Dojo Foundation -- a new musical system

Thoughts and responses regarding the research at acousticlearning.com.
SunFishSeven
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Dojo Foundation -- a new musical system

Post by SunFishSeven » Sun Aug 08, 2010 10:28 pm

http://www.toneme.org/

The first picture on the website should give you everything you need to understand this.

I don't really know what to say here. Working on this system has exhausted me -- I'm looking to connect with individuals who can understand what I am doing.

this system bridges the ' absolute versus relative SolFa ' conundrum. by associating the absolute pitch with a consonant sound, and the pitch relative to tonal centre by a vowel sound, a musical language is created.

I think this language would be a powerful tool for teaching musical concepts, especially to children.

I think that perfect pitch would come as a natural consequence from this method of teaching.

the method is still in an experimental stage -- I still have a lot of difficult decisions to make as regards the written notation.

I would like to point out -- in this work I'm starting from scratch. I'm examining why the conventional musical system is based around the C major scale, and showing that while it was a sensible choice a thousand years ago, this is no longer the case. Since the introduction of tempered tuning systems, it makes more sense to define the 12 basic pitch classes and use this as a working basis.

I am not familiar with 'We hear and play' -- I cannot find much information about this method on the Internet. I would be interested to know how much overlap there is.

Sam

aruffo
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Post by aruffo » Tue Aug 10, 2010 11:23 am

I must confess that the first image reminds me somewhat of the Codex Seraphinianus... it may be a primer, but it serves to explain only to those who are already familiar with the concepts.

That is, I'm not sure how this proposed system would represent a natural expression of music...

aruffo
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Post by aruffo » Tue Aug 10, 2010 11:24 am

And I feel like a bit of a dunce for never even thinking to question why C is the note (and if so, why isn't it called A?). What have you learned?

Sleeper
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Post by Sleeper » Tue Aug 10, 2010 4:37 pm

I could have sworn we talked about that before here. My guess it that at one time the aeolian mode was the "main" mode rather than ionian. C ionian and A aeolian encompass the same notes (ie., the white notes on a piano), but the former starts on C and the latter starts on A.

paul-donnelly
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Post by paul-donnelly » Wed Aug 11, 2010 12:12 am

I'm looking at your TODO section in red there, and I have a few comments.

First, "equal divisions of the octave" is probably the term you want for contemporary mainstream tuning.

Second, I'll wager that the reason the two systems generate similar pitch classes is because the latter was chosen to conform roughly to the former, and the former likely to the dominant tuning system of the time. In our musical tradition, I don't think a tuning that didn't produce in-tune fourths and fifths could catch on, so that sort of limits your options.

As for which is more natural or elegant, I don't think those are the right questions. The question is which has the most desirable properties for your music. The question is: which notes do you need? Take a look at the graphs on this page.

http://sonic-arts.org/td/erlich/entropy.htm

If you accept the argument there, I think you'll agree that a scale that didn't place notes at the most striking minima would be deliberately strange. But what of the other sections of the graph, nearer the maxima? My contention is that in general, the specifics of notes in those areas are not important. Consistency could be important, but precise values are probably not. Since Pythagorean tuning and 12 equal divisions agree on the big issues (what is a fifth, for example), they both are equally in accord with nature, and I don't see how one can be placed above the other. Now, Pythagorean tuning might have desirable harmonic properties in certain situations, especially if you're willing to let it generate more than 12 notes for you (since powers of 3 will never produce a power of 2, Pythagorean tuning will never repeat at the octave), and 12 equal divisions might allow for free-ish transposition with a limited number of notes (hence fewer parts on your piano or organ), but neither has any claim to primacy.

I did say that in general, fine-tuning of more ambiguous intervals is not important, but I do think that music with pretensions to nuance can't afford to ignore the difference, and neither one size fits all solution is likely to be satisfactory. When writing this music, it might be appropriate to select a small set of carefully chosen pitches (like a drone composer might do), or it might be appropriate to use a nearly unbounded set (Ben Johnston used over 1200 individual pitches in his 7th string quartet), or most likely an intermediate number based on the notes needed for the harmonies you want. In any case, attention to specific tunings is crucial.

The upshot is that in my opinion, any system attempting to expose the structure of music needs to take into account both the fact that there are many more than 12 notes, all of which have real musical purpose, but also that there are contexts in which the overall musical purpose can be satisfied by any note that's close enough. Ignoring the first fact means obscuring the harmonic series, which is in my opinion fundamental to harmony, but ignoring the second means making distinctions where none belong. Put another way: while 12 equal divisions is clearly adequate for many purposes, it's not possible, using that system, to indicate a pattern as simple as the harmonic series which, while it doesn't necessarily need to be played precisely, would be very unclear if not written so. How can we elucidate or even investigate the principles of music when notation is at odds with the phenomena it describes?

