User talk:Rperlner
Octatonic Groove
Hi Rperlner, welcome to the Wiki đ Thanks for sharing your pieces! (the 48-EDO version makes more sense to me) Best regards --Xenwolf (talk) 10:29, 31 October 2020 (UTC)
- BTW, the page on the octatonic scale https://en.xen.wiki/w/Octatonic_scale looks very minimal at present, which seems a bit odd for such a widely used scale. Would that be the natural place to add my idea regarding partially detempering the octatonic scale (treating it as a rank-3 2:3:5:7:17 subgroup temperament, with 50/49 and 85/84 tempered out, but not 36/35)? What else ought to be added? --Rperlner (talk) 18:57, 30 November 2020 (UTC)
Thanks! Yeah, Everyone I've talked to seems to like the 48-EDO version better. I also have a 26 edo version I like quite a lot, which I'll get around to uploading eventually. Pleased to meet you. -- Rperlner
Scherzo in 26 EDO
Hi Ray,
your Scherzo in 26 EDO sounds great. The notation looks quite uncommon to readers of classic music but interesting. After a bit of calculation I found out that the accidentals actually cause a 1\26 shift. Notating the piece in "B" causes that no double-flats have to be used (also F# and C# would allow this). I think we should have at least one article about circle-of-fifths notation(s) in the XenWiki. Thanks for sharing. --Xenwolf (talk) 13:24, 14 November 2020 (UTC)
PS: the sixfold forte in the 3rd-last bar before Fine seems like a glitch to me.
I'm glad you liked my scherzo. I did indeed choose the key of B to try to minimize double accidentals. (Strictly speaking, anything can be notated without double flats, since Dx = Cbb etc. in 26 edo). Regarding circle-of-fifths notation. Is it not covered (albeit briefly) by https://en.xen.wiki/w/Alternative_symbols_for_ups_and_downs_notation ? Or did you have something more devoted specifically to the traditional usage of #s and bs in pythagorean and meantone tunings? (Note: There were a number of ETs the article claimed couldn't be notated in Musescore. I was able to confirm that they can be notated in the version of Musescore with the n-tet tuner plugin that I have, using the double sharp and double flat arrow accidentals. I removed the inaccurate sentences.) Regarding the sixfold forte. I did mean to put it in. Musescore just wouldn't play that note loud enough so I tried extreme measures. It probably shouldn't be taken as instructions to any human performers who might actually want to play it some day. --Ray
Removal
Seems that you summarized by describing what you did, unfortunately not why. Let me ask here instead: are multiple sharps and flats now possible. Where is the limit for this? --Xenwolf (talk) 20:41, 18 November 2020 (UTC)
Sorry about that. I intended to, but accidentally saved the changes before I put the comment in. These systems can be used in musescore. Musescore has double sharp, double flat, and double sharp and double flat with arrows, and was able to spot check that these work. The Musescore plugin documentation also says Musescore plugin to retune and pitch up/down notes in any EDO ranked from flat-2 to sharp-8. (Supports all EDOs from 5-72 except 59, 66, and 71. Also supports larger edos up to 117 that are rated with a sharpness of up to sharp-8). See https://github.com/euwbah/musescore-n-tet-plugins/blob/master/README.md
- No need to apologize. Good to know.
- Another question for refinement: Is there a way to use triple, quadruple etc. sharps and flats? I know that these are not available in classic notation but theoretically it's possible even if unusual to reach every note in higher order EDOs (above 35) entirely by stacking fifths. --Xenwolf (talk) 21:51, 18 November 2020 (UTC)
- I don't see any way to use triple/quadruple flats/sharps in MuseScore, and the same readme as I quoted before says: "Triple flats and sharps and not supported as MuseScore does not provide these accidentals." --Ray
- Only double flats through double sharps are available as of MuseScore 3.5, whereas in edos with very flat fifth, triple or more are often required to access all the notes. As I said in Talk:Circle-of-fifths notation:
- > Without higher-order sharp/flats, larger edos are very limited. 26edo, for example, requires Gx to Abb to access every note in the key of C major. Now modulate to any key with more than three accidentals and boom.
- Fortunately, MuseScore 3.6 will introduce triple sharp/flats, but that still doesn't release edos as flat as 33 or 40. FloraC (talk) 05:52, 19 November 2020 (UTC)
- I think these need to be finalized first, and as it stands, things are really complicated for EDOs that don't temper out the Rastma- think 159edo, which I'm trying to come up with a good notation system for... Oh, and yes, I do indeed plan on having my notation system use variations of the demisharp, sesquisharp, demiflat and sesquiflat accidentals- I mean, I do have a background in 24edo after all... --Aura (talk) 03:34, 23 November 2020 (UTC)
- Has anything changed since the state reflected by the last comments in https://en.xen.wiki/w/Talk:159edo_notation (October 16th, I think)? In general what you're proposing seems reasonable. One additional thing I might hope for, is that in systems that temper out the Rastma, the accidentals that differ by a Rastma be taken as synonyms of the normal quartertone accidentals by the Musescore plugin. I like being able to switch the tuning from one EDO to another and have it sound as similar as possible given the EDOs. P.S. On the subject of the Rastma, I recently noticed that the tridecimal equivalent of the Rastma, 512/507 i.e. what you temper out to make 16/13 half of a perfect fifth wasn't in the table of small commas https://en.xen.wiki/w/Small_comma and added it. I got a somewhat non-catchy name for it from http://www.huygens-fokker.org/docs/intervals.html . Any opinion on whether I could give it a catchier name e.g. Tridecimal Rastma? --Rperlner (talk) 04:16, 24 November 2020 (UTC)
- The most recent comments in the last section of the 159edo notation talk page reflect the current state of affairs for the most part, but something tells me we have yet to finalize things. I'm glad you think my proposals to be mostly reasonable, and I do agree that in systems that temper out the Rastma, the accidentals that differ by a Rastma should be taken as synonyms of the normal quartertone accidentals by the Musescore plugin. I'd be happy to get your input on this, and we need to get Xenwolf back into this as well. --Aura (talk) 05:25, 24 November 2020 (UTC)
- You say that you like being able to switch the tuning from one EDO to another and have it sound as similar as possible given the EDOs... Well, I must point out that 159edo can pull some serious shenanigans on this front, mimicking 12edo, 14edo, 17edo, 19edo, 22edo, 24edo, 27edo, 31edo, 35edo, and 41edo- yes, I'm currently writing a song that changes between these different retunings mid-piece. Yes, that means I would like to see representation of both 81/80 and the rastma, and I do have some ideas for that- namely separating out the syntonic arrows into their own glyphs, which then can be combined with another combining glyph representing the rastma. --Aura (talk) 05:25, 24 November 2020 (UTC)
- Tridecimal Rastma doesn't sound like the most catchy name for 512/507, and "Rastma" itself seems to be related to "Rast", which is a term from Turkish, Arabic and Persian music. Therefore, we need something better, and I'll be happy to discuss this with you. --Aura (talk) 05:25, 24 November 2020 (UTC)
- Regarding picking a name for the 512/507 comma, I have two lines of thoughts. First, In Pajara-10, I have found it useful to split the chroma in half to introduce 13-limit (as well as 19, and 23 limit) intervals. This seems most directly related, in terms of scale structure, to tempering out 512/507, although the 169/168 buzurghisma/ dhanvantarisma is also tempered out in the process. Not sure what name this implies, but that 13-limit extension of Pajara should probably be added to the wiki as well, although I'm not sure how to fill in some of the fields "e.g. Nice value" off the top of my head.--Rperlner (talk) 22:24, 24 November 2020 (UTC)
- My second line of thought is that One might interpret Maqam Huzam as 1 - 13/12 - 16/13=39/32 - 13/10 - 20/13 - 13/8 - 20/11 - 2. This necessarily suggests 512/507 is tempered out and would suggest the name "Huzama" for the comma. OTOH, Huzam could also be interpreted as 1 - 12/11 - 27/22 - 9/7 - 14/9 - 18/11=44/27 - 20/11 - 2. --Rperlner (talk) 22:24, 24 November 2020 (UTC)
