User:CritDeathX/Sam's 17-note Well Temperament: Difference between revisions

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<small>''(in case you're confused by this, a similar equation can be found [[wikipedia:Alpha_scale|on the Wikipedia page for Wendy Carlos' alpha scale]])''</small>

With this, we get 0.05797208485 as our answer so far. That's only on log2 though, so we multiply this answer by 1200, giving us 69.5665018267c, a [[cent]] flat from one step of 17EDO. Next thing you do is you load this up on the ''Rank-2 temperament'' thing on [https://sevish.com/scaleworkshop/ the Scale Workshop website], load it up for 17 notes, and you got yourself a 1L16s scale, which we'll be calling our little [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(69.5665018267%2C%202%2F1)&data=69.566502%0A139.133004%0A208.699505%0A278.266007%0A347.832509%0A417.399011%0A486.965513%0A556.532015%0A626.098516%0A695.665018%0A765.231520%0A834.798022%0A904.364524%0A973.931026%0A1043.497527%0A1113.064029%0A1200.000000&freq=440&midi=69&vert=1&horiz=3&colors=&waveform=triangle&ampenv=organ 17-note well temperament] (at least if i understand this enough).

With this, we get 0.05797208485 as our answer so far. That's only on log2 though, so we multiply this answer by 1200, giving us 69.5665018267c, a [[cent]] flat from one step of 17EDO. Next thing you do is you load this up on the ''Rank-2 temperament'' thing on [https://sevish.com/scaleworkshop/ the Scale Workshop website], load it up for 17 notes, and you got yourself a 1L16s scale that starts on C, which we'll be calling our little [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(69.5665018267%2C%202%2F1)&data=69.566502%0A139.133004%0A208.699505%0A278.266007%0A347.832509%0A417.399011%0A486.965513%0A556.532015%0A626.098516%0A695.665018%0A765.231520%0A834.798022%0A904.364524%0A973.931026%0A1043.497527%0A1113.064029%0A1200.000000&freq=440&midi=69&vert=1&horiz=3&colors=&waveform=triangle&ampenv=organ 17-note well temperament] (at least if i understand this enough).

== The Scale ==

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Something to note here is that similar to [[pseudo-semaphore]], there's two different types of fifths; you got 486.97c (713.03c) and 695.67c.

The comma this tempers out is ''((25/24)^6)/(14/11)'', for which the [[monzo]] is ''|19 6 12 1 1>''. It also tempers out [[99/98]], which I certainly find interesting.

The comma this tempers out is ''[[User:CritDeathX/Sam's Neo-Gothic Comma|((25/24)^6)/(14/11)]]'', for which the [[monzo]] is ''|-19 -6 12 -1 1>''. It also tempers out [[99/98]], which I certainly find interesting.

The best limit I could think of is ''2.3.6.7.11.13.23''. I imagine there's probably a better way to demonstrate this limit, though.

The average difference from JI for 17EDO was 8c (taking the lowest difference for intervals with 2 approximations), but the average for my temperament was only 3.5c. Impressive, honestly.

An alternative generator could be 69.9628521248c, though this doesn't make much of a difference (to my knowledge).

== Retuning ==

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== ''Closed Up'' ==

This was a piece I decided to whip up cause [[User:Xenwolf|Xenwolf]] mentioned that retuning 12EDO pieces probably isn't the best way to demonstrate this. I've made sure to try and at least use all the notes and show examples of chords that could be made (including a huge harmonic series cluster!). Enjoy this little thing.

This was a piece I decided to whip up cause [[User:Xenwolf|Xenwolf]] mentioned that [https://en.xen.wiki/w/User_talk:CritDeathX#Retuned_piece retuning 12EDO pieces probably isn't the best way to demonstrate this]. I've made sure to try and at least use all the notes and show examples of chords that could be made (including a huge harmonic series cluster!). Enjoy this little thing.

