17ed5: Difference between revisions

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'''[[Ed5|Division of the 5th harmonic]] into 17 equal parts''' (17ED5) is a good [[hyperpyth]] tuning. The step size is about 163.9008 cents, corresponding to 7.3215 [[EDO]].

A hyperpyth tuning, 17ED5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ED5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after ~~5ed5~~, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.

== Division of the 5/1 into 17 tones ==

A hyperpyth tuning, 17ED5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ED5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ED5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.

But wait, an interesting pattern emerges:

22ED5 focuses on 9/5

[[22ed5|22ED5]] focuses on 9/5

27ED5 focuses on 13/5

[[27ed5|27ED5]] focuses on 13/5

29ED5 focuses on 17/5

[[29ed5|29ED5]] focuses on 17/5

(and 34=17*2)

Line 15:

Line 17:

so: 22+27+29=78=39*2

and behold, of the lot, 39ED5 offers the best balance between those intervals.

and behold, of the lot, [[39ed5|39ED5]] offers the best balance between those intervals.

{| class="wikitable"

Line 115:

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|}

~~[[Category:Ed5]]~~

== Harmonics ==

~~[[Category:Edonoi]]~~

{{Harmonics in equal

| steps = 17

| num = 5

| denom = 1

}}

{{Harmonics in equal

| steps = 17

| num = 5

| denom = 1

| start = 12

| collapsed = 1

}}

[[Category:Hyperpyth]]

[[Category:Todo:add sound example]]

@@ Line 1: / Line 1: @@
+{{Infobox ET}}
 '''[[Ed5|Division of the 5th harmonic]] into 17 equal parts''' (17ED5) is a good [[hyperpyth]] tuning. The step size is about 163.9008 cents, corresponding to 7.3215 [[EDO]].
-A hyperpyth tuning, 17ED5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ED5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ed5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.
+== Division of the 5/1 into 17 tones ==
+A hyperpyth tuning, 17ED5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ED5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ED5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.
 But wait, an interesting pattern emerges:
-ED5 focuses on 9/5
+[[22ed5|22ED5]] focuses on 9/5
-ED5 focuses on 13/5
+[[27ed5|27ED5]] focuses on 13/5
-ED5 focuses on 17/5
+[[29ed5|29ED5]] focuses on 17/5
 (and 34=17*2)
@@ Line 15: / Line 17: @@
 so: 22+27+29=78=39*2
-and behold, of the lot, 39ED5 offers the best balance between those intervals.
+and behold, of the lot, [[39ed5|39ED5]] offers the best balance between those intervals.
 {| class="wikitable"
@@ Line 115: / Line 117: @@
 |}
-[[Category:Ed5]]
+== Harmonics ==
-[[Category:Edonoi]]
+{{Harmonics in equal
+| steps = 17
+| num = 5
+| denom = 1
+}}
+{{Harmonics in equal
+| steps = 17
+| num = 5
+| denom = 1
+| start = 12
+| collapsed = 1
+}}
 [[Category:Hyperpyth]]
 [[Category:Todo:add sound example]]