My 20 cents anyway. I think the idea of indicating both pitch class and relationship to a tonal center in note names is an interesting one, although reducing harmony to 12 pitches doesn't seem very progressive to me. Your idea could potentially be better than the current system, although perhaps working from diatonic scales is the natural way to work.

SunFishSeven
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Codex Seraphinianus

Post by SunFishSeven » Wed Aug 11, 2010 9:26 pm

Thank you Chris for enriching my world -- I had never heard of this book, but now I have to get it! The lovemaking couple turning into an alligator... I cannot resist!

Yes -- it is a lot of material to put onto a single page. Yes, that page is intended for someone who understands musical theory. however, I have sent it to a couple of friends both of whom are without musical training yet keenly intelligent, and they were both able to comprehend it.

for most people music exists as a meta-conceptual language. we appreciate the beauty of the pattern, yet we have no explicit conceptual framework for studying or communicating these patterns, other than music itself. it is a language unto itself. we can hear a wrong note strike out in a piece of Vivaldi.

musical theory provides a conceptual basis; to my understanding it is at best a poor one, and in places deliberately misleading. It appears in places highly illogical -- it creates a logic that contradicts the logic of common sense. For example, the letters A B C D E F G are contiguous. but on a piano keyboard E is contiguous to F, whereas there exists an extra note between F and G. also the black notes do not have unique labels: F# and Gb seem to share the same physical note. and F# is a natural note in the key of G, whereas F-natural is not natural in that key. It is termed ' accidental ', as if some accident has occurred.

and then we look at the positioning of notes on the stave. it really is a challenge to figure out what is going on. Can you remember back to the first days of learning these things at school?

this system is not intuitive. I don't think any sane person could argue against that:

the system I am suggesting comprises a linguistic ( phonetic ) framework, as well as a conceptual ( visual ) framework.

by associating musical sounds with phonetic utterances, we can create a map into a part of our brain that is beautifully setup for handling these sorts of cross associations. for example, when you hear a 'C', it means something different depending on the context -- if you were in the key of C major it is your tonic. if you are in Bb it is your super tonic.

in my proposed system, Do Re Mi in C major would come out as Dar Reh Mi, and in Bb major as Kar Deh Ri. in A minor the first three notes would be Lah Teh Day.

so Dar, Deh, Day -- all of these are the physical note C. but in different contexts. and by singing in this system the brain would quickly learn that Dar associates with Reh and Mi, whereas 'Day' associates with Lah Teh

it is unfortunate that English (a non-phonetic language) has become the global standard. ;) on the paper I can use phonetic symbols, and it is much neater.

do you see, Chris? this follows directly from the point you leave off on your main page. you spot that Sesame Street teaches M as in monkey, meatball, hampster. and you are trying to apply the same principle to music.

well, here it is! I contend that learning this system through singing would teach perfect pitch to a child. I am going to try it out myself -- I will be surprised if it doesn't work for me.

{12 consonants}x{12 vowels} = 144 base phoneme pairs. and if anyone balks at that, just remember that we were taught our times tables at school at least up to 12x12.

SunFishSeven
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'logarithmic divisions of the octave'

Post by SunFishSeven » Wed Aug 11, 2010 10:13 pm

Paul, thanks for the reply -- there is much food for thought here.

firstly, I instinctively do not like the term 'equal divisions of the octave'. my inner aesthete is repelled -- these pitches are placed on a logarithmic scale. equal suggests linear.

the key is equivalence: one major key is equivalent to another in this system.

I am calling it chromatic tuning, the reason being the mathematical nature of the construction. whereas in the Pythagorean system new notes are generated one perfect fifth apart, in the chromatic system we generate consecutive semitones. to be specific, t_(k+1) = 2^(1/12) * t_k. for example, 'C#' = 2^(1/12) * 'C'

did you have a look at my history page? http://dojofoundation.wikispaces.com/History

together with the main page, this gives my best understanding of what has transpired, as regards tuning systems.

you say some things that I think are not correct: for example,
Since Pythagorean tuning and 12 equal divisions agree on the big issues (what is a fifth, for example), they both are equally in accord with nature


I think you will find if you do the maths, that if you line up the C's between the tuning systems, you will find that every one of the remaining 11 tones is out. only the C's match up.

I agree with you when you say that one size fits all is not going to work. Music in the Pythagorean tuning system is possibly going to sound more resonant, as the system derives from the principle of 2 standing waves vibrating on a string, compared with 3 standing waves vibrating on the same string. this gives us our perfect fifth, and from this perfect fifth Everything else is generated.

in this regard, the Pythagorean system is closer to nature. closer to the physical. And the chromatic system is more abstract -- it requires complex mathematics for its generation, whereas the Pythagorean system can be generated from a single string.

you write:
How can we elucidate or even investigate the principles of music when notation is at odds with the phenomena it describes?

this criticism would be better levelled at the existing system of music. Everyone today is playing on instruments tuned to the chromatic system. when we play F# and Gb, we are playing the same note. Yet the notation is not acknowledging this.

