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I'd like to make YouTube videos that clarify commonly confusing topics such as why keys are built on fifths - the reason being that, musically speaking, C & G are closer than C & D.

The question is - does the explanation that follows reasonably explain how notes in a scale don't increment in the same way as counting numbers - that the next note 'up' from C (in a C-major scale) is G, not D.

And if this explanation doesn't what words would you prefer to describe the G, the 'next note up' the scale?

=== Begin: Explanation ===============

Learning music can be hard because music looks like it's numbers, except with letters, but you can't add or subtract music like numbers.

For example with numbers we count 1,2,3, etc. We don't count 1,3,8,5 because 2 is numerically closest to 1. In other words we count numbers by the smallest increment, which for basic (integer) numbers is to counting by ones.

But it's not the same for scale notes because we're talking about sound and not physical objects you can count 1,2,3,etc.

A sound like a hand clap can be a massive combination of different frequency waves.

But a note in a scale is a 'pure' sound because it's just one frequency. For example middle C has a frequency of 262Hz.

(Hz is Hertz. Hertz is vibrations per second. If you play a middle C note through a speaker that speaker cone is literally shaking at 262 times per second... which means the distance that speaker cone flexes is super small.)

This means you can't count sounds as you do with numbers. The frequency of a "C" added to the frequency of a "D" doesn't give you the frequency of an "E" note.

Instead, to 'count musically', the next note up the scale, a C-scale of C,D,E,F,G,A,B for this example, is actually G.

The reason is that the musical distances between the scale notes are selected based on how similar/dissimilar they are to each other. The G note has a frequency that is a closer multiple to C than the D note.

Play a C note and then a G note. Do you hear how they sound more similar than a C then D note?

Even though the G note is five letters away it sounds 'closer', more similar, to the C note than a D note. Sound-wise, musically-wise, if the C note is the number one then the G is more like the number 2 than the D note even though D is literally the very next musical letter upward.

=== End: Explanation ===============

* ADENDUM *

What I figured out from discussion with User45266 is that I have to explain relative and absolute before I introduce the musical aspect.

Specifically it's absolute pitch, the frequency ... C,D,E, etc. vs the relative pitch, the multiple of the frequency between two pitches - the interval. Intervals vs. pitches seems to be the core distinction.

Thank you User45266.

closed as unclear what you're asking by ggcg, Camille Goudeseune, user45266, Dom Sep 25 at 22:31

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  • Comments are not for extended discussion; this conversation has been moved to chat. – Dom Sep 25 at 22:30
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I feel like the words like "similar notes" and "next up on the scale" are a bit ambiguous and you're not using their acutal definitions

In your case, you are proposing C and G are similar because G is essentialy a "closer" multiple than D which uses a confusing and vague word "closer". Also, when you say built on fifths, it is assumed that you are talking about the circle of fifths because building on fifths from C would give you C lydian (for the first 7 notes).

So since you are talking about Circle of Fifths then the easiest explanation to explain why two keys are similar and that is because their associated scales are very similar. E.g C major and G major have one different note (F and F#).

So overall, G is not the next note of scale of C but its the "next" on the circle of fifths.

  • @Rosie I've edited it because it might be confusing. However, when I talk about notes it more specifically talks about what we are comparing, while scale can be a bit broader. Also, I'm not sure if its clear but I mean notes between them as in the difference in notes used by their corresponding scales. – Vitulus Sep 25 at 10:36
  • Yep, you're right. What I figured out last night from my exchange with User45266 is that I have to explain relative and absolute before I introduce the musical aspect. Specifically it's absolute pitch, the frequency ... C,D,E, etc. vs the relative pitch, the multiple of the frequency between two pitches - the interval. Intervals vs. pitches seems to be the core distinction. Do you agree? – Randy Zeitman Sep 25 at 13:16
  • @RandyZeitman well intervals and pitches is the core of music theory so I'll agree. Althought perfect pitch and relative pitch are probably not the best terms because they refer to the ability to tell pitches and intervals not pitches and intervals themselves. – Vitulus Sep 25 at 22:36
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Sorry, but what you've written is a confused mess.

To take one section:

"The reason is that the musical distances between the scale notes are selected based on how similar/dissimilar they are to each other. The G note has a frequency that is a closer multiple to C than the D note.

Play a C note and then a G note. Do you hear how they sound more similar than a C then D note?

