Godtone

* 34: The first good approximation of the 5-prime-limit due to being the first reasonably accurate tuning of [[Kleismic family|kleismic]] and [[srutal archagall]] which are IMO the best 5-limit temperaments that observe the [[81/80|syntonic comma]]. 19 is also a tuning for kleismic but feels like it doesn't do justice to the accuracy and pristineness of kleismic to me, plus its harmonic interpretation is pretty lacking. And 22 is very obviously to Has the sharp 3/2's of 17 EDO, and as 17 EDO is a good colour system, 34 EDO is a natural extension. Also is a very logical "completion" of 17 due to giving a very logical 2.3.5.13.17(.23)-subgroup interpretation of the sqrt(2).sqrt(3) subgroup with some really intriguing possibilities. If you're lacking in inspiration and its wide array of supported MOSSes aren't inspiration enough, try taking a look at the diaschismic-tetracot continuum ([[2048/2025]])ⁿ / ([[20000/19683]]).

80 EDO MOSS gens table:

 

(1\10: 120c)

(~1\9: 135c (~~8L1s))

(1\8: 150c)

7L1s: 165c

6L1s: 180c (7L6s) (note 195c (6L7s) is extreme with L/s=6.5)

5L1s: 210c (6L5s), 225c (5L6s)

(1\5: 240c)

5L4s: 255c

4L5s: 270c, 285c

(1\4: 300c)

4L7s: 315c

(~~1\11: 330c (~7L4s))

7L3s: 345c

3L4s: 360c

3L7s: 375c, 390c

3L8s: 405c, 420c, 435c (all also ofc 3L5s; biased to 435c)

(3\8: 450c)

5L3s: 465c

(2\5: 480c)

5L2s: 495c, 510c

7L2s: 525c

2L7s: 540c, 555c, 570c, 585c (all also ofc 2L5s; biased to 540c)

==== 87 EDO interval colours/types (seconds and thirds) ====

41.4c fifth-tone

55.2c ultraminor (AKA quarter-tone)

82.8c neominor

 

== MOSS names i think are pretty ==

Note: I am only considering octave-period MOSSes here. Table is an edited version of the standardised version at [[TAMNAMS#Mos_pattern_names]]. I made a few small changes of personal preference:

 

* [[4L 1s]] I call "pentoid" after [[Bug_family#Pentoid|the 11-limit 4&5 exotemperament]] for which practically the entire tuning range of the MOSS is valid due to its impractically low accuracy/high damage (this is evidenced by it also being supported by patent val in EDOs 4+5=9 (the basic tuning) and 4+5+4=14 (the hard tuning), and by the 13b val (the soft tuning) where you take the (only barely) second-best fifth).

 

* [[1L 6s]] I find significant as a 7-note scale underlying all nL1s scales for n>=7. I have named it "onyx", which has a variety of aesthetic reasonings for it: "1Ln-ic's" and "nL1-ic's (like, the -ic suffix applied to MOSS names, collectivised for 1Lns and nL1s) sounds like "one-el-en-ics" or "en-el-one-ics" which abbreviated sort of sounds like "one-ics" => "onyx". Then "onyx" sounds sort of like "one-six". Furthermore the onyx mineral comes in many colours and types, which seems fitting given this is the parent scale for a wide variety of MOSSes; specifically of interest being [[7L 1s]] (pine), [[8L 1s]] (subneutralic) and [[9L 1s]] (sinatonic). Finally, the name "onyx" is also supposed to be vaguely reminiscent of "anti-archaeotonic" as "chi" (the greek letter) is written like an "x" (this is related to why "christmas" is abbreviated sometimes as "X-mas") and other than that, the letters "o" and "n" and their sounds are also present in "archaeotonic", and "x" is vaguely reminiscent of negation and multiplication. There is also something like a "y" sound in "archaeotonic" in the "aeo" part (depending partially on your pronounciation).

