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Yet Another Button Diagram For The Ec Treble


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#55 Wolf Molkentin

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Posted 15 May 2013 - 12:30 AM

 

Let me add one point: Frankly, I hadn't been aware of the fact that the naming of intervals simply derives from counting staff positions (or white keys, or EC middle row buttons). Prior to taking part in this current discussion I had been of the opinion that the difference of, for instance, an augmented unisone and a minor second would be one regarding the diatonic function, i.e.: that F# to G would have to be regarded as minor second just as part of a Gmaj scale (or one of the relatives). Now I have learned, that the basic concept is not just diatonic based, but more specific upon the single "world" of Cmaj/Amin/Ddor/Gmix a.s.f. and not be transferred to other keys.

 

I'm not sure I understand what you're saying here. Are they not both true? What meaning does counting letters have if not in a diatonic context? F#-G and Gb-G sound the same out of context. The intervals have different names because of how they are used (and the expectations that they create in the listener) in the context of the diatonic scale.

 

David, thank you for the reply! I seem to have learned from it that even the somehow distracting use of bb and ## ensures just the portability of the basic white-key concept into any given key. The same is pretty obvious regarding the - functional - minor second.

 

But just to ensure that I've got it right now I'd like to come back to the - non-functional - augmented unisone as well. Talking, for instance, about Schubert and his frequent "shadowing" from Major to Minor, regarded as one first step of, say, weakening the diatonic funktionality: F#-F (in the key of D) equals E-Eb (in the key of C); no (minor) second in any event.

 

This leads me back to my attempt to refine the formula regarding Don's chart one more time: The step from sharp to natural equals the step from natural to flat as every three notes share the same staff position.

 

After all, I find that diatonic issue (which I have always been into) all the more fascinating! Very productive thread for me as well...

 

I hesitate to add that notorious ceterum censeo of mine, but... anyway! I am regarding Piano and EC (and the German 20b concertina, as contrasted with the 30b-onwards Anglo due to its kind of irregular row of accidentals) as basically diatonic instruments because all the tones are  strictly organised around the naturals (which might fit the Crane as well, apart from its recently discussed irregularity).

 

Might well be that I'll fall on at least one pair of sympathetic ears in this context...  :)



#56 JimLucas

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Posted 15 May 2013 - 03:43 AM

 I am regarding Piano and EC (and the German 20b concertina, as contrasted with the 30b-onwards Anglo due to its kind of irregular row of accidentals) as basically diatonic instruments because all the tones are  strictly organised around the naturals (which might fit the Crane as well, apart from its recently discussed irregularity).

 

Yes, so is the Crane, and so is the Maccann, for that matter.  All usually organized around the diatonic scale in the key of C.

 

But... all except the anglo are also organized around the chromatic scale.  The English and Crane clearly have reserved columns specifically for the accidentals and fixed patterns for their placement.  So does the (uniform) Maccann, except that to completely fulfill that criterion one would need 7 columns, with two of them (one for naturals and one for accidentals) only half filled.  Instead those two half-dense columns have been interwoven into a single column.

 

But the piano is the most "obvious" yet overlooked example of diatonic and chromatic scales having shared status.  On a (properly constructed) piano, all the white keys are equally spaced (of equal width) at the diatonic "front" of the keyboard, but at the chromatic "back" of the keyboard all the keys -- both white and black -- are equally spaced.



#57 Łukasz Martynowicz

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Posted 15 May 2013 - 06:04 AM

@sjm: "I wonder if this is because the previous sounds have established some sort of mental expectation of what parts of a scale should sound like - and then the actual sound does not match this expectation." - that is EXACTLY what diatonic and other non-symetrical scales do! Think of it as "formating" your brain - it gets used to steps of a scale (played both melodicaly or in chords) just like it gets used to stairs: you can climb stairs of any height as long as they are all same height, but if one will have different you will trip or stomp on it. Our brains are very good at finding patterns (or making them up :D). Listen to some examples of whole-tone scale on YT - it is a scale with all notes two semitones apart. When you'll listen to it directly after listening to something "normal" (diatonic) it will sound awkward. But If you'll just loop it, it will become completely normal after just few repetitions. And this is a scale that leaves no expectations - it is even, "flat", symmetrical. It won't force you to stop on tonic note, because there is no tonic note.. It wouldn't force you to arrange your improvisation in any way, so as long as you'll stick to the scale "anything goes". That's why it is so popular within jazz. I've read about it only recently, but for me, it is a great reference point and should be (maybe is, I don't know :)) taught (or just introduced) before diatonic scales, to give foundations to understanding how and why diatonic scales work as they do.