- A couple updates. I see the fundamental issue as being whether the practice of Maqam Huzam in Arabic traditional music is implying 13 limit ratios. I already know Maqam Huzam is notated with quartertone accidentals, so this would be a fair reason for calling 512/507 the Huzama if the implied ratios are 13-limit. I think the clearest indicator is whether the interval Ed-Ab is tuned closer to 13/10 or 9/7. Unfortunately, actual pitch measurements of Arab rather than Turkish scales seem hard to come by. I found a couple of theoretical sources which would imply this interval is tuned closer to 9/7 e.g. https://www.alsiadi.com/Maqam_Huzam.html and the "Egyptian tuning of Amin Ad-Dik" reported in table 4.12 of Ozan Yarman's doctoral Thesis. However, literal 24-EDO would imply 13/10ths, and that has a long history in Arabic theory and practice (e.g. I've seen multiple reports that Arabic qanuns typically don't have notes outside 24edo.) Another point in favor of 13/10 is that the 9/7 tuning results in an unusually wide Augmented second from Ab to B (The augmented seconds in Hijaz tetrachords are generally described as being smaller than a 12-edo minor third, but this would be larger.) In any event, I may try to contact Ozan Yarman as his email is listed on some of his papers. His specialty appears to be Turkish rather than Arabic music, but he seems knowledgeable about both. --Rperlner (talk) 03:48, 4 December 2020 (UTC)
- The name for 44/27 will have to be related to that of 27/22. I personally call 44/27 the "Lesser Alpharabian Neutral Sixth" with 18/11 being the "Greater Alpharabian Neutral Sixth". The reason why I would do this is because both 44/27 and 18/11 result from modifying Pythagorean intervals by 33/32. I call 27/22 the "Greater Alpharabian Neutral Third" and 11/9 the "Lesser Alpharabian Neutral Third" for the same reasons. --Aura (talk) 22:57, 24 November 2020 (UTC)
- As an aside, I do think it would be helpful if we also looked at Alpharabian tuning and My Ideas on Tonality for ideas on how to deal with interval names and stuff such. --Aura (talk) 05:33, 24 November 2020 (UTC)
- You said that you left a comment on Talk:Circle-of-fifths notation but I don't find it there. Maybe you only previewed it but forgot to save. --Xenwolf (talk) 06:26, 19 November 2020 (UTC)
Space Tour and 159edo
I have an update myself. I recently finished a song that I call "Space Tour". This song demonstrates what 159edo is capable of by means of a near-perfect approximation. I'd like to hear what you think of the song. --Aura (talk) 04:09, 4 December 2020 (UTC)
- Neat song! I like the idea of building to a large tonality by exploring smaller regular subsets. It reminds me of your earlier work âAnticipationâ, which I also liked quite a lot. And I agree that 159 EDO retains a lot of the character of the smaller temperaments it is approximating. I also liked the general sound quality. What software do you use? âRperlner (talk) 14:31, 4 December 2020 (UTC)
Oh, and I should have thought of this earlier, but when you contact Ozan Yarman, feel free to tell him about my work with 159edo, as he seems to have been at least somewhat interested in 159edo in the past. --Aura (talk) 04:13, 4 December 2020 (UTC)
Diatonic Modes
Hey, I listened to your Phrygian Fugue in both 55edo and 12edo, and I have to say your approach to the diatonic modes seems to differ from mine. I also want to ask- what you think about Locrian mode? --Aura (talk) 22:44, 5 December 2020 (UTC)
- Interesting. How do you see your approach and mine to the diatonic modes differing? Regarding Locrian mode. I haven't written anything extensive in Locrian Mode as yet, but I have done species counterpoint exercises in it, and it seems entirely workable, at least for that purpose. I don't feel like I can really get a restful feeling on a diminished triad, but there's no reason you need to include the 5th if you want to rest on the tonic. I mean, that's the standard treatment of a V7-I cadence, even in the obviously-tonal major mode. Clearly in Locrian, a normal V-I cadence isn't an option, but that's true in Phrygian too for all practical purposes, and I clearly think you can make a song out of that. --Rperlner (talk) 03:40, 6 December 2020 (UTC)
- Did you know that "Space Tour" actually uses Locrian mode? It actually occurs in the following portions of the song:
- 0:14-1:12
- 7:30-8:30
- 14:52-17:04
- Furthermore, as per my relevant comment on the Space Tour page on reddit, I even give examples of how Locrian chord progressions operate. What I didn't mention on reddit is that Locrian is even capable of circle progressions with just a fixed set of pitches if you play your cards right. --Aura (talk) 04:08, 6 December 2020 (UTC)
- For a more thorough example of my treatment on the other modes, see my page on the matter. I'll admit that one of the sample songs needs replacing, but still. --Aura (talk) 04:09, 6 December 2020 (UTC)
- I hadnât noticed that these passages were in Locrian, but now that you mention it, I especially like the choice in your 12 EDO section as a way to set up the 2EDO passage. I do have a question regarding your general statements about using Locrian: I entirely agree that an incomplete tonic chord (lacking the 5th) is a good way to establish a tonal center. But you also say that several other chords need to be incomplete (lacking a 3rd). Iâve generally found complete triads to be entirely usable (except for the tonic) in Locrian. Why do you see the need for incomplete chords on other scale degrees? Rperlner (talk) 18:38, 6 December 2020 (UTC)
- Voice leading is one of the major concerns, and, more important than that is the need to ensure that the Tonic still retains the feeling of being the tonal center. The way most of the other chords in Locrian are structured when in their complete form often makes it seem like some other note is the actual tonal center, and that's the sort of thing that destabilizes Locrian mode- at least to the ears of many music theorists. --Aura (talk) 18:45, 6 December 2020 (UTC)
- I'm not saying that complete chords on other scale degrees aren't usable at all, but you still have to be careful with the few that you can actually get away with when the Tonic chord is reduced to just the Tonic and the Mediant. A notorious example of a chord that you don't want to have in complete form under any circumstances is the Submediant chord as it contains the entire Locrian tonic chord, and makes it seem like the Submediant chord is actually the tonal center. An even more notorious example is the chord built on the flat-2 as that chord is particularly likely to be tonicized if it is in complete form, and it requires careful setups and follow-ups to use it even in incomplete form. --Aura (talk) 19:23, 6 December 2020 (UTC)
- I see where you're coming from, but in my experience, these chords do not seem as problematic as you suggest. Even something normal like: i(83)-VI-II(6)-i(dim,64)-bV sounds fine to my ear, with the Locrian root clearly sounding like the tonic, as long as the voice leading is what you'd expect ignoring that it's in Locrian. It probably helps that the first 3 chords are just tonic, submediant, Neapolitan from common practice music. I uploaded an image of some of my (not that) old counterpoints for reference on how I write in Locrian. https://en.xen.wiki/w/File:Locrian_Counterpoints.jpg . I'm also writing a Fugue in Locrian, at your (sort of) suggestion (sounds best in 12 EDO, somewhat boringly), but it will likely take a few weeks. --Rperlner (talk) 00:46, 9 December 2020 (UTC)
- It may work for brief periods of time- especially when you introduce the perfect fifth above the tonic as an accidental- but over time, the more normal stuff seems to have a way of destabilizing the mode, and yes, the fact that the first three chords are tonic, submediant (a.k.a. contramediant) and Neapolitan (a.k.a. reverse lead) are part of what make it workable in this case, but I'd be wary of of using the diminished tonic triad right after a neapolitan chord- you may get away with that every once in a while assuming you use the right inversion, but you won't get away with it every time, and definitely not if you attempt it too frequently. I mean, whereas most people attempt to work with shorter passages in Locrian at most- and even then they use fairly simple versions of the chords- I try to work with it for longer passages using richer, more extensive chord structures. --Aura (talk) 02:30, 9 December 2020 (UTC)
Email exchange with Dr. Ozan Yarman
I am posting an email exchange I had with Dr Ozan Yarman on the possible naming of the tridecimal neutral thirds comma (512/507) "Huzamma".
Hello Dr. Yarman,
My name is Ray Perlner. I am interested in microtonal composition and have recently been looking into Turkish and Arabic traditions in tuning.
I recently joined Xenharmonic wiki, a major online resource on the theory of musical tuning. One of my first edits has been to add to the list of commas -- the comma that is implied to be tempered out when using quarter-tone accidentals to notate 13-limit intervals, 512/507. As a follow up, I have been looking into choosing a catchier name for the comma than the present name, "tridecimal neutral thirds comma."
