User talk:Rperlner: Difference between revisions

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::::: 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. --[[User:Rperlner|Rperlner]] ([[User talk: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 (1/1-6/5-32/27) 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. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:46, 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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 04:12, 22 December 2020 (UTC)

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:::::::::::: Is me or is the fugue's subject- when harmonically stable- often counterbalanced by the contrasting sections where the more extensive harmonic development and key changes takes place? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:17, 6 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/ --[[User:Rperlner|Rperlner]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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.) --[[User:Rperlner|Rperlner]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 4 January 2021 (UTC)

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:::::::::::: 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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 01:05, 6 January 2021 (UTC)

:::::::::::::: Looks like the so-called "purists" in the Music Theory department really were wrong about the IVM-VM-IM after all. Still, the usage of the IIm-VM-IM cadence does have serious merits- especially in an Ionian circle progression containing the final cadence. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 01:15, 6 January 2021 (UTC)

::::::::::::::: Agreed. From my spot checking, it definitely seemed to me like Bach usually preferred ii V I final cadences to IV V I, as the former are much more common in his music.--[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 15:38, 12 January 2021 (UTC)

:::::::::::::: Now, as I'm looking over the counterpoint rules [[Wikipedia:Counterpoint|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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 15:38, 12 January 2021 (UTC)

:::::::::::::::: I'm checking a bit of that now, and so far, I'm finding a good chunk of this stuff interesting. I'll see how much of this I can apply to what I'm doing. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:16, 13 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. --[[User:Aura|Aura]] ([[User talk: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 [[Wikipedia:Guerino Mazzola|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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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? --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 15:26, 12 January 2021 (UTC)

:: Okay, I contacted him, and he replied saying only that his microtonal counterpoint theories are to be found in his book "Computational Counterpoint Worlds". Perhaps we should both read it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:35, 13 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 --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:09, 11 January 2021 (UTC)

== Welcome to Dystopia ==

Hey Ray, I just finished "[[:File:Welcome to Dystopia.mp3|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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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 --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 21:18, 7 July 2021 (UTC)

::Well, we can talk about it some time if you'd like. I've been using Discord for over two years now, so I can show you at least a few things about some of the basic functionalities and stuff like that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:23, 8 July 2021 (UTC)

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 ::::: 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. --[[User:Rperlner|Rperlner]] ([[User talk: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 (1/1-6/5-32/27) 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. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:46, 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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 04:12, 22 December 2020 (UTC)
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 :::::::::::: Is me or is the fugue's subject- when harmonically stable- often counterbalanced by the contrasting sections where the more extensive harmonic development and key changes takes place? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:17, 6 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/ --[[User:Rperlner|Rperlner]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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.) --[[User:Rperlner|Rperlner]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:12, 4 January 2021 (UTC)
@@ Line 486: / Line 494: @@
 :::::::::::: 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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 01:05, 6 January 2021 (UTC)
+:::::::::::::: Looks like the so-called "purists" in the Music Theory department really were wrong about the IVM-VM-IM after all.  Still, the usage of the IIm-VM-IM cadence does have serious merits- especially in an Ionian circle progression containing the final cadence. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 01:15, 6 January 2021 (UTC)
+::::::::::::::: Agreed. From my spot checking, it definitely seemed to me like Bach usually preferred ii V I final cadences to IV V I, as the former are much more common in his music.--[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 15:38, 12 January 2021 (UTC)
+:::::::::::::: Now, as I'm looking over the counterpoint rules [[Wikipedia:Counterpoint|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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 15:38, 12 January 2021 (UTC)
+:::::::::::::::: I'm checking a bit of that now, and so far, I'm finding a good chunk of this stuff interesting.  I'll see how much of this I can apply to what I'm doing. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:16, 13 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. --[[User:Aura|Aura]] ([[User talk: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 [[Wikipedia:Guerino Mazzola|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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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? --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 15:26, 12 January 2021 (UTC)
+:: Okay, I contacted him, and he replied saying only that his microtonal counterpoint theories are to be found in his book "Computational Counterpoint Worlds".  Perhaps we should both read it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:35, 13 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 --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:09, 11 January 2021 (UTC)
+== Welcome to Dystopia  ==
+Hey Ray, I just finished "[[:File:Welcome to Dystopia.mp3|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. --[[User:Aura|Aura]] ([[User talk: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. --[[User:Rperlner|Rperlner]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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 --[[User:Rperlner|Rperlner]] ([[User talk:Rperlner|talk]]) 21:18, 7 July 2021 (UTC)
+::Well, we can talk about it some time if you'd like.  I've been using Discord for over two years now, so I can show you at least a few things about some of the basic functionalities and stuff like that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:23, 8 July 2021 (UTC)