 

@diatonic instruments: For me, it's a secondary matter, that an instrument is diatonic or chromatic - I can do just fine on any that has logical and cyclic layout. That's why I have given up anglo and was frustrated by clarinet. I find EC, Wicki-Hayden, or various chromatic button accordion isomorphic layouts far more musical, as they incorporate in a very clear way the fundamental principle of octave consonance and cyclic nature of music. Of course piano keyboard has this property "embedded" in the layout, and octaves do look the same throughout whole range, but I personally don't like it for its linear construction. Concept of pitch is usually taught as a linear space of staff or a circular space of octave, but it's both at the same time - so for me the most adequate representation of musical space would be a 3d, conical spiral. This way a piano is a built along the spiral and two dimensional layouts are built "across" or are a "side view" of it.



#58 Wolf Molkentin

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Posted 15 May 2013 - 07:12 AM

 

 I am regarding Piano and EC (and the German 20b concertina, as contrasted with the 30b-onwards Anglo due to its kind of irregular row of accidentals) as basically diatonic instruments because all the tones are  strictly organised around the naturals (which might fit the Crane as well, apart from its recently discussed irregularity).

 

Yes, so is the Crane, and so is the Maccann, for that matter.  All usually organized around the diatonic scale in the key of C.

 

But... all except the anglo are also organized around the chromatic scale.  The English and Crane clearly have reserved columns specifically for the accidentals and fixed patterns for their placement.  So does the (uniform) Maccann, except that to completely fulfill that criterion one would need 7 columns, with two of them (one for naturals and one for accidentals) only half filled.  Instead those two half-dense columns have been interwoven into a single column.

 

But the piano is the most "obvious" yet overlooked example of diatonic and chromatic scales having shared status.  On a (properly constructed) piano, all the white keys are equally spaced (of equal width) at the diatonic "front" of the keyboard, but at the chromatic "back" of the keyboard all the keys -- both white and black -- are equally spaced.

 

 

We agree on this matter, don't we? Diatonic scales complemented to fully chromatic; and that's what I cherish with "my" piano and EC (and certainly would with one ot the above-mentioned Duets as well).

 

Besides, from my (limited) experience (with an attic found of some sort) there could hardly be imagined an instrument being "lesser" diatonic than a bandoneon. But OTOH there is just as little chromatic order. Turned out as completely maddening for me...



#59 Łukasz Martynowicz

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Posted 15 May 2013 - 10:53 AM

@Wolf: "Diatonic scales complemented to fully chromatic" - historically they did, but from more holistic approach they are a subset of a chromatic system (and further microtonal or contiuous pitch music) and they are easier (for me at least) to understand that way. I think of it in a same way as of Newton-Einstein approach to gravity or (kind of) Ptolemaic-Copernican model of planetary movement. Without wider context diatonic scales require a lot of theory to understand how they work and all of the different intervals functions, scale modes, chord progressions etc.. are a little bit like deferents and epicycles in Ptolemaic model. In fact, they were both build up on same principles - mathematics at that time was much more a dogmatic set of beliefs than a well explained and coherent knowledge. E.g. Pythagorean tuning was introduced based on belief, that simple fractions are pure and perfect and not because it's somehow fundamental to music in general. And using a perfect fifth was best available way to tune a string intrument. It was Pythagoras who first found, that square root cannot be written as a simple fraction and that was a fundamental revolution back then - such "impure number".... Music theory was more in a domain of philosophy and dogma than strict science, so it's full of patches and arbitrary beliefs, "schools", practices and so on.. Some of them are fundamentaly true, some are just a consequence of previous choices.. Indian music is based on completely different division of octave to 22 steps and is as beatifull and rich as western, diatonic music. 



#60 Anglo-Irishman

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Posted 15 May 2013 - 02:03 PM

@Wolf: "Diatonic scales complemented to fully chromatic" - historically they did, but from more holistic approach they are a subset of a chromatic system (and further microtonal or contiuous pitch music) and they are easier (for me at least) to understand that way.

 

Lukasz,

Confining ourselves to European music, it is my observation that basic melodies and harmonies are built on the diatonic scale and its modes (a mode consisting of the same notes, but using a note other than the 1st step as the home note or tonic). This applies to traditional European musics, and also to all but the most modern academic music. If this were not so, there would be no point in putting a key signature at the start of a classical score - we would use accidentals where necessary!