In discussing this on my talk page ( https://en.xen.wiki/w/User_talk:Rperlner ) with another user, Aura, we came upon a possible name for the comma, the "Huzamma," based on the Arabic Maqam Huzam, on the grounds that it is notated with quarter-tone accidentals, and may be used in a way that implies 13-limit intervals. But, neither of us was entirely sure about the latter point and we wanted to consult someone more knowledgeable about the subject before committing to the name. Aura, who is a big fan of your work in 159EDO and has also worked with 159EDO, recommended you. Do you have any thoughts on the 13-limit implications of Maqam Huzam, or the naming of the 512/507 comma?
Thank You,
Ray Perlner
Dear Ray, very glad you wrote to me. Sorry for my delay in responding to you and to Aura. I've been exhausted these past days and had to rest the whole day until late hours.
Now, back to the tridecimal neutral thirds comma. If I understand you correctly, one initially has, for instance,
13/10 454.214 cents
and
72/55 466.278 cents 55/42 466.851 cents
representing the Karjighar makam's ascending "perde hisar" in the former case (tonic is acute Bb), and the Huzzam makam's ascending "perde hisar" in the latter case (tonic is C). For the descending melody scenarios these ratios go down a notch (13/10 may become Huzzam's "perde huzzam" in descent).
Were the desire to temper them to a single median or mean note, one would first need find the primes to generate them and temper one or more of those primes to approximate values so as to converge to a single note. But you more specifically require, if I understand correctly,
13/10 times 512/507 = 6656 / 5070 = 256/195 = 471.2036 cents for the "ascending or nominal perde huzzam" which is "perde hisar"
or otherwise
55/42 divided by 512/507 = 27,885 / 21,504 = 9295 / 7168 = 449.8611 cents for the descending or the real namesake "perde huzzam".
Let's pick the former route for simplicity. Thus we have "13/10" as the lowerbound and "256/195" as the upperbound, while the actual target is somewhere between. The prime factors for 256/195 are "2^8 / (3*5*13)". The prime factors for 13/10 are straightforwardly "13 / (2*5)". We can dismiss the "13th harmonic" specifically and focus instead on the octave "2" and/or the octave+fifth "3" and/or the two octaves+major third "5".
Therefore, as an example:
[1199 + 1199 + 1199 + 1199 + 1199 + 1199 + 1199 + 1199 cents] - [ 1909.9446 + 2780 + 4,440.5277 cents]
=
[4,440.5277] - [1199 + 2780]
making 461.5277 cents as some sort of median where we tempered out the 512/507 comma by dint of 1 cent clipped octaves and somewhat wider fifths and narrower major thirds than pure.
Under these circumstances, tempering out the 512/507 comma does indeed reduce the nominal "perde hisar" of Huzzam makam and its "perde huzzam" counterpart in descent to be the same pitch. Thus, verily, you may rename 512/507 to "hĂźzzama" or the "hisarite/hisarine comma".
Yet, bear in mind that it is in fact Karjighar makam that rather delineates 13-limit ratios while Huzzam maqam may rather delineate 11-limit ratios. That is because Karjighar concludes like Ushshaq, which transcends the 11-limit or quarter-tonal perde segah to an evel lower tridecimal perde segah which many, including myself, call "perde ushshaq".
Cordially, Dr. Oz.
Dear Dr. Oz.
Thanks for the reply. It was in fact quite prompt from my perspective. Do not worry about needing rest. We all do. What you write makes sense, but I think my guess about tempering of 512/507 in Maqam Huzam may have been subtly different from what you thought I had in mind.
The interval I suspected might be tempered was in fact that between the 1st and 3rd scale degrees of Maqam Huzam (perde segah and perde neva, I believe.) Here the idea is that the context of the other perdes in the Maqam may suggest this interval is either 16/13 or 39/32 (differing by the 512/507 comma I need a name for.) Here I suspect the other perdes in the Maqam may be heard as being related to the tonic by relatively simple intervals that either suggest perde neva should be at 16/13 or 39/32. In particular the only simple intervals that are near the roughly 450 cent interval from perde segah to perde hisar are 9/7 and 13/10. If this interval is the latter, it would suggest to me that perde neva should be an interval of 16/15th lower, i.e. at 39/32. Likewise, the next scale degree after hisar (I assume it is perde gevast or perde mahur. I typically see it written as b natural when the tonic is e half flat. e.g. https://www.maqamworld.com/en/maqam/huzam.php) is roughly 450 cents below the octave above the tonic, so one might assume it is 20/13 if perde hisar is 13/10. This would suggest that perde neva should be a just major 3rd below perde mahur here, and therefore tuned to 16/13.
In sum, if we can interpret the full scale as something like 1: 13/12 : 16/13 or 39/32 : 13/10 : 20/13 : 13/8 : 20/11: 2, it seems like tempering 512/507 could be important to the musical structure of Maqam Huzam. Alternatively, one could see the 512/507 comma as related from a purely notational perspective to any scale where the 13/12 interval is written using quartertone accidentals in a notation that assumes two chromatic quartertones are equal to a chromatic semitone.
Let me know if the above seems reasonable. Also, you mention the low perde segah that occurs in the Karjighar and Ushshaq Maqams a ratio of approximately 13/12 above the tonic. This might make sense to me in the context of a 12:13:14:16 tetrachord, but this would make the tuning of perde cargah surprisingly low, given that it is written as a note often played on open strings on an Oud for example. Can you give some insight into what is going on here?
Best, Ray
Dear Ray, 13-limit is too low for HĂźzzam in the Turkish understanding. But perde hisar, instead of the tonic perde segah, can be focused on to temper out 512/507 the way I indicated or in a similar fashion.
Cordially, Dr. Oz.
Dear Dr. Oz.
Thank you for your responses. May I reproduce this exchange (with proper attribution) on my talk page.
Best, Ray
Dear Ray,
Just to be on the safe side, I tried the scale you indicated:
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 16/13 359.472338 tridecimal neutral third 3: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 4: 13/10 454.213948 tridecimal semi-diminished fourth 5: 20/13 745.786052 tridecimal semi-augmented fifth 6: 13/8 840.527662 tridecimal neutral sixth 7: 20/11 1034.995772 large minor seventh 8: 2/1 1200.000000 octave
and confirm that 13/10 should be replaced by 4/3 if one should insist on a 13-limit architecture for conformity with an outlandish Turkish understanding of HĂźzzam:
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 117/64 1044.437664 7: 15/8 1088.268715 classic major seventh 8: 2/1 1200.000000 octave
In such a case, where would you have the tridecimal neutral thirds comma eliminated if not regarding between 16/13 and 4/3? Thus, maybe by keeping 4/3 in place and raising the whole structure tonic-wise up by a third or fourth of a syntonic comma?
How about then my HĂźzzam (Turkish Segah, Huzzam and Mustear ver.2 with perde segah on E by Dr. Oz.) key-transposed to C:
0: 1/1 0.000000 unison, perfect prime 1: 392/363 133.060927 2: 40/33 333.040771 3: 175/132 488.180391 4: 147/110 501.975158 5: 3/2 701.955001 perfect fifth 6: 196/121 835.015928 two (undecimal diminished fourth or major third) 7: 20/11 1034.995772 large minor seventh 8: 12544/6655 1097.384272 9: 441/220 1203.930158 Werckmeister's undecimal septenarian schisma +1 octave
where I already understand your 512/507 to be tempered out in the desired manner?
Also, I missed the part about 12:13:14:16 earlier. To tell the truth, some people in Turkey insist perde chargah gets lowered by dint of just such an Ushshaq tetrachord in descent perhaps?
By all means, do refer to what I wrote here in its entirety on your Talk page. I would be interested in what other microtonalists engaged with maqam/makam/mugham/dastgah/etc... think about the whole issue.
Cordially, Dr. Oz.
--Rperlner (talk) 00:04, 9 December 2020 (UTC)
Here is the continuation of my conversation:
Dear Dr. Oz
I have posted the conversation so far on my talk page: https://en.xen.wiki/w/User_talk:Rperlner#Email_exchange_with_Dr._Ozan_Yarman Thank you for granting me permission to do so.
I have a couple of follow up questions, if you donât mind. First of all, when you say you âtried the scale I indicatedâ what exactly do you mean by that? Did you look it up somewhere, or did you listen to it in some software, or something else entirely?