I think there should be a clear distinction between notation for music composed for the Pythagorean system, which uses a potentially infinite basis of pitches, and notation for music composed for the chromatic system, which uses only 12.

what we have at the moment is the first notation attempting to cater for both categories.

I have a hunch that it would be far clearer and cleaner for the second notation ( that I am working on ) to bend backwards and extend to express the first category. however, this is going out on a limb.

your final comment is interesting:
Your idea could potentially be better than the current system, although perhaps working from diatonic scales is the natural way to work.


what I am suggesting is to zoom out a level. instead of taking the diatonic scale to be the basis ( which is what conventional musical theory does ), I am suggesting: zoom out. take the ring of 12 elements as the basis. then the diatonic scale is a secondary construction over this basis: it is the pattern Y n Y n Y Y n Y n Y n Y superimposed over this ring.

and modulation becomes movement around the ring.

this is the framework that Chopin and Rachmaninov were using.

the problem with taking the diatonic scale as the basis is that when we modulate to another diatonic scale, this is seen from the perspective of the original. it is conceptualised as applying a botch to the original. Which quickly becomes messy.

I wager that it would be possible to correctly depict this movement from my proposed chromatic framework. eg A violinist would be able to use my chromatic notation and play Vivaldi with Pythagorean tuning. even though my notation would be representing F# and Gb as the same element, the context would be clear and they could play the appropriate pitch.

certainly I think it is worth investigating.

But all of this is very high-level brainwork -- if we are looking at a musical system to teach the children, I propose that the 12 tone system such as mine is used initially, and an exploration into the world of the Pythagorean system is taken as a more advanced study. I think that my system could successfully teach the basics of harmonising a melody, constructing chords, modulating etc and with this understanding a child would be set in good stead to uncover the nuances of classical harmony.

this was my motivation for this work -- I was offered a teaching position in a music school and could not overcome my reluctance to teach the conventional system.

Sam

PS you linked to a page with some very interesting Graphs. however, I found the page quite indecipherable. Could you give a concise understanding of what these graphs are conveying?

TS
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Re: Dojo Foundation -- a new musical system

Post by TS » Thu Aug 12, 2010 2:59 am

SunFishSeven wrote:It appears in places highly illogical -- it creates a logic that contradicts the logic of common sense. For example, the letters A B C D E F G are contiguous. but on a piano keyboard E is contiguous to F, whereas there exists an extra note between F and G. also the black notes do not have unique labels: F# and Gb seem to share the same physical note. and F# is a natural note in the key of G, whereas F-natural is not natural in that key. It is termed ' accidental ', as if some accident has occurred.

and then we look at the positioning of notes on the stave. it really is a challenge to figure out what is going on. Can you remember back to the first days of learning these things at school?

this system is not intuitive.


If your approach is to learn to play the piano like a mechanical device, looking at notes on the page and pressing corresponding keys on the keyboard, then it might not be intuitive why F# and Gb share the same note. But if your approach is to learn to read music for the musical meaning, then you will start with a scale.
Let's say you start with the C-major scale. It has notes that are called A, B, C, D, E, F, G.
Then let's look at the G-major scale. It has notes that are called A, B, C, D, E, F, G, exactly the same as C-major, but in this case the note F is altered, it is "sharpened" or "raised". It is still the note F, it's just a "sharper" F.
Then let's look at D-major. It has notes that are called (surprise!) A, B, C, D, E, F, G, exactly the same as C- or G-major. Only in this case the notes F and C are altered, "raised" or "sharpened".

Every scale has the same seven notes, A, B, C, D, E, F, G, some of them only have slight alterations to them depending on the scale. This is because the natural basis for music is a seven tone scale.

The reason why G-major has F# but not Gb, even when they can be played with the same key on a piano, is that in G-major the F note is altered but the G note is not. From a mechanical point of view this might seem illogical, but from a mechanical point of view you're not seeing the music, you're only seeing the mechanical motions of playing the piano or any other instrument.

Actually this system of notation is a combination of relative and absolute information. The relative part is that each scale degree has a unique letter name, and the absolute part is that the letter names also correspond to absolute pitches.

By the way, while some people say that a skilled violinist will play a different pitch for F# than for Gb, I don't believe this at all. I think this is only a justification for the notation system used by people who don't really understand how the system is supposed to work, who don't know the real justification.

SunFishSeven wrote: firstly, I instinctively do not like the term 'equal divisions of the octave'. my inner aesthete is repelled -- these pitches are placed on a logarithmic scale. equal suggests linear.


