# Scales with zero or negative intervals and other bs



## ncfiala (Apr 3, 2012)

First, some definitions. An interval is a positive integer multiple of half steps. A scale is a sequence of intervals adding up to 12 half steps. Therefore, we can identify scales with (additive) compositions (ordered partitions) of the integer 12. We could take into account the playing of the same string on the same fret multiple times in a row by allowing an interval to be a non-negative integer multiple of half steps. Then scales could be identitified with weak compositions of 12. We could also take into account "backtracking" by allowing an interval to be any integer multiple of half steps. Finally, we could allow for scales that don't repeat every octave but instead repeat after some number of octaves by allowing a scale to be a sequence of intervals adding up to any integer multiple of 12. The concatenation of two scales is then again a scale. In this way the set of scales is given the structure of a non-commutative monoid (if we allow the empty scale). The subset of scales with only positive intervals, but that may not repeat every octave, would be a subsemigroup. What is this good for? Nothing but my mind runs rampant.


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## PortalNathrakh (Apr 3, 2012)

ncfiala said:


> What is this good for? Nothing but my mind runs rampant.



This thread in a nutshell.


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## Thep (Apr 3, 2012)

ncfiala said:


> First, some definitions. An interval is a positive integer multiple of half steps. A scale is a sequence of intervals adding up to 12 half steps. Therefore, we can identify scales with (additive) compositions (ordered partitions) of the integer 12. We could take into account the playing of the same string on the same fret multiple times in a row by allowing an interval to be a non-negative integer multiple of half steps. Then scales could be identitified with weak compositions of 12. We could also take into account "backtracking" by allowing an interval to be any integer multiple of half steps. Finally, we could allow for scales that don't repeat every octave but instead repeat after some number of octaves by allowing a scale to be a sequence of intervals adding up to any integer multiple of 12. The concatenation of two scales is then again a scale. In this way the set of scales is given the structure of a non-commutative monoid (if we allow the empty scale). The subset of scales with only positive intervals, but that may not repeat every octave, would be a subsemigroup. What is this good for? Nothing but my mind runs rampant.



Paragraphs, son.


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## Gothic Headhunter (Apr 3, 2012)

I'm sorry, what did you say? I was with you up till "First, some definitions."


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## mr_rainmaker (Apr 3, 2012)

none of this matters unless you resolve your musical statment at the end... ie: cadence.
Cadence (music) - Wikipedia, the free encyclopedia


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## pentecost (Apr 3, 2012)

ncfiala said:


> We could take into account the playing of the same string on the same fret multiple times in a row by allowing an interval to be a non-negative integer multiple of half steps.


which wouldn't accomplish anything... the whole idea of being 'additive' shouldn't be tossed to make the round hole more square. the original definitions you've put in play don't specify a number of notes in said scale, adding a null is redundant. it's already there.


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## Augminished (Apr 3, 2012)

Does anyone else feel like they just got yelled at and lectured? 

Close to two years of theory in school and never have I been this confused. 

I feel like a just walked in to a door that had notes on it but they were negative.


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## groovemasta (Apr 3, 2012)




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## niffnoff (Apr 4, 2012)

Hey guys what's goi- WHOAH WHAT THE FU-

Seriously though, my head hurts now, what's the point in any of that OP


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## JStraitiff (Apr 4, 2012)

Perhaps if you formatted the original post a little we would be compelled to read. Separate the definitions using line breaks and then the rest below that.

Paragraph per topic


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## ncfiala (Apr 4, 2012)

Sorry, I was pretty much just thinking out loud. Or rather thinking in print. As a mathematician, I try to abstract and generalize everything. I can't turn it off. The question is does the abstraction and generalization have any real world use or value. In this case, and in many cases, it probably doesn't. But that usually doesn't stop us from doing it anyway.


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## ixlramp (Apr 4, 2012)

I feel you might find microtonal and 'just-intonation' music theory interesting.


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## Explorer (Apr 4, 2012)

A friend of mine obsessed about what he called "spiral" scales, which didn't have all the notes in each octave, instead repeating the "scales" over two and three octaves. 

I'm ready to hear something compelling arising from this thinking. Otherwise, I'd say you just sound like you've been hitting the weed and daydreaming. "Hey... I was just thinkin'... isn't that cosmic?" *laugh*

Short version: I would love a cupcake... I'm just thinkin' out loud... what do you think of that idea?


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## fantom (Apr 5, 2012)

So after reading that a few times... maybe I missed something. But for the sake of a fun mathematics discussion (in 1 paragraph), can you clarify something for me? How did you go from elements of the monoid being notes to scales? If you treat your operator as combining scales, you're forcing an ordered sequence to be elements. This pretty much generates all permutations of notes rather quickly with no purpose. If you just meant that notes are elements, then you have to drop the notion of a scale when dealing with a monoid, because all you can do is an single operator to combine two relative intervals to produce a third interval. So say what?


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## mm66554 (Apr 5, 2012)

Sorry but you sound like you just started a qualification in either maths or computer programming and are hyped up to somehow prove your newly aquired knowledge (or words) on an unrelated internet forum.
Instead of thinking scales, think in terms of notes, that in itself makes "negative intervals" obsolete as they are already encompassed within keys, inverted chords etc. If you want to create your own scales based off intervals the only way is to experiment and see what sounds best. Every scale will repeat at the octave if a semi-tones is your lowest incriment, that's just how it is, even if you force yourself not to play the octave another instrument such as bass almost certainly will.


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## ixlramp (Apr 5, 2012)

Explorer said:


> A friend of mine obsessed about what he called "spiral" scales, which didn't have all the notes in each octave, instead repeating the "scales" over two and three octaves.


Interesting.


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## Augminished (Apr 5, 2012)

I'm sorry but i'm still confused are we talking about scales or math? 

If its math I have to get into math mode and then I can conquer you ALL.

PS I know shit about math so ya.


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## ncfiala (Apr 5, 2012)

mm66554 said:


> Sorry but you sound like you just started a qualification in either maths or computer programming and are hyped up to somehow prove your newly aquired knowledge (or words) on an unrelated internet forum.
> Instead of thinking scales, think in terms of notes, that in itself makes "negative intervals" obsolete as they are already encompassed within keys, inverted chords etc. If you want to create your own scales based off intervals the only way is to experiment and see what sounds best. Every scale will repeat at the octave if a semi-tones is your lowest incriment, that's just how it is, even if you force yourself not to play the octave another instrument such as bass almost certainly will.


 
Actually I have a Ph.D. in mathematics. And I certainly wouldn't call mathematics and music unrelated.

And it's not true that any sequence of intervals will repeat every octave. A sequece of intervals will repeat every octave if and only if it adds up to a divisor of 12.