 

It is important to note that the natural, diatinic scale consists of larger and smaller intervals. Today, we tend to refer to them as whole tones and semitones, but this is only an approximation. The major 3rd is flatter and the pure 5th sharper than if they were each made up of equal semitones. A major chord made up of a root and such a 3rd and 5th sounds perfect. 

 

The perfection, however, quickly fades when we build an instrument - piano, concertina, guitar - that has to be capable of playing in several keys. Because, for instance, what is the 3rd of the diatonic scale of C is the 5th of the diatonic scale of A. So if the instrument is tuned to the diatonic scale of C, the 5th of A will be flat, and if you tune it to the diatonic scale of A, the 3rd of C will be sharp. In both cases, the major chords will sound "sour." To remedy this, and make the chords of C major and A major sound equally pleasant, we have (after a long process) adopted equal temperament for fully chromatic instruments.

 

The converse of this is, of course, that a diatonic scale cannot be regarded as a subset of the equal-tempered, chromatic scale. Conceptually, equal temperament makes it possible to play any diatonic scale, but practically, each diatonic scale is less harmonious than if it were played on a diatonic instrument in "just," i.e. natural tuning with unequal intervals.

 

In the autoharp community - autoharp music lives from its rich harmonies - a real dichotomy is seen between diatonic and chromatic autoharps. An autoharp with only 7 strings per octave is usually tuned "just", i.e. so that all the chords sound "sweet." A chromatic autoharp, with 12 strings per octave and chord bars that enable 3 or more keys, has to be tuned to equal temperament (or at least some form of meantone) if none of the chords are to sound "sour."

 

The final proof that "diatonic" is not a subset of "chromatic" is the fact that a just-tuned, diatonic autoharp, when played together with equal-tempered, chromatic instruments that are nominally playing in the autoharp's key, just does not sound in tune, however "sweet" it may sound by itself.

 

Cheers,

John



#61 Łukasz Martynowicz

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Posted 15 May 2013 - 03:54 PM

John,

of course I agree, that natural diatonic scale in just tuning is not just a subset of equally temperamented chromatic scale in terms of how they sound. I know, that just tuning sound sweeter, because that's the physics of vibrating strings - one cannot argue with that :) I know, that diatonic circle of fifths is something matematicaly different than chromatic circle of fifths. And I am aware, that whole music written earlier than 1900 is diatonic. I do not say, that diatonic is in any way obsolete, useless or wrong...

 

What I'm saying only aplies to understanding why diatonic scales work as they do, why they produce "expectations in the listener" - and that concept can be understood easier (in my opinion) while analysing them in context of other scales, especially chromatic symmetrical ones and whole-tone scale. And that's what jazz and modern academic music is doing.

 

Again, there are two layers (not as separate this time as earlier) - how do notes and intervals sound and what they feel like in psychological way. Whether in natural, just tuning or any temperamented one, diatonic functions remain the same. If it were not the case, only diatonic autoharps would exist and only music played on trully diatonic instruments would have it's psychological impact. And all non-western, non-Pythagorean music would be noise rather than music and we know, that it is not. So diatonic music is just a subset of something larger, but "just" has no negative meaning attached. What I was wrong about was calling this larger entity a chromatic scale. Maybe this time it's clearer what I have in mind...



#62 Łukasz Martynowicz

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Posted 15 May 2013 - 04:08 PM

One more thing - just as with planetary movements, realising that circle is not the most perfect, "godly" shape and that planets move on elipses made progress of astronomy possible, the idea that there can be other types of semitones and octave can be divided differently have opened music to whole new ideas. Of course, that doesn't change the fact, that our brains prefer circles over elipses and just tuning over temperamented one.


Edited by Łukasz Martynowicz, 15 May 2013 - 04:09 PM.


#63 David Barnert

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Posted 15 May 2013 - 10:22 PM

But just to ensure that I've got it right now I'd like to come back to the - non-functional - augmented unisone as well. Talking, for instance, about Schubert and his frequent "shadowing" from Major to Minor, regarded as one first step of, say, weakening the diatonic funktionality: F#-F (in the key of D) equals E-Eb (in the key of C); no (minor) second in any event.