 

* [[4L 3s]] I noticed is unique in that out of [[1L 6s]], [[2L 5s]], [[3L 4s]], [[4L 3s]] and [[5L 2s]] it is the only MOSS pattern that doesn't have both of its child MOSSes named and included. Note that it makes sense to make an exception for [[6L 1s]] as the large number of large steps and small number of small steps makes the range of valid tunings for the generator(s) the most strict of all the 7-note MOSSes. Anyway, as generators close to 6/5 corresponding to [[kleismic]] temperament seem to be of especial importance for this MOSS, I consider the [[4L 7s]] pattern important enough to be named, and it had a proposed name of "kleistonic", a name I think is fitting. As a result, [[7L 4s]] could be named "anti-kleistonic", but I think its actually sort of the more natural extension of the [[4L 3s]] scale pattern which has sharper minor thirds in less complex tunings, hence I've opted for naming it "suprasmitonic" instead after its (and to a lesser extent smitonic's) supraminor third generator AKA "sharp minor third" - the origin of the name "smitonic". Note that another reason I think [[4L 7s]] is worth distinguishing and naming is because kleismic temperaments tend to need both more generators and very hard tunings for [[4L 3s]], as evidenced by the basic tuning of [[11edo]] being way too sharp for kleismic and the hard tuning of [[15edo]] being the sharpest kleismic that could ever make some sense (as it requires, for instance, accepting 720c as an approximation of 3/2 and 400c as an approximation of 5/4). The interval prefixes/abbreviations for [[7L 4s]] are "ssmi" to show preference in comparing it to the underlying [[4L 3s]] scale and as a shortenage of "sharp supraminor third" and "suprasmitonic" correspondingly.

 

* I gave names for the interval prefixes and interval name abbreviations for [[5L 7s]] (p-chromatic) and [[7L 5s]] (m-chromatic). For [[7L 5s]] I picked "chrome" as it is strongly befitting of meantone as meantone does the 7-limit efficiently, elegantly and colourfully, and because its a contraction of "chromatic" and the "me" in "meantone". Pronounced like the word. For [[5L 7s]], in contrast with [[5L 7s]] which is mellow and harmonic, [[5L 7s]] is sharp and active, perhaps like fire, hence I picked "pyr-" from "pyro" and from "[py]thago[r]ean", with the letters "pyr" of course also being for "[p]a[r]a[py]th", "su[p]e[rpy]th" and "ult[r]a[py]yth".

 

* Similarly to how I made an exception for the 1Lns scale form of [[1L 6s]], I'm also making an exception to include the multiMOSS of [[6L 2s]] as [[Diaschismic_family#Echidna|echidna]] (from which the MOSS derives its name) is a strong and important temperament to me with a period of half an octave and where one generator is both 11/10 and 9/7 depending on from which direction you view it, as 11/10 * 9/7 is extremely close to half an octave, the period for this MOSS scale. ("MultiMOSS" stands for "multi-period Moment Of Symmetry Scale".) '''However,''' this would not be included if I were to have this as "the semi-official [[TAMNAMS]] minimal MOSS name list", because this is a true exception to a lot of the design principles behind choosing this set of MOSSes to name and recognise as important.

 

{| class="wikitable center-all"

!colspan=5| 5-note mosses

! Pattern !! Name !! Interval prefix<ref name=prefix>used in interval names, e.g. ''perfect 3-oneirostep''</ref> !! Abbreviation<ref name=abbr>used in abbreviations of interval names, e.g. ''P3ons''</ref> !! Notes

| [[2L 3s]] || pentic || pent- || pent || Shortening of pentatonic.

| [[3L 4s]] || mosh || mosh- || mosh || Graham Breed's name, from ''[[mohajira]]-ish''.

| [[4L 5s]] || orwelloid || or- || or || From [[orwell]] temperament.