Even though the G note is five letters away it sounds 'closer', more similar, to the C note than a D note. Sound-wise, musically-wise, if the C note is the number one then the G is more like the number 2 than the D note even though D is literally the very next musical letter upward."

You've invented a concept 'musical distance' which conflicts with the basic (musical) fact that C is closer to D than it is to G. If you're writing a melody, C, D, E is more likely than C, G, C. Both 'sound-wise' and 'musically-wise'

I can sort of see what you're getting at. But in looking for a 'new' way to explain it, I'm afraid you've just succeeded in being confusing.

  • Yep, you're right. What I figured out last night from my exchange with User45266 is that I have to explain relative and absolute before I introduce the musical aspect. Specifically it's absolute pitch, the frequency ... C,D,E, etc. vs the relative pitch, the multiple of the frequency between two pitches - the interval. Intervals vs. pitches seems to be the core distinction. Do you agree? – Randy Zeitman Sep 25 at 13:13
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Well, I'm sorry, but after more than half a century of making music, I can't even work out what your "explanation" is trying to explain.

The idea that the note G somehow sounds "closer" to C than the next note in the scale, D, doesn't make any sense at all. If you play a keyboard, The "next note after C" is C sharp, not D, and it is certainly not G. If you play a guitar, or a tin whistle, or a harp, the "next note" is also the next one in some type of scale.

On the other hand if you are trying to say that the chord of G major sounds "closer" to C major than D minor (or D major?) there might be some logic to that - but first, you have to explain what chords are, and how common practice harmony works. Explaining that without first explaining scales (where D is the closest note to C) is going to be an interesting challenge.

In fact, a conventional "explanation" why a G chord is "closest" to a C chord might be that the leading note B is the closest note to the tonic C.

But whether or not that makes any sense, common practice harmony isn't a useful tool to understand all the music genres that don't use it.

All the stuff about pure tones, frequencies, the amplitude of loudspeaker cone movement, etc, is completely irrelevant. An student who is intelligent enough to see that will go elsewhere to find a better explanation. A student who takes everything at face value will just end up confused, and/or with a head full of disconnected factoids. (One of my high school teachers used to write "MWW" in the margin next to those sort of digressions when marking work - and "MWW" stood for "Much Wind and Waffle.")

All this needs a complete pedagogical rethink, IMO.

  • Yep, you're right. What I figured out last night from my exchange with User45266 is that I have to explain relative and absolute before I introduce the musical aspect. Specifically it's absolute pitch, the frequency ... C,D,E, etc. vs the relative pitch, the multiple of the frequency between two pitches - the interval. Intervals vs. pitches seems to be the core distinction. Do you agree? – Randy Zeitman Sep 25 at 13:15
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"Closer" is a term that gets used within musical discussion in a way that doesn't agree with what your question describes.

In certain situations, it makes sense for music theorists to consider G more similar to C than D is. However, this is not true of all situations.

The common example of fifths-based "closeness" is that of major scales. C major, obviously, has no sharps or flats. G major has one sharp, and D major has two sharps. So, to get from G major to C major, only one note has to be altered. From D major, two notes need to be "unsharpened". Theorists realise the value of conceptualizing scales as related by number of notes altered between the two scales rather than by root motion, and it's easy to see that this follows a pattern of perfect fifths (or fourths in the other direction). More on that below ("circle of fifths").

On the other hand, in a melody written in C major, the note G is much farther away from C than D is. Common sense, and this part is kind of math-like. Letter names can be compared similarly to numbers: They can be counted, like C, D, E, F, and so on, and because of this they have an order and can be treated similarly to numbers on a number line. You actually could "add" and subtract notes (four semitones up from C is E, so one could say "E minus C equals 4"), but not by frequency, since our brains perceive frequency changes on a logarithmic scale. One must therefore make musical measurements in semitones and tones, or more precisely, in cents.


Addressing Inaccuracies:

"Play a C note and then a G note. Do you hear how they sound more similar than a C then D note?

"Even though the G note is five letters away it sounds 'closer', more similar, to the C note than a D note. Sound-wise, musically-wise, if the C note is the number one then the G is more like the number 2 than the D note even though D is literally the very next musical letter upward."

Intervals are another way in which one could say something's "closer" than another. C and G make a perfect fifth, and by definition, a perfect fifth is a further/larger distance than a major second (C-D). However, you may have confused the concepts of interval size and consonance/dissonance.

