User talk:Godtone

Welcome

Hello there! I'm glad to finally see someone else here who thinks that powers of two in the denominator are important. That said, I would add that numerators with powers of two also have a similar effect (shared harmonics that suggest the Tonic as a fundamental of sorts), and thus also help to establish a sense of tonality. I call the type of consonance exhibited by intervals with powers of two in the numerator and the denominator "connectivity", though it arguably needs a better name. I also have a lower threshold for intervals that can meaningfully be distinguished- this being at around 7 cents- the reason being that intervals of that size are still noticeable when the two notes are played side by side, and that intervals that are 7-10 cents in difference from one another can still be exploited to seamlessly modulate between keys that are not on the same series of fifths. I also deal in 11-limit harmony quite frequently, and I should mention that I prefer 27/16 over 5/3 for the major sixth above the Tonic because of both the virtual fundamental effect and connectivity-related reasons. --Aura (talk) 01:25, 18 December 2020 (UTC)

Hello Godtone. If there is anything you need, please ask. --Xenwolf (talk) 08:08, 18 December 2020 (UTC)

Hi uhm, how do I reply "properly" (if there is a way to reply "properly") so that it shows up like a comment on the talk page? As of now I'm just trying to replicate the plaintext markdown. Another thing is where do I read on conventions/etc. on editing pages for commas/intervals and EDOs? --Godtone (talk) 10:12, 18 December 2020 (UTC)

Yes, replying is by indenting by one (via colons at line start). This convention is restricted to talk (or diskussion) pages. Written conventions are a work in progress. Currently the "rules" for these three sorts of pages are a bit under construction. The pages Xenharmonic Wiki:Conventions and Xenharmonic Wiki:Things to do (including discussions), and maybe also Template talk:Infobox ET may give you an idea... --Xenwolf (talk) 14:34, 18 December 2020 (UTC)

Hi Aura, I've considered the issues you raised with my stopping points before for the most part. The reason I disinclude 14/13 is, while it is noticeable when played side-by-side with 13/12, I think this is an idealised situation for judgement because in a lot of music in practice, the notes won't be as clear, won't be played as long, will be played with other notes/sounds that serve to obfuscate their precise judgement and will be played with not-too-precise - or worse inharmonic - timbres, plus it should also be considered that a lot of the range of human pitch hearing is of significantly lower precision than in its optimal range of frequencies. The final reason for disincluding 14/13 is basically what I said in my explanation: I find the difference between 13/12 and 14/13 to be uncomfortably small, and so wouldn't want to have to differentiate them, meanwhile 13/12 is pretty distinct from 12/11 or 15/14. As for powers of 2 in the numerator, I find that this generalises to a 2^n in a chord usually helping with orientation significantly, however, I don't find that the presence of factors of 2 in a numerator necessarily help with orientation if there are other factors there, plus if we allow that sort of thinking, shouldn't 9/7 be considered to be fairly "connected" just because it can be written as 18/14 or 36/28? I do think there is a little validity to this reasoning, but overall I think powers of 2 are more pleasing and orienting when in the denominator, although I admit 2^n in the numerator is a special case. Having said that, I personally dislike 16/15 as it sounds too complex to me and it doesn't sound very "connected" to me while 8/7 sounds somewhat connected. I'm also keeping the superparticulars in consideration slightly on the minimal side because of later thoughts of mine introducing more complexity (as there is plenty of ratios that can be built from these superparticulars alone for example). My last point is that maybe you misunderstood my intent for this limit as a melodic one rather than a harmonic one. A 10c difference is far from nothing harmonically, but melodically it is very little. I focus on the melodic rather than the harmonic as the harmonic can be very precise with very precise and harmonic timbres, and approximating pure JI with rank one temperaments eventually seems slightly futile (at that point, why not just JI?), hence me drawing the line where I have. Sorry for the verbose response; hope this gives some insight. (Further insights will hopefully come when I add more to my user page later.) Godtone (talk) 13:15, 18 December 2020 (UTC)