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## ncfiala (Apr 5, 2012)

fantom said:


> So after reading that a few times... maybe I missed something. But for the sake of a fun mathematics discussion (in 1 paragraph), can you clarify something for me? How did you go from elements of the monoid being notes to scales? If you treat your operator as combining scales, you're forcing an ordered sequence to be elements. This pretty much generates all permutations of notes rather quickly with no purpose. If you just meant that notes are elements, then you have to drop the notion of a scale when dealing with a monoid, because all you can do is an single operator to combine two relative intervals to produce a third interval. So say what?


 
The elements of the monoid are sequences (of intervals) and the operation is concatenation of sequences. It's just like when you form the free monoid on the strings over some alphabet.


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## niffnoff (Apr 5, 2012)

... what in the hell am I reading and why does my head hurt and why do I feel like I'm about to explode...

can someone break down the math into a simpler term for us who may not be at a PHD level.


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## Augminished (Apr 5, 2012)

^ I agree it sounds interesting but I have no fucking clue what any of it means. 

ncfiala break it down in to simpler terms and it might make for a great topic.


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## ncfiala (Apr 5, 2012)

niffnoff said:


> ... what in the hell am I reading and why does my head hurt and why do I feel like I'm about to explode...
> 
> can someone break down the math into a simpler term for us who may not be at a PHD level.


 
It really doesn't matter dude. It just helps me to put things into an abstract context that I'm familiar with. It helps me to think about things in different ways. You can never have too many different perspectives on any subject. But it's probably not going to be useful to anyone else, or even to me for that matter. 

Also, the math is actually really simple but I don't think it's worth your time to figure it. Just go practice, which is what I need to go do just as soon as I finish painting this beat up Donkey Kong Jr. cab.


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## niffnoff (Apr 5, 2012)

ncfiala said:


> But it's probably not going to be useful to anyone else, or even to me for that matter.


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## Necris (Apr 5, 2012)

Sounds like you're thinking along the lines of synthetic scales and non-octave tunings to me.


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## JStraitiff (Apr 5, 2012)

I just realized you're the same guy who was posting about about theory and obsessing about learning everything about theory.


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## Trespass (Apr 5, 2012)

The problem here isn't mathematical, it's psychological.

The human brain only accepts so many relationships between pitches, vertical or linear as consonant. You would do better to extrapolate new, non-octave based scales/temperaments mathematically by understanding how consonance works.

Check out the Bohlen-Pierce scale, and the theory behind while it's a consonant alternative to the chromatic scale.


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## lurgar (Apr 6, 2012)




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## morrowcosom (Apr 6, 2012)

Allan Holdsworth uses a bunch of scales of 8 or 9 notes that resolve over 3 octaves. You could just make up a scale of nine notes and put 3 notes in each octave (note 1=octave 1, note 2=octave 2, note 3=octave 3, note 4=octave 1......you get it. Permutate your ass off to your heart's content) 

You could make 24 notes in an octave on a guitar by ascending in quarter steps by using small bends. 

You are getting me lost on the complex math terminology. Just find a way to convert your thoughts from math to english to get more help. Make your thoughts easy to understand for your intended audience in order to more effectively communicate with us. 

I was just thinking outloud too. I busted out of a poker tournament in 10th place last night after being short stacked at 12 big blinds and shoving all-in in middle position with pocket tens.


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## Explorer (Apr 6, 2012)

ncfiala said:


> And it's not true that any sequence of intervals will repeat every octave. A sequece of intervals will repeat every octave if and only if it adds up to a divisor of 12.



I'm not disagreeing that one can define "scales" which "span" more than one octave... but doing so can only be done by ignoring one of the things which the human ear can do immediately: recognize one given pitch, regardless of which octave, as the same as the same pitch at a different octave. It's what the ear and brain do. 

So, in order to say that a scale won't repeat every octave, one can only so assert by denying the way humans hear and make music, and putting in the condition that playing a note is okay in one octave but not in another. 

Again, I"m ready to be impressed, but not really expecting to be.


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## Cabinet (Apr 6, 2012)

Please SchecterWhore save us!


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## Trespass (Apr 7, 2012)

Explorer said:


> I'm not disagreeing that one can define "scales" which "span" more than one octave... but doing so can only be done by ignoring one of the things which the human ear can do immediately: recognize one given pitch, regardless of which octave, as the same as the same pitch at a different octave. It's what the ear and brain do.
> 
> So, in order to say that a scale won't repeat every octave, one can only so assert by denying the way humans hear and make music, and putting in the condition that playing a note is okay in one octave but not in another.
> 
> Again, I"m ready to be impressed, but not really expecting to be.



The Bohlen Pierce scale repeats at what would be an octave and a fifth in 12 tone temperament.

Bohlen



> The Bohlen&#8211;Pierce scale (BP scale) is a musical scale that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the diatonic scale.[1] Compared with octave-repeating scales, its intervals are more consonant with certain types of acoustic spectra.
> 
> 3:1 serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave). ( play (help·info)) This interval is a perfect twelfth in diatonic nomenclature (perfect fifth when reduced by an octave), but as this terminology is based on step sizes and functions not used in the BP scale, it is often called by a new name, tritave ( play (help·info)), in BP contexts, referring to its role as a pseudooctave, and using the prefix "tri-" (three) to distinguish it from the octave.


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## Mr. Big Noodles (Apr 7, 2012)

Trespass, I'm not terribly familiar with Bohlen-Pierce intonation. Could you explain how one would make music with said scale outside of running up and down the collection, or perhaps how octave equivalence is defeated in using the scale?


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## tacotiklah (Apr 7, 2012)

My question is, how the hell is this in any way applicable to actual playing situations? 
Unless you own a micro-tonal guitar (which many of us don't) this is pretty much of no real day-to-day use as far as I can tell.
Sorry to sound like a douche, but I in no way understood or was intrigued by the OP. Perhaps it's just a failing on my part, but I honestly feel that regarding theory, unless it has real use to the actual playing of an instrument, it's pretty pointless.


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## ixlramp (Apr 7, 2012)

Here's Elaine Walker (with a 13ED3 'vertical keyboard' she made) with some Bohlen Pierce music in 13 equal steps per tritave (tritave = tripling of frequency = 19.02 semitones). Harmonically alien and difficult on the ear at first, but with it's own strange consistency:


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## Trespass (Apr 7, 2012)

SchecterWhore said:


> Trespass, I'm not terribly familiar with Bohlen-Pierce intonation. Could you explain how one would make music with said scale outside of running up and down the collection, or perhaps how octave equivalence is defeated in using the scale?



Sorry, I don't understand the question. It's a collection of pitches, you make music with it just like one makes music with conventional 12TET pitches. Melody over harmony. Unlike a lot of other theoretical scales, this does produce a sizeable amount of consonant intervals.