 

This leads me back to my attempt to refine the formula regarding Don's chart one more time: The step from sharp to natural equals the step from natural to flat as every three notes share the same staff position.

 

After all, I find that diatonic issue (which I have always been into) all the more fascinating! Very productive thread for me as well...

 

I hesitate to add that notorious ceterum censeo of mine, but... anyway! I am regarding Piano and EC (and the German 20b concertina, as contrasted with the 30b-onwards Anglo due to its kind of irregular row of accidentals) as basically diatonic instruments because all the tones are  strictly organised around the naturals (which might fit the Crane as well, apart from its recently discussed irregularity).

 

Might well be that I'll fall on at least one pair of sympathetic ears in this context...  :)

 

Wolf, this is a very interesting discussion and I'd like to be able to help you here, but I can't quite parse the question you're trying to ask.

 

 

On a (properly constructed) piano, all the white keys are equally spaced (of equal width) at the diatonic "front" of the keyboard, but at the chromatic "back" of the keyboard all the keys -- both white and black -- are equally spaced.

 

This is not obvious, but it's true. Did you ever take a close look at a piano keyboard? A real one, not an electronic PLO (Piano-Like-Object). There is more space between the black keys (measuring from center to center) than the white keys. The notches in the white keys that make room for the black keys are not symmetrical. F#, for instance, takes a bigger bite out of F than of G. G# is symmetrical, and Bb leans into B. This actually fits the human hand optimally and makes playing easier. But it also makes the black keys and the skinny parts of the white keys the same width and evenly spaced, as they would pretty much have to be in order to strike the evenly-spaced courses of strings.

 

 

PianoKeys.gif



#64 Wolf Molkentin

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Posted 16 May 2013 - 02:54 AM

 

But just to ensure that I've got it right now I'd like to come back to the - non-functional - augmented unisone as well. Talking, for instance, about Schubert and his frequent "shadowing" from Major to Minor, regarded as one first step of, say, weakening the diatonic funktionality: F#-F (in the key of D) equals E-Eb (in the key of C); no (minor) second in any event.

 

This leads me back to my attempt to refine the formula regarding Don's chart one more time: The step from sharp to natural equals the step from natural to flat as every three notes share the same staff position.

 

Wolf, this is a very interesting discussion and I'd like to be able to help you here, but I can't quite parse the question you're trying to ask.

 

David, the second half of my post (regarding the ceterum censeo) has already been answered by Jim (leading to your further remarks on how the piano keyboard being measured), for what reason I omitted this item in the first place.

 

The first half just dealt with my understanding of analogical relationships of both staff notation and piano (and as well the EC's) keyboard to diatonic scales whilst advancing within the circle of fifths. I believe to have learned that due to the grounding of any note of any diatonic scale on just one natural tone (as being part of the Cmaj and parallel modes) / white key / center row button the naming of intervals is strictly running in parallel with their diatonic function. Maybe this is just too obvious from your point of view, whereas mine had been somehow obscured temporarily.



#65 Wolf Molkentin

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Posted 16 May 2013 - 03:27 AM

@Wolf: "Diatonic scales complemented to fully chromatic" - historically they did, but from more holistic approach they are a subset of a chromatic system (and further microtonal or contiuous pitch music) and they are easier (for me at least) to understand that way. I think of it in a same way as of Newton-Einstein approach to gravity or (kind of) Ptolemaic-Copernican model of planetary movement. Without wider context diatonic scales require a lot of theory to understand how they work and all of the different intervals functions, scale modes, chord progressions etc.. are a little bit like deferents and epicycles in Ptolemaic model. In fact, they were both build up on same principles - mathematics at that time was much more a dogmatic set of beliefs than a well explained and coherent knowledge. E.g. Pythagorean tuning was introduced based on belief, that simple fractions are pure and perfect and not because it's somehow fundamental to music in general. And using a perfect fifth was best available way to tune a string intrument. It was Pythagoras who first found, that square root cannot be written as a simple fraction and that was a fundamental revolution back then - such "impure number".... Music theory was more in a domain of philosophy and dogma than strict science, so it's full of patches and arbitrary beliefs, "schools", practices and so on.. Some of them are fundamentaly true, some are just a consequence of previous choices.. Indian music is based on completely different division of octave to 22 steps and is as beatifull and rich as western, diatonic music. 

 

Łukasz, altbeit having dealt just with keyboards myself, I find the comparision between diatonic scales and the Ptolemaic epicycles (which are beautiful in terms of art) quite interesting.

