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Differences between tweeter designs?

andreasmaaan

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Uploaded the crossover simulation files on wetransfer:
https://we.tl/t-qagYM37ZMt

Thanks :) Looking forward to trying those out.

Not sure what could be causing the discrepancy between 1.6KHz and 2KHz. Perhaps the deep null is just at a different position at 1.6KHz that you managed to miss in the specific angles you modelled?

As for the music theory research it's too long a story to converse about casually sadly. Really need to write a thick book in the future :)
What I can tell though is a controversial thing.. I've found that the brain quantizes the interval space into perfect octaves (2/1) and perfect fifths (3/2), corresponding to the western notation system actually. This can in it's pure / just form be described as an extended Pythagorean tuning (and I find what is classically though of as "just intonation" with 5/4 major thirds etc is incorrect, extended Pythagorean is the true "just intonation". We further find that especially in polyphonic music musical context is more important that actual tuning, for instance if a chord behaves as for instance a dominant 7th we can tune that minor seventh as an augmented sixth as if it is a German sixth chord (which is a Pythagorean comma higher when tuned just) but we will only hear it as a slightly out of tune minor seventh in this instance. In traditional monophonic music we are more free to hear the interval as tuned, in Turkish/Arab/Persian music often more complex intervals are used (we used to have them in the west as well before polyphony set in), for instance Turkish rast is G-A-Cb-C-D-E-Gb-G instead of western major G-A-B-C-D-E-F#-G. It gets too complex to explain here how to harmonize these more remote intervals in a musical way, as I wrote earlier with the German sixth vs dominant seventh chord we can't just harmonize this by replacing a major third in a major or minor triad with an augmented fourth as we'll still hear it as an out of tune major third. Long story to explain my harmonic theory for harmonizing such intervals correctly.
And now to get slightly back on topic :) If we tune (correctly spelled, simple western well understood) music to extended Pythagorean tuning, we actually get an increase in soundquality! 12-tone equal temperament "floats" which gives an overal phasy haze to the music which hides fines details and hinders tranparancy with polyphonic music. Extended Pythagorean tuning is transparent (though this will also show clear any errors in timbre etc, it's a double edged sword. But if your music is otherwise very high quality a simple change of tuning can lift it to a higher level.)

This is really fascinating. Sorry to ask you to explain a bit more, just wanting to try to understood a bit better:
  • Do the brains of people not exposed to predominantly Western tonalities during their development also quantize to perfect octaves and fifths?
  • What do you mean by "tune" in the context of e.g. "tune that minor seventh as an augmented sixth" or "out of tune major third"? The latter to my simple brain would mean that a note or all the notes in the chord were not tuned to concert pitch, but I assume you mean something different here?
  • In terms of the Turkish rast for example, what is the difference e.g. between the Turkish Cb and the B in standard Western tuning?
  • What do you mean by "transparent" in the context of "Extended Pythagorean tuning is transparent"?
  • And finally, what do you mean by "high quality" in the context of that last paragraph of yours I quoted? Are you talking about tuning already-recorded music here, or are you talking about how musical instruments should be tuned (or something else)?
Anyway I'm going to read up on extended Pythagorean tuning and just intonation so no doubt that will clear up some of these questions...

EDIT: @Thomas savage maybe these last couple of posts could be moved to a new thread? :)
 
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andreasmaaan

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Re new thread , if you want one create it and a let me know the posts you want moved (the numbers are at top right hand corner) .

Many thanks :) On second thought, let's wait and see if @JustIntonation has time to elaborate on this topic a bit more. If so, I'll start a new thread and let you know.
 

Thomas savage

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Many thanks :) On second thought, let's wait and see if @JustIntonation has time to elaborate on this topic a bit more. If so, I'll start a new thread and let you know.
That would be polite as it’s his thread and topic.
 
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JustIntonation

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Thanks :) Looking forward to trying those out.

Not sure what could be causing the discrepancy between 1.6KHz and 2KHz. Perhaps the deep null is just at a different position at 1.6KHz that you managed to miss in the specific angles you modelled?

No the deep null is at A100 for 2kHz.
I'll make the A100 deep null / cancellation axis for 1.6kHz later today and upload it as well.