There have been a few symphonic works composed with it (mainly with VST instruments), and organs and clarinets have been re purposed to BP. 

To get into this kind of music, I personally found the need to "cleanse" my bias towards 12TET pitches by listening to lots of microtonal music. There was a microtonal Podcast on iTunes that had hours of microtonal piano music, string music, some BP stuff. After "training" my brain to accept non-12TET, going back felt dissonant.


To be realistic, I don't think that society is ready for BP or any alternative division at the moment. When 12TET music has been harmonically exhausted (in hundreds of years?), I think we'll start to see alternative pitch collections being adopted by academia and classical/jazz music circles.


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## JStraitiff (Apr 7, 2012)

Microtonailty is silly. If i find a reason to use tones outside the standard scale, i use a bend and every single time its for ambiance or effect. Look at warrel dane. He uses microtonality for effect all the time hahahaha


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## Mr. Big Noodles (Apr 8, 2012)

ghstofperdition said:


> My question is, how the hell is this in any way applicable to actual playing situations?
> Unless you own a micro-tonal guitar (which many of us don't) this is pretty much of no real day-to-day use as far as I can tell.
> Sorry to sound like a douche, but I in no way understood or was intrigued by the OP. Perhaps it's just a failing on my part, but I honestly feel that regarding theory, unless it has real use to the actual playing of an instrument, it's pretty pointless.



+1. I don't know what the OP is going on about.



ixlramp said:


> Here's Elaine Walker (with a 13ED3 'vertical keyboard' she made) with some Bohlen Pierce music in 13 equal steps per tritave (tritave = tripling of frequency = 19.02 semitones). Harmonically alien and difficult on the ear at first, but with it's own strange consistency:



I've checked out some of her music before. It's really cool. I wish I had a better understanding of its workings, and whether her music and the instruments she's designed are 100% kosher to the BP concept.



Trespass said:


> Sorry, I don't understand the question. It's a collection of pitches, you make music with it just like one makes music with conventional 12TET pitches. Melody over harmony. Unlike a lot of other theoretical scales, this does produce a sizeable amount of consonant intervals.



But what's different about it? What I don't get is the whole tritave thing. Are we to suppose that the BP scale is contained within a "twelfth", and that the same scale can be extended to the next tritave and still assume the same pitch classes? I'm not trying to shoot this down, I just have difficulty in conceiving of music that says that green is red and orange is purple.



> To get into this kind of music, I personally found the need to "cleanse" my bias towards 12TET pitches by listening to lots of microtonal music. There was a microtonal Podcast on iTunes that had hours of microtonal piano music, string music, some BP stuff. After "training" my brain to accept non-12TET, going back felt dissonant.
> 
> ...
> 
> To be realistic, I don't think that society is ready for BP or any alternative division at the moment. When 12TET music has been harmonically exhausted (in hundreds of years?), I think we'll start to see alternative pitch collections being adopted by academia and classical/jazz music circles.


I think I have a take on this.

There are longstanding musical traditions that make use of different temperaments, notably in the music of Turkey and the former Ottoman states, India, Polynesia, and pretty much everywhere else in the world that developed a musical system independent of European influence. Thing is, these cultures don't really focus on pitch that much. Sure, they recognize it, but classical music in India is in one key the entire time and the tonic pitch is whatever the principal player feels like. Similarly, Chippewa fipple flutes are tuned based on the dimensions of the maker's arm (a process called "grandfather tuning"). Highly idiosyncratic. How do Westerners describe pitch? A=440Hz, 100 cents to the half-step, twelve half-steps to the octave, different numbers for each octave based on a relationship of the pitches within that octave to C... There is an obsession with definition and organization. Western culture likes standards, as evidenced by the bureaucracies of Rome and the Christian Church, not to mention countless other institutions since then. The scientific method and peer review come to mind. This pattern is at the core of Western society's success, so it is therefore inextricably linked to everything that we do.

The move from just tuning to equal temperament was made not to make music sound better (or whatever), but in order to make tonality easier. Around the same time that this happened, all of the esoteric instruments of the Baroque chamber ensemble were systematically phased out to make way for a few families of instruments that could cover more ground at the expense of timbre. The pattern for the last sixty years or so has been one that allows these odd things back in. So, there is an established interest in serpent concerti and bizarre pitch systems, but these are and always will be oddities in the Western world. In order for something to reach success, it must also demonstrate consistency and the ability to pander to simplicity, even at the expense of beauty.


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## Explorer (Apr 8, 2012)

Trespass said:


> To be realistic, I don't think that society is ready for BP or any alternative division at the moment.



I'd argue that, given how the human ear perceives octaves, inventing a synthetic system which completely tosses that out will never gain acceptance. 

Similarly, taste buds sense a few components, and a food which tosses out those flavor components from consideration will never gain acceptance. 

And, like food, both familiar and exotic musics have octaves in common, and familiar and exotic foods are appreciated by most people. It's silly to say that there aren't people who don't enjoy food and music from across cultural divides.

However, for what it's worth, I greatly enjoyed the idea that people will eventually tire of the normal flavors, and will eventually embrace chewing gum with the breath-freshening power of tungsten....

----

Short version: A system which plays to a given set of sensory apparatus should take that sensory apparatus into account. Ignoring an important aspect of that apparatus is ignoring a fundamental reality.


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## All_¥our_Bass (Apr 8, 2012)

SchecterWhore said:


> Trespass, I'm not terribly familiar with Bohlen-Pierce intonation. Could you explain how one would make music with said scale outside of running up and down the collection, or perhaps how octave equivalence is defeated in using the scale?


There is no octave in that tuning/scale, there are some things that are close but not close enough and they clash horribly.


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## Necris (Apr 8, 2012)

I've come up with a few EDT temperaments (equal divsions of the tritave, like bohlen pierce which is 13-EDT) that I have found to be easy to digest, my favorite of which I hope to modify a guitar and bass to play in soon. I think higher divisions of the tritave (20 or more equal divisions) are much less foreign sounding to the ear. Unequal divisions can sound good as well but are not particularly applicable to guitar in any meaningful way.


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## Mr. Big Noodles (Apr 8, 2012)

All_¥our_Bass;2951213 said:


> There is no octave in that tuning/scale, there are some things that are close but not close enough and they clash horribly.



I understand that, and my question is still unanswered. How does Bohlen-Pierce intonation account for the fact that the second partial of any tone is an octave above that tone, and sounds like it is the same tone but only higher? What happens if I have a BP clarinet and a BP piccolo flute, and I want them to double at the octave? Does one of those instruments not exist, due to the tenets of the tuning system? The idea of new tuning systems based on 3:1 is nice, but it really seems like you have to fake it; saying that the octave isn't there requires one to reject octave equivalence, which creates the doubling conundrum I've described above; saying that the same function is fulfilled by tritave equivalence requires one to create a theoretical model in which the laws of physics are set aside in order to make the system work.