"The reason is that the musical distances between the scale notes are selected based on how similar/dissimilar they are to each other. The G note has a frequency that is a closer multiple to C than the D note."

A perfect fifth may be represented as a ratio containing smaller integers than a major second (at least in Just Intonation), but that doesn't make it "closer" than a perfect fifth. We talk about interval size and ratio simplification in very specific ways, but we don't say intervals that are more mathematically simple are "closer".

"But a note in a scale is a 'pure' sound because it's just one frequency. For example middle C has a frequency of 262Hz."

Minor quibble: A note in a scale is not a "pure tone": The only sounds that produce only one frequency are sine waves. We musicians just interpret musical notes as having only one fundamental frequency (thank you, brain!).

"Instead, to 'count musically', the next note up the scale, a C-scale of C,D,E,F,G,A,B for this example, is actually G."

False. The next note in the scale is D, because after C comes D. You may be thinking of the circle of fifths, for which G does come after C (going from C major to G major adds one sharp, so one spot to the right). Don't overthink it; the notes are in alphabetical order for a reason: to make it obvious approximately how far they are apart relative to one another.

Counterexamples to the claims that G is closer to C than D is: Octaves are large leaps, even though their ratios are as simple as can be. Minor seconds are small leaps, though their frequency ratios are not simple.


So, one might wonder: "Who's to say anything's closer than anything else? Sounds cannot have distance!" Well, this is true, but when you get down to it, sounds don't really have letter names, either. Music Theory is an entirely human construct, apart from various physical properties within acoustics. Therefore, all the concepts and terminology within music weren't discovered, they were invented. Those terms and ideas exist because the musical community believes them to be an aid in understanding music as a whole.

We music theorists have decided that it makes sense to refer to interval size with distance, occasionally. A three-octave leap is farther than a two-octave interval, and two octave intervals are "closer" together than three-octave intervals. But we also find it useful to label some constructs as more related in ways besides interval size. Most would say that a C7 chord is more related to an F chord than an A7 chord is, but we wouldn't say it's "closer." We might say "more closely related", or "closer on the circle of fifths", but not "closer", because "closeness" is strictly defined as interval size, and "closeness" is entirely separate from "relatedness".

  • Yes, the next note in the scale is D. And it is musically. So you're right and my wording is lacking. Hence the question. What I need help saying is that G is the next note if you were 'counting by consonance'. That is, for example with numbers, three is three times more than one. But E doesn't sound three times more than C although it's the third note. (con't). – Randy Zeitman Sep 25 at 5:57
  • G "sounds like" C more than D does because it's frequency is closer to an even multiple of C than any other note in the scale. This is not coincidence, it's by design. Sonically G is 'next' to C just as 2 is after 1. This is the idea I'm trying to convey ... keys are the musical analogy to counting numbers by 1's. With numbers the difference between numbers is the same ... one ... the increment is additive ... you keep adding one to get the number that is 'one more'. (con't) – Randy Zeitman Sep 25 at 6:00
  • But in music 'one more' works by frequency and the physics of that means it's not additive but multiplicative (I don't know a better word). For example the frequency of G compared to C is 3:2, the "interval ratio" ... while D to C is 9:8. As Wikipedia explains, and I am trying to explain more simply... – Randy Zeitman Sep 25 at 6:04
  • "Ratios, rather than direct frequency measurements, allow musicians to work with relative pitch measurements applicable to many instruments in an intuitive manner, whereas one rarely has the frequencies of fixed pitched instruments memorized and rarely has the capabilities to measure the changes of adjustable pitch instruments (electronic tuner)." en.wikipedia.org/wiki/Interval_ratio – Randy Zeitman Sep 25 at 6:05
  • @RandyZeitman Perhaps the phrase you're looking for is "closer on the circle of fifths"? Or, specifically for harmony, G is "more closely related" to C than D is? And the note G sounds more like C than D does? Maybe, but that's subjective. I can see how one could argue that the circle-of-fifths relationship pattern between notes is more important than the ascending-frequency order, but this isn't how musicians think about notes. They don't conceive of the note G as right next to C, maybe partly because since D is closer frequency-wise, D is closer on the actual instrument... – user45266 Sep 25 at 6:05
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The simplest way to explain is to say that after the first harmonic on a given note (say C), the very next one is a P5 higher (G). Then the second harmonic of G itself is D, and so on.