 

Nevertheless, the somehow restricted diatonic theory (as having emerged in the course of the centuries) seems to explain and further a certain praxis.  As you have already pointed out regarding Pythagoras there definitely had some choices to me made, just because there are no "pure" maths of melody and harmony. OTOH continuous pitch wouldn't have generated a universe of musical culture on its own terms as the (admittedly arbitrary) diatonic scales have.

 

My main interest has always been for the "world" of parallel modes and transcending modulations. This parallels or specifies my general interest for culture, objective spirit (prominently including "dogma" as well as the law) and the fascinating fact of their immanent regularities being rooted in arbitrations.

 

As a musician I (whilst appreciating the wider "theoretical", say Newton-Einstein way of looking to music by all means) love to swim around in that (arbitrary but never ending) ocean of traditional notes and relations..., now and again pushing forward to new borders and adjacent territories...  :) 

 

(typos corrected)


Edited by blue eyed sailor, 16 May 2013 - 03:29 AM.


#66 Wolf Molkentin

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Posted 16 May 2013 - 03:34 AM

There is more space between the black keys (measuring from center to center) than the white keys.

 

 

PianoKeys.gif

 

 

Definitely (even contrary to illusion)! Playing the piano for some 45 years myself I hadn't been aware of this!  :)



#67 Łukasz Martynowicz

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Posted 16 May 2013 - 04:47 AM

Again this thread led me to further reading - this time on the subject of diatonic scales and different tunings and I understand now, why equal temperament tuning was such an achievement. We cannot simply say, that music of pre 1900 was diatonic, as different historical tunings made different things possible and music was written with "diatonic language" but for specific tunings. And that just tuning had to be sacrificed for something else not beacause we wanted to be able to play music in any key on one instrument, but to close an octave and make some of the intervals sound more consonant, thus enabling added complexity to composed music.

 

Wolf, again, I do not say, that diatonic scales are in any way limiting. In fact, while I may "sail off" the boundaries of diatonic system in this thread, my point of focus is still on understanding why do they work as they do and academic nauture of this aproach is separate from just enjoying the music itself :) This thread have helped me to understand why I do like pre-1900 music, why I do like early XX century music (both popular and classical) and why I don't like most of jazz

and most of contemporary academic music.  

 

This thread is a crash course on music theory for me, and has given me so much... Thank you all :)



#68 Anglo-Irishman

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Posted 17 May 2013 - 10:23 AM

Friends,

Now that this thread has quietened down a little, perhaps we should put the whole interesting topic into perspective.

 

It is a philosophical truism that science does not define the natural world - it merely attempts to describe it. And music theory is a branch of science, involving lots of maths and physics. Music itself was there before there were musicologists, and even today, it thrives in places where there are no musicologists to worry about it.

 

The value of musicology for us musicians is that the way it describes our music makes us more aware of what we are doing, so that we can perhaps do it better.

 

Another truism - a linguistic one, this time - is that writing does not define language, it only reflects speech. The same is true of musical notation and music. To say, for instance, that classical musicians play music "as it is written" is an over-simplification; what they do is play the music "as the composer must have heard it in his head in order to write it the way he did." 

 

As long as we remember that musicology is not music, and notation is not music either, we can benefit from being scientific and literate.

 

In this, music is like the real world - because it is a part of the real world!

 

Cheers,

John



#69 cboody

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Posted 18 May 2013 - 12:52 AM

Thanks John, good stuff there.  As a musicologist (at least once upon a time) I think your statements are spot on.  Musicologists place music in historical context or attempt to explain musical content in ways that allow sensible consistent ways of looking at quite different musics (after all the term really means "'sciencing' about music").  I've known some musicologists who forget that what we are about is studying music and not about music itself.  But, the good ones always remember.

 

As to notation and its relation to actual music:  Notation is a guide.  It is no more than that.  It is NEVER a complete representation of music except in some isolated instances in 20th century music.  To properly play any music, be it Irish Trad, Morris Dance, Baroque concertos, classical works, romantic works, Dixieland, big band jazz, or whatever one needs to begin by listening and (secondarily) studying the genre.  There's a reason those early music groups perform from early notation:  They've learned that the original notation provides clues that get lost in the translation to our notation.  And they learned that by immersing themselves in the music, and not just the study of the music.

 

This note is way off topic and I apologize, but John really pushed my buttons with his very important summative comments.





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