Octave itself is a logarithmic concept. Octaves are placed on a logarithmic scale. Octaves don't exist on a linear scale. Therefore I don't see how anything that's mentioned in connection with octaves can suggest linearity.

SunFishSeven wrote: in this regard, the Pythagorean system is closer to nature. closer to the physical. And the chromatic system is more abstract -- it requires complex mathematics for its generation, whereas the Pythagorean system can be generated from a single string.


The Pythagorean system is mathematically simpler to calculate than equal temperament, but actually equal temperament is the one that's closer to nature, closer to the physical, closer to the vibrating bodies.
Here is a table that compares Pythagorean and equal temperament to just tuning, which is the natural tuning. Looking at that table you can see that Pythagorean tuning gets the fifth, fourth and major second perfectly right, but the Pythagorean tuning is actually worse than equal temperament for most other notes. And even the ones where Pythagorean gets closer to nature than equal temperament, the difference is not very much.

SunFishSeven
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Post by SunFishSeven » Thu Aug 12, 2010 9:46 pm

If your approach is to learn to play the piano like a mechanical device, looking at notes on the page and pressing corresponding keys on the keyboard, then it might not be intuitive why F# and Gb share the same note. But if your approach is to learn to read music for the musical meaning, then you will start with a scale.
Let's say you start with the C-major scale. It has notes that are called A, B, C, D, E, F, G.
Then let's look at the G-major scale. It has notes that are called A, B, C, D, E, F, G, exactly the same as C-major, but in this case the note F is altered, it is "sharpened" or "raised". It is still the note F, it's just a "sharper" F.
Then let's look at D-major. It has notes that are called (surprise!) A, B, C, D, E, F, G, exactly the same as C- or G-major. Only in this case the notes F and C are altered, "raised" or "sharpened".

Every scale has the same seven notes, A, B, C, D, E, F, G, some of them only have slight alterations to them depending on the scale. This is because the natural basis for music is a seven tone scale.


I am aware of this logic that preserves the seven distinct letter names A, B, C, D, E, F, G in each scale.

I have covered all of this material on the website, although I really could do with some feedback -- it has got to be too much of a jumble and I don't know how to organise or manage it now -- too many things I want to say at the same time, and if I split it into sub pages then that doesn't feel right either.

my point is that there is no actual benefit in this preservation. you could say there is some conceptual neatness to it. But it is conceptually quite horrible. the root of the problem is that it is trying to express the G major scale in terms of the C major scale. it tries to express everything in terms of the C major scale.

I disagree with your argument:
Then let's look at the G-major scale. It has notes that are called A, B, C, D, E, F, G, exactly the same as C-major, but in this case the note F is altered, it is "sharpened" or "raised". It is still the note F, it's just a "sharper" F.


this is not true at all. It is a completely different note. look at its position relative to F in the cycle of fifths. It's pitch class happens to lie between that of F and that of G. it has only been designated 'F sharp' for the convenience of preserving the seven letter names. this whole concept of ' raising ' the seventh note is as far as I can see nothing more than a mnemonic -- a crutch to help the learner. to actually understand what is going on one would do better to visualise: http://dojofoundation.wikispaces.com/file/view/MathLoRes.jpg

as I have said above, the problem with the conventional notation is that it attempts to express everything in terms of the C major scale. another way of stating this is to say that it is using as its basis the major scale.

Every scale has the same seven notes, A, B, C, D, E, F, G, some of them only have slight alterations to them depending on the scale. This is because the natural basis for music is a seven tone scale.


it sounds like you are trying to brush something under the carpet: 'slight alterations' ...

choosing the diatonic scale as a basis is bound to create problems. An arbitrary one must be chosen as an anchor point, since in any non-tempered tuning system there are infinitely many potential candidates.

I go one level deeper. By choosing a basis at a deeper level (http://dojofoundation.wikispaces.com/file/view/TonemeBasis.png the 12 diatonic scales arrange themselves symmetrically around an empty centre.

the shift is from having C major at the centre to having an empty centre. with an empty centre the equivalence between keys can be accurately and readily conceptualised.

this conceptualisation is only possible with a finite basis; ie a tempered tuning system.

the tempered tuning system has changed the topological structure -- and this has been swept under the carpet. It should have been celebrated, but I can find no research to this end.

By the way, while some people say that a skilled violinist will play a different pitch for F# than for Gb, I don't believe this at all. I think this is only a justification for the notation system used by people who don't really understand how the system is supposed to work, who don't know the real justification.


hmm This shows that you don't understand what you are talking about. If you are really interested in engaging in this discussion, you should seek to understand why in a classical tuning F# is a different pitch from Gb. you can find a clear explanation on my site -- this should be a good start: http://dojofoundation.wikispaces.com/History

Sam

TS
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Post by TS » Fri Aug 13, 2010 4:55 am

SunFishSeven wrote: my point is that there is no actual benefit in this preservation. you could say there is some conceptual neatness to it. But it is conceptually quite horrible. the root of the problem is that it is trying to express the G major scale in terms of the C major scale. it tries to express everything in terms of the C major scale.