All I want to know is if there is anything beyond a tritave in Bohlen-Pierce intonation, and what happens in that second tritave. Is the idea to create an extended 156-tone scale (13TET over the space of a P12, and it takes twelve P12's to get back where you started... 16 octaves above the original pitch)? If you're just using wonky intervals to make individual chords or tones sound a certain way, why not say that it's an adjustment system rather than a scale or system of tonality?


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## Necris (Apr 8, 2012)

JStraitiff said:


> Microtonailty is silly. If i find a reason to use tones outside the standard scale, i use a bend and every single time its for ambiance or effect. Look at warrel dane. He uses microtonality for effect all the time hahahaha


You realize your argument is strikingly similar to that of 6 string guitarists who say "Why would you ever need a 7?"


SchecterWhore, I linked your post to a friend of mine, this is what he had to say:

"


> I understand that, and my question is still unanswered. How does Bohlen-Pierce intonation account for the fact that the second partial of any tone is an octave above that tone, and sounds like it is the same tone but only higher?


 There is no 2/1 ratio, and if you try to double a note at the octave it will sound dissonant, as the BP system is like 8.2-equal divisions of the octave if you consider it an octave system. It is not though, and you get a dissonance curve up to 3:1 instead.
Also, the basis of the BP system is ODD harmonics. so 4:5:6 is out, and 3:5:7 is in. that means instead of 4:5:6:8 (with an octave on the outside) you get 3:5:7:9 (with a tritave on the outside [or a perfect twelfth]) 

This is why people have such interest in the Bohlen Pierce system, it does not go near many even harmonics, and is easy to snap your brain into. 




> What happens if I have a BP clarinet and a BP piccolo flute, and I want them to double at the octave?


There are no octaves in BP. 



> Does one of those instruments not exist, due to the tenets of the tuning system? The idea of new tuning systems based on 3:1 is nice, but it really seems like you have to fake it; saying that the octave isn't there requires one to reject octave equivalence, which creates the doubling conundrum I've described above; saying that the same function is fulfilled by tritave equivalence requires one to create a theoretical model in which the laws of physics are set aside in order to make the system work.


Somewhat right, but wrong that you need to "fake" anything. 
BP is a system based on 3, and no even harmonics whatsoever, clarinets were chosen for their square wave timbre so that one can perceive a the same note but higher at 3:1 without even partials.

Notes aren't doubled, theyre tripled, hence 3:1, not 2:1.....this is a very simple concept you might be overthinking. 

Stringed instruments can simply cancel the octave by picking at 2/1, from whichever distance the originating tone is. ( so pick 1/2 way between your left hand and the bridge and you cancel even harmonics- Brian May knows this trick )

Finally, the theoretical model is no different from the one that holds up western music theory. 




> All I want to know is if there is anything beyond a tritave in Bohlen-Pierce intonation, and what happens in that second tritave.


Yes you get 9:1 when multiplying the 3:1, instead of 4:1 when multiplying two octaves of 2:1. does this answer your question?
you can go past 81:1 in BP if you wanted- up to you. 




> Is the idea to create an extended 156-tone scale (13TET over the space of a P12, and it takes twelve P12's to get back where you started... 16 octaves above the original pitch)? If you're just using wonky intervals to make individual chords or tones sound a certain way, why not say that it's an adjustment system rather than a scale or system of tonality?


No that is not the idea."


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## ixlramp (Apr 8, 2012)

^ What Necris' friend said.

In the second tritave the pitches of the scale are repeated, the scale repeats infinitely at the just/natural interval 3/1 = tritave = 3rd harmonic = 19.02 semitones. Since BP is odd-harmonic-based it it uses the most consonant odd-harmonic just/natural interval 3/1 as the scale repeat interval.

As well as 'octave similarity' ... there is also 'tritave similarity' based on the natural similarity of the tritave to the fundamental, all the harmonics of the tritave are contained within the harmonics of the root pitch. It is another completely natural choice for a repeat interval.

Even for a microtonal enthusiast BP can sound 'far out' and difficult (it does to me) since the 'tritave similarity' is working against the familiar 'octave similarity'.

If i play a root-12th interval on my guitar it does indeed, in a strange way, sound like the 'same pitch but higher'.

http://www.nonoctave.com/tuning/twelfth.html

The BP system of pitches is initially derived as an unequal step just/natural intonation system. The derivation of BP is similar to the derivation of 'traditional just intonation' from the natural harmonics, but with odd harmonics only. The equal step 13EDT system is just a rough approximation of just/natural BP, in the same way that modern 12ET is a rough approximation of 'traditional just intonation'.


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## Mr. Big Noodles (Apr 8, 2012)

Edit: ixlramp answered some of my questions before I could post. Thank you. I'm still confused about tritave repetition. I just hear a twelfth. But, if that's what you say it is, more power to you.



Necris said:


> I linked your post to a friend of mine, this is what he had to say.



Thanks for the information.



> There are no octaves in BP.


I was expecting a more complete answer than this. 

How does a consort of BP instruments work? Will a BP bass clarinet be able to play in the same context as a BP clarinet in the alto or soprano range? Are they capable of playing identical notes in the registers where they overlap (for example, as a B-flat bass clarinet and a B-flat soprano clarinet in 12TET can both play together at E3-F5)? Is the pitch content of "tritave 1" (3:1) and "tritave 2" (9:1) assumed to be identical, or is it different from one to the next? In 2:1 music, I can write a melody that goes C4 B3 C4 D4 E4, and change its character by transposing it down an octave (C3 B2 C3 D3 E3) or by transposing it up an octave (C5 B4 C5 D5 E5). What is the parallel in BP music? or is there one?



> Notes aren't doubled, theyre tripled, hence 3:1, not 2:1.....this is a very simple concept you might be overthinking.


So, does the 'perfect twelfth' (tritave) serve the same function as the perfect octave in 12TET (and every other established pitch system in the world)? It's this very concept that troubles me. Do you have any BP notation that I can look at with a recording? I listen to some of this stuff on YouTube, and it sounds cool, but I don't hear anything that I haven't heard in any other microtonal music. It's evident that it's a little more involved than a maqam in which the second note is played two commas flat, or anything else where something is simply a quarter-tone sharp or flat.



> Stringed instruments can simply cancel the octave by picking at 2/1, from whichever distance the originating tone is. ( so pick 1/2 way between your left hand and the bridge and you cancel even harmonics- Brian May knows this trick )


I don't see how this is relevant. An instrument's timbre doesn't affect its pitch availability. Are odd-harmonic timbres desirable in BP music, because even harmonics are problematic? because odd harmonics are easier to play on instruments that overblow at the third partial?