It sounds like you confuse "connectivity" with "concordance"- the latter of which is discussed on the harmonic entropy article, "connectivity" and "concordance" are both types of consonance, but they are different in that "connectivity" only exists between the fundamental and its partials- that is, overtones and undertones as well as their octave-reduced counterparts. Oh, and yes, you can actually get away with something like 27/16 or even 32/19 when it comes to connectivity. Only ratios with numerators and or denominators that are pure powers of two (such as 1, 2, 4, 8, 16, 32, etc.) count as demonstrating "connectivity", so ratios like 4/3 or 16/15 actually count when it comes to connectivity whereas 15/14 doesn't. I'll be honest, 16/15 doesn't really sound all that complex to me- in fact it actually sounds pretty simple, and the fact that a power of two is in the numerator (resulting in a shared harmonic) actually helps with orientation- not to mention that its inverse is 15/8, a very pleasing major seventh that is easily bridged by the likes of ratios like 5/4 and 3/2. Meanwhile, 15/14 has to be placed somewhere else in the melody and harmony in order to function properly as 15/14 is less than ideal as the distance between your Lead and your Tonic precisely because of the missing fundamental effect- yes, I've checked, and I can actually hear the difference between them in terms of the missing fundamental effect. Did I mention that you can omit 7/4 from the overtone scale between the 8th and 16th harmonics and still end up with a scale demonstrating Rothenberg propriety, whereas you can't do that if you omit 15/8? Yes, I work heavily with complex harmony, and so, the melody should be able to go well with the harmony without being mistuned- key changes, or even a series of rapid-fire key changes, are another story, as in those cases, the harmony is deliberately mistuned for the sake of transitions and a sense of instability. It is true that there as such a thing as an EDO that is too big, however, the reason I'm still a fan of something like 159edo is because in JI, you frequently have to deal with commas that are less than 3.5 cents- which are unnoticeable even when two notes differing by that amount are played together- and compared to all those different notes in JI differing by commas that size, something like 159edo brings a great deal of simplification. As to a verbose response? That's par for the course at times as far as I'm concerned. --Aura (talk) 16:13, 18 December 2020 (UTC)

I guess at the end of the day, my point is that harmony has a way of exerting some measure of control over the tuning of the notes in the melody, and thus the intervals that are used as a result. If your preference is different, well, that's the way it is, but nevertheless, more precise tunings do matter, and although there appears to be some degree of tolerance for mistuning, such as in how 27/16 and 32/19 are virtually indistinguishable, I'd still prefer to take some finer distinctions more seriously. --Aura (talk) 19:52, 18 December 2020 (UTC)

15/8 is a pretty different case to 16/15 IMO, and one of the reasons for preferring 15/14 and 17/16 over 16/15 is because they represent better intervals for stepping upwards while 16/15 represents a good interval for stepping downwards, plus personal preference as aforementioned. Also consider that 15/8 can be expressed as (3/2)(5/4), both already existing in the list of superparticulars, while 16/15 = (4/3)/(5/4) and so is again implicit in existing superparticulars. This means that the lower superparticulars can be used to emphasize/help evidence these subtler intervals' existences in a chord. In other words, I believe prioritising the accuracy of the simpler superparticulars is worth sacrificing the accuracy of some more complex ones but that specific complex superparticulars of interest should ideally especially be represented with accuracy. For example, for stepping up, 15/14 is a pleasing wider minor second to me with a nice ring to it, and 17/16 a darker, more shimmery and slightly more familiar alternative. And it isn't that I don't take finer distinctions more seriously, just that, in the context of approximate systems, you (IMO) kind of compromise their 'seriousness' (with respect to JI) anyway, and I see simplification as a good thing. Also, IMO, 16/15's power of 2 isn't very easy to hear unless there are more tones emphasizing the 16 and I think this applies more generally for intervals whose numerators are powers of 2 greater than 8. Oh and out of curiosity, what is the largest (in cents) comma you're comfortable with (intentionally) tempering? Godtone (talk) 21:57, 20 December 2020 (UTC)

Well, I can indeed hear 16/15's power of two with just the two notes involved- particularly when the notes are set up high. I've done the experiments with Audacity using nearly pure tones, and 16/15 is the interval that strikes me as being the most natural for a leading tone in either direction. It may be true that I do compromise the seriousness of JI in some respects when it comes to those smaller commas, but the largest comma I'm comfortable with intentionally and directly tempering out for sure (outside of the 12edo-based systems that I'm actually quite familiar with) is the keenanisma, which is only about 4.503 cents, and even then, that is situational. When it comes to commas regarding fifths, I'd have to say Mercator's comma- which is about 3.615 cents wide- is the best, as it's the smallest 3-limit comma that can be tempered out for an EDO while still ending up with a reasonable step size. --Aura (talk) 22:34, 20 December 2020 (UTC)

Excuse me, I think I see what you mean about 16/15 being good for stepping downwards- that is, you're talking about the difference between your Tonic and the note a semitone below it. When I was talking about 16/15's power of two, I was thinking of just such an arrangement. I understand why you might prefer 17/16 in particular for the interval between the Tonic and the note located a Semitone above it, however, I have to admit that I'm not just limited to the most common ideas for diatonic modes, or even Bass-Up tonality. I also work with both Locrian mode Treble-Down tonality. --Aura (talk) 02:44, 21 December 2020 (UTC)