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= ARCHIVED WIKISPACES DISCUSSION BELOW =
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'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.
== Daniel Anthony Stearns ==


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He is credited with having coined the term but there is no reference for this? Is it true at all? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:39, 22 November 2020 (UTC)


== Approximations for just intonation and meantone ==
: There are two "sources" now, both of them posts on the tuning list with zero replies. I find they make very little sense so it's hard to consider these real sources. – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 09:15, 18 May 2025 (UTC)
My program generated this:


Good for 3-limit:
:: Not sure how you will find better in-writing documentation, but if you ask anyone who was on the tuning list at that time, they'll tell you that it was Daniel who coined it. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:58, 18 May 2025 (UTC)
 
1 2 3 5 7 12 29 41 53 200 253 306 359 665 8286 8951 9616 10281 10946 11611 12276 12941 13606 14271 14936 15601 31867
 
Good for 5-limit:
 
1 2 3 7 9 10 12 19 22 31 34 53 118 289 323 441 494 559 612 1171 1783 2513 3684 4296 12276 16572 20868 25164 48545
 
Good for 7-limit:
 
1 2 3 4 5 7 9 10 12 15 19 21 22 31 53 84 87 94 99 118 130 140 171 270 410 441 612 935 966 1053 1106 1277 1547 1578 2954 3125 3566 6691 9816 11664 14789 18355 39835 48545 54624 58190 59768 63334
 
Good for 11-limit:
 
1 2 3 4 5 6 7 9 10 12 15 22 26 31 41 63 72 87 109 161 202 224 270 494 612 742 764 836 1012 1084 1106 1308 1417 1578 3426 4843 6421 6691 10698 12276 18355 19461 21039 22887 25046 26894 31737 33585 35163 41854 53046 54624
 
Good for 13-limit:
 
1 2 3 4 5 6 7 9 10 15 16 17 19 20 22 24 26 31 37 46 50 53 63 77 84 87 130 140 161 183 207 217 224 270 494 851 1075 1282 1578 2159 2190 2684 3265 3535 4573 5004 5585 6079 8269 8539 13854 14124 16808 20203 22887 28742 32007 37011 50434 50928 51629 54624 56202 59467 64471 65052
 
Good for 2.3.7:
 
1 2 3 4 5 17 21 26 31 36 41 77 89 94 130 135 265 306 436 571 1277 3125 4402 4708 5414 5679 5985 7262 8539 10387 17649 18926
 
Good for 2.9.5:
 
1 2 3 4 5 6 25 28 34 40 41 47 53 59 289 323 382 435 441 494 500 553 559 612 1171 1230 1783 1842 4296 6138 10434 14730 25164 39894 48545 52841 58979 63275
 
Good for meantone:
 
1 2 3 4 5 7 12 19 31 50 102 114 121 133 152 171 205 326 338 357 376 407 764 1171 2718 3125 4296 14059 18355 22651 26947 31243
 
For just intonation, I weighted the error of harmonics of primes in each limit/subgroup. For meantone, I weighted 5/4, 6/5 and a flat fifth.
 
- '''PiotrGrochowski''' August 23, 2016, 01:46:57 AM UTC-0700
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== rework of table(s) ==
Great idea to split them, much more helpful now :) Thanks, spt3125!
 
- '''xenwolf''' May 28, 2014, 02:36:47 AM UTC-0700
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I agree too with that changes !
 
- '''Osmiorisbendi''' May 28, 2014, 11:05:12 AM UTC-0700
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great, glad you like :)
 
- '''spt3125''' May 29, 2014, 06:21:34 PM UTC-0700
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== 39 ==
39, which is less than six cents sharp, quite a bit less sharp than 22, belongs on the list of "reasonably good" fifths.
 
- '''genewardsmith''' July 20, 2011, 05:02:51 PM UTC-0700
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ok
 
- '''Osmiorisbendi''' July 21, 2011, 12:30:34 AM UTC-0700
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I don't understand Gene's revert of JosephRuhf's edit.  39-EDO only has one circle of fifths, since 23 is coprime with 39.
 