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## Adam Of Angels (Apr 8, 2012)

Explorer said:


> A system which plays to a given set of sensory apparatus should take that sensory apparatus into account. Ignoring an important aspect of that apparatus is ignoring a fundamental reality.


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## ixlramp (Apr 8, 2012)

A Bohlen Pierce 9 string piccolo guitar / touch-guitar with 2 tritaves of frets ...







Elaine is using the equal tempered / equal step BP scale in the video above, which is even more difficult on the ears than just-intonation BP. That performance was from a recent BP conference that gained some media coverage. However i feel BP is a bad choice for introducing the masses to microtonality due to it's difficulty, it is likely to only re-inforce the perception of microtonality as unlistenable.

If i may answer questions not directed at me ...

>Are they capable of playing identical notes in the registers where they overlap?

Yes.

>Is the pitch content of "tritave 1" (3:1) and "tritave 2" (9:1) assumed to be identical?

Yes, both 3/1 and 9/1 are tonic notes and the scale degrees are relative to them.

>In 2:1 music, I can write a melody that goes C4 B3 C4 D4 E4, and change its character by transposing it down an octave (C3 B2 C3 D3 E3) or by transposing it up an octave (C5 B4 C5 D5 
E5). What is the parallel in BP music?

You transpose up or down by a tritave = 3/1 = 19.02 cents

>So, does the 'perfect twelfth' (tritave) serve the same function as the perfect octave in 12TET?

Yes.

>Are odd-harmonic timbres desirable in BP music, because even harmonics are problematic? because odd harmonics are easier to play on instruments that overblow at the third partial?

Odd harmonic instruments (clarinet, sax) are sometimes used since the BP system is derived from odd harmonics, it's just makes a good match.

Weird stuff indeed, BP is not to my taste, although interesting to hear.


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## Necris (Apr 8, 2012)

"


> I was expecting a more complete answer than this.



Why would you want anything more than there are no 2/1's (aka octaves pertaining to the diatonic scale) - in the BP system. thats all there is to it! 



> How does a consort of BP instruments work? Will a BP bass clarinet be able to play in the same context as a BP clarinet in the alto or soprano range?



They work well.. There was a 3 day symposium of this.. You could ask Nora-Lovisa Müller yourself though she plays and owns both.. 
these instruments do play together, as long as there is a fixed reference pitch or unison note. Right now there is no "standard" as some people use the clarinets with 440hz reference and others use MIDI with BP at 262hz. I have seen people do both, it just requires setting the MIDI at 440 instead of 262. 

Right now only guitars, keyboards, and clarinets exist in BP. 



> Are they capable of playing identical notes in the registers where they overlap (for example, as a B-flat bass clarinet and a B-flat soprano clarinet in 12TET can both play together at E3-F5)?



Yes. but like i said above, ask the master.



> Is the pitch content of "tritave 1" (3:1) and "tritave 2" (9:1) assumed to be identical, or is it different from one to the next?



If you can hear in multiples of three instead of 2, yes.



> In 2:1 music, I can write a melody that goes C4 B3 C4 D4 E4, and change its character by transposing it down an octave (C3 B2 C3 D3 E3) or by transposing it up an octave (C5 B4 C5 D5 E5). What is the parallel in BP music? or is there one?



BP is treated as a stretched chroma - so yes there is one, I'd imagine it's a strong 3.5.7. subgroup sound. why don't you try it for yourself if you want to know?



> So, does the 'perfect twelfth' (tritave) serve the same function as the perfect octave in 12TET (and every other established pitch system in the world)? It's this very concept that troubles me. Do you have any BP notation that I can look at with a recording? I listen to some of this stuff on YouTube, and it sounds cool, but I don't hear anything that I haven't heard in any other microtonal music. It's evident that it's a little more involved than a maqam in which the second note is played two commas flat, or anything else where something is simply a quarter-tone sharp or flat.



Yes it does repeat the same. yes perfect twelfth does ONLY come from the 12-tone diatonic scale categorical perception which I figured you'd be most familiar with.



.. But in the bohlen pierce scale world it's the tritave. it's just a signal word, similar to how oct- pertains to the number 8 and there are 7 notes in the diatonic [7] scale--- but instead of calling it the Decade like Heinz Bohlen wanted, Tritave seems to have stuck with everyone. 

BP notation can be based on any rank-2 diatonic-type scales in 13-tones with 2 step sizes, Large and small. (rank-2 is like myhill's property) one example is Sirius [7]: 2221222, LLsLLL.... 3125:3067 vanishes and it's generated by the minor third. 
Right now it's based on a scale called Lambda that Heinz Bohlen Made, consisting of the more pure harmonics from the scale. Which you can find online on the BP site, maintained by the scale's creator. The BP "Diatonic" (211212121) vanishes 245:243, and is based on primes 3,5,7. 

The Maqam comment is way off here. This music has nothing to do with traditional whole tones, fourths or fifths..or dividing them

You might hear a similarity between this and other microtonal music because they all touch onto the 7th harmonic and up. especially bp- being a 7-limit temperament itself. Most music on youtube that is labelled as Microtonal is going to have the 7th harmonic and others that appear that 12 doesnt have- hence the interest in these scales. 

Im not trying to talk over your head or be rude here, Im just pointing things out and trying to answer your questions to the best of my ability... 

If you want to discuss at length these ideas just talk to Paul Erlich. He'll reply to every message you write, with the correct answer. I promise...



> I don't see how this is relevant. An instrument's timbre doesn't affect its pitch availability. Are odd-harmonic timbres desirable in BP music, because even harmonics are problematic? because odd harmonics are easier to play on instruments that overblow at the third partial?



....Strings have even partials in the timbre. consider the sound of a clarinet to a guitar. huge difference there in timbre. try picking a classical guitar in the middle of the string, you cancel the 2/1- thats all i was saying...

"


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## ncfiala (Apr 9, 2012)

What the hell, I have no idea what you guys are talking about. But that's ok. I like being confused. It forces me to learn. I don't think the conversation even has anything to do with my post anymore, but who cares. Any interesting discussion is a good thing.

And why are people giving me negative rep (anonymously) and telling me to leave? If you're not interested then just move on. I have no interest in the billions of ridiculous "djent" threads so I just don't read them, I don't tell the guys to leave the forum.


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## Mr. Big Noodles (Apr 9, 2012)

Necris said:


> Why would you want anything more than there are no 2/1's (aka octaves pertaining to the diatonic scale) - in the BP system. thats all there is to it!