Keep in mind, if itâs the latter, that assuming the 507/512 comma is tempered out, the cents values would need to be altered, for example all the intervals with 13 in the numerator might be ~8.5 cents larger than their just values, and those with 13 in the denominator might be ~8.5 cents flat, or alternatively you might use an equal temperament like 34 EDO that tempers this comma out in its patent val.
Taking the first approach would result in a scale like 0, 147, 351, 463, 737, 849, 1035, 1200. Alternatively, I could see the 1035 being raised to 1080 (on the way up?) to represent 13/7.
Second of all, when you say âoutlandish Turkish understanding of Huzzamâ I assume you mean the analysis comes from parts of Turkey away from the major population centers? Typically, the English word âoutlandishâ means absurd or ridiculous, but the former understanding makes more sense in context.
By the way, this âoutlandishâ Turkish scale looks like it should work the same way as the scale I had in mind, with the pitch marked at 16/13 needing to be lowered to 39/32 in order to make a perfect fourth with 13/8 and outline the Hijaz tetrachord in the middle of the scale.
Finally, can you comment on the Arabic understandings of Huzam, which is what I originally had in mind? This scale is notated several places using quartertone notation, and it is similar to the Turkish scales you mention, but, at least taking the notation literally, does not have either a perfect fourth or a perfect 5th above the tonic. Both perfect intervals seem like too strong relationships with the tonic to be missed by the notation if they are really present in the Arabic scale.
Best, Ray
Dear Ray, I meant raising 1/1 and 4/3 up while keeping the 13/12 and 16/13, etc... in place. Sorry if I expressed myself in a roundabout fashion.
The scale you indicated that I took as reference was when you said " ... if we can interpret the full scale as something like 1: 13/12 : 16/13 or 39/32 : 13/10 : 20/13 : 13/8 : 20/11: 2, ..."
Yes, by outlandish I tend to mean more Arabicized-Kurdicized parts of southeastern Turkey, and maybe Lazica and Georgic lands of the Pontus. By that I mean no racism of course. Take it rather as a pun on the actual ridiculousness of the supremacism of "white-Turks" of "de facto Turkey" close to the Aegean.
Thus, I meant the other way round than what you said here:
> Taking the first approach would result in a scale like 0, 147, 351, 463, 737, 849, 1035, 1200. Alternatively, I could see the 1035 being raised to 1080 (on the way up?) to represent 13/7.
I think Sami Abu Shumays would be a better source to comment on the Arabic Huzzam. The issue is, if I had to say something about it, to quartertonalize some pitches and to semitonalize some others.
Cordially, Dr. Oz.
Dear Dr. Oz
Thank you for your recommendation to ask Sami Abu Shumays about Arabic tunings of Huzam. I shall look him up.
I do have a question about your last email, though. I am not sure I understand what you mean by "raising 1/1 and 4/3 up while keeping the 13/12 and 16/13, etc... in place. " It seems doing that would not temper out the 512/507 comma. It seems like tempering that comma tends to raise the representation of the 13th harmonic, so these pitches (not containing any factors of 13) would need to move in opposite directions against 13/12, which has 13 in the numerator, and 16/13, which has 13 in the denominator. I could only see that strategy working if it was 14/13 and 16/13, say.
In any event, can I take as a summary of this exchange that, while there are a variety of versions of Huzzam in use in Turkish and neighboring regions, some of them may reasonably be analyzed as tempering out the 512/507 comma?
Finally, Aura requests that I ask you for comment on his composition https://en.xen.wiki/w/File:Space_Tour.mp3 . I think he sees you as somewhat of a kindred spirit due to your shared interest in 159 EDO, which this composition uses. While I'm asking about compositions, you may also want to check out one of mine https://en.xen.wiki/w/File:A_stroll_through_some_retuned_maqams.mp3 , which tries to interpret maqams as scales in 34 edo and use them contrapuntally.
Best, Ray
Dear Ray, forgive me once more for the late reply. Here is the situation regarding what I'm trying to say but failing at it...
> How about then my HĂźzzam (Turkish Segah, Huzzam and Mustear ver.2 with perde segah on E by Dr. Oz.) key-transposed to C: > > 0: 1/1 0.000000 unison, perfect prime PERDE SEGAH > 1: 392/363 133.060927 > 2: 40/33 333.040771 > 3: 175/132 488.180391 > 4: 147/110 501.975158 > 5: 3/2 701.955001 perfect fifth > 6: 196/121 835.015928 two (undecimal diminished fourth or major third) > 7: 20/11 1034.995772 large minor seventh > 8: 12544/6655 1097.384272 > 9: 441/220 1203.930158 Werckmeister's undecimal septenarian schisma +1 octave
Consider then the 175/132 (488 cents) as our "tempered pitch" vis-a-vis an imaginary tridecimal perde hisar counterpart which we can assume to be 169/128 (481 cents) located downwards from 4/3 (if you will forego my 441/220 "brighter octave" attempt leading to 147/110 as the "perfect fourth").
Were we to re-position the whole thing so as to start HĂźzzam on E that I personally nominate as perde segah (where C is now 1/1 and hence the ordinary Arabic-wise consistent perde rast):
0: 1/1 0.000000 unison, perfect prime 1: 55/49 199.979843 quasi-equal major second 2: 64/55 262.368344 3: 25/21 301.846520 BP second, quasi-tempered minor third 4: 99/80 368.914230 PERDE SEGAH 5: 147/110 501.975158 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 16731/10240 849.969554 9: 105/64 857.094621 septimal neutral sixth (tempered? hisar) 10: 1323/800 870.889388 11: 99/56 986.402038 12: 297/160 1070.869231 13: 441/220 1203.930158 Werckmeister's undecimal septenarian schisma +1 octave
and replace the 105/64 with 64/39, we could re-express the whole thing as:
0: 1/1 0.000000 unison, perfect prime 1: 55/49 199.979843 quasi-equal major second 2: 64/55 262.368344 3: 25/21 301.846520 BP second, quasi-tempered minor third 4: 99/80 368.914230 PERDE SEGAH 5: 147/110 501.975158 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 13/8 840.527662 tridecimal neutral sixth (UNTEMPERED HiSAR) 9: 64/39 857.517337 39th subharmonic (TEMPERED? HiSAR) 10: 1323/800 870.889388 DiK HiSAR 11: 99/56 986.402038 12: 297/160 1070.869231 13: 441/220 1203.930158 Werckmeister's undecimal septenarian schisma +1 octave
To further undo my "brighter 441/220 octave" setup, you can replace the last unwieldy 1323/800 "dik hisar" with 33/20 and even the 147/110 "perde chargah" with 4/3 so that the whole panorama between segah and dik hisar will be revealed according to our liking:
4: 99/80 368.914230 PERDE SEGAH 5: 4/3 498.044999 perfect fourth PERDE CHARGAH (for HĂźzzam+Segah) 6: 7/5 582.512193 septimal or Huygens' tritone (PERDE HiCAZ for MĂźstear) 7: 3/2 701.955001 perfect fifth PERDE NEVA 8: 13/8 840.527662 tridecimal neutral sixth UNTEMPERED HÄ°SAR 9: 64/39 857.517337 39th subharmonic TEMPERED? HÄ°SAR 10: 33/20 866.959229 DiK HiSAR (for makams Segah and MĂźstear)
Feel free to add this additional discourse to your TALK page if you so desire.
Cordially, Dr. Oz.
P.S. I'm listening to Aura's "Space Tour" as it is raining outside at 10:00 during night time here. The beeping sounds in the beginning and end are nice, but the choir and later the calliope does not always mesh so well I think. On the other hand I very much like the occasional microtonal pitch level changes. However there are too many octave and unison passages that I would rather replace with some microtonal flavored chords and more microtonal commatic/quartertonal/etc... level shifts. Anyway, it gets much better halfway and towards the end. I recommend that he doesn't shy away from being xenharmonically bold! (which I should also try myself...) The story is also catchy! Regardless of any criticism, I support 159-tET endeavors of this kind. :)
P.S.2 After that I took a look at your song. I very much appreciate 34-tET as a very valid alternative that just so happened to perform even better than 41-tET for approximating Turkish masters' "histogram autopeaks" in my latest published study here:
Ozan Yarman: âSearch for an Optimal Tonal-System for an Authentic Turkish Soundscape,â Near Eastern Musicology Online 5 9 |2020-11|p.âŻ73â111.