This same problem is present in your dojo-system also. You give the example of Do, Re, Mi in C-major: Da, Re, Mi, and the same in D-major: Ra, Me, Shi. The syllables that begin with R and M in C-major represent the same pitches as the syllables that begin with R and M in D-major, so by having R and M represent the same pitches in both C-major and D-major, you are actually trying to express everything in terms of the C major scale.

The root of the problem is that if you try to create a musically relevant system that includes absolute information then you will generate a system with a lot of stuff to memorise. It's the same with the dojo-system. You could leave out the relative stuff, in which case you would have a system with only 12 consonants to memorise but which would be musically useless. You could also leave out the absolute stuff, in which case you would have a system with only 12 vowels to memorise, musically a more useful system, but lacking absolute information. If you want to have both, then you will end up with 144 combinations to memorize.

You can remove the absolute information from conventional notation by a trick using the circle of fifths. If you travel the circle you will notice that every step adds or removes a sharp or a flat to/from the key signature. Knowing this you can count the number of sharps or flats in the key signature and then look up the key from the circle of fifths. Now you know the scale, and you can place 'do' on the line that is the root tone of that scale, and the other syllables correspondingly. You don't actually have to look at the sharps and flats at the beginning of the line and think "oh, notes on these lines should be sharp/flat, I'll try to remember that as I go along".

If you don't have absolute pitch then using this trick to remove the absolute information is pretty much the only thing you can do to read music. The other option is to be a mechanical player piano that just translates dots on paper to finger-presses on keys.

Similarly with the dojo system, if you don't have absolute pitch then the only thing you can do is to remove the consonants and use only the vowels, which reduces the system to just solfege with different syllables.

You write at the dojofoundation wiki:
For example, the scale of Db Harmonic Minor comprises {Db, Eb, Fb, Gb, Ab, Bbb, C}. This is ghastly!

If you had absolute pitch, you could just read those names and immediately hear the scale in your mind. Not so bad after all! If you don't have absolute pitch, you could examine those names, compare them to a chart of some sort, and eventually figure out that it's a harmonic minor scale. The point is that if you don't have absolute pitch, naming individual notes out of context is useless. You could have just read that it's harmonic minor, the root is a note called D (an altered D in this case, but a D nonetheless), and all the other degrees follow alphabetically, D, E, F, G, A, B, C. Yes, those notes are altered, some are flatted, one is even double flatted, but you would just think they are the degrees of a harmonic minor scale labeled in alphabetical order, and ignore the accidentals.

This exactly same uselessness of absolute information applies to the dojo system of naming individual notes.

You could argue that teaching the full dojo system to children might lead them to develop absolute pitch, but the conventional musical notation already has all the same features as the dojo system and it seems children don't develop absolute pitch by just learning the conventional system. This could also be because the conventional system is mostly taught wrong, which I think it is, since so many people don't seem to understand how the system works, leading them to use faulty arguments like "skilled violinists play a different pitch for F# and Gb".

SunFishSeven wrote:hmm This shows that you don't understand what you are talking about. If you are really interested in engaging in this discussion, you should seek to understand why in a classical tuning F# is a different pitch from Gb. you can find a clear explanation on my site -- this should be a good start: http://dojofoundation.wikispaces.com/History

Sam


No, I think this shows that you, among countless other people, don't understand the musical notation system.

First, the Pythagorean tuning system, where you stack fifths or fourths to derive all notes from one note, is not the natural tuning system. The natural tuning is called the "just tuning".

It should also be noted that the "classical tuning" you are talking about (stacking of fifths, Pythagorean style) was dead and buried long before Bach or Vivaldi or Mozart or Beethoven were born.

When a skilled violinist is playing a piece in equal temperament, he will notice that some intervals do not sound pure. That is because these intervals differ from just tuning, the natural tuning. The skilled violinist will then adjust the pitches just a little bit towards just tuning, so that the intervals sound pure again. The just tuning is what the skilled violinist is striving for, because it is the natural tuning.

Now, the argument is that the musical notation system somehow contains the information on which notes should be corrected like this, in that the same note can be called Gb or F# depending on context, and this indicates whether the note should be corrected sharp, flat, or not at all.

Here then is an example that demonstrates the misunderstanding in this argument:
Let's say that a violinist is playing a piece in the key of D-minor. He plays a D, and then he plays an F, which is the minor third degree of the D-minor scale. He notices that in equal temperament the F is too flat, so he corrects the F and makes it a little sharper.
Let's then say that the same violinist is playing a piece in the key of C-major. He plays a C, and then an F, which is the perfect fourth degree of the C-major scale. He notices that in equal temperament the F is just a bit too sharp, so he corrects the F and makes it a little more flat.