Because octave equivalency is a constant in all of the music that I've ever experienced. The idea of the tritave is alien. I expected more than a claim that it just is. I'm willing have my own perception challenged, but I need substantiation in order to be convinced and to convince myself.



> The Maqam comment is way off here. This music has nothing to do with traditional whole tones, fourths or fifths..or dividing them
> 
> You might hear a similarity between this and other microtonal music because they all touch onto the 7th harmonic and up. especially bp- being a 7-limit temperament itself. Most music on youtube that is labelled as Microtonal is going to have the 7th harmonic and others that appear that 12 doesnt have- hence the interest in these scales.


I was remarking on one of the approaches to microtonality that I know, not relating maqam theory to 12TET, BP, or any other divisional system. I know microtones as things that occur outside of 12TET and just tuning; the commonality is that I hear notes outside of the Western chromatic scale in both BP and Ottoman music. This comment isn't way off at all, I'm remarking that my lack of familiarity with Bohlen-Pierce intonation means that my context for understanding it is dictated by relationships that I can draw from my own experience. I've encountered microtonality as minute alteration to diatonic or chromatic tones (like a guitar bend, or using 24TET to get closer to just intonation, or slightly raising a leading tone to emphasize the gravity of the tonic), or in non-standard divisions of the octave (such as slendro tuning). BP is closer to the latter, but as I mentioned before, the octave is still the reality in the case of something like the slendro scale.



> Im not trying to talk over your head or be rude here, Im just pointing things out and trying to answer your questions to the best of my ability...


Thank you for doing so. My confrontation is only in the spirit that I might learn something. Also, muchas gracias for the names. I'll check them out and come up with some questions when I feel like I'm not wasting too much of their time. 



> ....Strings have even partials in the timbre. consider the sound of a clarinet to a guitar. huge difference there in timbre. try picking a classical guitar in the middle of the string, you cancel the 2/1- thats all i was saying...


I still don't see the relevance in bringing it up, then, but that's okay. Instruments whose waveforms favor odd partials are used in 2:1 music all the time, after all. It would seem to me that letting a violin play arco on an open string, or a euphonium playing at the third partial (with different tubing to account for the new intonation) wouldn't pose any sort of offense, since most people will hear whatever the playing note is (using standard techniques; sul ponticello is excluded here) and not the partials above it.



ncfiala said:


> What the hell, I have no idea what you guys are talking about. But that's ok. I like being confused. It forces me to learn. I don't think the conversation even has anything to do with my post anymore, but who cares. Any interesting discussion is a good thing.
> 
> And why are people giving me negative rep (anonymously) and telling me to leave? If you're not interested then just move on. I have no interest in the billions of ridiculous "djent" threads so I just don't read them, I don't tell the guys to leave the forum.



Don't worry, haters gonna hate. If you feel that your postulations are worth hearing, then carry on. Just be prepared to support them. I personally think it's cool to have you around, since you bring a different perspective than these forums are accustomed to. However, I think that the ideas you presented in the first post in this thread are beyond what scales are and how they function and would be better applied to other aspects of harmony. For scales alone, that kind of math is overkill. Feel free to prove me wrong.


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## Explorer (Apr 9, 2012)

Regarding octave equivalence, there is evidence that not just humans, but also animals perceive notes a perfect octave apart, or two or more perfect octaves apart, as equivalent. 

So, it seems the argument for the existence of this "scale which cannot possibly fit into one octave" is that it can't because we have to pretend it doesn't. 

I don't find that all that amazing, just as I didn't find my friend's "spirals" to be so amazing. I'm not saying that people shouldn't pursue what they want, of course.

What I *am* saying, though, is that one can say the color blue doesn't exist all one wants, or the number 2, but that doesn't make it so.


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## JStraitiff (Apr 9, 2012)

ncfiala said:


> What the hell, I have no idea what you guys are talking about. But that's ok. I like being confused. It forces me to learn. I don't think the conversation even has anything to do with my post anymore, but who cares. Any interesting discussion is a good thing.
> 
> And why are people giving me negative rep (anonymously) and telling me to leave? If you're not interested then just move on. I have no interest in the billions of ridiculous "djent" threads so I just don't read them, I don't tell the guys to leave the forum.



You need to be careful about publicly complaining about rep or you WILL find you way out the door very quickly. A large portion of bans are due to this.

I dont think that you should leave just because you approach things in a different way. Do i think you are over thinking EVERYTHING? Yes. I absolutely do. Music is not a science. Its an art. Art is not drawn using rulers and protractors, it is drawn with a hand. Generally at least. 

There are people, who just like you, have tried to approach it this way and produce music that is just emotionless and calculated. Sure understanding why you do what you do and the concepts around music will of course be beneficial to making more complex music but at the end of the day the music needs to come from inside you or it will suck. I understand that you approach things this way in general due to your background and occupation, but i urge you to put down the books and just jam for a while. Dont think about the notes, dont think about the key, dont think about the progression. Just play and feel your way around. Start anywhere and just play what you think would sound best next by instinct.

That is YOUR music. If you feel like taking it further, record the melody you came up with and THEN sit down and figure out what you are playing theory wise. Thats where theory really applies.


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## Mr. Big Noodles (Apr 9, 2012)

JStraitiff: I don't know that a scientific approach is bad. If teaching has taught me one thing, it's that learning strategies vary from individual to individual in ways that defy definition. I've had students that need me to hold their hand every step along the way, and students that hardly need any structure at all. Frankly, I question if the latter group even needs me. Then, there are people who don't know what they have and think that they should go another way. I had a guitar student whose goal was to learn the fretboard so that they could gain proficiency in sight-reading. They played another instrument before, and insisted that we start at the very beginning so that nothing was missed. My response was that it was silly and pointless to start all the way back there, because they already knew that material and would be quickly bored. I gave this kid the location of a minor third on one string (played melodically), then the same minor third in a different position on two strings (played melodically or harmonically), and then called out a bunch of intervals and note names for him to find (with minimal help from me) and he had a map of the fretboard at the end of the first lesson. How does this pertain? ncfiala's strength is that he has developed pattern recognition and manipulation through the study of mathematics. Music is entirely built of patterns, so that's a nice thing to have. If his interest in music is mathematical, then by all means should he draw the common thread. We all make aesthetic choices, and those choices are entirely independent of how one is shoehorned into art. That said, ncfiala, I'd love to see what you could come up with if you could wrap your head around set theory and motivic development. Form is awesome if you're a pattern person. Harmony and tonality are also very interesting, particularly once you get into modulation.

Always a good site to check out: Ricci Adams' Musictheory.net


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## Mr. Big Noodles (Apr 9, 2012)

It's cyclical. A negative interval is just an interval that has the opposite trajectory. We don't use that terminology when referring to musical intervals. Instead, we talk about inversion: a word that has about a million different meanings.

