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#19 cboody

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Posted 11 May 2013 - 01:22 AM

David has it right.  Take it from someone who taught the stuff for longer than he would care to remember.  Even when considering tuning schemes other than equal temperament you'll generally find the terms used this way.  However, please note that while the numbering of half steps on the chart is correct in describing the size of the mentioned intervals it can be confusing.  I think that is what Geoff is referring to.  David's example is a good one.  If you think about the letters the number of letters involved in the interval (counting upward) determines unison, second, third, fourth etc.  So, any C (Cb C# C or even Cbb or C##) to any E (I don't have to repeat the possibilities do I ? :) ) is some kind of third. What kind can be determined by counting the half steps and following the conventions so C-E is Major 3rd, C-Eb minor third, C-Ebb (or C#-Eb) is a diminished third, and Cb-E (or C-E#) is an augmented third.  You can do the same thing with other intervals too.  Things can get confusing though.  Consider F-B is an augmented 4th while F-Cb is a dimished 5th.  Or maybe don't consider that :)

 

I hope this clarifies a bit and doesn't just add to the confusion.  Please note this does not consider tuning issues which, as pointed out above, can result in different sizes of particular intervals so that D#-E and Eb-E may not just have different names (minor second and augmented unison), but also slightly different sizes when measured in 100ths of a semitone (cents).  That is a whole different issue.



#20 JimLucas

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Posted 11 May 2013 - 03:25 AM

And so the interval from G# to Ab is what, a demented second?  B)

 

Seriously, though, it seems to me that for discussing the concepts Don was trying to deal with there should be a simpler language than a nomenclature system that requires an advanced degree just to parse it.  Especially since many (most?) of us today play instruments in equal temperament, where many (most?) of the distinctions embodied in that complex nomenclature don't actually exist.

 

And it seems to me that such a system does exist... one in which (e.g.) the intervals C-Db and C#-D are both called "minor second", .  I've been using it for more than 50 years, and so did my various (amateur) orchestral and choral directors.  And if I understood Don correctly, he learned about that system, too, simply by searching the internet.



#21 David Barnert

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Posted 11 May 2013 - 06:41 AM

Seriously, though, it seems to me that for discussing the concepts Don was trying to deal with there should be a simpler language than a nomenclature system that requires an advanced degree just to parse it.  Especially since many (most?) of us today play instruments in equal temperament, where many (most?) of the distinctions embodied in that complex nomenclature don't actually exist.

I'm sorry... Which system are you referring to here? It sounds like you're objecting to the one cboody and I are describing (was that a referrence to my 6 semesters of college-level music theory I have mentioned elsewhere and cboody's "taught the stuff for longer than he would care to remember"?), but then you go on to describe that same system.

And it seems to me that such a system does exist... one in which (e.g.) the intervals C-Db and C#-D are both called "minor second", .  I've been using it for more than 50 years, and so did my various (amateur) orchestral and choral directors.  And if I understood Don correctly, he learned about that system, too, simply by searching the internet.

It seems to me that we're all in agreement here except Geoff, who comes no closer to claiming an advanced degree than:

I cannot ever remember covering this subject during my musical education, which is still  on going, of course



#22 blue eyed sailor

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Posted 12 May 2013 - 05:39 AM

Just to clarify (as I hope): The basic feature of the diagramme of Dons' is, regarding semitones, just the step trom natural to flat or sharp (which is from the center rows to the outer rows). Here the count of "1" leads to "Minor 2nd", which wouldn't be in accord with what David and cbody have outlined.

 

Thus he'd be in need of just another "system" (if there is a fitting one), or the freedom of creating a new nomenclature just for the purpose of his project...



#23 David Barnert

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Posted 12 May 2013 - 07:31 AM

Just to clarify (as I hope): The basic feature of the diagramme of Dons' is, regarding semitones, just the step trom natural to flat or sharp (which is from the center rows to the outer rows). Here the count of "1" leads to "Minor 2nd", which wouldn't be in accord with what David and cbody have outlined.

 

Thus he'd be in need of just another "system" (if there is a fitting one), or the freedom of creating a new nomenclature just for the purpose of his project...

That's true. And he's assigned the same number to the pairs of notes that are enharmonic equivalents (Jim's "demented 2nd"), although the table on the right doesn't suggest what to call it. But I don't think either of these rises to the level of necessitating abandoning the system, only accepting that it isn't perfect, useful as it is.



#24 JimLucas

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Posted 12 May 2013 - 08:28 AM

Seriously, though, it seems to me that for discussing the concepts Don was trying to deal with there should be a simpler language than a nomenclature system that requires an advanced degree just to parse it.  Especially since many (most?) of us today play instruments in equal temperament, where many (most?) of the distinctions embodied in that complex nomenclature don't actually exist.