> 15 AUGUST 2020, Nemo Journal (last revision draft), O. Yarman, "SEARCH FOR THE OPTIMAL TONE-SYSTEM FOR AN AUTHENTIC TURKISH SOUNDSCAPE: WEIGHING SEVERAL MORE THEORETICAL MODELS ON MAKAM MUSIC AGAINST PITCH-HISTOGRAMS". > http://www.ozanyarman.com/files/WeighingAgainstHistograms_SEARCH_FOR_THE_OPTIMAL_TONE-SYSTEM.pdf > ---CONCOMITANT COMPUTATIONAL MUSICOLOGY SET: http://www.ozanyarman.com/files/searchfortheoptimaltonesystem.zip
So, I congratulate you and Aura for your deep interest in microtonality and Makam music!
--Rperlner (talk) 01:04, 13 December 2020 (UTC)
Posting a couple more followup emails:
Dear Dr Oz.
Thanks. That makes much more sense. My only quibble then would be that it seems like it would make more sense to use 5/4 and 5/3 respectively for the tuning of Perde Segah and Dik Hisar wrt Perde Rast in the context of Turkish music, as these ratios are simpler than 99/80 and 33/20, and just as close to the measurements given in table 4 of your paper on Yarman-36, for example. This would then tend to suggest the size of the bounding interval of the Turkish Huzzam tetrachord should be 13/10. With these values in place, it seems clear that the tempering you suggest on Hisar is still possible, although I'm not sure exactly what musical context would motivate one to do so. One gets a simpler relation with Chargah, for example, if Hisar is tempered to 64/39, but the same could be said if Hisar is instead tempered to, say 44/27, which is closer to 13/8.
Thanks for your comments on my and Aura's music, and I'm glad to see some study of 34 EDO in the context of Makam music.
Best, Ray
Dear Ray, the "untempered low hisar" is, for my tastes at the very least, much too below in general for Turkish HĂźzzam (better suited for Karjighar?) -- while 5/4 as the tonic (viz., perde segah) in comparision to a 1/1 perde rast pivot is too high as a finalis (Rauf Yekta argued a century ago for the schismatic Pythagorean equivalent as the true segah while 5/4 was for him an "approximate ratio"). The idea is to create as close a semblance to a perfect fourth as can be between segah and hisar while not deviating from the HĂźzzam gestalt where perde hisar is "quartertonal" (not "commatic"). In fact the presence of just such a perfect fourth thereat is a requisite per se for the Turkish HĂźzzam as far as I understand it.
In the paper I shared with you, Yarman-36 did not perform so well compared to 34-tET and 29-tET. Still it was a good try and even so, my 5/4 is lower and "beats proportionally" in major chords at home keys.
Cordially, Dr. Oz.
p.s. I follow the practice of using entire lowercase for perde names and single uppercase for maqam names. It helps communication better in my opinion. --Rperlner (talk) 04:25, 22 December 2020 (UTC)
- Truth be told, I don't know a lot about Arabic/Turkish/Persian music, but from the sounds of things, 512/507 should be named after "hisar". Since the "rastma" has the "-ma" suffix, perhaps we should call 512/507 the "hisarma". --Aura (talk) 00:46, 9 December 2020 (UTC)
- On another note, I wonder what he'll think about my own work on 159edo. I mean, the main reason I'm a fan of his work on 159edo is because he seems to be among only a handful of other people who have even bothered to seriously consider a mega-edo such as 159edo in the first place. Perhaps, if he's open to listening to a more Western take on 159edo, he can listen to "Space Tour". I'd like to hear what he thinks about that- assuming such Western music is even his cup of tea in the first place- at least in any practical sense. --Aura (talk) 00:46, 9 December 2020 (UTC)
- It's true that other people have expressed interest in other mega-edos, but in these cases, most of the the mega-edos in question suffer from having too small of a step size, while another one, 152edo, is not as consistent in the 17-odd limit. --Aura (talk) 02:19, 9 December 2020 (UTC)
- Hi Aura. Just replying to check that you saw I posted more emails from the exchange with Dr. Yarman, including his comments on your Space Tour. Regarding the original topic: Dr Yarman's observations have mostly concerned the Turkish tuning of Huzzam, which is different from the Arabic tuning I originally had in mind. I agree that it is possible to temper 512/507 in a way that only affects the tuning of Hisar in the Turkish variant, but, I'm still not sure it makes sense to temper 512/507 as opposed to say 352/351 in that case. On Dr. Yarman's recommendation, I also plan to follow up with Sami Abu Shumays on the Arabic version of Huzam, and whether it makes sense to think of that as tempering 512/507. --Rperlner (talk) 04:17, 15 December 2020 (UTC)
- I saw it. Aside from the fact that he doesn't seem to know that the "calliope" is actually supposed to be a pan flute, I should point out that many sci-fi songs have gotten away with choirs before, most notably, Halo's rather famous main theme. I realize that there should probably be sounds where the choir uses other vowels, and the pan flute should have more variation in technique, but I did what I could with Musescore's soundfonts, that said, there are likely tricks that I don't know for some things regarding the pan flute. I realize that the pan flute is one of the least expected instruments to show up in a sci-fi-based song, but as he unexpectedly notes from later on in the song, it can actually work, as the pan flute actually appears in most of the later sections, including the ending. --Aura (talk) 15:02, 15 December 2020 (UTC)
- Now that I think about it, the pan flute, when implemented correctly, is one of the best instruments to use in a sci-fi piece, because its more organic sound provides for a nice contrast with all the synth sounds and their more mechanized feel. I mean, from my experience, science and tech cannot account for everything, contrary to what some may think, and with that it mind, it makes sense to pick an instrument like the pan flute. It may not mesh with others expectations for what sci-fi should soundlike, but other than that, I see no problem with using it. --Aura (talk) 15:19, 15 December 2020 (UTC)
Stroll impressions
Hi Ray,
Thanks for sharing A stroll through some retuned maqams. Listening to it was an interesting short trip. I really liked the part from 00:46 to 01:02 (Maqam Saba?). Well, I have to admit that the contrapuntal elaborations at the beginning and end did not convince my heavily Baroque-biased ears, but maybe I just misinterpret the melodic lines. If it isn't to much work, would it be possible to add a more detailed timing info to the description? --Xenwolf (talk) 09:12, 11 December 2020 (UTC)
- Hi Xenwolf. I added a bunch more detail into the description. Thanks for the comments. My favorite bit is also 0:46 to 1:02. I'd be interested in knowing which parts of the beginning and end didn't seem so effective. In my defense, I don't think I was really trying to sound Baroque at any point in this song. Despite my protestations to the contrary, I was, in fact, going for a somewhat Middle Eastern vibe, albeit adapting techniques I use when I'm trying to sound Baroque, and knowing in advance that I would fail at sounding authentically Middle Eastern. --Rperlner (talk) 03:47, 12 December 2020 (UTC)
- Hi Ray, interesting that this piece is in 34 EDO, I added a link to it in 34edo #Music. Concerning the notation you are using on the description page: Is there a place where I can read more about it? --Xenwolf (talk) 08:27, 14 December 2020 (UTC)
Locrian Tunings in Different EDOs
Hey Ray, you mentioned that Locrian seems to sound best in 12edo. May I ask which kinds of JI intervals you were approximating when trying to tune Locrian in other EDOs? I think that may have an impact on good Locrian sounds in different EDOs. --Aura (talk) 20:42, 12 December 2020 (UTC)
- My Locrian fugue is done now: https://en.xen.wiki/w/File:Locrian_Fugue.mp3 . I also uploaded a 31 edo version, so you can confirm for yourself it sounds worse: https://en.xen.wiki/w/File:Locrian_Fugue_31_edo.mp3 . As I said on the description page for the 12 EDO version, I think the reason I like 12 EDO for this particular piece (not necessarily claiming this applies to everything in Locrian) is that the subject can be heard as an elaboration of a 5:6:7:8 tetrad in 12 EDO, but not so much other tunings. That said, I was not thinking of just ratios when composing this. Just the usual counterpoint rules: 3rd and 6ths are imperfect consonances and can be used freely in harmony, perfect 5ths and octaves are perfect consonances (i.e. parallels are to be avoided.) Perfect 4ths with the bass and 7ths with the root of a chord are dissonances that like to resolve by having the upper voice fall to a 3rd. Augmented intervals like to expand, diminished intervals like to contract, Avoid dissonant leaps in melodic motion. Handle dissonances as suspensions, passing tones, neighbor tones etc. --Rperlner (talk) 01:45, 13 December 2020 (UTC)