Edit: Not to reignite this, but I have to point out a discrepancy.



ixlramp said:


> Odd harmonic instruments (clarinet, sax) are sometimes used since the BP system is derived from odd harmonics, it's just makes a good match.



Saxophones are "even harmonic" instruments. Stopped conical instruments (saxophone, bassoon, oboe, horn, euphonium, tuba, cornet, flugelhorn) overblow at the octave. Stopped cylindrical instruments (clarinet, trumpet, trombone, baritone horn) overblow at the twelfth. The exception to the latter is the flute, as they're open-ended cylinders, and overblow at the octave.

Also, an empty bottle of Laphroaig 10-year has a harmonic series consisting of fundamental, octave, then major thirteenth. Don't know what it is after that, getting the next partial was difficult and everybody was getting pissed off at me.


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## ncfiala (Apr 9, 2012)

JStraitiff said:


> You need to be careful about publicly complaining about rep or you WILL find you way out the door very quickly. A large portion of bans are due to this.
> 
> I dont think that you should leave just because you approach things in a different way. Do i think you are over thinking EVERYTHING? Yes. I absolutely do. Music is not a science. Its an art. Art is not drawn using rulers and protractors, it is drawn with a hand. Generally at least.
> 
> ...


 
People get banned for talking about rep? What the hell? And I wasn't complaining about it. Negative rep me to your heart's content. It doesn't bother me in the slightest. It just doesn't make sense to me. And to do it anonymously? Pretty pussy if you ask me. But whatever. If I get banned then I get banned. There will always be another forum to go to.

Your way of just feeling my way around just doesn't work for me. We probably just like very different music. Ron Jarzombek makes pretty "calculated" music and he is one of my favorite guitarists.


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## ncfiala (Apr 9, 2012)

SchecterWhore said:


> It's cyclical. A negative interval is just an interval that has the opposite trajectory. We don't use that terminology when referring to musical intervals. Instead, we talk about inversion: a word that has about a million different meanings.


 
One of the reasons I wanted to allow zero and negative intervals is another construction (it's not really necessary for the original construction). If I allow zero and negative intervals then any two n-interval scales can be added or subtracted coordinate-wise to produce another scale. Also, we can multiply a scale coordinate-wise by any integer to produce another scale. This would endow the set of n-interval scales with the structure of what is called a Z-module.

These "scales" with zero and negative intervals may seem stupid and artificial, but we do this kind of thing frequently in mathematics. We might have some set of objects that we wish to analyze but the set lacks "structure". So we embed the set in a larger set that does have "structure" and that allows us to bring to bear mathematical machinery that we couldn't use before. This usually entails creating objects that are somewhat "artificial". As a mathematical formalist it doesn't bother me since I think it's all artificial.


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## Necris (Apr 9, 2012)

JStraitiff said:


> I dont think that you should leave just because you approach things in a different way. Do i think you are over thinking EVERYTHING? Yes. I absolutely do. Music is not a science. Its an art. Art is not drawn using rulers and protractors, it is drawn with a hand. Generally at least.



Art and Science are not even vaguely mutually exclusive. 

A musical piece can have a structure created for it long before a note is ever written. Some will do what you do and I and many others do play their instrument until something of interest pops up and build the piece from there. Others may draw out a loose or detailed graphic representation of the piece to be written as a guideline (I do this occasionally) or write a verbal outline of the piece (slow, fast, louder, slowing down). These 3 examples are among an infinite number of ways to approach the creation of a piece of music and to say that one particular approach will always produce "emotionless and calculated" music is outright ridiculous.


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## Necris (Apr 9, 2012)

Explorer said:


> Regarding octave equivalence, there is evidence that not just humans, but also animals perceive notes a perfect octave apart, or two or more perfect octaves apart, as equivalent.
> 
> So, it seems the argument for the existence of this "scale which cannot possibly fit into one octave" is that it can't because we have to pretend it doesn't.


There is no pretending necessary. A perfect octave is 1200 cents above the original note C1 to C2 for example. The closest the equal tempered form of the Bohlen-Pierce scale comes to that continuing with the C to _ example is C to Jb which is an interval of 1170 cents which is called the BP Eighth (in the Just Intonation version it is an interval of 49/25 or 1165 cents) , you can look at that as a narrowed octave if you like but it still is not a perfect octave and is noticeably different in pitch to the human ear. Continuing along that interval would bring you from Jb to E and then from E to B and so on and so forth.


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## ixlramp (Apr 9, 2012)

SchecterWhore said:


> Saxophones are "even harmonic" instruments.


Cool, thanks for the correct info


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## Mr. Big Noodles (Apr 9, 2012)

ncfiala said:


> One of the reasons I wanted to allow zero and negative intervals is another construction (it's not really necessary for the original construction). If I allow zero and negative intervals then any two n-interval scales can be added or subtracted coordinate-wise to produce another scale. Also, we can multiply a scale coordinate-wise by any integer to produce another scale. This would endow the set of n-interval scales with the structure of what is called a Z-module.
> 
> These "scales" with zero and negative intervals may seem stupid and artificial, but we do this kind of thing frequently in mathematics. We might have some set of objects that we wish to analyze but the set lacks "structure". So we embed the set in a larger set that does have "structure" and that allows us to bring to bear mathematical machinery that we couldn't use before. This usually entails creating objects that are somewhat "artificial". As a mathematical formalist it doesn't bother me since I think it's all artificial.



I lack the mathematical understanding to see what you mean, so I don't know if what I'm thinking is necessarily what you mean. Can you give an example of what you're thinking in music terms?


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## ixlramp (Apr 10, 2012)

Necris said:


> I've come up with a few EDT temperaments (equal divsions of the tritave, like bohlen pierce which is 13-EDT) that I have found to be easy to digest, my favorite of which I hope to modify a guitar and bass to play in soon.


I'm intrigued by this Necris ... how many divisions has your favourite?

Thought i'd mention there is a (currently rather quiet) forum for microtonal guitar here: Microtonal Guitarist - Index. Public registration was disabled due to spammers but if anyone wants to join send me a PM with your email address and username of choice and i'll register you in manually (i'm a minor admin there).

Some BP electronic music:



BP guitar synth (audio and video are mostly unsynched):



Nora playing BP tenor clarinet:



Mad hyperactive fractal generated electronic BP music with synchronised visuals and visual reverb:


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## Konfyouzd (Apr 10, 2012)

Explorer said:


> A friend of mine obsessed about what he called "spiral" scales, which didn't have all the notes in each octave, instead repeating the "scales" over two and three octaves.
> 
> I'm ready to hear something compelling arising from this thinking. Otherwise, I'd say you just sound like you've been hitting the weed and daydreaming. "Hey... I was just thinkin'... isn't that cosmic?" *laugh*
> 
> Short version: I would love a cupcake... I'm just thinkin' out loud... what do you think of that idea?