I'm sorry... Which system are you referring to here? It sounds like you're objecting to the one cboody and I are describing (was that a referrence to my 6 semesters of college-level music theory I have mentioned elsewhere and cboody's "taught the stuff for longer than he would care to remember"?), but then you go on to describe that same system.

And it seems to me that such a system does exist... one in which (e.g.) the intervals C-Db and C#-D are both called "minor second", .  I've been using it for more than 50 years, and so did my various (amateur) orchestral and choral directors.  And if I understood Don correctly, he learned about that system, too, simply by searching the internet.

David, you're right that I was confused, though not just about who said what.  I completely muddled my "examples".
 
It's C-C# and Db-D that I think should also be considered "minor seconds", not some sort of "unison", while C#-Db should be named as a kind of "unison"... "argumented", perhaps?  ;)  Certainly, in an equal-tempered scale, it is acoustically a true unison.  And even in other temperaments, it seems counter intuitive to me that anything named "xyz-second" could be a narrower interval than something named "qrs-unison"

#25 David Barnert

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Posted 12 May 2013 - 09:04 AM

It's C-C# and Db-D that I think should also be considered "minor seconds", not some sort of "unison", while C#-Db should be named as a kind of "unison"... "argumented", perhaps?  ;)  Certainly, in an equal-tempered scale, it is acoustically a true unison.  And even in other temperaments, it seems counter intuitive to me that anything named "xyz-second" could be a narrower interval than something named "qrs-unison"

Perhaps you're right that there should be a system as you describe, which now emerges as different from what cboody and I are describing. But I'm not aware that one exists. Have you really been using such a system for 50 years?



#26 Łukasz Martynowicz

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Posted 12 May 2013 - 09:31 AM

@cboody: thank you very much for your explanation! As I'm completely self-taught musician I had a very hard time understanding intevals - they seemed completely unlogical and obscure, because a simple result of mathematical calculation or sound perception was translated to (what seemed like) completely unintuitive naming convention. Now I understand how there are two completely separate levels: one of mathematical proportion and second resulting from history of western music being an ongoing expansion of primitive pentatonic scales to diatonic and chromatic by an increasing number of patches and that my confusion comes from trying to understand all of this based on simple mathematics and not whole history of music...

 

I completely agree with JimLucas that "there should be a simpler language than a nomenclature system that requires an advanced degree just to parse it". From my point of view, both traditional staff and interval naming is a great from composer point of view (and for those who need an analytical insight into music they play) but could be much, much simpler for players. For example, I find this form of music notation: http://musicnotation...chard-parncutt/ much more readable than conventional staff - you don't need to remember sharps and flats, melody line is clearly visible, chords of given kind look always the same regardles of root, etc.. Main drawbacks of all of chromatic staves is that they "forget" what composer had in mind: "is that D a D or a C## or Ebb"... But for players of equally temperamented instruments who just want to play music this is completely nonexistent or unimportant matter.

 

In other words, in my oppinion (from player, not composer point of view), music can be pain in the back if you try to learn and understand piano and classic staff notation, or an easy walk, if you play on isomorphoc keyboard of any kind and use chromatic notation... 



#27 inventor

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Posted 12 May 2013 - 12:34 PM

In reply to Anglo-Irishmans earlier enquiry about doing something similar for the Crane Duet. You will find a diagram of just this in my "Duet Concertina Workshop Tutor", where the button pattern for the Crane duet has to be slightly distorted (less distorted if you have a Crabb Crane); and also (undistorted) for the Hayden Duet. It is not possible to do something similar for either the Maccann or Jeffries duets. 

Inventor.



#28 Don Taylor

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Posted 12 May 2013 - 02:01 PM

You will find a diagram of just this in my "Duet Concertina Workshop Tutor",

http://www.concertin...kshop-Tutor.pdf



#29 Anglo-Irishman

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Posted 12 May 2013 - 02:21 PM

In reply to Anglo-Irishmans earlier enquiry about doing something similar for the Crane Duet. You will find a diagram of just this in my "Duet Concertina Workshop Tutor"

 

Thanks, Inventor!

 

I have the Crane-relevant pages of your tutor in my Crane Learning Binder. I found your approach to chord shapes very useful, but had overlooked the buttons-to-stave diagram.

 

Cheers,

John



#30 Anglo-Irishman

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Posted 12 May 2013 - 03:14 PM

I completely agree with JimLucas that "there should be a simpler language than a nomenclature system that requires an advanced degree just to parse it".