- Okay, I just listened to your Locrian fugue, and I'll admit I had a hard time identifying the Tonic in the chord progressions of this piece. One thing I should take note of quickly is that the Flat-Five- which I call the Tyrant- operates best in Locrian mode when it approximates 64/45 or something in that vicinity. This is because the chord based on the Tyrant actually relies on the interval between the Tonic and the Tyrant in order to provide the strong sense of contrast that makes Locrian mode work best in non-meantone EDOs, the harmonic connection between the Tonic and 64/45 also helps immensely. Hence this is one of the techniques I used in "Space Tour" for writing the Locrian section in 53edo. When the Flat-Five interval is less than 600 cents wide, it actually sounds like it wants to expand rather than contract according to the relevant section of Wikipedia's article on the Tritone, and the reasoning behind this as stated in the article actually makes sense. Thus, in order to actually have the kinds of harmonic motion that lends itself to establishing a more solid sense of Tonality, you might want to consider a different tuning, and more carefully consider my comments in regards to Locrian chord progressions. --Aura (talk) 04:39, 13 December 2020 (UTC)
- Hi Aura. I have considered your advice, but I am not convinced it can be applied to writing a fugue (at least not a fugue in the style of JS Bach, which is roughly what I was going for, aside from the use of a modal subject.) First of all, fugues generally modulate a lot, so it is expected and desirable that there be passages where the tonic is not immediately clear. As long as the tonality is clear at the beginning and end, transitions are smooth, and the piece continually feels like it's going somewhere (whether the destination is clear or not), it should be effective. This applies to a number of other forms in the common practice period as well, such as Sonata Allegro form and scherzo. Second of all, fugues rely on transposing a melody by a variety of intervals other than an octave. This can be difficult to do if the scale structure is irregular. I'm not going to say it's impossible to do with 5-limit-JI-like diatonics as you have suggested, but it's much harder and there's not much precedent for it in the repertoire. Fugues have almost exclusively used Meantone tunings and Meantone-like well temperaments. Where scales like you suggest for diatonic modes have been used effectively is in Indian Raga music, but these are typically played over a drone of a perfect fifth on the tonic -- about as static a harmony as one could possibly imagine. From what I've seen of your works, they are not quite that harmonically static, but they are still neither polyphonic (you seem to use simple melody and accompaniment texture) nor especially modulatory (you modulate sometimes, but they seem more like brief transitions between long stable passages than the driving force behind the structure of a piece.) I would be interested to see how you would approach more polyphonic textures, and forms with more harmonic development. Finally, I'd like to make a brief point about the proper resolution of augmented 4ths and diminished 5ths in the common practice style: It seems pretty clear to me that the proper resolution has more to do with the scale structure providing context for the interval, than the tuning of the interval itself. The fundamental issue is that if two voices a certain interval apart resolve inward by step to a third, then the original interval is, by definition, some sort of 5th. It just so happens that in meantone temperaments the diminished 5th is larger than the augmented 4th, as a side effect of making 5-limit thirds more pure. But, this is not always the case. e.g. Using a historically accurate tuning for Bach's Well Tempered Clavier, the preludes and fugues in remote keys will have augmented 4ths larger than diminished 5ths, but you can check for yourself that they still overwhelmingly resolve the standard way. I also tested the limits of this phenomenon by rendering scale segments outlining a diminished 5th and augmented 4th (BCDEF and FGAB) in extremely non-meantone temperaments using Musescore, and seeing what dyad sounds best after them. In both cases it was C raised by a comma and E, as would be expected from common practice rules about resolving tritones. Tuning may have some effect, but scale structure is far more important. --Rperlner (talk) 04:03, 15 December 2020 (UTC)
- Okay, so scale structure is a more significant predictor of the resolution of tritone-like intervals. I've done polyphony before, but when I do so, it mostly centers around melodies and countermelodies. The accompaniment would be much the same style as in other pieces of mine, however, for something like a fugue, I guess that means I'll have to make more transitions, and make them closer together to see how it works. At this point, I don't seem to have a good inspiration for such a song. --Aura (talk) 15:02, 15 December 2020 (UTC)
- So, I'm reworking one of my other pieces, but it seems to me that the more extensive harmonic development seen in Baroque-style pieces registers to me as a series of rapid-fire key changes. Furthermore, they seem to provide a sense of being unmoored- that is, they create such instability as to express a sense of disorientation, and that to the point where a resolution doesn't really feel like a resolution without careful setup. Therefore, my approach would involve trying to make the destination more clear towards the end of the song especially. What's more, as I incorporate the rapid-fire key changes using Xenharmonic intervals, I find that these key changes are significantly more difficult to work out- though you do reap some interesting rewards for doing this correctly. --Aura (talk) 21:44, 17 December 2020 (UTC)
- Interesting. As another (related only via your writings on Locrian mode) suggestion: You might want to look into Maqam Lami, the Arabic equivalent of the Western Locrian scale as described, for example, here: https://offtonic.com/theory/book/7-9.html#kurd-family . It is described using Pythagorean tuning there and elsewhere, but Arabic intonation is reasonably variable, and at least one diatonic mode is described using JI (or a 53 EDO approximation thereof.) See https://offtonic.com/theory/book/7-9.html#ajam-family. It seems to me that the natural way to extend this JI aesthetic, to the Kurd tetrachords used to construct Maqam Lami, would be to tune them as 1 : 16/15 : 6/5 : 4/3. I think this results in the same Locrian scale as yours, up to a Keenanisma. Maqam Lami is a relatively recent invention and somewhat rarely used, but it is used, so the way it is handled in Arabic music may give you ideas that match with your existing ideas about how to handle the mode. --Rperlner (talk) 02:25, 19 December 2020 (UTC)
- I just looked at the links you sent, and it seems that Maqam Lami- despite the similarities- isn't treated the same way as I prefer to treat Locrian mode. I should mention that while the fourth is often slightly tonicized in Maqam Lami, the fact is that I'd prefer to work with the sixth and even the Flat Fifth when working in Locrian mode, and no, I'd rather not attempt to tonicize them. --Aura (talk) 03:46, 19 December 2020 (UTC)
- In other news, I experimented with replacing the meantone scale with a JI-like scale in Locrian Fugue, using 53 EDO and up and down arrow accidentals (and adjusting for modulations/transposition). I also tried strengthening the effect and getting the smaller minor 3rds to approximate 7/6 using the same accidentals and 34 or 22 EDO tuning. The problem with the obvious 1 : 16/15 : 6/5 : 4/3 : 64/45 =? 7/5 : 8/5 : 9/5 : 2 Locrian scale is that there's a prominent leap of a wolf 4th from D to A in the second measure of the subject, which sounds wonky. I also tried correcting it to a perfect fourth (raising the A by a comma when in B Locrian), but the whole thing still seems a bit off balance, so I still prefer 12 EDO for this song. An interesting experiment, nonetheless. --Rperlner (talk) 02:25, 19 December 2020 (UTC)