I fuckin love you, man.


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## All_¥our_Bass (Apr 10, 2012)

For EDTs I prefer 26, 34, or 39 notes, since I find the 147cent BP "chromatic tone" to be a bit too large.


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## Konfyouzd (Apr 10, 2012)

Is the purpose of this to translate the way you think into music or just figuring out new ways to divide the fretboard? If I've learned anything it's that simply knowing where your fingers go is less productive than one might think.


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## JStraitiff (Apr 10, 2012)

Lol called the rep thing


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## Mr. Big Noodles (Apr 10, 2012)




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## Osorio (Apr 11, 2012)

ixlramp said:


> Here's Elaine Walker (with a 13ED3 'vertical keyboard' she made) with some Bohlen Pierce music in 13 equal steps per tritave (tritave = tripling of frequency = 19.02 semitones). Harmonically alien and difficult on the ear at first, but with it's own strange consistency:




Holy crap, I loved that. What the fuck is wrong with me?! 
Thanks for sharing!


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## ixlramp (Apr 11, 2012)

Have you seen this one too?


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## Necris (Apr 11, 2012)

Explorer said:


> A friend of mine obsessed about what he called "spiral" scales, which didn't have all the notes in each octave, instead repeating the "scales" over two and three octaves.



I _may _have stumbled across a legitimate counterpart to whatever your friend was obsessing over a little while ago. Granted not in 12-EDO.
In 14-EDO there is a Mode called "Gould's Nonatonic" which contains the following notes in the Key of C:
C D D\ E\ F G G\ A\ B\ C
if you play the following repeating pattern within that mode
1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 
You get 
*C* D D\ E\ G G\ A\ B\ D D\ E\ F G\ A\ B\ *C* D\ Etc. etc.

C to C over a span of 2 octaves. Aesthetically it sounds somewhat similar to a harmonic minor scale.
It appears to be a moment of symmetry which equals 3L + 12S (3 Large + 12 Small), I was looking for a Moment of Symmetry that has already been found that is equivalent to that but the closest I could find was Magic [13] which is 3L + 10s.

Edit: Apparently it's Mohavila, a cross between Mohajira and Mavila.


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## Osorio (Apr 11, 2012)

ixlramp said:


> Have you seen this one too?



Fantastic  The examples you posted above are excellent as well. I really liked the electronic music and the fractal-generated piece. Simply superb. BP has earned a new fan.
Has Elaine Walker made an album or something that I can get with her songs? I really dig the stuff so far.


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## Necris (Apr 11, 2012)

venneer said:


> Fantastic  The examples you posted above are excellent as well. I really liked the electronic music and the fractal-generated piece. Simply superb. BP has earned a new fan.
> Has Elaine Walker made an album or something that I can get with her songs? I really dig the stuff so far.


music


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## Osorio (Apr 11, 2012)

The computer programming major in me is having so many eargasms it's not even funny. Thank you so much! 

Something just hit me, it's kinda of a absolutely pointless comment, but at any rate: Listening to this type of thing if you have Perfect Pitch should be the most frightening of nightmares. How would one coupe with this...? I can imagine the frustration of someone who trained to attain perfect pitch and then stumble onto something like this... I can almost hear Darth Vader on the background: "NOOOOOOOOOOO!!!". But I digress...


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## Quitty (Apr 11, 2012)

I wonder if anyone's familiar with Olivier Messiaen.



If you find it overly... difficult, just note that Fredrik Thordendal is just a copycat (i'm kidding, fanboys. Chill), forward to 3:50 and let it play for a minute. 
I nearly shat my pants the first time i heard it. Felt like someone was molesting something beautiful inside my ear canals.

The thing with Messiaen, and the reason i think he's relevant to this thread, is that he transcribed, explained and built a musical theorem around the scales, modes and progressions played in Vingdt Regards - and as you can hear, it's a pretty funky theorem.

Lots of it is mathy, some concerns multi-octave scales, some are modes of microtonal scales that only use western frequencies.
I find there's something very emotional and intuitive about some of his progressions, chords and scales - 
and i think that bit around 4:00 is a great example - it's the very definition of 'almost'.
It's a terrible version, by the way - there's a far better version played by someone who's name i can't recall, but i can't find it -
so on the off chance that anyone knows a different version, i'd love to hear it.


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## ixlramp (Apr 11, 2012)

EDIT


venneer said:


> Has Elaine Walker made an album or something that I can get with her songs? I really dig the stuff so far.


Check out her youtube channel, and also that of billystiltner for lots of excellent fractal music ...



Lots of free micro electronic music, contemporary styles grooves and beats at split notes: split-notes microtonal netlabel


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## Sciurid (Apr 13, 2012)

Hello Folks,

Just wanted to chime in on the BP discussion - I find it quite an easy scale to work with, and within a few hours of playing around you can start hearing tritaves working like octaves. I'll make a video that has a melody played in different tritaves, but for now:


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## Sciurid (Apr 13, 2012)

This example is a melody heard first in a low register, then up 1 tritave, then with both sounding together.

Tritave comparison by Dustin Schallert on SoundCloud - Create, record and share your sounds for free


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## ixlramp (Apr 14, 2012)

Thanks for that, i can certainly hear the 'tritave similarity'. It's the exact same process that makes octaves sound similar but with a tripling of frequency rather than a doubling, so the octave is not special, it's just the simplest, most consonant and obvious choice for a repeat interval. Makes me wonder about scales repeating at the 5th harmonic (27.86 semitones), with the process of 'quintave / pentave similarlty'.


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## Mr. Big Noodles (Apr 15, 2012)

Sciurid said:


> This example is a melody heard first in a low register, then up 1 tritave, then with both sounding together.
> 
> Tritave comparison by Dustin Schallert on SoundCloud - Create, record and share your sounds for free



Thanks for the input. I still don't hear tritave similarity the same as octave similarity, but this discussion is making me think of the octave as just another interval. By the way, I enjoyed the melody. Did you compose it?


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## Explorer (Apr 15, 2012)

Having parsed this out as follows in my mind...



ixlramp said:


> ...(T)he octave is not special.
> 
> It's just the simplest, most consonant and obvious choice for a repeat interval.



...It sounds like the octave *is* special, and you even listed the reasons why.

I know, obvious observation is obvious, but that makes me wonder... if it is actually the simplest, most consonant and obvious choice for a repeat interval, then why don't you consider that unique and special set of characteristics enough to make it special?


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## ixlramp (Apr 16, 2012)

I do see what you mean


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