Did you notice what happened? The skilled violinist played the same note, F, and the note even had the same name the whole time, and yet the same note with the same name had a different pitch.

The argument is that the same note has two names, Gb and F#, because it has two slightly different tunings depending on context, and this is the reason for the naming scheme. "Gb is slightly different than F#, a skilled violinist can play the difference"
But the argument fails completely when you take that example of F. "F is slightly different than F, a skilled violinist can play the difference". So why isn't there a different name for these two Fs? Well, it's because the names were never meant to imply anything about the tuning of these pitches, or how a skilled violinist should play them.

SunFishSeven
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Post by SunFishSeven » Fri Aug 13, 2010 6:01 am

ok it seems you do know what you're talking about, so my apologies.

However, seeing as you are keenly engaging in this discussion, I wonder if you could stretch a little to see what I am talking about:

you say:
This same problem is present in your dojo-system also. You give the example of Do, Re, Mi in C-major: Da, Re, Mi, and the same in D-major: Ra, Me, Shi. The syllables that begin with R and M in C-major represent the same pitches as the syllables that begin with R and M in D-major, so by having R and M represent the same pitches in both C-major and D-major, you are actually trying to express everything in terms of the C major scale.


now, this last statement is false. it would take me a lot of words to explain why, but if need be I can. But it would be great if you could see it without my explaining. but if not, I will be happy to explain.

Many thanks for elaborating on the F#/Gb argument. That helps me to see things more clearly. That a written note is not defining a pitch -- the pitch depends on the context. I will update my website. Of course it is a constant compromise between being scientifically accurate (which will lose almost everyone's interest) and generally accessible ( which leads to inaccuracy ).

My system should also be flexible enough to do the same, by using 12 basic categories, the pitches of which can be bent depending on context.

so for the purposes of a piano, these pitches would need to be fixed. But for a violin they would be allowed to move freely.

As you point out, use of the vocal Dojo system would require 144 basic phoneme pairs. I notice people are scared even to move from seven note to 12 note SolFa, which is ludicrous. These people should just give up and watch TV or something. An easy life is always possible for the price of mundanity. this is not going to take too long to assimilate. Certain combinations will crop up together frequently, just as with language, only with language there are thousands of words.

and mastering it would be an art, bending the pitches in the same way you described. but this bending would go hand-in-hand with the phonetic content.

if you don't have perfect pitch, you would need to tune yourself in before you sing, otherwise you would be failing to reinforce and build perfect pitch.

another aspect I'm very interested in is that it would offer a musical comprehension at the linguistic level. almost everyone is capable of comprehending musical ideas simply as is -- this is a great tune -- that tune sucks etc. as a language unto itself. and those who study musical theory become capable of comprehension at a conceptual level. But comprehension at a linguistic level... this interests me.

anyway, many thanks for the last post. That material is really valuable to my understanding.

I just ask that you be not too hasty to shoot the system down, lest the shots land off target and cause clutter. A good shot to the heart of the matter is the Grail of evolution.

TS
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Post by TS » Fri Aug 13, 2010 7:35 am

SunFishSeven wrote: you say:
...
, so by having R and M represent the same pitches in both C-major and D-major, you are actually trying to express everything in terms of the C major scale.


now, this last statement is false. it would take me a lot of words to explain why, but if need be I can. But it would be great if you could see it without my explaining. but if not, I will be happy to explain.


I think I can see that, but I think there is also a way of seeing that the conventional system isn't based just on the C-major scale either. Just as much as you can say that the conventional system tries to express everything in terms of the C-major scale, you could say that it tries to express everything in terms of the A-minor scale. And you could go on, saying that it tries to express everything in terms of the G-mixolydian scale, or the D-dorian scale, or the F-lydian scale, or the B-locrian scale, and so on. So there really isn't one scale that everything is based on, there are more like seven absolute anchors spread across the frequency spectrum, and different scales can be built by combining these anchors, and applying modifications in some cases.

The fundamental problem is in including information about absolute pitches when to most people this information is meaningless. If you want to understand the conventional system you have to learn to ignore the absolute aspects and colour in the relative bits with your imagination, or you have to have absolute pitch. I am afraid that this same fundamental problem will appear in any system that tries to incorporate absolute information to non-absolute pitch people.


SunFishSeven wrote: I notice people are scared even to move from seven note to 12 note SolFa, which is ludicrous. ... ... this is not going to take too long to assimilate. Certain combinations will crop up together frequently, just as with language, only with language there are thousands of words.

What I think will happen is that the combinations that will show up together frequently will be the 7 note scales, so you would first learn 12 note solfege, and then end up using 7 note solfege anyway.