- I'm sorry, I should have mentioned both that I use wolf fifths and wolf fourths deliberately and that they are not simply mistuned knock-offs of the 3/2 perfect fifth and the 4/3 perfect fourth, rather, they are intervals with their own distinct character and functionality, and they should be treated as such- a lesson I've had to learn the hard way, and a lesson that I should have shared with you earlier. From the feedback I've gotten, I'd say they have a way of predisposing the chords they are found in towards having certain functions. For example, the 40/27 wolf fifth between A and E in the key of C major has a way of making deceptive cadences all the more powerful on account of the subtle tension provided by their seemingly "off" sound- as if it hammers home to the listener that "we're not done yet". This same subtle tension means that whenever this chord appears, there is bound to be either an increase in tension, or a decrease in tension. For example, a 1/1-32/27-40/27 minor chord on the sixth scale degree of C major (root related to the Tonic by 27/26) will usually be followed up by either G-Dominant-7 (1/1-5/4-3/2-16/9) or B-Diminished (1/1-6/5-64/45) for an increase in tension, or alternatively, F-Major (1/1-81/64-3/2) or D-Minor (1/1-32/27-3/2) for a decrease in tension. A similar functionality exists for the open wolf dyad on the third scale degree of Locrian, as the 1/1-1024/693-2/1 open wolf dyad on the third scale degree of B Locrian (root related to the Tonic by 77/64) will usually be followed up by either F-Major (1/1-3/2-5/2) for an increase in tension, or alternatively, B-Minor (1/1-77/64-2/1) or G-Open (1/1-385/256-2/1) for a decrease in tension. Such is the way that wolf fifths in general seem to function the best. With that, I guess it can be said that one of the main lessons to be learned here is that Locrian's behavior in non-meantone settings is markedly different in some ways from its behavior in meantone settings, and that people's expectations as to how Locrian ought to function can get in the way very easily. That said, I think that if you wish to express things like anger, anxiety and lament, Locrian is just the mode for you. This is especially true in non-meantone settings, as those strident wolf fifths only add to the intensity of the aforementioned feelings, enhancing the mode's more well-known usage in heavy metal and other genres like it. Conversely, if you wish to pull something with a more Baroque-style using Locrian in a non-meantone setting, I'd say this is more difficult, but ultimately worth it if you're trying to express anger, anxiety and lament. Therefore, I'd recommend trying to write more Baroque-style pieces in Locrian using some of the advice I've given you- especially concerning how wolf fifths are best used- as I want to see what comes of that sort of experimentation. --Aura (talk) 03:46, 19 December 2020 (UTC)
- I should point out that the D A wolf fourth leap does kind of work the way you say it should in that the A immediately resolves to the tonic B. However, the resolution doesn't seem very effective. Resolving the wolf fourth outward to the G sounds much smoother to my ear, but of course G is not the tonic I'm looking for. Again I see this as a scale structure thing, where the wolf fourth is wide due to being made from two 9/8 wholetones and a 16/15 semitone instead of a 9/8 a 10/9 and a 16/15. It seems more effective to resolve the interval by expanding out by a 10/9 wholetone and restoring balance than contracting to a minor third by taking back the extra 9/8 whole tone. Anyway, I'll let you know if I ever make another attempt to make a non-meantone diatonic fugue work. --Rperlner (talk) 04:12, 22 December 2020 (UTC)
- Your observations about the resolutions of the wolf fourth are spot on. Indeed, it is not for nothing that the D-A wolf fourth's resolution to B-Minor is not a final resolution- although this provides a decrease in tension, this decrease in tension can be compared to the calm before a storm. In fact, when a given musical phrase contains the D-Wolf-Open-to-B-Minor motion, that motion is often followed up by a motion to F-Major to create a Tyrant half cadence, which closes out that particular musical phrase. The D-A wolf fifth can be thought of as the parallel to the Tyrant chord in the same way that E-Minor is the Dominant Parallel in C-Major- the parallel chord is usually not as strong as the chord to which it acts as the parallel. As to the resolution from the D-A wolf fifth to G-Open, this is followed up by C-Open (1/1-3/2-2/1-3/1) as the chord on the Flat-2 (root related to the Tonic by 16/15), which is in turn followed up by a full Tyrant cadence consisting of F-Major (1/1-3/2-5/2) followed by B-Minor (1/1-2/1-77/32-4/1). Dare I point out that the entire sequence is actually part of Locrian's circle progression, which goes like this- B-Minor, E-Open, A-Open, D-Wolf-Open, G-Open, C-Open, F-Major, and finally, B-Minor. Locrian's circle progression is the strongest progression that Locrian mode has to offer, and because of that, it's best saved for closing out a lengthy passage. --Aura (talk) 05:13, 22 December 2020 (UTC)
- A brief comment on the Locrian circle progression: Root motion by 5ths between open 5th chords presents a pretty limited range of options for voice leading. Voices can either be held fixed, move by step, or leap by a perfect 4th or 5th. The former may be able to be decorated by a neighbor tone figure, the step may be treated as a 9-8 suspension, and the fourth leap may be filled in with passing tones (although this will put the 3rd back in the first chord.) This leaves out a number of the more common contrapuntal decorations you find in the baroque style (e.g. the 7-6 and 4-3 suspensions and their standard elaborations as well as the humble single passing tone.) I'd also note that, except at cadences, I don't think much about what chords I'm using when writing in a fugal style. It's very much a chords from voice leading process as opposed to vice-versa. I guess this isn't necessarily at odds with your advice to use the circle progression at the end of a lengthy passage (i.e. around the cadence). --Rperlner (talk) 19:58, 5 January 2021 (UTC)
- Locrian mode seems to have a way of being more restricted in terms available chord progressions than other modes, and cadences often need more of a set up in Locrian than in some of the others. I'm not saying that your approach to the voice leading and chord progressions is totally off base- it's not- but you do kind of have to plan ahead as you set up your voice leading so that you keep things within the confines of Locrian's style of tonality. This is all the more true for those types of fugue in which you have a main leitmotif that repeats itself at random times throughout your fugue as with Fugue in G Minor by Bach. Nevertheless, I do think I see at least one really good option for decorating the B-Minor (1/1-77/64-2/1) at the start of the circle progression- namely by adding the minor seventh to create (1/1-77/64-16/9-2/1), as this is a common variation of the Tonic chord in non-final environments anyway. I also see melodies involving a passing Flat-2 (located at 16/15 above the Tonic) as being readily available for this purpose. --Aura (talk) 23:27, 5 January 2021 (UTC)
- Those are called "episodes". That said, fugues certainly modulate outside of episodes. See for example this analysis of my favorite Bach fugue (Not my analysis. I found it via some quick Googling): https://tonic-chord.com/bach-prelude-and-fugue-no-4-in-c%E2%99%AF-minor-bwv-849-analysis/ --Rperlner (talk) 01:17, 6 January 2021 (UTC)
- Okay then. It seems to me that I personally would prefer the Subject and Answer of a fugue to be more lengthy passages in more stable keys, even though the Subject is in the original Tonic key while the Answer is in the key located a perfect fifth above the original- at least when we're not working in Locrian mode, as for a Locrian fugue, the Answer seems to need to be in the key located a perfect fourth above the original due to having a flat five. --Aura (talk) 01:38, 6 January 2021 (UTC)
- I see why you like Bach's little fugue in G then. Very long and very tonally stable subject. It leans pretty heavily on the dominant and the raised leading tone to get this effect, so it's not obvious how to do something like that in Locrian. Speaking of Locrian, I think it is possible to have the answer be a transposition up a perfect 5th of the subject, as is common for fugues based on other modes, but up a 4th is certainly easier and it's what I did for my Locrian fugue. (I had the for voices entering on B, E, D and B respectively.) --Rperlner (talk) 15:50, 12 January 2021 (UTC)
- I do know that while Locrian mode doesn't have a perfect fifth above the Tonic, and thus cannot resort to establishing Tonality in those more typical fashions, it does have access to Minor's lowered seventh scale degree, the Subtonic, which not only acts as the melodic anchor in place of a proper Dominant but also establishes tonality through a sort of "back door"- all due to the parallel relationship between a Dominant and a Subtonic. I must also point out that the Subtonic is the Serviant of the Serviant in much the same way that a Supertonic is the Dominant of the Dominant, meaning the Subtonic is very easy to hit from a chord progression standpoint. This is why the Tyrant chord must include some iteration of its third, because the third of the Tyrant chord is the lowered seventh scale degree, and can thus establish tonality through the aforementioned mechanism. A cantus firmus in Locrian must rely heavily on the lowered seventh scale for much the same reason, and at the same time, since a flat fifth without the backing of the lowered seventh has a way of negating tonality, the flat fifth must be avoided in the cantus firmus, but can be unlocked for counterpointed melodies when the cantus firmus has the Subtonic. The same thing is true with the flat sixth, but for different reasons, with the flat sixth being unlocked in counterpointed melodies where the cantus firmus has either the Mediant or the Serviant. --Aura (talk) 20:28, 13 January 2021 (UTC)