This is really fascinating. Sorry to ask you to explain a bit more, just wanting to try to understood a bit better:
  • Do the brains of people not exposed to predominantly Western tonalities during their development also quantize to perfect octaves and fifths?
  • What do you mean by "tune" in the context of e.g. "tune that minor seventh as an augmented sixth" or "out of tune major third"? The latter to my simple brain would mean that a note or all the notes in the chord were not tuned to concert pitch, but I assume you mean something different here?
  • In terms of the Turkish rast for example, what is the difference e.g. between the Turkish Cb and the B in standard Western tuning?
  • What do you mean by "transparent" in the context of "Extended Pythagorean tuning is transparent"?
  • And finally, what do you mean by "high quality" in the context of that last paragraph of yours I quoted? Are you talking about tuning already-recorded music here, or are you talking about how musical instruments should be tuned (or something else)?
Anyway I'm going to read up on extended Pythagorean tuning and just intonation so no doubt that will clear up some of these questions...

EDIT: @Thomas savage maybe these last couple of posts could be moved to a new thread? :)
Ah nice that you find it fascinating :)
- I believe the evidence is very much in favor that we are all born with this way of quantizing the musical interval space. Though not everybody agrees with me here. Though you can imagine someone from a tribe never in contact with the western world being presented two things, an audio recording of a piece by Bach, and an audio recording of a letter by Bach in German. He will be able to understand musically the piece / its intervals etc, though some aspects of it are culturally and it doesn't say whether he'll like it or not etc. The audio recording of the German letter though will be complete gibberish to him, he'll have to learn the German language first (which isn't a blank slate either, a language. Here Chomsky wrote a few things about universal grammar. But the basic "grammar" of music is what makes the intervals, we do not have to learn it.)

- By "in tune" I mean the ratio of the interval. For instance in 12-tone equal temperament the octave is tuned as 2/1 ratio, 1200 cents. for instance 100Hz an octave above is 200Hz. And an octave above 200Hz is 400Hz. In 12-tone equal temperament the perfect fifth is tune as 700 cents. This is about 2 cents short of 3/2 which is about 702 cents. As you can see all the intervals come from a chain of perfect fifths and octaves, here is the western major scale in fifths: F-C-G-D-A-E-B and in 12-tone equal temperament every fifth has a 2 cent error so they add up. The augmented fourth F-B is about 12 cents too low in equal temperament. A major third is about 8 cents too low in equal temperament. (though as a twist of nature the correct tuning for the major third of about 408 cents can in many circumstances appear to sound harsher than an equal tempered major third of 400 cents. This is due to the fifth harmonic / overtone of about 386 cents. And this is one of the main reasons why people have been led to a wrong path regarding tuning in the past and many still today.

- The difference between Cb and B is in relation to the G.
G - Cb is the interval of a diminished fourth. G - B is the interval of a major third, A - Cb is the interval of a diminished third, A - B is the interval of a major second, Cb - C is the interval of an augmented prime, B - C is the interval of a minor second. These are different intervals as far as our brain is concerned (even if we tune them exactly the same on an equal tempered instrument).
In monophonic music we can indicate the interval by tuning difference alone. This is what makes up the Turkish / Arab / Persian "quartertones", augmented seconds and diminished thirds. (often the difference is exaggerated a bit in tuning)

- With "transparant" I mean that the "haze" of floating intervals of equal temperament is removed (for fixed pitch instruments / electronic music etc). Take for instance the equal tempered perfect fifth at 700 cents and the Pythagorean perfect fifth of 702 cents. The third harmonic overtone is 3/1 and is 1902 cents which is 1200 cents + 702 cents. If the perfect fifth for instance C - G is tuned to 700 cents there is a 2 cents discrpancy between the third harmonic of C and the second harmonic of G which will slowly go in and out of phase. This produces a slightly hazy soundquality to the music. It holds for other intervals as well, and not even just because of the harmonics but that's another story don't want to make it too long.

- With high quality I mean that if you're using a subpar sampled piano for instance with correct Pythagorean tuning then any timbre deviation and any tuning deviation will be heard much more clearly which will often lead to errors in the sampled set jumping forward which were not so noticeable when playing that sampled piano in 12-tone equal temperament.

