For clarity, my essay is by all means serious about septimal harmony, even tho they're pretty basic. Not only that understanding harmony in 2.3.7 is preliminary of full 7-limit, but moreover, using full 7-limit doesn't imply that full 7-limit ratios need to be present in every individual chord. For one, I covered how certain septimal chords may resolve to classical ones. That's an instance of full 7-limit harmony as the ratios involved in the progression can't be explained but by viewing them as in the very same space.
My honest suggestion is to try stuff on your own. "Primes interacting" or whatever sounds like crackpottery - there are many possible ways to mistune the JI system into some edo and it will be optimal, if you are after such musical system - you need only three simple intervals to get something that differs by something else for example by 2401/2400, so tempering is needed for sure unlike in 5-limit where small commas are more complex. There is no universal 7-limit theory that will cover any possible tempered chord progression (since you talk about interacting - for sure they don't interact in JI), you may try 171 edo, if you want pseudo JI.
I think there is a misunderstanding here. Prime harmonics interact with each other thru chord progressions like 3/4-21/16-9/4 > 1-5/4-3/2, where 21/16 resolves to 5/4 by 21/20. I dunno what you meant by your usage of "interaction". I'm pretty sure we were talking about how chords work in ji, not tempered systems.
Seximal isn't a human-scale system imo. Human is a sophisticated being and we call for sophisticated systems. Seximal may work for some certain subhuman civilizations. I can also imagine they use octal in computing and define the constant of circle as a quarter of tau.
i think "twenzy" would be better, since it's almost the same as twenty, but the zy makes it cleast it's dozenal rather than decimal. not sure what to call the "teens" tho
Contemporary 12et 4/4 rhythm is nothing but a modern construction, just like modern architecture – they're purposefully international. The true western centrist view is to associate it to the western. Historically western classical music didn't use 12et until Schoenberg, whose school did use 12et but that deviated from western tradition ever more than not. And ofc, the more attribution of 12et to the western, the more colonization criticisms will be drawn towards them.
Western music is the only tradition in which any ET is used (and only as of fairly recently). Indonesian slendro is close to 5ET but not exact, a lot of Thai music uses a system close to 7ET but not exact, and although 24ET is used in modern Arabic music, traditional Maqam music does not divide the octave equally.
Normally, I might be sympathetic to something like this as I'm not always a big fan of contemporary art, but I fail to see how using tunings that differ from a tuning that was only used relatively recently in the West constitutes an attack on the basic foundations of Western Civ. The founders of our civilization (the Greeks) used scales in their music that would be considered highly microtonal today (use of the enharmonic genus in tetrachords, for example). The idea of 12 tone equal temperament wasn't even first developed in the West. The Chinese knew about it before we did.
Hello, I like your music works, but I must point out your misconceptions about the history of architecture demonstrated in this post. Modern architecture is not part of contemporary art. What you referred to as modern architecture should be postmodern architecture. You recognized Art Deco and Wright; these are modern. The ugly/controversial buildings of the following era are postmodern. Their opinions and approaches are vastly different and can never be mixed. Hope that clears things up.
Hmm... how would we do that? I have to admit that one of my main concerns is step size- I don't want to not be able to hear a difference between adjacent steps. I mean, if you can't hear a difference between two adjacent steps when said steps are played simultaneously... That said, a good temperament that links our two favorite temperaments would be quite useful...
When working with tonal music, most people don't really "think in 12et". Instead, they "think in meantone". That is because the most important identity in 12et is that four steps along the circle of fifths gives a consonant third. Other facts in 12et ain't as helpful in constructing tonality.
What you proposed are more commonly called 7edf (7 equal divisions of fifth) and 4ed5/4 (4 equal divisions of 5/4). They are, along with 12edo (12 equal divisions of octave), different tunings of 12et (12 equal temperament).
I can't distinguish any of them, not even 17edo from others. I hear the difference when switching, but after the section runs for a while, all of them sound consonant. The timbre doesn't help to show the differences.
Yes, but these chords in the article are 2.3.7 subgroup, this doesn't cover the full 7-limit.
For clarity, my essay is by all means serious about septimal harmony, even tho they're pretty basic. Not only that understanding harmony in 2.3.7 is preliminary of full 7-limit, but moreover, using full 7-limit doesn't imply that full 7-limit ratios need to be present in every individual chord. For one, I covered how certain septimal chords may resolve to classical ones. That's an instance of full 7-limit harmony as the ratios involved in the progression can't be explained but by viewing them as in the very same space.
