finger-picker - Posted - 01/01/2021:  10:53:44

I've been studying the circle of fifths/fourths lately as I educate myself more on the music theory aspects of my playing and had a question that stumped my music major wife. I noticed in the case of the keys C#/Cb, the third and seventh degrees of E#/B# and Fb/Cb are technically F/C and E/B, respectively, correct? Then I got to thinking, well, can you only ever have a total of 7 sharps or 7 flats in a key or is it theoretically possible to continue working yourself around the Circle into double sharp and double flat key territory? I doubt this will add any significant contribution to my actual playing, just curious.

C# D# E# F# G# A# B# (C# Major) - 7 Sharps
Cb Db Eb Fb Gb Ab Bb (Cb Major) - 7 flats

Thanks

 

trapdoor2 - Posted - 01/01/2021:  11:04:22

It is really just a spelling convention. Yes, there are small pitch differences between enharmonic notes (E# vs F, etc.) but convention says one doesn't use double-sharp or double flat to name a key.

Texasbanjo - Posted - 01/01/2021:  11:10:03

Got this from a theory book:



Generally speaking, there are enough keys to cover all, using purely sharps or flats. With seven sharps, that takes us into C? major, which can, in 12tet, be re-written as D?. The latter has five flats.



With seven flats, that takes us into C? major, which can be written as B major, with five sharps. There are very few occasions where a composer would need, or want to use more sharps/flats in a key signature, so going even further and using double sharps (x) or double flats (??) is not going to be helpful to any instrument player. If particular scales have to use double either, it's due to particular notes needing to be written as such.



Having double either in a key signature is therefore somewhat pointless, as the 'simple' ones cover all that's needed. Thus, theoretical.

NOTE:  The ?s are supposed to be flat notations but on my computer, it came out as a ?



Does that help answer your question?

Edited by - Texasbanjo on 01/01/2021 11:12:46

banjoy - Posted - 01/01/2021:  11:31:30

Theoretically, sure, you can do whatever you want. But why?



Practically, no, not at all. If you double sharp a C (C##) it's a D. C double flat, you have a Bb. What would the point be, theoretically?



C## D## E## F## G## A## B##  would be identical to D E F# G A B C# ... a scale which already exists on the Circle.

Cbb Dbb Ebb Fbb Gbb Abb Bbb would be identical to Bb C D Eb F G A ... a scale that already exists on the Circle.

It's called a Circle because it starts over. What you are describing is a spiral, which could go on forever. And remember, any scale has only 7 notes before it repeats an octave higher at the 8th note (1st note repeated at octave). There are only 7 notes to modify before it all starts over again (Circle).

Double Sharp and Double Flat notes do exist as accidentals outside a key signature, but now, you're deep in some weeds and they don't comprise a scale.

I think I'm explaining this correctly. I'll shut up now LOL.

Edited by - banjoy on 01/01/2021 11:44:32

finger-picker - Posted - 01/01/2021:  11:57:23

Yes to all - that clears up my question, thanks

G Edward Porgie - Posted - 01/01/2021:  13:08:58

There are subtle differences in C# and Db, E# and F, B and Cb, when one is in just temperament, but equal temperament, which is what is used in traditional Western music and music theory, removes those differences by stretching some intervals and shrinking others. The key of C# thus becomes Db, Cb becomes B, and E# becomes F, simplifying everything from notation to modulation to a new key. 

If a person were to play in just temperament, where the intervals are based on the harmonic series created by the root note of the chosen key, it's doubtful that anyone could go far enough to utilize much of the circle of fifths. One could probably go from the C chord to the D7, then G7, back to C, but much beyond that, the chords would most likely sound sour. 

 

davidppp - Posted - 01/01/2021:  13:38:51

Here's something that I find really cool about the Circle of Fifths: About 2500 years ago, the Greeks got excited about the integer frequency ratios of nice sounding intervals. An octave is a factor of 2, and a fifth is a factor of 3/2. They occur naturally in the vibrations of thin strings, air in straight pipes, and in our singing voices. And I've read that animals can be taught to recognize those. If you go around the Circle of Fifths by increasing by factors of 3/2, i.e., 12 steps, you don't actually get to the seventh octave of the starting pitch. The overshoot of about 1% is called the Pythagorean comma -- because those guys knew about it! Supposedly it contributed to their thinking about "irrational" numbers (which also figure in the eponymous Theorem). Of course, the circle closes if you use the equal temperament version of a 5th.

Old Hickory - Posted - 01/01/2021:  14:29:53

quote:

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Originally posted by trapdoor2

Yes, there are small pitch differences between enharmonic notes (E# vs F, etc.) . . .

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Demonstrate that on a piano, please.  

trapdoor2 - Posted - 01/01/2021:  14:38:11

quote:

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Originally posted by Old Hickory

quote:

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Originally posted by trapdoor2

Yes, there are small pitch differences between enharmonic notes (E# vs F, etc.) . . .

