~~.

== Theory ==

730edo is a very strong 5-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out the [[counterschisma]], {{monzo| -69 45 -1 }}, the minortone comma, {{monzo| -16 35 -17 }}, the kwazy comma, {{monzo| -53 10 16 }}, the whoosh comma, {{monzo| 37 25 -33 }}, and the pirate comma, {{monzo| -90 -15 49 }}. In the 7-limit it tempers out [[4375/4374]] and {{monzo| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.

[[W. S. B. Woolhouse]] proposed 730edo<ref name="summary">[http://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joe Monzo]]</ref> as a [[Interval size measure|logarithmic measure of interval size]], sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12, which can be regarded as either a good thing or a bad one.

=== Prime harmonics ===

== Intervals ==

W. S. B. Woolhouse, in his 1835 essay<ref name="essay">[https://archive.org/details/essayonmusicali00woolgoog/page/n34/mode/2up Essay on musical intervals, harmonics, and the temperament of the musical scale, &c], 1835 by Wesley Stoker Barker Woolhouse</ref>, proposed:

~~...~~ dividing the octave into 730 equal intervals, which we shall call ''degrees'', the elemental intervals will be:

… dividing the octave into 730 equal intervals, which we shall call ''degrees'', the elemental intervals will be:

<pre>

Major-tone, t = 124

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Comma, c = 13

</pre>

~~...~~

…

These numbers present a more accurate measurement of the musical scale than any other, unless we go to very high numbers. The greatest error which can arise from their natural or melodious combinations is that of the fifth, and does not amount to one half of the error of the major-tone above mentioned.

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</blockquote>

== Woolhouse diatonic scale ==

== Scales ==

=== Woolhouse diatonic scale ===

Woolhouse defined the following diatonic/heptonic scale for 730edo<ref name="essay" />.

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== References ==

[[Category:Equal divisions of the octave|###]]

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-The '''730 equal divisions of the octave''' ('''730edo'''), or the '''730(-tone) equal temperament''' ('''730tet''', '''730et''') divides the [[octave]] into 730 [[equal]] parts of 1.644 [[cent]]s each. It is a very strong five-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out the [[counterschisma]], {{monzo| -69 45 -1 }}, the minortone comma, {{monzo| -16 35 -17 }}, the kwazy comma, {{monzo| -53 10 16 }}, the whoosh comma, {{monzo| 37 25 -33 }}, and the pirate comma, {{monzo| -90 -15 49 }}. In the 7-limit it tempers out [[4375/4374]] and {{monzo| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.
+{{Infobox ET
+| Prime factorization = 2 × 5 × 73
+| Step size = 1.64384¢
+| Fifth = 427\730 (701.92¢)
+| Semitones = 69:55 (113.42¢ : 90.41¢)
+| Consistency = 15
+}}
+{{EDO intro|730}}
-W. S. B. Woolhouse proposed 730edo<ref name="summary">[http://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by Joe Monzo</ref> as a [[Interval size measure|logarithmic measure of interval size]], sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12, which can be regarded as either a good thing or a bad one.
+== Theory ==
+edo is a very strong 5-limit system, but is also distinctly consistent up to the [[15-odd-limit]]. It tempers out the [[counterschisma]], {{monzo| -69 45 -1 }}, the minortone comma, {{monzo| -16 35 -17 }}, the kwazy comma, {{monzo| -53 10 16 }}, the whoosh comma, {{monzo| 37 25 -33 }}, and the pirate comma, {{monzo| -90 -15 49 }}. In the 7-limit it tempers out [[4375/4374]] and {{monzo| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.
-{{Primes in edo|730}}
+[[W. S. B. Woolhouse]] proposed 730edo<ref name="summary">[http://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joe Monzo]]</ref> as a [[Interval size measure|logarithmic measure of interval size]], sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12, which can be regarded as either a good thing or a bad one.
+=== Prime harmonics ===
+{{Harmonics in equal|730|columns=11}}
 == Intervals ==
 W. S. B. Woolhouse, in his 1835 essay<ref name="essay">[https://archive.org/details/essayonmusicali00woolgoog/page/n34/mode/2up Essay on musical intervals, harmonics, and the temperament of the musical scale, &c], 1835 by Wesley Stoker Barker Woolhouse</ref>, proposed:
 <blockquote>
-... dividing the octave into 730 equal intervals, which we shall call ''degrees'', the elemental intervals will be:
+… dividing the octave into 730 equal intervals, which we shall call ''degrees'', the elemental intervals will be:
 <pre>
        Major-tone, t = 124
@@ Line 17: / Line 27: @@
        Comma,      c =  13
 </pre>
-...
+…
 These numbers present a more accurate measurement of the musical scale than any other, unless we go to very high numbers. The greatest error which can arise from their natural or melodious combinations is that of the fifth, and does not amount to one half of the error of the major-tone above mentioned.
@@ Line 33: / Line 43: @@
 </blockquote>
-== Woolhouse diatonic scale ==
+== Scales ==
+=== Woolhouse diatonic scale ===
 Woolhouse defined the following diatonic/heptonic scale for 730edo<ref name="essay" />.
@@ Line 85: / Line 95: @@
 == References ==
 <references />
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->