If I were to create a new notation system for music, I would try to create a system that uses symbols written on a single line, one after another, just like written language. You can teach a child to draw a familiar word even when the child doesn't actually know how to read or write. You can show that DOG is a half circle, a full circle and a partially angled spiral, and the child can then draw a familiar word, and know what it means. But you can't really teach a child to draw a familiar tune. First you'd have to draw the staff lines, then the clef, then the key signature, then you have to count the lines to know where the dots should be drawn, and then you have to mark the rhythms.

If a system were to promote musical literacy it would have to be convenient enough to use even for small things. You should be able to take a pen and sticky note and write a simple melody on it in an instant. You should also be able to read it without counting which line a certain dot is on, and what the key signature is.

paul-donnelly
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Re: 'logarithmic divisions of the octave'

Post by paul-donnelly » Fri Aug 13, 2010 8:49 pm

SunFishSeven wrote: did you have a look at my history page? http://dojofoundation.wikispaces.com/History

I think your details on Gregorian chant are off. It revolved not around the major scale (in fact, the Ionian mode was not officially a part of the theoritical system until around a millenium after the system's first use), but around 8 modes, four authentic and four plagal. This is from Knud Jeppesen's Counterpoint.

It seems odd to me to call the Pythagorean notes "harmonic" (this is what you're doing, correct?). I would have used that word to refer to notes derived from the harmonics of a fundamental. The fifth certainly is, and the fourth (fifth below) is an undertone, but from that point the Pythagorean scale diverges from being harmonic. The best it manages is rational-number ratios to the fundamental.

I think you may be confused regarding the relationship of Pythagorean tuning to the harmonics of a string. Pythagorean tuning proceeds by fifths exclusively, and to make it repeat at the octave, you need to take your spiral of fifths and transpose it to each other octave. Stacking fifths will never produce an octave. The harmonics you get by touching a string do not follow the same series. They proceed: fundamental, octave, octave+fifth, two octaves, octave+major third (flatter than the equal-division third), two octaves and a fifth, harmonic seventh (which is a bit flatter than the equal-division minor seventh that two stacked fourths produce), three octaves, and it continues in this way, not by fifths but by multiplying by the fundamental. The series is f*n, where f is the fundamental and n is the harmonic. Harmonics of 20 Hz: 20*1, 20*2 , 20*3, 20*4, 20*5, 20*6, 20*7, 20*8.... You can transpose those to the octave as well: 1/1, 1/1, 3/2, 1/1, 5/4, 3/2, 7/4, 1/1.... Notice that the harmonics, besides not being the same ratios as Pythagorean tuning, do include octaves (several times over, in fact).

SunFishSeven wrote:
Since Pythagorean tuning and 12 equal divisions agree on the big issues (what is a fifth, for example), they both are equally in accord with nature

I think you will find if you do the maths, that if you line up the C's between the tuning systems, you will find that every one of the remaining 11 tones is out. only the C's match up.

To be sure. But the fifth is 702 cents in Pythagorean tuning, and 700 cents in the other. The fourth: 498 versus 500. Indistinguishable from one another, and both enough close enough to the minima on that graph that I would say they fill the scale positions perfectly. These minima I consider natural positions for notes to be in, and since both scales are equally good fits, I think you can see where I'm coming from. Both scales go somewhat crazy after this point, and you're left asking yourself why any interval would be more natural than any other. You could come up with a theoretical reason, but would it have any correlation to human perception?

SunFishSeven wrote:
How can we elucidate or even investigate the principles of music when notation is at odds with the phenomena it describes?

this criticism would be better levelled at the existing system of music. Everyone today is playing on instruments tuned to the chromatic system. when we play F# and Gb, we are playing the same note. Yet the notation is not acknowledging this.

It probably applies very well to the existing system too.

SunFishSeven wrote:PS you linked to a page with some very interesting Graphs. however, I found the page quite indecipherable. Could you give a concise understanding of what these graphs are conveying?

The page puts forth the idea that for any interval played, there's for the hearer a degree of uncertainty about which one it might be. The graphs chart the uncertianty for an octave of pitches proceeding smoothly and not by scale degrees. Minima are areas of low uncertainty (702 Hz, for example, which is the general area where the fifth always falls), and maxima are particuarly uncertain zones. The measure is based on how many rational-number intervals with numerators below N (which varies from graph to graph) fall at a given point in the octave, and regions with greater density have less definite intervals. This is the source of my thinking on "naturalness", because while there are a few points where a particular interval is overwhelmingly prime, how can we decide which kind of third is the standard when there are so many equally good choices?