- As for reading up on this. I can strongly advice against it. The internet is a mess regarding this subject. What I'm sharing above is in part because of original research I've done for the past 12-years. Most of what's on the internet is simply completely wrong and there's no easy way to tell truth apart from error for you I'm afraid. Getting into microtuning leads most people completely astray and their music suffers a very great deal, both because they spend too much time on weird mathematical constructions behind tuning and mostly because the result will almost always sound very much out of tune.
Only thing I can recommend is to experiment with very simple western music which is well understood and tune it Pythagorean according to the correct written enharmonics. You can only do this if you've studied music theory and know how to spell correctly. And even this is somewhat bothersome as most instruments inc VST's etc are not made to be easily retuned.
And anything going beyond this I can only strongly strongly advice against as you'll probably end up making things more out of tune that 12-tone equal temperament :) (edit: not that I question your individual musical hearing or anything like that. But it's a snake pit for everybody also the very best. Even many scientists who are famous in other areas, like Helmholtz, Mersenne, Kepler, etc etc wrote completely wrong things regarding tuning. They fell into the traps and never got out. And you can't even read about this because nobody knows what's right. This is a very hard part of the brain to study, it is not like sound and the auditory cortex etc but something else alltogether.)

edit: to make it extra clear. Only worth tuning very well understood "common practice" music to Pythagorean based on standard common practice harmonic theory and spelling.
Please don't attempt to do this with jazz/blues etc or late romantic period music etc. Especially jazz/blues is basically a mess in theory and spelling. With 12-tone equal temperament this doesn't matter much as when you spell a note wrong (for instance a G# instead of an Ab) it doesn't matter for the tuning. But for Pythagorean tuning this difference is audible. And when our brain interprets a note as a Ab and you tune it as a G# it is out of tune, and can be quite audible. Not very nice for your audience.
 
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RayDunzl

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I experimented with different numbers of notes per octave once I realized how to code it.

Easley Blackwood is one who has investigated other counts musically.

00:00 Fanfare in 19-Note Equal Tuning, Op. 28a

12 Microtonal Etudes for Electronic Music Media, Op. 28:
02:31 Andantino - 16 notes per octave
06:24 Allegro volando - 18 notes per octave
09:03 Suite in four movements - 21 notes per octave
13:57 Allegro moderato - 23 notes per octave
17:20 Sostenuto - 13 notes per octave
20:38 Lento - 15 notes per octave
24:20 Con moto - 17 notes per octave
27:18 Andante ma non troppo - 22 notes per octave
32:00 Moderato - 24 notes per octave
35:08 Allegramente - 14 notes per octave
37:58 Comodo - 20 notes per octave
41:59 Allegro moderato -19 notes per octave

Suite for Guitar in 15-Note Equal Tuning, Op. 33:
46:14 I. Prelude
49:06 Sarabande
51:55 Gavotte (Tempo di gavotta)
53:01 IV. Gigue

---

Then there's Sevish, if your ear is tuned to more modern sounding microtonal compositions...

https://www.youtube.com/results?search_query=Sevish
 
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JustIntonation

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I experimented with different numbers of notes per octave once I realized how to code it.

Easley Blackwood is one who has investigated other counts musically.

00:00 Fanfare in 19-Note Equal Tuning, Op. 28a

12 Microtonal Etudes for Electronic Music Media, Op. 28:
02:31 Andantino - 16 notes per octave
06:24 Allegro volando - 18 notes per octave
09:03 Suite in four movements - 21 notes per octave
13:57 Allegro moderato - 23 notes per octave
17:20 Sostenuto - 13 notes per octave
20:38 Lento - 15 notes per octave
24:20 Con moto - 17 notes per octave
27:18 Andante ma non troppo - 22 notes per octave
32:00 Moderato - 24 notes per octave
35:08 Allegramente - 14 notes per octave
37:58 Comodo - 20 notes per octave
41:59 Allegro moderato -19 notes per octave

Suite for Guitar in 15-Note Equal Tuning, Op. 33:
46:14 I. Prelude
49:06 Sarabande
51:55 Gavotte (Tempo di gavotta)
53:01 IV. Gigue

---

Then there's Sevish, if your ear is tuned to more modern sounding microtonal compositions...

https://www.youtube.com/results?search_query=Sevish

Well these are the kinds of things I meant with the direction not to take and sounding out of tune ;)
But for those who can enjoy this, have fun of course!
 

RayDunzl

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Well these are the kinds of things I meant with the direction not to take and sounding out of tune ;)
But for those who can enjoy this, have fun of course!

I think they emphasize how conditioned(?) we are to twelve tone and its variations... Everything else just tends to sound a bit wrong.

Maybe if you listen to microtonal exclusively for a few weeks it will mess you up.

The mathematical intervals apparently are what we like. Frequency intervals of the 12th root of two - 12 tones making an octave. Almost insiginificant (in my opinion) are the exact frequencies of the progression. I don't know if it is inbred or just habit to like those intervals.