 

There is a very much simpler notation that is widely used by singers in the UK - tonic sol-fa. This used syllables to represent the steps of the diatonic scale, and is pitch independent. A competent sol-fa reader can sing a tune or part in any key, as long as you give him/her the tonic chord and the starting note. The absolute pitch is always given in the form "doh=C" or "doh=Bb", etc.

 

I have an old Scottish Psalm book in tonic sol-fa, and thought it would be neat to transcribe some of the tunes (which are often really beautiful) into standard notation. So I made myself a sort of transcribing disc: a larger disc with the 12 semitones of the chromatic scale marked around the edge, and a smaller, concentric disc with the 7 steps of the diatonic scale, marked doh, re, mi, fa, so la, ti. Turn the "doh" to the chromatic key-note indicated for the tune, and you can read off the absolute pitches of re, mi, etc.

 

In Release 1 of my disc, I used the more frequent of each pair of enharmonics: Ab, Bb, C#, Eb, F#. However, for the key of E, this resulted in mi being Ab and fa being A-natural. (Which as we now know, is a no-no! fa should be G# in this case.)

 

So Release 1.1 had both forms of each enharmonic marked on it: G#/Ab, A#/Bb, etc. I added a little window to the inner disc, which indicates which enharmonic is to be used: for doh=E, for example, a "#" is shown, which means that you need G#, C#, D# and F# rather than the equivalent flats.

 

This works perfectly for the keys represented in the Psalm book. But I did a function test for the key of C#, and hit a problem! This gave me re=D# and mi=F (no E of any kind!) and, worse still, fa=F# (F-natural and F# in one scale - no-no!). So what I needed was the enharmonic of F-natural, which would be E#. This makes the scale C#, D#, E#, F#, G#, A# ... and we need a B# to avoid the clash between C and C#!

 

Since then, I've been experimenting with enharmonics or natural notes, and even double-sharps, but have not yet found the totally consistent sequence. Thankfully, this is, in every sense of the word, academic. I can transcribe the entire Psalm book with Release 1.1 of my disc, because none of the tunes have more than 4 sharps or flats. There will probably be no Release 2!

 

Cheers,

John



#31 Łukasz Martynowicz

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Posted 12 May 2013 - 05:15 PM

John, there is a simpler way to translate tonic sol-fa to any key, with proper note names... Just treat it as in C or Cm and mark it on any "infinite" (non-wraping) isomorphic layout (e.g. Wicki-Hayden) and then just move it around keeping the shape of it. 

 

The whole idea of isomorphism (both in notation and instrument layout, as thoroughly explained here: http://musicnotation...ory/isomorphism) simplifies almost anything in music theory, changing many of difficult to memorize relations and concepts to simple geometric shapes, so great deal of music theory can be deducted from the keyboard itself. For example: diatonic functions of chords and triads used on each degree of a scale can be read from Hayden keyboard directly, just by trying to fit the triad on each degree in an overall shape of a scale. For C major scale, this gives you respectively C, Dm, Em, F, G, Am and B diminished - just by trying to fit every chord on "datonic scale hex" of ten buttons in 3-4-3 layout. With isomorphic layouts whole thinking about music theory becomes thinking about geometric relations between notes, transposition is simple spatial translation etc... It is most illogical for me, that in every music school there is an obligatory piano class, just to teach people music theory, while piano is one of those instruments where distinction between D# and Eb don't matter! On any isomorphic keyboard the difference between sharps/flats and their functions becomes obvious just by looking at the keyboard...

 

Łukasz



#32 David Barnert

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Posted 12 May 2013 - 09:11 PM

Now I understand how there are two completely separate levels: one of mathematical proportion and second resulting from history of western music being an ongoing expansion of primitive pentatonic scales to diatonic and chromatic by an increasing number of patches and that my confusion comes from trying to understand all of this based on simple mathematics and not whole history of music...

Exactly. And, I might add, very insightful for a self-taught musician.

I completely agree with JimLucas that "there should be a simpler language than a nomenclature system that requires an advanced degree just to parse it".

People have been trying to simplify the language of music for centuries and it just keeps getting more complicated, for the reasons you yourself discuss, above.



#33 cboody

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Posted 12 May 2013 - 11:36 PM

And so the interval from G# to Ab is what, a demented second?  B)

 

Seriously, though, it seems to me that for discussing the concepts Don was trying to deal with there should be a simpler language than a nomenclature system that requires an advanced degree just to parse it.  Especially since many (most?) of us today play instruments in equal temperament, where many (most?) of the distinctions embodied in that complex nomenclature don't actually exist.

