tpainton - Posted - 01/31/2025:  18:56:21

From another post I was directed to McKeon's  Music Theory for the Banjo Player. I'm literally on page 10 and I am already curious.. and I'll admit.. I have been my whole life.  Why is there no B sharp?  I mean, on a piano, can't we just plop a black key down between the B and C key and tune that to be a 1/2 step?  This is the part that just breaks my brain.  I'm very technical and it seems like if the arrow can always fly 1/2 the distance and never strike it's target, why cant we create a 1/2 step between B and C and between D and F?!  Is it because, "it just would not sound right" and if so, why not?   This very fundamental principal has stymied me for 50+ years and to my analytical brain, seems to make the major scale unnecessarily confusing. 

Now. I KNOW I"M WRONG.  But I need to know why I am wrong.  To me, it just seems like a bizarre constant that nobody has ever defined for me.  

Thank you so much for any insights.  

stanleytone - Posted - 01/31/2025:  19:35:47

chatgpt.com/share/679d965a-c5d...419e1da00
Dont know if this linkbworks or not

tonygo - Posted - 01/31/2025:  21:33:40

quote:

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Originally posted by tpainton

From another post I was directed to McKeon's  Music Theory for the Banjo Player. I'm literally on page 10 and I am already curious.. and I'll admit.. I have been my whole life.  Why is there no B sharp?  I mean, on a piano, can't we just plop a black key down between the B and C key and tune that to be a 1/2 step?  This is the part that just breaks my brain.  I'm very technical and it seems like if the arrow can always fly 1/2 the distance and never strike it's target, why cant we create a 1/2 step between B and C and between D and F?!  Is it because, "it just would not sound right" and if so, why not?   This very fundamental principal has stymied me for 50+ years and to my analytical brain, seems to make the major scale unnecessarily confusing. 

Now. I KNOW I"M WRONG.  But I need to know why I am wrong.  To me, it just seems like a bizarre constant that nobody has ever defined for me.  

Thank you so much for any insights.  

If a scale has needs to have say 

G scale G A B C D E F#G   the F# is because you can't have it be Gfat and then G.  In the say Bflat scale Bb C D Eb F G A Bb  you can't have a D and a Dsharp so you have Eflat. This is as i understand it to prevent confusion and ease of communication. So you say G A B C D E F# G  and not  G A B C D E Gb G and Bb C D  Eb F G A Bb and not  Bb C D D# F G A Bb,

Culloden - Posted - 01/31/2025:  21:47:29

A musical scale is a mathematical equation that follows a pattern of whole steps and half steps. Somewhere in the sequence, there had to be short intervals to make the scale sound right. B to C and E to F are the two places where the short intervals were placed. All this was figured out hundreds of years ago by people who were smarter than I am.

trapdoor2 - Posted - 01/31/2025:  22:31:33

Go read the Wiki on "music intervals".



You named the cause though. The system was built on notes that sound right. Notes that sound best together are called "perfect" intervals. The best are the unisons, two of the same note or two octaves notes. The next are "perfect 4ths" and "perfect 5ths". Then there are decending orders of dissonance. Eventually, over thousands of years, 12 tones were identified (western music). The naming system evolved...not systematically or scientifically but by humans being humans: Chaos.

Eulalie - Posted - 02/01/2025:  04:37:52

To answer your question, B-sharp and F-flat actually do exist—theoretically speaking. It all depends upon the context and the key signature of a piece of music. Mostly those intervals emerge in modern compositions composed by people who like to play mathematical games, starting a piece of music in keys with an excessive number of flats or sharps. But music theorists from the 16th and 17th centuries demonstrated that the use of such odd intervals was theoretically possible in highly chromatic music that modulates from its original key.

The best way to understand this is to think of such intervals as "leading tones" that are a half-step away from the next higher pitch. Our modern diatonic scale normally has a half-step (the equivalent of one fret) between the seventh degree of the scale and the root of the scale one octave (eight tones) above the starting place. In that event, a B-sharp occurs as the leading tone to the key of C-sharp. Obviously, a B-sharp on the piano keyboard or the fingerboard of the banjo is the same note as C. This is called an enharmonic spelling of the note, which again relies upon the key signature of the piece.


We banjo players don't play many tunes in the key of C-sharp, and we're likely to just play in the key of C using a capo if called upon.

Ira Gitlin - Posted - 02/01/2025:  06:49:57

There are theoretical reasons (as Eulalie says) for calling a note "E#" instead of "F", or "C-flat" instead of "B". But that doesn't look like what tpainton is asking. The question seems to be, "Why can't we have a note halfway between E and F, and another one halfway between B and C?" The answer is simply (?) we could, but those would be notes that our system of music doesn't use.