If anything, 39-EDO should be in the first list, and not in the second.
 
- '''Sarzadoce''' September 23, 2012, 05:16:47 PM UTC-0700
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Sorry, I thought it was saying 39 had more than one circle of fifths. Also, I should mention "so there" was not commentary, but an artifact of space limitations. I was cut off.
 
- '''genewardsmith''' September 23, 2012, 06:05:06 PM UTC-0700
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Hahahahaha that is hilarious. Gene meant to be like "so there are N circles of fifths..." but the software made it sound like he was saying "so there!"
 
- '''keenanpepper''' September 26, 2012, 03:07:18 PM UTC-0700
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== Red edo links in the table... ==
...should net be removed, if the (future) pages are referenced more than once (from the edo page itself). You can check this by looking on the 'Backllinks' option in the 'page' menu of the non existing page.
 
for example look at
 
http://xenharmonic.wikispaces.com/page/links/128edo
 
Best regards :)
 
- '''xenwolf''' March 25, 2011, 03:33:43 AM UTC-0700
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I see no sense in having a link if the page behind it does not exist at all. If a certain EDO is important, there will sure be informations about it that can be written on its page.
 
- '''hstraub''' March 25, 2011, 06:01:32 AM UTC-0700
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Hi hstraub,
 
the idea is that we increase the probability to get new articles created that are really needed is higher if they are listed on such a prominent place. BTW: It's not I who reverted your changes, please have a look on the article history.
 
ps. I use to format interesting topics into links. I ask for an deeper explanation of the background this way.
 
- '''xenwolf''' March 25, 2011, 11:40:18 AM UTC-0700
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== edo classification ==
What do you think: does it make sense to classify this lot of edos by size?
 
<ul><li>macrotonic</li><li>microtonic</li><li>commatic</li><li>nanotonic</li></ul>
 
...or something else?
 
- '''xenwolf''' March 23, 2011, 05:58:48 AM UTC-0700
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What about this bound:
 
Macro: 0 to 16
 
Micro: 13 to 55
 
Comma: 31 to 612 (as 31edo uses diesis and 612edo uses schisma)
 
Nano: 218 to 15601
 
Accurate: 22, 34, 41, 53
 
Inaccurate: 21, 25, 28, 30, 35 (these temper out limma or apotome)
 
- '''PiotrGrochowski''' August 12, 2016, 02:12:03 AM UTC-0700
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Accurate: 22, 34, 41, 53 because they are good in 5-limit and don't temper out 81/80
 
- '''PiotrGrochowski''' August 12, 2016, 02:12:53 AM UTC-0700
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Accurate: 22, 34, 41, 53 because they are good in 5-limit and don't temper out 81/80
 
- '''PiotrGrochowski''' August 12, 2016, 02:12:53 AM UTC-0700
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Why it makes a double post?
 
- '''PiotrGrochowski''' August 12, 2016, 02:13:15 AM UTC-0700
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Why it makes a double post?
 
- '''PiotrGrochowski''' August 12, 2016, 02:13:16 AM UTC-0700
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Lower bound:
 
Macro: 0 to 12
 
Micro: 17 to 30
 
Comma: 56 to 217
 
Nano: 613 to 15601
 
- '''PiotrGrochowski''' August 12, 2016, 02:22:43 AM UTC-0700
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MacroEDD: 0 ~ 17
 
PluscuamEDD: 14 ~ 57
 
MicroEDD: 46 ~ 667
 
CommaEDD: 306 ~ 15601
 
NanoEDD: 6079 ~ ∞
 
My suggerence, dears (-;
 
- '''Osmiorisbendi''' August 12, 2016, 05:03:32 PM UTC-0700
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I think comma should start at 31~56 not 306, as 31edo bases on diesis and 55edo can be used for guitar that it may belong in micro...
 