Change the playing speed of a recording by a little bit, you can easily adapt (at least I do) as the ratios between the notes remain the same, change the intervals and it just doesn't work right any more.
 
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JustIntonation

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I think they emphasize how conditioned(?) we are to twelve tone and its variations... Everything else just tends to sound a bit wrong.

Maybe if you listen to microtonal exclusively for a few weeks it will mess you up.

The mathematical intervals apparently are what we like. Frequency intervals of the 12th root of two - 12 tones making an octave. Almost insiginificant (in my opinion) are the exact frequencies of the progression. I don't know if it is inbred or just habit to like those intervals.

Change the playing speed of a recording by a little bit, you can easily adapt (at least I do) as the ratios between the notes remain the same, change the intervals and it just doesn't work right any more.

I've spent the past 12 years doing full time research into music theory, specifically microtonal theory. I'm also the owner of justintonation.com (nothing there at the moment).
I was on the old yahoo tuning lists, etc. Know everybody in that scene and all the microtonal music and all the different theories :)
Furthermore I've retuned close to a thousand pieces of classical music to various tuning systems, including various forms of 5-limit and higher limit rational intonation (often mistakenly called just intonation) and just about anything else you can think of.
I don't know of anybody else in the world who has done this to anywhere near the extent I did. (and that was just the first 4-5 years of my research)
So I will not get messed up by listening as you suggest ;)
 

RayDunzl

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RayDunzl

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Which "traditional" music doesn't use the 12 tone intervals we're all so familiar with, or a subset (a few cycles difference on the intervals doesn't necessarily count), so I can go look them up and listen to some samples?
 

RayDunzl

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Back to the thread topic - my tweeters are roughly 720 square inches each, and are crossed to the woofer at 180Hz.
 
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JustIntonation

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Which "traditional" music doesn't use the 12 tone intervals we're all so familiar with, or a subset (a few cycles difference on the intervals doesn't necessarily count), so I can go look them up and listen to some samples?

Basically all traditional Turkish makam music, Arab maqam, Persian classical music, and surrounding countries use microtones that indeed express different intervals than the ones we're used to in western melodies. Also Indian classical music, though this is often less noticeable I was just listening to Aruna Sairam (can be found a lot on youtube too, just looked up this one as example
starts getting pretty to me around 3min) but the microtones are certainly there. They just don't sound out of tune :)
Almost all of it is monophonic (drones etc don't count as polyphony). Though I know of some music that expresses some of the more remote intervals in a polyphonic context too from 70's Ethiopian jazz (sometimes mix of Ethiopian music and western jazz) which can be found in the Ethiopiques series.
 
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JustIntonation

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Back to the thread topic - my tweeters are roughly 720 square inches each, and are crossed to the woofer at 180Hz.
Aah electrostat :)
I may end up getting a ribon or AMT still.. should have some similarities to electrostatic treble.
 
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JustIntonation

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That's good to know.
Btw, I didn't mean to mmm ah don't know how to word this, but come across the wrong way..
But I know very well how one can train oneself to listen for different things in music. For instance to listen to how a in 4:5:6 major triad the 5/4 tuned major third sounds "synchronous" that buzzy sound and convince oneself that this is in tune etc.
It's a long story. But one very simple thing I can advice is to tune normal common practice classical music to a variety of tuning system, preferably piano music as the piano will make pitch quite clear. And then really listen to the melodies and overal in-tune sensation, not just for how chords "buzz".
Another thing is that what I tried to explain earlier is that the brain takes context over relatively small tuning differences. On can tune a piece by for instance Bach in many different tuning systems but as long as the deviation doesn't approach a full semitone then we'll hear it as the same music, only "coloured" differently.
The core of tuning is to first know which interval one is expressing, and only then what is in tune for that interval according to how our brain quantizes the intervals. One can then also effectively "colour" the tuning if one chooses. Some musicians manage to use "out of tune colouration" as an added expressive things to good effect in my opinion (Aphex Twin comes to mind).

Btw I don't mind going well off topic personally. Though if a moderator finds this is not a good thing on this forum feel free to move this part of the thread :) (or let me know if and how I should do this)

Though I'm not interested in going really deep about tuning theory here. I've had my fair share of endless discussion on this subject for many year already hehe :)
 

Sal1950

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Reading thru these "speaker builder" threads makes me so wish I still had the room and tools to experiment with a few designs.
Oh well, that's life in retirement sized digs and communities. :(
 

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