IMPORTANT NOTE: there seems to be a bug for subgroup mappings at the moment, pending investigation, but ideally usage of subgroups should be made far easier too:

def cs(scale_in):

sg = lim(ol)

def et_badness(ivs,v,badness=lambda rel_err,x,et2: rel_err**2 * et2**2,weighting=lambda x: iv_complexity(x),combine='avg',et2=0):

if weighting==1 or weighting in ['unweighted','trivial','basic']:

weighting = lambda x: 1

elif weighting=='sensitive':

weighting = lambda x: iv_complexity(x)**2

if type(v)==int:

return combine([ badness3args(abs( map_iv(v,x) - steps(x,et2) ), x, et2) * weighting(x) for x in ivs ]) / (ivs_sum_weights_cache if using_avg else 1)

def optimal_edo_sequence(ivs_or_edo_badness,edo_set=range(2,311+1),weighting=lambda x: iv_complexity(x),combine='avg'):

et_badness_judger = lambda edo: et_badness(ivs,edo,weighting=weighting,combine=combine)

if current < best_edo:

def strict_optimal_edo_sequence(ivs,edo_set=range(2,311+1),weighting=lambda x: iv_complexity(x),combine='avg'):

return optimal_edo_sequence(lambda edo: et_badness(ivs,edo,lambda rel_err: rel_err**2,weighting,combine),edo_set)

</syntaxhighlight>

=== Important 23-limit EDOs ===

Produced with the help of my above code and corrected with love. Below are theoretically important [[23-limit]] [[EDO]]s in that they do an increasingly better job at representing the [[27-odd-limit]] minus zero or one of composite odds 25 and 27. The exception is that if an EDO (such as 94) achieves less than 2 inconsistencies in the [[25-odd-limit]] or no-25's [[27-odd-limit]] then we don't consider a record to be set to give a chance to larger EDOs that are often interesting for having better approximations (of the intervals mentioned or of other intervals in higher limits). The logical stopping point is [[311edo]] due to its extreme efficiency and elegance as a [[23-limit]] and [[41-limit]] temperament (plus a handful of optional large primes). Please note that there may be one or two important 23-limit EDOs missing here, because I've only checked patent val and occasionally a non-patent-val will perform better for consistency, however, one can argue that a patent val representation should be a requirement for any serious 23-limit EDO.

It should hopefully go without saying that by "serious 23-limit EDO" I mean in terms of archetypal and structural importance; to me it's obvious, with the exception of maybe EDOs 46 and 53 (corresponding to [[Eros]] (rank 3) and maybe also [[Amity]] (rank 2)), that any 23-limit EDO must have at least 77 notes, to allow for the fitting of a submajor third ([[21/17]] plus various higher-complexity submajor thirds), a superneutral third ([[16/13]]), a subneutral third ([[11/9]]) and a supraminor third (most notably [[17/14]] and [[23/19]]; equated in any "small" system) between 5/4 and 6/5, corresponding to splitting 25/24 into 5 equal parts. If you do this with one part equated to [[81/80]] you get [[absurdity]], explaining its non-absurdity and, to the contrary, ''intuitiveness'', as a [[29-limit]] temperament (given that prime 29 is essentially free for multiples of 7 EDO). If you instead choose to exaggerate 81/80 to 2 parts you get an extension of 5-limit [[artoneutral]] (I specify 5-limit as [[80edo]], one logical tuning for it, uses a different mapping for 7).

== Novation Launchpad isomorphic keyboard code ==

The code and usage/debugging instructions are the same as for the Novation Launchpad Pro MK3, so see [[#Novation Launchpad Pro MK3 isomorphic keyboard code]].

 

Note that in theory, any Launchpad with programmer mode should work, so any MK3 model such as the Launchpad X and the cheaper (but not velocity-sensitive) mini version of that should work.

 

A launchpad X is potentially recommendable as having more comfortable/similar side/control buttons so that you get what feels more like a proper 9x9 grid (also due to being less costly), as the Pro MK3 has hard side-buttons that require significantly more pressure, though in both cases note that these buttons do not have pressure sensitivity so depend on the default velocity outputted by the program.

(More generally, Launchpads are '''''very''''' affordable xen MIDI instruments, nearly optimal for xen in that (with the help of the code below) they provide a fully customisable isomorphic MIDI keyboard with custom highlighting options. Also note that the tuning itself is not specified by the program; only the layout, though for the aforementioned large tunings the code will give you a .scl file to use, with all such .scl files using the same MIDI mapping, but requiring the base MIDI note/reference being 0.)