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Demonstrate that on a piano, please.  

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Yah, better with strings. Piano ain't never in tune anyway...

Ozark Banjerman - Posted - 01/01/2021:  18:28:07

quote:

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Originally posted by Old Hickory

quote:

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Originally posted by trapdoor2

Yes, there are small pitch differences between enharmonic notes (E# vs F, etc.) . . .

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Demonstrate that on a piano, please.  

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Here you go: m.youtube.com/watch?v=7GhAuZH6phs

rfink1913 - Posted - 01/01/2021:  18:44:49

Two points (from a professional pedant and music theory nerd):



1. Yes, in equal temperament there is no sounding difference between sharps and flats. But there are still good reasons to use double sharps and double flats, maybe not in a key signature, but certainly as accidentals on the page. It's a matter of "spelling": in tonal music, sharping a note implies that it will rise (F# goes to G) and flatting a note implies that it will fall (Eb goes to D). So the chord progression II-V-I in C# major - three major chords -- should be spelled:



A#-B#-C#

Fx-G#-G#

D#-D#-E#

(Piano players see that kind of "D# major" chord, the one with the double sharp F -- that's what the "x" means -- all over the place in works by, say, Chopin.)

Why not just write an Eb major triad there? Well why not right awl the English wards any weigh ewe kin? If you're expecting people to read at sight, you've got to learn to spell correctly, and not just go for the sound. If I am reading along in C#, and the composer/arranger throws in an Eb chord because it's "easier" to write, it actually makes it harder for me to understand.

(We can get into a whole thing about when a composer should change wholesale from sharps to flats. Perhaps because of lingering associations with non-equal tempered music of the past, European composers still retained a sense that flat keys and sharp keys were "different" right up to the 20th century. If you're brought up in the classical culture, music in sharp keys just "looks" different -- edgier, more energetic -- on the page than the same music written with flats.)

2. This may seem totally irrelevant to the banjo. Probably the only people playing in C# major on the fretted banjo are Bela Fleck and some egghead graduates of the Berklee School.

(They call it Ax-L-U-Fb-G-R-Bbb-S-S...)

But I read an elegant piece of banjo musicology where the author argued that, if you looked at the fingering diagrams in some old banjo tutors from the mid-19th century, you could tell by where the book instructed you to put your fingers for different chords that the intervals being fingered (not fretted, this is before frets) were not in equal temperament. Thus sharps and flats could be different, at least in theory, with the G# as the third of E slightly different to the Ab as fifth of Db.

This rabbit hole goes deep...  :) 

Ira Gitlin - Posted - 01/02/2021:  07:28:24

And even if you're not using the KEYS of C# or Cb, the notes in question will often come up in chords or passages. For you bluegrass guys, imagine playing "The Old Home Place" in the key of A. That second chord is a C#7. If you wanted to convey that in writing to one of your classical friends, you'd write it out as C#-E#-G#-B.



To a trained musician, that looks at a glance like a C#7 chord. If you were to write it out as C#-F-G#-B, it would just look puzzling at first glance. (See Robert Fink's more detailed discussion of proper musical "spelling" above.)



Analogous considerations apply in naming entire chords. For instance, Am7 (A-C-E-G) and C6 (C-E-G-A) contain all the same notes as each other. But a chord chart that has an E7 followed by an Am7 is telling the musician to do something very standard--a V-I resolution, while a chart that gives E7 followed by C6 will cause a brief moment of "Huh?!?" This can make a big difference when a substitute player is relying on the chart to play an unfamiliar tune at a gig.



(Similarly, it drives me crazy to hear John Hartford call F# "G-flat" in the lyrics to "My Rag".)



youtube.com/watch?v=QBZFebgYU_I

Edited by - Ira Gitlin on 01/02/2021 07:30:43

G Edward Porgie - Posted - 01/02/2021:  11:06:55

quote:

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Originally posted by Old Hickory

quote:

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Originally posted by trapdoor2

Yes, there are small pitch differences between enharmonic notes (E# vs F, etc.) . . .

---

Demonstrate that on a piano, please.  

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A piano is tuned to equal temperament, so there is no difference. What trapdoor says is true when in just temperament. Apparently you missed what has actually been said about these two and the differences between them. (That's not unusual. Most people are only familiar with one tuning system, which is the equal tempered system in use in Western music for a few centuries.)

If a piano were to be tuned in just temperament, it would require , if I recall, 64 keys per octave so that all notes (B and Cb, E# and F, etc. could be played properly.

Old Hickory - Posted - 01/02/2021:  14:21:25

quote:

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Originally posted by Ira Gitlin

. . . imagine playing "The Old Home Place" in the key of A. That second chord is a C#7. If you wanted to convey that in writing to one of your classical friends, you'd write it out as C#-E#-G#-B.

---

Well, I do play Old Home Place in A when I call it a jam, and since I use a capo to play as if in G, it never occurred to me think about how the C#7 would be "spelled" by someone playing without capo. Now that you bring it up, I'm going to continue not to think about it.