No meso or pluscuam categories!
 
- '''PiotrGrochowski''' August 13, 2016, 03:23:35 AM UTC-0700
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I think comma should start at 31~56 not 306, as 31edo bases on diesis and 55edo can be used for guitar that it may belong in micro...
 
No meso or pluscuam categories!
 
- '''PiotrGrochowski''' August 13, 2016, 03:23:35 AM UTC-0700
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I think comma should start at 31~56 not 306, as 31edo bases on diesis and 55edo can be used for guitar that it may belong in micro...
 
No meso or pluscuam categories!
 
- '''PiotrGrochowski''' August 13, 2016, 03:23:36 AM UTC-0700
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And why not Pluscuam/Meso?
 
For example, 23-EDD is not sufficiently "micro" acoustically.
 
Pluscuam/Meso is precisely a type of classification for a top-limit fretted instruments.
 
For me, 57-EDD represents an extreme umbral for fretted guitar.
 
46-EDD begins to be very tiny intervals by ear, adequate starting as 'Micro'.
 
!!!!!
 
- '''Osmiorisbendi''' August 13, 2016, 11:20:56 AM UTC-0700
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Macro: 1-11
 
Micro: 13 and on
 
Fine: 22 and on
 
Finer: 34 and on
 
- '''PiotrGrochowski''' June 09, 2017, 11:52:35 AM UTC-0700
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Hello Titim Deft,
 
nice to hear from you. :)
 
I came to this question, when I thought about the extreme small steps in ~250edos and the usability of a cromatic scales from ~10edos to ~30edos (at ~50edo and above there isn't this chromatic feeling).
 
I relatively agree with you concerning the distribution. I find the borders should be less strict, the edo's fitness for a particular purpose does not disappear suddenly bejond one of these borders. What about something like this:
 
<ul><li>1edo ~ 18edo be MACROTONALS</li><li>12edo ~ 60edo be MICROTONALS</li><li>40edo ~ 250edo be COMMATONALS, and</li><li>200edo ~ 15601edo be NANOTONALS</li></ul>
 
The borders and also the names could (and should!) be discussed some more. Are you member on the yahoo group? (I'm not) Do you see any chance to discuss it there?
 
Best regards!
 
- '''xenwolf''' March 24, 2011, 01:02:03 AM UTC-0700
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Hi mr. PEU (again) (:
 
So, you have the idea of 'Limit-Range' for separate those groups of EDOs. Is not bad the idea, but i insist in the inmediately Limit that separates MACROTONALS of the MICROTONALS; that is:
 
<ul><li>1edo ~ 16edo= MACROTONALS, and</li><li>17edo ~ upper= MICROTONALS.</li></ul>Personally, i don't feel 17edo like a "Macrotonal", Because 17edo represents, in esense, the Low Limit for 1/3-tones (That 'Tone' that vary between 151 ~ 216,7 Cents [Ratios 12/11 until 17/15]{but in some cases you can 'stretch out' the tone between 25/23 until 25/22 for the 'Tone'}); In many cases, I based with respect the equal divisions for these 'Tones', and the 11edo until 16edo FITS with that setting.
 
And now, with respect the others EDOs, this should be the 'way':
 
<ul><li>17edo ~ 55edo be MICROTONALS (because 55edo is the highest limit for fretting a guitar of 26 Inches (660mm) with 94 frets on the neck (that is equivalent to 20,5 frets in 12edo).</li><li>40edo ~ 289edo be COMMATONALS (because 289edo supports very accurate the 1253/1250 Ratio (or Comma)); and</li><li>218edo ~ 15601edo be NANOTONALS (Particulary I choose <big><big><big><big><big><big>[[218edo]]<small><small><small><small><small><small>, because this EDO contains with much accurate the Ratios 7/4, 11/8, 9/7, 8/7, 9/8, 10/9, 11/10, 17/16 and very interesting accurate to the Pi Ratio [1981,7954 Cents Pi ; 1981,6514 Cents the 360\218edo]. 218edo contains a 'possible Comma' which is the Ratio 65207/65000). The size of 1\218 is 5,5046 Cents, but you can use the size of 5,5 Cents like a approximation too).</li></ul>I hope that the rest of the Microtonal (or Ekmelic) people can be agree with this order.
 