== Novation Launchpad Pro MK3 isomorphic keyboard code ==

This code is licensed under the AGPLv3 (https://www.gnu.org/licenses/agpl-3.0.html), a version of the [[wikipedia:Affero General Public License|AGPL]] corresponding to the [[wikipedia:GNU General Public License#Version 3|GPLv3]].

 

'''It should be compatible with any Launchpad that has programmer mode; it has been confirmed to work for the Launchpad X so will likely also work for a Launchpad Mini MK3.'''

 

NOTE: I discovered it was possible to use custom colour palettes after I'd spent a lot of time making these rainbows using the rather limited and uneven set of factory colours. I haven't tested using this yet, but for those who want to take that route to achieve a more even rainbow, here is the link: https://fw.mat1jaczyyy.com/

 

ALSO: This should go without saying but take care of your launchpad! If you wipe it don't expect it to be properly responsive until fully dry and even then wiping it can have risks if the liquid goes inside. Similarly, do not bang it and probably don't leave it upside down (especially if for long periods of time) in case it causes the velocity sensitivity to go weird. Treat it as an instrument. If you do all this, it should be fine to use it for its intended purpose: just don't press ''too'' hard; try not press with more velocity than the buttons actually require, if possible. (Because of my silliness (not heeding such obvious procedures) there is a possibility that I may have weared my launchpad slightly in that I think I now require more pressure for the pressure-sensitive pads. I thought it responsible to add this note about taking care of your launchpad, as we are technically using it in a nonstandard way by treating the buttons as though they were just insensitive pads that require extra velocity/pressure.)

 

 

The most potentially difficult part is that depending on what OS you are using, how you have Python installed, what version, etc. there can be complications so that running <code>pip install rtmidi</code> in a terminal does not work. I list potential issues below, so please read carefully for something applicable to your case if it isn't going smoothly.

 

0. Technically not an issue with rtmidi, but an easy one to solve: you forgot to update the firmware of your launchpad to be up-to-date via the official site: https://components.novationmusic.com/

 

1. The easiest issue is if you have a version of Python 2 installed (regardless of whether you have Python 3 installed), then sometimes <code>pip</code> and <code>python</code> refer to Python 2, so use <code>pip3</code> and <code>python3</code> instead wherever applicable. Alternatively, if you don't need Python 2, uninstalling it may help.

 

2. If you installed Python 3 but it doesn't work on command line, maybe you haven't used an official installer, as that usually shouldn't be an issue, or if you did use an official installer, you may not have marked the checkbox that makes it change PATH environment variables for you automatically, in which case adding the location of the Python 3 (and potentially pip) executables should fix it.

 

3. <code>rtmidi</code> seems to install but there's issues when trying to use it; installing <code>python-rtmidi</code> may help in such a case. That's why I have "pip install mido && pip install python-rtmidi" with a note about the loopMIDI requirement on Windows as the default/simplest installation recommendation present at the beginning of the code where I <code>import mido</code>.

 

4. If you are getting a long error where towards the end there is <code>error: Microsoft Visual C++ 14.0 or greater is required.</code> (which might happen if you are using an older version of Windows) then try <code>pip install --only-binary :all: rtmidi</code> which will save you a huge amount of trouble if it works. Versions apparently should be available for almost every relevant version of Python 3, so if it isn't, try a different version of Python 3 if you know how. If your system doesn't use Python 3 and you installed it, it should definitely be safe to uninstall the current version.

 

4.1. I haven't seen this issue, but possibly if <code>pip install --only-binary :all: rtmidi</code> seems to work but then brings an error when trying to use the code, try <code>pip install --only-binary :all: python-rtmidi</code> in case it helps.

 

5. If you are on Windows, make sure you have [https://www.tobias-erichsen.de/software/loopmidi.html loopMIDI] installed and running with the default port name! (The default name should work; the code searches for a name starting with "loop".)

 

'''Mix and match these solutions as you find them potentially relevant to your situation, and hopefully you should be able to get it working.'''

 

print( str(steps)+'\\'+str(edo) if args.get('backslash') or args.get('backslashes') else int(.5 + 10000 * steps/edo*1200)/10000 )