[[File:Closed Up.mp3|left|frameless]]

@@ Line 17: / Line 17: @@
 <small>''(in case you're confused by this, a similar equation can be found [[wikipedia:Alpha_scale|on the Wikipedia page for Wendy Carlos' alpha scale]])''</small>
-With this, we get 0.05797208485 as our answer so far. That's only on log2 though, so we multiply this answer by 1200, giving us 69.5665018267c, a [[cent]] flat from one step of 17EDO. Next thing you do is you load this up on the ''Rank-2 temperament'' thing on [https://sevish.com/scaleworkshop/ the Scale Workshop website], load it up for 17 notes, and you got yourself a 1L16s scale, which we'll be calling our little [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(69.5665018267%2C%202%2F1)&data=69.566502%0A139.133004%0A208.699505%0A278.266007%0A347.832509%0A417.399011%0A486.965513%0A556.532015%0A626.098516%0A695.665018%0A765.231520%0A834.798022%0A904.364524%0A973.931026%0A1043.497527%0A1113.064029%0A1200.000000&freq=440&midi=69&vert=1&horiz=3&colors=&waveform=triangle&ampenv=organ 17-note well temperament] (at least if i understand this enough).
+With this, we get 0.05797208485 as our answer so far. That's only on log2 though, so we multiply this answer by 1200, giving us 69.5665018267c, a [[cent]] flat from one step of 17EDO. Next thing you do is you load this up on the ''Rank-2 temperament'' thing on [https://sevish.com/scaleworkshop/ the Scale Workshop website], load it up for 17 notes, and you got yourself a 1L16s scale that starts on C, which we'll be calling our little [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(69.5665018267%2C%202%2F1)&data=69.566502%0A139.133004%0A208.699505%0A278.266007%0A347.832509%0A417.399011%0A486.965513%0A556.532015%0A626.098516%0A695.665018%0A765.231520%0A834.798022%0A904.364524%0A973.931026%0A1043.497527%0A1113.064029%0A1200.000000&freq=440&midi=69&vert=1&horiz=3&colors=&waveform=triangle&ampenv=organ 17-note well temperament] (at least if i understand this enough).
 == The Scale ==
@@ Line 217: / Line 217: @@
 Something to note here is that similar to [[pseudo-semaphore]], there's two different types of fifths; you got 486.97c (713.03c) and 695.67c.
-The comma this tempers out is ''((25/24)^6)/(14/11)'', for which the [[monzo]] is ''|19 6 12 1 1>''. It also tempers out [[99/98]], which I certainly find interesting.
+The comma this tempers out is ''[[User:CritDeathX/Sam's Neo-Gothic Comma|((25/24)^6)/(14/11)]]'', for which the [[monzo]] is ''|-19 -6 12 -1 1>''. It also tempers out [[99/98]], which I certainly find interesting.
 The best limit I could think of is ''2.3.6.7.11.13.23''. I imagine there's probably a better way to demonstrate this limit, though.
+The average difference from JI for 17EDO was 8c (taking the lowest difference for intervals with 2 approximations), but the average for my temperament was only 3.5c. Impressive, honestly.
+An alternative generator could be 69.9628521248c, though this doesn't make much of a difference (to my knowledge).
 == Retuning ==
@@ Line 227: / Line 231: @@
 == ''Closed Up'' ==
-This was a piece I decided to whip up cause [[User:Xenwolf|Xenwolf]] mentioned that retuning 12EDO pieces probably isn't the best way to demonstrate this. I've made sure to try and at least use all the notes and show examples of chords that could be made (including a huge harmonic series cluster!). Enjoy this little thing.
+This was a piece I decided to whip up cause [[User:Xenwolf|Xenwolf]] mentioned that [https://en.xen.wiki/w/User_talk:CritDeathX#Retuned_piece retuning 12EDO pieces probably isn't the best way to demonstrate this]. I've made sure to try and at least use all the notes and show examples of chords that could be made (including a huge harmonic series cluster!). Enjoy this little thing.
 [[File:Closed Up.mp3|left|frameless]]