User:CritDeathX/Sam's 17-note Well Temperament: Difference between revisions
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== Random Ramblings To Reason Why I Did This == | == Random Ramblings To Reason Why I Did This == | ||
Okay, so lets get one thing straight (not me): I love my [http://dkeenan.com/Music/NobleMediant.txt Neo-Gothic] intervals. The sound of a [[14/11]] somehow works and calls back to my [[12edo|12EDO]]-self as its rapid warbles | Okay, so lets get one thing straight (not me): I love my [http://dkeenan.com/Music/NobleMediant.txt Neo-Gothic] intervals. The sound of a [[14/11]] somehow works and calls back to my [[12edo|12EDO]]-self as its rapid warbles make my brain excited. [[13/11]] also works for the same reason. | ||
The problem for me is that I don't wanna use a large [[EDO]] to approximate these well, nor do I wanna compose in [[Just intonation|JI]]. So, the natural assumption (for me, at least) is to look at [[17edo|17EDO]] and see if that works. | The problem for me is that I don't wanna use a large [[EDO]] to approximate these well, nor do I wanna compose in [[Just intonation|JI]]. So, the natural assumption (for me, at least) is to look at [[17edo|17EDO]] and see if that works. | ||
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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> | <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 | 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&env=organ 17-note well temperament] (at least if i understand this enough). | ||
== The Scale == | == The Scale == | ||
| Line 46: | Line 46: | ||
| -1.1c | | -1.1c | ||
| | | | ||
|25/24 | |[[25/24]] | ||
| | | | ||
|70.59 | |70.59 | ||
| Line 56: | Line 56: | ||
| +0.5c | | +0.5c | ||
| | | | ||
|13/12 | |[[13/12]] | ||
| | | | ||
|141.18 | |141.18 | ||
| Line 66: | Line 66: | ||
| +4.8c | | +4.8c | ||
| | | | ||
|9/8 | |[[9/8]] | ||
| | | | ||
|211.76 | |211.76 | ||
| Line 76: | Line 76: | ||
| -10.9c, -3.1c | | -10.9c, -3.1c | ||
| | | | ||
|13/11, 20/17 | |[[13/11]], [[20/17]] | ||
| | | | ||
|282.35 | |282.35 | ||
| Line 86: | Line 86: | ||
| +0.8c | | +0.8c | ||
| | | | ||
|11/9 | |[[11/9]] | ||
| | | | ||
|352.94 | |352.94 | ||
| Line 96: | Line 96: | ||
| -0.1c | | -0.1c | ||
| | | | ||
|14/11 | |[[14/11]] | ||
| | | | ||
|423.53 | |423.53 | ||
| Line 106: | Line 106: | ||
| -11c | | -11c | ||
| | | | ||
|4/3 | |[[4/3]] | ||
| | | | ||
|494.12 | |494.12 | ||
| Line 116: | Line 116: | ||
| +5.2c | | +5.2c | ||
| | | | ||
|11/8 | |[[11/8]] | ||
| | | | ||
|564.71 | |564.71 | ||
| Line 126: | Line 126: | ||
| -2.2c | | -2.2c | ||
| | | | ||
|23/16 | |[[23/16]] | ||
| | | | ||
|635.29 | |635.29 | ||
| Line 136: | Line 136: | ||
| -6.3c | | -6.3c | ||
| | | | ||
|3/2 | |[[3/2]] | ||
| | | | ||
|705.88 | |705.88 | ||
| Line 146: | Line 146: | ||
| +0.3c | | +0.3c | ||
| | | | ||
|14/9 | |[[14/9]] | ||
| | | | ||
|776.47 | |776.47 | ||
| Line 156: | Line 156: | ||
| -5.7c | | -5.7c | ||
| | | | ||
|13/8 | |[[13/8]] | ||
| | | | ||
|847.06 | |847.06 | ||
| Line 166: | Line 166: | ||
| +1.5c | | +1.5c | ||
| | | | ||
|27/16 | |[[27/16]] | ||
| | | | ||
|917.65 | |917.65 | ||
| Line 176: | Line 176: | ||
| +5.1c | | +5.1c | ||
| | | | ||
|7/4 | |[[7/4]] | ||
| | | | ||
|988.24 | |988.24 | ||
| Line 186: | Line 186: | ||
| -5.9c | | -5.9c | ||
| | | | ||
|11/6 | |[[11/6]] | ||
| | | | ||
|1058.82 | |1058.82 | ||
| Line 196: | Line 196: | ||
| +12c, +1.9c | | +12c, +1.9c | ||
| | | | ||
|17/9, 19/10 | |[[17/9]], [[19/10]] | ||
| | | | ||
|1129.41 | |1129.41 | ||
| 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. | 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''. I imagine there's probably a better way to demonstrate this limit, though. | 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 == | |||
I retuned Rachmaninoff's first prelude of the 13 Preludes into this temperament. That's it. | |||
[[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]] | |||