10ed7/3: Difference between revisions

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== Theory==

== Theory ==

~~This tuning tempers out [[16/15]] in the [[5-limit]]; [[28~~/~~27]],~~ [[~~50/49~~]], ~~and [[36/35]] in~~ the [[~~7-limit]]; [[22/21~~]]~~, [[56/55]], 77/75~~, and [[55/54]] ~~in the [[11-limit]]; [[26/25]], [[52/49]], 65/63, [[66/65|66/65,]] [[78/77]],~~ and [[40/39]] in the [[~~13-limit]]; [[34/33~~]], ~~51/49,~~ [[52/51]]~~, 75/68, 77/68, and 51/50 in the [[17-limit]]; [[20/19]], [[64/57]], [[76/75]], [[77/76]],~~ and [[39/~~38]] in the [[19-limit~~]]~~; [[24/~~23~~]],~~ [[70/~~69|70/69,~~]] and ~~[[46/45]] in the~~ [[23~~-limit]]; [[30~~/29]], ~~58/57, and~~ [[32/29]] ~~in the [[29-limit]]; 33/31, [[63/62]], 65/62,~~ and ~~34/31 in the~~ [[~~31-limit]]; 38~~/~~37, 39/37, 75/74, 77/74, and 40/37 in the [[37-limit~~]]; [[42/41]] and 44/41 in the [[41-limit]]; 43/42, 43/41, and 44/43 in the [[43-limit]]; [[47/46]], [[48/47]], and 47/45 in the [[47-limit]]; 54/53, 56/53, and 55/53 in the [[53-limit]]; 59/58, 60/59, [[64/59]], and 59/57 in the [[59-limit]]; 62/61, [[65/61]], 66/61, and 63/61 in the [[61-limit]]; 69/67, 72/67, and 70/67 in the [[67-limit]]; [[71/67]], 71/69, 72/71, and [[71/70]] in the [[71-limit]]; 73/68, 75/73, 76/73, 77/73, 78/73; and 74/73 in the [[73-limit]]; and 81/79 in the [[~~79-limit~~]].

10ed7/3 is essentially a tritave stretch of [[13edt]], the equalized [[Bohlen–Pierce]] scale, and as a result tempers out [[245/243]] and [[3125/3087]] in the [[3.5.7 subgroup]], as well as [[529/525]] and [[1127/1125]] when prime 23 is introduced. It fails to represent any other primes of note within 20 cents. Making this stretch makes [[5/1]] and [[23/1]] closer to just compared to 13edt, while both [[3/1]] and [[7/1]] are about 5 [[cents]] sharp of just.

==Intervals==

=== Harmonics ===

{{Harmonics in equal|10|7|3|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 10ed7/3 (continued)}}

== Intervals ==

~~==Harmonics==~~

~~{{Harmonics in equal~~

~~| steps = 10~~

~~| num = 7~~

~~| denom = 3~~

~~| intervals = prime~~

}}

~~{{Harmonics in equal~~

~~| steps = 10~~

~~| num = 7~~

~~| denom = 3~~

~~| start = 12~~

~~| collapsed = 1~~

~~| intervals = prime~~

}}

@@ Line 2: / Line 2: @@
 {{ED intro}}
-== Theory==
+== Theory ==
-This tuning tempers out [[16/15]] in the [[5-limit]]; [[28/27]], [[50/49]], and [[36/35]] in the [[7-limit]]; [[22/21]], [[56/55]], 77/75, and [[55/54]] in the [[11-limit]]; [[26/25]], [[52/49]], 65/63, [[66/65|66/65,]] [[78/77]], and [[40/39]] in the [[13-limit]]; [[34/33]], 51/49, [[52/51]], 75/68, 77/68, and 51/50 in the [[17-limit]]; [[20/19]], [[64/57]], [[76/75]], [[77/76]], and [[39/38]] in the [[19-limit]]; [[24/23]], [[70/69|70/69,]] and [[46/45]] in the [[23-limit]]; [[30/29]], 58/57, and [[32/29]] in the [[29-limit]]; 33/31, [[63/62]], 65/62,  and 34/31 in the [[31-limit]]; 38/37, 39/37, 75/74, 77/74, and 40/37 in the [[37-limit]]; [[42/41]] and 44/41 in the [[41-limit]]; 43/42, 43/41, and 44/43 in the [[43-limit]]; [[47/46]], [[48/47]], and 47/45 in the [[47-limit]]; 54/53, 56/53, and 55/53 in the [[53-limit]]; 59/58, 60/59, [[64/59]], and 59/57 in the [[59-limit]]; 62/61, [[65/61]], 66/61, and 63/61 in the [[61-limit]]; 69/67, 72/67, and 70/67 in the [[67-limit]]; [[71/67]], 71/69, 72/71, and [[71/70]] in the [[71-limit]]; 73/68, 75/73, 76/73, 77/73, 78/73; and 74/73 in the [[73-limit]]; and 81/79 in the [[79-limit]].
+ed7/3 is essentially a tritave stretch of [[13edt]], the equalized [[Bohlen–Pierce]] scale, and as a result tempers out [[245/243]] and [[3125/3087]] in the [[3.5.7 subgroup]], as well as [[529/525]] and [[1127/1125]] when prime 23 is introduced. It fails to represent any other primes of note within 20 cents. Making this stretch makes [[5/1]] and [[23/1]] closer to just compared to 13edt, while both [[3/1]] and [[7/1]] are about 5 [[cents]] sharp of just.
-==Intervals==
+=== Harmonics ===
+{{Harmonics in equal|10|7|3|columns=11}}
+{{Harmonics in equal|10|7|3|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 10ed7/3 (continued)}}
+== Intervals ==
 {{Interval table}}
-==Harmonics==
-{{Harmonics in equal
-| steps = 10
-| num = 7
-| denom = 3
-| intervals = prime
-}}
-{{Harmonics in equal
-| steps = 10
-| num = 7
-| denom = 3
-| start = 12
-| collapsed = 1
-| intervals = prime
-}}