Greetings (:
 
- '''Osmiorisbendi''' March 24, 2011, 02:52:28 PM UTC-0700
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I like your Numbers, the limits I gave were only random examples (except the 50edo experience).
 
Ok, your macro-micro border I would like to question. What do you think about
 
  MACRO &lt;= 12edo &lt; MICRO
 
it categorizes all edos with steps finer than a semitone as microtonal - in my opinion this hits best the common sense.
 
Best regards!
 
- '''xenwolf''' March 25, 2011, 03:28:48 AM UTC-0700
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Ok. If is for the common sense i agree.
 
So the limits would be like a:
 
<ul><li>1edo ~ 16edo MACROTONALS, and</li><li>13edo ~ upper MICROTONALS</li></ul>Greetings (:
 
- '''Osmiorisbendi''' March 25, 2011, 12:50:26 PM UTC-0700
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Sounds good to me :)
 
What do you think: is such a classification from your point of view also acceptable for other Xenharmonics?
 
Best :)
 
- '''xenwolf''' March 25, 2011, 01:01:42 PM UTC-0700
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i guess
 
i am sure
 
(:
 
- '''Osmiorisbendi''' March 25, 2011, 01:45:43 PM UTC-0700
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We've already said 1-11 is macrotonal elsewhere on the Xenwiki so we should stick with that.
 
- '''genewardsmith''' March 28, 2011, 05:06:55 PM UTC-0700
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Hello Genewardsmith,
 
(1) How would you classify 12edo then? Micro? Or is there a MESO category?
 
(2) What do you think about overlapping usability properties (compared to strict categories)?
 
(3) What do you think about the classification at all? (I see very different qualities in, for example, 11edo and 359edo)
 
- '''xenwolf''' March 29, 2011, 12:15:09 AM UTC-0700
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Meso would be fine by me. Could run 12-22, I suppose.
 
- '''genewardsmith''' March 29, 2011, 08:58:01 PM UTC-0700
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so we are here:
 
<ul><li>MACRO 1 to 11</li><li>MESO 12 to 22</li><li>MICRO 17 to 55</li><li>COMMA 40 to 250</li><li>NANO from 200 on</li></ul>Would a (first draft) diagram illustrate this better?
 
BTW: I find the strict border between MACRO and MESO not so good. What do the xenharmonic practitioners think about it?
 
- '''xenwolf''' March 30, 2011, 12:08:05 AM UTC-0700
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Why not ordened the EDO pages each 25 places?
 
- '''Osmiorisbendi''' September 02, 2011, 07:06:34 PM UTC-0700
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What about this bound:
 
Macro: 0 to 16
 
Micro: 13 to 55
 
Comma: 31 to 612 (as 31edo uses diesis and 612edo uses schisma)
 
Nano: 218 to 15601
 
Accurate: 22, 34, 41, 53
 
Inaccurate: 21, 25, 28, 30, 35 (these temper out limma or apotome)
 
- '''PiotrGrochowski''' August 12, 2016, 02:12:02 AM UTC-0700
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Hi, mr. PEU (:
 
I think the same thing.
 
I guess that would be:
 
<ul><li>1edo ~ 16edo be MACROTONALS</li><li>17edo ~ 52edo be MICROTONALS</li><li>53edo ~ 253edo be COMMATONALS, and</li><li>254edo ~ 15601edo be NANOTONALS</li></ul>Maybe considering too the 'FEMTOTONALS', being upper than 15601edo.
 
Greetings !!!'!!!!' [FOREVER ARMODUE]
 
- '''Osmiorisbendi''' March 23, 2011, 08:24:44 PM UTC-0700
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