 

And it seems to me that such a system does exist... one in which (e.g.) the intervals C-Db and C#-D are both called "minor second", .  I've been using it for more than 50 years, and so did my various (amateur) orchestral and choral directors.  And if I understood Don correctly, he learned about that system, too, simply by searching the internet.

 

Well, if you care it is a diminished second. And yes both of your examples are minor seconds.  Same I think as what I mentioned...  Where's the difference??



#34 blue eyed sailor

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Posted 13 May 2013 - 12:28 AM

And yes both of your examples are minor seconds.  Same I think as what I mentioned...  Where's the difference??

 
There had been some confusion which had been clarified (see above).
 
What Jim meant (in accord with Don's chart) was the following:
 

It's C-C# and Db-D that I think should also be considered "minor seconds".


Edited by blue eyed sailor, 13 May 2013 - 12:29 AM.


#35 Anglo-Irishman

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Posted 13 May 2013 - 03:41 AM

John, there is a simpler way to translate tonic sol-fa to any key, with proper note names... Just treat it as in C or Cm and mark it on any "infinite" (non-wraping) isomorphic layout (e.g. Wicki-Hayden) and then just move it around keeping the shape of it. 

 

Simpler??

I think my two concentric cardboard discs, with the chromatic scale on one and the diatonic scale in sol-fa notation on the other, are a lot simpler. Just turn "doh" to the desired key note, and read the rest off!

And cheaper, too! What would an instrument with a non-wrapping Hayden-Wicki keyboard cost? And how long would a non-wrapping Wicki keyboard be? Certainly longer than is manageable on a concertina!  

 

You have a point, in that the Hayden-Wicki system seems to me to be diatonic-oriented. In this, it resembles the bisonoric concertinas and accordions, in which each row only has the notes of a diatonic scale.  The Hayden duet has blocks of adjacent keys that only have the notes of a diatonic scale. (The superiority of the Hayden system is that it has a lot more blocks than an Anglo or Bandonoen has diatonic rows!) Tonic sol-fa notation is also essentially diatonic, and I could well imagine playing a Hayden from sol-fa notation. Just map the syllales (doh, re, mi ...) to the buttons in a block, and start the block on the given tonic note, and off you go! I imagine this would be simpler than reading standard notation for the Hayden, but I have no experience of this. Anone tried it?

 

Sol-fa notation is also isomorphic. It's intended for singers, and to a singer, a tune does not consist of a series of notes, but rather a series of intervals. For example, mi is always a major third above doh, and has the same "feel" to it, no matter what absolute key you're using.

 

In the article you cited, Brian Hayden advocates isomorphic notation for isomorphic instruments. So why not use tonic sol-fa for the Hayden duet? Both are inherently transposing-friendly!

Well, sol-fa literature is not widely available outside the UK, and even there it's used mainly for vocal music. So perhaps I could market my "Tonic Sol-fa to Standard Notation Transcribing Disc" to Hayden players. You can use it "backwards" to convert staff or ABC notation to tonic sol-fa! 

 

Cheers,

John



#36 Łukasz Martynowicz

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Posted 13 May 2013 - 04:52 AM

John,

maybe I should use word "fundamental" instead of "simpler" - I'm quite biased by my mathematic education and to me"simpler" means something "more comperhensible" . I understand the simplicity of use of your circle. I was only trying to point, that when using Hayden layout (you can do the transcription on just printed hex grid) the proper naming of notes is completely inherent property of the layout - you don't have to choose anything, you don't have to design v1.1 disc.. I don't mean, that your circle is complicated - just that it's an artificial tool designed for a specific purpose - easier to use than a table or a list of possible combinations, but as I understand, it's an "automated translator". What Brian Hayden invented (and what any other hexagonal isomorphic layout is) is (from mathematical point of view) just one hex with named intervals attached to sides of it. Rest of properties emerges from this. It is simpler in mathematical sense... That said, I am very courious on how your disc looks like - can you post a photo or an illustration of it?

 

I'm familiar with sol-fa (called solmizacja in Poland) - this is the first (and only) thing taught in primary school (we only have elementary music in our obligatory education). While it is isomorphic, it's not the best notation for duet instrument capable of playing multiple melody and harmony lines at once... Translating e.g. Yann Tiersen to readable sol-fa would be a rather hard endavour. But I agree, that using isomorphic notation with isomorphic instrument makes a lot more sense than using traditional staff with it. The only problem is the availability of music already transcribed to it or software that can do the conversion (Lilypond can do it, to some degree)...  

 

@David: "And, I might add, very insightful for a self-taught musician." - thank you, I'm trying my best, and such comment is very rewarding. 





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