My honest suggestion is to try stuff on your own. "Primes interacting" or whatever sounds like crackpottery - there are many possible ways to mistune the JI system into some edo and it will be optimal, if you are after such musical system - you need only three simple intervals to get something that differs by something else for example by 2401/2400, so tempering is needed for sure unlike in 5-limit where small commas are more complex. There is no universal 7-limit theory that will cover any possible tempered chord progression (since you talk about interacting - for sure they don't interact in JI), you may try 171 edo, if you want pseudo JI.
I think there is a misunderstanding here. Prime harmonics interact with each other thru chord progressions like 3/4-21/16-9/4 > 1-5/4-3/2, where 21/16 resolves to 5/4 by 21/20. I dunno what you meant by your usage of "interaction". I'm pretty sure we were talking about how chords work in ji, not tempered systems.
Nearly everyone would agree with you, no problem.
Unix time ftw.
Interesting! I had actually never heard of superparticular ratios before. I just spent a bunch of time listening to different ratios of notes.
Oof. Corrected.
Seximal isn't a human-scale system imo. Human is a sophisticated being and we call for sophisticated systems. Seximal may work for some certain subhuman civilizations. I can also imagine they use octal in computing and define the constant of circle as a quarter of tau.
i think "twenzy" would be better, since it's almost the same as twenty, but the zy makes it cleast it's dozenal rather than decimal. not sure what to call the "teens" tho
You don't need counterparts to "teens". Simply dozen-one, dozen-two, and so on.
Contemporary 12et 4/4 rhythm is nothing but a modern construction, just like modern architecture – they're purposefully international. The true western centrist view is to associate it to the western. Historically western classical music didn't use 12et until Schoenberg, whose school did use 12et but that deviated from western tradition ever more than not. And ofc, the more attribution of 12et to the western, the more colonization criticisms will be drawn towards them.
Western music is the only tradition in which any ET is used (and only as of fairly recently). Indonesian slendro is close to 5ET but not exact, a lot of Thai music uses a system close to 7ET but not exact, and although 24ET is used in modern Arabic music, traditional Maqam music does not divide the octave equally.
Schoenbergian music isn't really western, so basically western music didn't use any et, either.
Many people here already read eleven as "el" or "elv". I think you could just substitute "sept" for "seven" too.
They all sound identical to me.
Normally, I might be sympathetic to something like this as I'm not always a big fan of contemporary art, but I fail to see how using tunings that differ from a tuning that was only used relatively recently in the West constitutes an attack on the basic foundations of Western Civ. The founders of our civilization (the Greeks) used scales in their music that would be considered highly microtonal today (use of the enharmonic genus in tetrachords, for example). The idea of 12 tone equal temperament wasn't even first developed in the West. The Chinese knew about it before we did.
Hello, I like your music works, but I must point out your misconceptions about the history of architecture demonstrated in this post. Modern architecture is not part of contemporary art. What you referred to as modern architecture should be postmodern architecture. You recognized Art Deco and Wright; these are modern. The ugly/controversial buildings of the following era are postmodern. Their opinions and approaches are vastly different and can never be mixed. Hope that clears things up.
Okay, sorry. I just meant "modern" in the sense of "contemporary." I suppose "post 1900s" would have been more accurate.
I think the property you described is called monumentality, isn't it?
41 and 46 for general-purpose ji approximation.
Try 10edo. It's better suited for serialism than 12edo.
Approximation to harmonics 8-16: 5 5 4 4 4 3 3 3
Squares[8] ftw.
I prefer + for half-sharp.
@Xotla
I wonder if sharply tuned temperaments in general create a cyberpunk-ish sound. Sometimes I feel 27edo cyberpunk-ish. Now you picked 15edo…
Hmm... how would we do that? I have to admit that one of my main concerns is step size- I don't want to not be able to hear a difference between adjacent steps. I mean, if you can't hear a difference between two adjacent steps when said steps are played simultaneously... That said, a good temperament that links our two favorite temperaments would be quite useful...
Finding the temperament defined by 159 & 198 is easy.
Mind sharing what you use it for?
Notating just intonation
Uh, I asked the wrong question.
When working with tonal music, most people don't really "think in 12et". Instead, they "think in meantone". That is because the most important identity in 12et is that four steps along the circle of fifths gives a consonant third. Other facts in 12et ain't as helpful in constructing tonality.
What you proposed are more commonly called 7edf (7 equal divisions of fifth) and 4ed5/4 (4 equal divisions of 5/4). They are, along with 12edo (12 equal divisions of octave), different tunings of 12et (12 equal temperament).
AFAIK George Secor developed some well-temperaments for 17 and 29et.
do you have a link to any information about them?
http://anaphoria.com/Secor17puzzle.pdf
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Lol. But 31edo is, actually, a fifth tone (x
I can't distinguish any of them, not even 17edo from others. I hear the difference when switching, but after the section runs for a while, all of them sound consonant. The timbre doesn't help to show the differences.