- I just had a thought... Since the wolf fifth is a different interval from the perfect fifth with different properties, perhaps a succession of chords in root position such as the sequence G-Major (1/1-5/4-3/2), A-Wolf-Minor (1/1-32/27-40/27), B-Diminished (1/1-6/5-32/27), C-Major (1/1-5/4-3/2) in the key of C-Major could potentially be allowed in non-meantone settings, seeing as it seems to be that only two successive chords with parallel perfect fifths or octaves lead to the loss of independence among the different voices. Do you think this is a viable technique for things like fugues? --Aura (talk) 23:12, 4 January 2021 (UTC)
- The voice leading I think you're suggesting (Perfect 5th - Wolf 5th - Diminished 5th by upward parallel stepwise motion) sounds acceptable to my ear. It does not have the same clunky feeling as true parallel perfect 5ths between otherwise independent voices. The resolution of the diminished 5th by parallel motion to a perfect 5th is somewhat more questionable, as it is not the normal way to resolve this dissonance (normal is inward motion to a major or minor 3rd), although it may work in some contexts. There are of course ways to remove parallel 5ths between root position chords e.g. if G is voiced from bass to soprano as GDGB and A minor is voiced as ACEA. (Note, for the next chord, a root position diminished triad is not really a thing in common-practice 4-part voice leading texture, so it should probably be extended either to a (half/fully)-diminished 7th chord or a first inversion dominant 7th chord.) I actually prefer the parallel voice leading through the wolf 5th to this treatment, though (assuming you're not using a tempering that removes the wolf, or correcting the wolf to a perfect 5th) since otherwise the wolf sounds like an unresolved dissonance to me. As for whether this would work in a fugue, I think it might -- although having too much parallel motion in the voice leading creates a similar effect to doubling a voice in parallel 3rds -- which you absolutely can do in a fugue, but it's a special effect of sorts and shouldn't be used as the main texture. Rather, in a fugue, there should be a lot of contrary motion and voices moving in contrasting rhythmic patterns. --Rperlner (talk) 19:15, 5 January 2021 (UTC)
- Well, to be frank, since music of the common practice era was virtually all in some sort of meantone or other (as far as I know), and the distinct qualities and musical properties of wolf fifths were not recognized back then, it sounds to me like we can regard root position diminished triads as something unique to non-meantone tunings, just like with the wolf fifths and wolf fourths themselves- particularly since this sort of appearance of a diminished triad in root position is only really facilitated by the prior usage of the wolf fifth as in the example I provided. Besides, diminished triads do have other follow ups- most notably, B-Diminished in root position can be followed up by the second inversion of E-minor (1/1-6/5-3/2 in root position; root note related to the Tonic by 5/4). From the aforementioned second inversion E-minor, we can then use a first inversion A-Wolf-Minor as a follow up, and then go on to some inversion of G-Dominant-7. --Aura (talk) 21:29, 5 January 2021 (UTC)
- On another note, I have been told that the IVM-VM-IM chord progression wasn't used in common practice tonality, but I think we can nevertheless use it, as even the purists seem to accept the notion that the IV triad (1/1-81/64-3/2; related to the Tonic by 4/3)- as it occurs in this position- originated from a first inversion IIm7 where the root was seen as superfluous and thus removed. The purists may not like some of the implications that result from this development, but there is a sense in which it's their loss. That said, they do have a point about the IVM-VM-IM cadence being easily bastardized- I can only assume that this means that this cadence works best as a non-final phrase ending. --Aura (talk) 22:58, 5 January 2021 (UTC)
- I am confused. You mean this super common (Scarlatti and Bach are certainly common practice) progression? https://en.wikipedia.org/wiki/I%E2%80%93IV%E2%80%93V%E2%80%93I#:~:text=In%20music%2C%20I%E2%80%93IV%E2%80%93,an%20exposition%20of%20the%20tonality%3A&text=The%20progression%20is%20also%20often,end%20of%20works%20and%20sections. --Rperlner (talk) 23:38, 5 January 2021 (UTC)
- Yes, that is exactly the chord progression I'm referring to. If Bach used it, then that means the so-called "purists" were wrong. I guess one reason that the "purists" take the stance they do is because the IIm-VM-IM is a stronger motion and is thus better suited to close out the main body of a song in a number of ways. --Aura (talk) 23:56, 5 January 2021 (UTC)
- To be fair, the wiki example using Bach is a little wonky (over a tonic pedal and could be ii42 instead of IV). Here's a much clearer Bach example that ends with IV7 V7 I: https://www.youtube.com/watch?v=Gt2K1KYkblo&feature=emb_logo . Not that you need Bach. Any Western art music from about 1650-1900 counts. --Rperlner (talk) 01:05, 6 January 2021 (UTC)
- Now, as I'm looking over the counterpoint rules as listed on Wikipedia, the only rule I can think of that I can flout for sure is rule six- building from the bass upwards- and that courtesy of the existence of Treble-Down Tonality, which requires the reverse direction construction for sections that use it. --Aura (talk) 02:37, 6 January 2021 (UTC)
- BTW, if you're looking for info on counterpoint, I recommend Jacob Gran's youtube videos. Elam Rotem also has some good videos about the Renaissance tradition specifically, and a number go into detail regarding the Renaissance perspective on counterpoint (e.g. his video on cadences) as well as tuning. --Rperlner (talk) 15:38, 12 January 2021 (UTC)
- I know this may sound hard to believe, but in all my experimenting with different intervals, I've found that the wrong kind of interval involving small-number-ratios between the wrong two notes actually works against the formation of a sense of tonality. Conversely, a more tense-sounding interval in the right location- yes, even if the interval in question happens to be 40/27- can actually strengthen your sense of tonality. Yes, intervals with small-number-ratios are vital to establishing tonality, but because of their power, they have to be well-placed within the tonal system, or otherwise the sense of tonality shifts when you don't want it to. --Aura (talk) 04:50, 13 December 2020 (UTC)
Counterpoint in Microtonal Contexts
I was just doing some research on counterpoint, and it seems we need to talk to Guerino Mazzola to try and find out what he knows about counterpoint in the microtonal realm. We should also bring up our findings on the wolf fifth to him and see what he thinks- especially the bit about the functions of the wolf fifth that we've found. I'm particularly curious to hear what he has to say about the idea that the wolf fifth with its distinct function and subtle tension as well as the options for follow up that we've found. For example, the idea of a 1/1-32/27-40/27 minor chord on the sixth scale degree of C major (root related to the Tonic by 27/26) being followed up by either G-Dominant-7 (1/1-5/4-3/2-16/9) or B-Diminished (1/1-6/5-64/45) for an increase in tension, or alternatively, F-Major (1/1-81/64-3/2) or D-Minor (1/1-32/27-3/2) for a decrease in tension. While we're at it, we should talk about Treble-Down Tonality and the effects that has on things like counterpoint. --Aura (talk) 03:06, 6 January 2021 (UTC)
Personally I think Mazzola might be surprised to know that someone is interested not only in the 40/27 wolf fifth as a distinct musical interval and the potential that interval offers as a dissonance requiring resolution, but also in the possibilities of 11/8 and 16/11. I think he might even be surprised that someone has more than just a passing interest in both Locrian mode and the idea of Treble-Down Tonality. --Aura (talk) 03:25, 6 January 2021 (UTC)
- His email is listed on his website. https://www.encyclospace.org/ Why don't you contact him? --Rperlner (talk) 15:26, 12 January 2021 (UTC)
Reduce comma tables on EDO pages
Please have a look at Xenharmonic Wiki: Things to do #Comma tables in EDO_pages. Thanks --Xenwolf (talk) 09:09, 11 January 2021 (UTC)
Welcome to Dystopia
Hey Ray, I just finished "Welcome to Dystopia". This song involves multiple key changes and some degree of polyphony, especially in the later portions. I even added distorted vocals, which I couldn't add in the original version of this song as I didn't have either Audacity or a microphone at the time. --Aura (talk) 23:22, 5 February 2021 (UTC)
- Hi Aura. Nice song. I definitely think that the effects modulations and more varied textures add to the richness of the overall sound. --Rperlner (talk) 16:32, 11 February 2021 (UTC)
Discord Conversations
Hey, I've been wondering if you'd like to join some of the conversations on the Xenharmonic Alliance Discord Server. I personally think we could share more ideas if you were there. --Aura (talk) 13:35, 2 July 2021 (UTC)
- Hi Aura. I created a discord account. Still haven't looked closely enough to figure out what to do with it yet. BTW, I completed my set of modal fugues. You can find them here: https://www.youtube.com/playlist?list=PLkW9S8bpltfyhXXDcnsnF2d3Y08cm4vsp --Rperlner (talk) 21:18, 7 July 2021 (UTC)