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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[[File:Thirteen Preludes No. 1, tuned to sam's 17-tone temperament.wav]]

== ''Closed Up'' ==

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 225: / Line 229: @@
 [[File:Thirteen Preludes No. 1, tuned to sam's 17-tone temperament.wav]]
+== ''Closed Up'' ==
+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]]