RB3 - Posted - 02/01/2025:  07:34:15

tpainton,

In order to achieve the kind of understanding you're looking for, I think you're going to have to find a resource that provides a fundamental explanation of the history of the development of music theory and music notation.

banjoboyd - Posted - 02/01/2025:  08:20:08

The arrangement of white and black keys on a piano is asymetrical because the basic musical scale underlying Western music is asymetrical. What we know as the diatonic scale is really a product of stacking perfect fifths:



F - C - G - D - A - E - B



When we collapse that down and put the notes in order, We get



C D E F G A B C



which has the stepwise interval pattern



W W H W W W H



Rotating this sequence of steps gives us our various "modes": ionian AKA major, dorian, phrygian, etc.



So we can do a lot with only 7 notes (the "white keys"). We can see from the very beginning that E-F and B-C are half tones.



The trouble comes when we want to move (AKA modulate) that entire system up or down. If we want to move everything up by a perfect fifth and retain the same W W H W W W H sequence, we wind up having to drop one of the original notes (F) and insert a new one in its place (F#). Our two half steps were at E-F and B-C, now they're at B-C and F#-G. 



If you do the same procedure but move everything down by a perfect fifth, that's where Bb comes in as a substitute for B. Our two half steps were at E-F and B-C, now they're at E-F and A-Bb. Early keyboard makers decided to stick these alternate notes in-between the original 7 "white" keys rather than trying to rework the whole arrangement. And when we modulate up and down a bunch of times in this way, we basically wind up with 5 "black" keys; there are technically more, but some are very close in pitch so we just split the difference and represent them with the same key. That's why, as @Eulalie points out, there are such notes as E# and B#, but they're being represented by the keys we normally call F and C. When it comes to notation, the beauty of this system is that we only have one of each letter in a scale. In C# major for example -- C# D# E# F# G# A# B# C# -- we wouldn't want to write E# as F (even though they are the same sound) because then F and F# would appear next to each other. 



That's about as short and non-technical as I can make it. Pitch itself is a continuum, and we can always insert additional notes in between existing ones. We can't insert a half step between B and C because B-C is already a half step, by convention. We could insert an even smaller interval, like a quarter step (roughly 50 cents), giving us B quarter-sharp or C quarter-flat. You can find these kinds of intervals explicitly realized in some Middle Eastern music. They occur in passing in Western music (like when sliding between notes) but they aren't typically notated outside of some more experimental compositions. 



 

Eulalie - Posted - 02/01/2025:  09:03:49

quote:

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Originally posted by Ira Gitlin

There are theoretical reasons (as Eulalie says) for calling a note "E#" instead of "F", or "C-flat" instead of "B". But that doesn't look like what tpainton is asking. The question seems to be, "Why can't we have a note halfway between E and F, and another one halfway between B and C?" The answer is simply (?) we could, but those would be notes that our system of music doesn't use.

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Actually, there is an historical precedent for more notes per octave.  In the 1540s, Nicolo Vincentino devised a microtonal keyboard with 31 notes per octave.

My premise is and always has been that the keyboard as a reference point is what undermines Western music.  Prior to its ubiquitous use (17th century forward) musicians did hear and honor the difference between what we now call enharmonic notes (G# = Ab).  Singers would naturally adjust depending upon the context.  Unfretted string instruments like the violin can and do play so-called enharmonic notes differently, for instance a D-sharp in the key of B is intonated differently from an E-flat in the key of Bb.  Lutes and viols have moveable frets, making them adjustable depending upon the context.

Fixed keys on the keyboard led us to universal acceptance of an equal temperament that fudges thirds to the degree that perfect fourths, fifths and octaves are also as out-of-tune as thirds.  Same is true of stringed instruments with fixed frets. 

Unless you play fretless, the best solution is just tune your banjo as best you can and deal with it.

Old Hickory - Posted - 02/01/2025:  09:16:29

quote:

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Originally posted by tpainton

Now. I KNOW I"M WRONG.  But I need to know why I am wrong.  To me, it just seems like a bizarre constant that nobody has ever defined for me.  

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I was writing off-line while some great theory-based answers were posted.

To find more of the answer for yourself, I think you need to read about the development of the octave, scales, and "solfege" (do-re-mi note naming). Then discover how the specific major and minor scales were developed and settled on. Then the concept of the 12-tone octave that put un-named half-steps in between some of the do-re-mi notes.

And here, I'm probably already wrong, because musicians may have settled on letter names for the notes by then.

I don't know what note names were used in12-tone Pythagorean tuning, which might not have actually been developed by Pythagoras (6th century BCE) but earlier in ancient Mesopotamia. Anyway, this system -- used into the 16th century -- gave us the 12-tone octave, from which our major and minor scales use ony 7 different notes plus the octave. Pythagorean "just intonation" was replaced by 12-tone-equal-temperament that lets instruments play in multiple keys and sound mostly in tune.