Old Hickory - Posted - 01/02/2021:  14:27:19

quote:

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Originally posted by G Edward Porgie

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A piano is tuned to equal temperament, so there is no difference. What trapdoor says is true when in just temperament. Apparently you missed what has actually been said about these two and the differences between them. (That's not unusual. Most people are only familiar with one tuning system, which is the equal tempered system in use in Western music for a few centuries.)

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Apparently you missed that I was just making a joke. (That's not unusual. Most people who are extremely  knowledgeable about the intricacies and history of tuning systems aren't familiar with the types of jokes or sarcasm that have been around for a few centuries.)

G Edward Porgie - Posted - 01/02/2021:  14:46:39

quote:

---

Originally posted by Old Hickory

quote:

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Originally posted by G Edward Porgie

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A piano is tuned to equal temperament, so there is no difference. What trapdoor says is true when in just temperament. Apparently you missed what has actually been said about these two and the differences between them. (That's not unusual. Most people are only familiar with one tuning system, which is the equal tempered system in use in Western music for a few centuries.)

---

Apparently you missed that I was just making a joke. (That's not unusual. Most people who are extremely  knowledgeable about the intricacies and history of tuning systems aren't familiar with the types of jokes or sarcasm that have been around for a few centuries.)

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There are jokes and there are supposed jokes that are poorly delivered. That's also not unusual, and I, myself, sometimes am guilty of that.

Emoticons, in my opinion, are no substitute for good writing.  Emoticons, I would point out, have not been around for centuries, so they are still quite easily misinterpreted. 

I am a bit disappointed that I missed something, but I am also disappointed that you couldn't explain yourself without resorting to being snarky and sarcastic.

Old Hickory - Posted - 01/02/2021:  15:31:19

I’ll take it up with the guy who writes my material.

davidppp - Posted - 01/04/2021:  11:36:54

More weird stuff on temperament:

According to my sources, pianos aren't tuned to equal temperament anyway. They have what are called "stretched octaves." They get progressively sharper and sharper as you go up. That's a relic of their being tuned by ear (inharmonic overtones and such) and persists to this day with users of electronic tuners (unless the customer insists otherwise). (I know this from a stride piano player.) Furthermore, listener preference supposedly favors stretched octaves. (I suspect that's due to repeated exposure more than anything else.)

Equal temperament is well-defined and mathematically (if not sonically) motivated. "Pure" temperament may be well-defined, but it's only one of a zillion (read: infinity) of temperaments in actual use that attempt to maintain (small) integer ratios of intervals. There is no unique solution because it is impossible to keep everyone happy with a single choice. You simply cannot get all chords to have small integer pitch ratios. A cappella singers (at least some) avoid the problem by not having well-defined pitches for the notes. Rather, the harmonizing pitches squirm around until they hit the desired ratio. Really serious guitar players do that, too. I heard Adrian Legg say just that: "Of course you bend each note in a chord until it's right."

John R Harvey - Posted - 01/15/2021:  12:18:36

Here's how I understand notation:

Of the 21 note names, you can only build a major scale on 15 of them without double flatting or double sharping. 

You can build a major scale on these notes: Cb, Gb, Db, Ab, Eb, Bb, F, C, G, D, A, E, B, F#, C#

but not these: Fb, ... G#, D#, A#, E#, B#

In a major scale, you must use all 7 letters without skipping any or repeating any: 

c#, d#, e#, f#, g#, a#, b# = right

c#, d#, f, f#, g#, a#, c = wrong (skipped e & b, repeated f & c)

Ira Gitlin - Posted - 01/15/2021:  14:28:35

quote:

---

Originally posted by Ira Gitlin

And even if you're not using the KEYS of C# or Cb, the notes in question will often come up in chords or passages. For you bluegrass guys, imagine playing "The Old Home Place" in the key of A. That second chord is a C#7. If you wanted to convey that in writing to one of your classical friends, you'd write it out as C#-E#-G#-B.



To a trained musician, that looks at a glance like a C#7 chord. If you were to write it out as C#-F-G#-B, it would just look puzzling at first glance. (See Robert Fink's more detailed discussion of proper musical "spelling" above.)



Analogous considerations apply in naming entire chords. For instance, Am7 (A-C-E-G) and C6 (C-E-G-A) contain all the same notes as each other. But a chord chart that has an E7 followed by an Am7 is telling the musician to do something very standard--a V-I resolution, while a chart that gives E7 followed by C6 will cause a brief moment of "Huh?!?" This can make a big difference when a substitute player is relying on the chart to play an unfamiliar tune at a gig.



(Similarly, it drives me crazy to hear John Hartford call F# "G-flat" in the lyrics to "My Rag".)



youtube.com/watch?v=QBZFebgYU_I

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A good analogy, I think, would be confusing highway signage, or confusing punctuation in a written text that leads the reader to expect the sentence to go somewhere other than where the writer intended it to go.