SunFishSeven
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Post by SunFishSeven » Tue Aug 31, 2010 10:38 pm

I think I can see that, but I think there is also a way of seeing that the conventional system isn't based just on the C-major scale either. Just as much as you can say that the conventional system tries to express everything in terms of the C-major scale, you could say that it tries to express everything in terms of the A-minor scale. And you could go on, saying that it tries to express everything in terms of the G-mixolydian scale, or the D-dorian scale, or the F-lydian scale, or the B-locrian scale, and so on. So there really isn't one scale that everything is based on, there are more like seven absolute anchors spread across the frequency spectrum, and different scales can be built by combining these anchors, and applying modifications in some cases
.

really we are saying the same thing now. It is only the terminology that is being argued. it seems to me you are using ' scale ' when you should be using ' mode of the scale '. to my understanding there is no such thing as the A-minor scale. It is simply one of the seven modes of the C Major scale.

yes, seven anchors. Seven pitch classes. This is the historical basis.

The fundamental problem is in including information about absolute pitches when to most people this information is meaningless. If you want to understand the conventional system you have to learn to ignore the absolute aspects and colour in the relative bits with your imagination, or you have to have absolute pitch. I am afraid that this same fundamental problem will appear in any system that tries to incorporate absolute information to non-absolute pitch people.


absolute pitch information is not in anyway meaningless. Just -- hitherto meaning has not been attributed to it. and to say that to understand the conventional system you have to learn to ignore the absolute bits is plain wrong. to understand the conventional system it is not necessary to learn the absolute information. It is not as if one has to train oneself to ignore it. the opposite is true -- one has to train oneself to acquire it. And as aruffo points out on his website, there has never been a coherent mechanism for this training -- the brain learns by reward systems, and there is no naturally occurring reward for developing this skill. You care that the sound is the roar of a lion; you care not for the pitch at which he roars.

behind your words is an assumption that absolute pitch is either something people have or don't have. The truth is it is something that is acquired. Talking with people who possess the skill, unanimously they have said ' at one point I didn't have it, then I did '. if someone cannot say this, they have simply acquired the skill earlier back than they can remember.

And my work is to create a framework that facilitates and encourages this acquisition. Because perfect pitch is to my understanding an essential musical skill.

If I were to create a new notation system for music, I would try to create a system that uses symbols written on a single line, one after another, just like written language.


This is what my system does. by creating a linguistic representation, straightaway this can be written down: Dah Reh Mih.

I think your details on Gregorian chant are off. It revolved not around the major scale (in fact, the Ionian mode was not officially a part of the theoritical system until around a millenium after the system's first use), but around 8 modes, four authentic and four plagal. This is from Knud Jeppesen's Counterpoint.


Thank you for the correction! this does not, however, alter the point I'm making.

I am aware of the construction of the harmonic series. You are right! I should not be calling the Pythagorean notes harmonic, if that's what I'm doing. I have had my head in iPhone development for the past month so I haven't checked back to the website.

Definitely I should call them Pythagorean notes/Pythagorean system/Pythagorean basis etc

but if I remember correctly, I am just referring to their construction -- each new note is constructed as the first distinct harmonic from the previous one. So starting from C, G is the first distinct harmonic. (3 standing waves on the string). Starting from G, D. etc

TS
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Post by TS » Wed Sep 01, 2010 12:42 am

SunFishSeven wrote: absolute pitch information is not in anyway meaningless. Just -- hitherto meaning has not been attributed to it.


If you have absolute pitch, then absolute information is not meaningless. But if you don't have absolute pitch, then absolute information is meaningless, in a musical sense. You could still use the absolute information as a mechanical guide, showing you which key to press down.

You say that the conventional system is based on the C-major scale, but it is not, it's based on seven absolute pitches. The reason why you think it's based on a scale is because you are unable to understand what a pitch means, you can only understand a scale. This is the case for anyone who doesn't have absolute pitch.

If I show you a paper with a letter drawn on it, like the letter 'E', then would you know what it means? Would you be able to hear in your mind the sound that 'E' represents?
If I show you a staff with a note drawn on it, say the note 'Ab', then would you know what it means? Would you be able to hear in your mind the sound that 'Ab' represents? Without absolute pitch you wouldn't. But you could look at the key signature and see that the Ab appears to be the third degree in the key of F minor, or you could see that the Ab appears to form a major chord with two other notes, and when you've come to this point you've already abandoned the concept "A flat" and replaced it with "third degree of a minor key" or "root of a major chord".

SunFishSeven wrote: behind your words is an assumption that absolute pitch is either something people have or don't have.


Pregnancy is also something that people either have or don't have, but at the same time it's also an aquired thing. One doesn't rule out the other. You either understand what a pitch means, or you don't.

SunFishSeven wrote:
If I were to create a new notation system for music, I would try to create a system that uses symbols written on a single line, one after another, just like written language.


This is what my system does. by creating a linguistic representation, straightaway this can be written down: Dah Reh Mih.


You could do the same with conventional solfege: Do Re Mi, or just numbers: 1, 2, 3, but it's still missing the rhythm aspect. I don't know if it's possible to code both pitch and rhythm on one line.

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