But this still doesn't answer the question of who decided to apply names to just 7 of the notes and have 5 in-between semitones be called sharps or flats of their adjacent named notes. Or when. 

My guess is it doesn't matter. Maybe it works better than any other system. I wish you luck in finding the answer.

-  -  -  -  -  -  -  -

If you're asking why don't we keep our current system but also add notes in between B-C and E-F, then the answer is as Ira and Ethan said: Those would be notes that aren't needed in our current system of music. B-C and E-F are already a half-step apart. So a note in between those pairs would be a quarter tone. Maybe a blues guitarist bends notes into quarter tones sometimes, but not always or only those two.

-  -  -  -  -  -  -

A lot of words to say I don't know.

Edited by - Old Hickory on 02/01/2025 09:26:20

Eulalie - Posted - 02/01/2025:  09:50:50

quote:

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Originally posted by Old Hickory

But this still doesn't answer the question of who decided to apply names to just 7 of the notes and have 5 in-between semitones be called sharps or flats of their adjacent named notes. Or when.

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This is likely getting into the weeds, but if the question is as you stated, the notes of the scale were first named by Guido d'Arezzo about one thousand years ago. The initial names of the notes were derived from "Ut queant laxis," a medieval Latin chant hymn, which is the source for what we have come to know as the solfege syllables (Ut, Re, Mi, Fa, Sol, La). Taking the first syllable of each phrase of the text, the tune of the hymn begins on an intervallic step above the previous phrase, creating six tones of a musical scale, and the basis for the hexachord, which was in use for about 900 years before we arrived at our modern derivation of the scale.  When we added the seventh syllable of the scale "SI" the leading tone syllable came from the ending words of the hymn, "Sancte Iohannes" (there was no "J" in the alphabet at the time, so "I" was substituted).

The letter names came later, and dovetailed with the scale to identify point of "mutation" or modulation of the six-note scale.  For instance, one referred to F fa sol la, or A la mi re.  Interesting stuff, and it's explained in our video on the original tune. 

youtube.com/watch?v=viu-PhML3D8

Ira Gitlin - Posted - 02/01/2025:  09:53:23

quote:

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Originally posted by Eulalie

quote:

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Originally posted by Ira Gitlin

There are theoretical reasons (as Eulalie says) for calling a note "E#" instead of "F", or "C-flat" instead of "B". But that doesn't look like what tpainton is asking. The question seems to be, "Why can't we have a note halfway between E and F, and another one halfway between B and C?" The answer is simply (?) we could, but those would be notes that our system of music doesn't use.

---

Actually, there is an historical precedent for more notes per octave.  In the 1540s, Nicolo Vincentino devised a microtonal keyboard with 31 notes per octave.

My premise is and always has been that the keyboard as a reference point is what undermines Western music.  Prior to its ubiquitous use (17th century forward) musicians did hear and honor the difference between what we now call enharmonic notes (G# = Ab).  Singers would naturally adjust depending upon the context.  Unfretted string instruments like the violin can and do play so-called enharmonic notes differently, for instance a D-sharp in the key of B is intonated differently from an E-flat in the key of Bb.  Lutes and viols have moveable frets, making them adjustable depending upon the context.

Fixed keys on the keyboard led us to universal acceptance of an equal temperament that fudges thirds to the degree that perfect fourths, fifths and octaves are also as out-of-tune as thirds.  Same is true of stringed instruments with fixed frets. 

Unless you play fretless, the best solution is just tune your banjo as best you can and deal with it.

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I'm aware of all that.

Old Hickory - Posted - 02/01/2025:  14:22:11

quote:

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Originally posted by Eulalie

quote:

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Originally posted by Old Hickory

But this still doesn't answer the question of who decided to apply names to just 7 of the notes and have 5 in-between semitones be called sharps or flats of their adjacent named notes. Or when.

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This is likely getting into the weeds, but if the question is as you stated, the notes of the scale were first named by Guido d'Arezzo about one thousand years ago.

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Thanks.

I was characterizing what I thought the original question was. The OP specifically asked why there's no B# or E#. I assume the fixing of the note names as we have them is part of the answer.

Because of all the information that's been shared here, I'd say it's nothing tht anyone needs to know in order to play banjo.

Corwyn - Posted - 02/01/2025:  16:42:37

quote:

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Originally posted by tpainton

why cant we create a 1/2 step between B and C and between D and F?! 

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Because there is only a 1/2 step between B and C.

As to why that is?  Music is full of these seeming inconsistencies and hide-bound traditions, and we can either go along, or re-do the whole enterprise from scratch.

Thank you kindly.