  • That's sound like it has great potential but I'm not personally clear what how harmonic is what I've been mistakenly calling 'similar'. – Randy Zeitman Sep 25 at 13:12
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You can't use a term like close/closer comparing different dimensions.*)

One dimension are the scales the other the circle of fifths and frequencies (overtones).

From the sight of scales D is closer to C, regarding the fifths G is closer to C.

*) this is like comparing e.g. a country closer to another by geographical distance or in respectively to the political system:

From the geographical point of view Switzerland is closer to Turkey than to the USA, but regarding the political system it might be closer to the USA than to the Turkey.

  • Why can't one use closer for any number of qualities? A nickel is closer to a penny in value than a dime but a dime is closer to a nickel in appearance. For this situation it's absolute pitch, the frequency ... C,D,E, etc. vs the relative pitch, the multiple of the ƒ between two pitches. This is what I figured out last night from my exchange with User45266. I have to explain relative and absolute before I introduce the musical aspect. Does this sound more useful to you? – Randy Zeitman Sep 25 at 13:10
  • You can if it's the same quality or dimension. But scales and overtones are different. Of course you will be more successful with the overtones. – Albrecht Hügli Sep 25 at 13:13
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As others have said, "closer" is meaningless at best, and confusing at worst. The correct and musically meaningful phrase that you want to use is "most consonant".

Starting with a given pitch, the most consonant pitch is itself (duh!). The next most consonant pitch is anything that is one or more octaves away. But after accounting for the trivial case, and the case of octave equivalence, the next most consonant pitch is the fifth above.

  • Closer is NOT meaningless, it just has to be defined and used constantly. I do not think the OP is talking about consonance and dissonance. But only he knows what's in his head. – ggcg Sep 25 at 18:34
  • @Caleb Nicely said. Upvote. As for what others say ... I don't know why they say what they say. Notes have both an absolute and relative relationship. Every successive note has a higher frequency - the absolute relationship. However the relationship between the frequencies of notes, how closely one is a multiple of the other, the intervals such as minor3rd and perfect fifth, are the relative relationship. In other words G sounds more similar to C because it's relative, interval, relationship means C and G are more consonant than C and D despite C and D being closer in ƒ than C and G. – Randy Zeitman Sep 26 at 11:05
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C and G are not closer than C and D and keys are NOT "built on 5ths".

Keys in Western music are built with the major scale, a pattern of steps that is always the same {{W, W, H}, W, {W, W, H}}. This is also defined by playing the same tetrachord on the starting note of the key and again a whole step after the last note. The inner {} define the tetrachord. The Key of C the Key of F and the Key of G are all "similar", not close, because the differ by only one single note. The note G is no where "near" the note C in frequency space but the sets of notes have 6 of 7 notes in common, so as sets they are very similar and the concept of closeness in sets can be defined by the number of differing elements, or the size of the complement of their intersection relative to their union, or relative to the chromatic scale.

Example(s):

Key of F: {C, D, E, F, G, A, Bb, C}

Key of C: {C, D, E, F, G, A, B, C}

Key of G: {C, D, E, F#, G, A, B, C}

Obviously we play the major scale starting on the key name but the notation is meant to point out the fact there these sets are almost the same. Also note that you can change key up a 5th simply by raising the 4th of the key you are currently in by a half step. The 4th of F is Bb, raise it up and you're in C. The 4th of C is F, raise it and go to G. This logic works for changing key up a 4th but you flatten the 7th of the key you are in. Again, start in C and just drop the 7th of C and you are in the key of F. This makes modulation in the circle of 5th (or 4th) very easy both from a voice leading perspective and mechanically on instruments like the guitar, you can cover a lot of ground in one position if you know where your 4ths and 7ths are.

One can also see this pattern emerge by continuing the tetrachord sequence in both directions, you simply get what you get! The keys follow this pattern naturally. Since the tetrachord is a basic unit of melody (a lot of Western melodic themes are based on it) using it makes sense. You could try a different unit and see what emerges. But to your question, there is no CLOSER key to the key you are in than that which differs by only one note.

  • C and G are not closer, but 'similar' despite that G is 'higher' than D. This is because interval relationships are cyclical. I don't understand why you say keys are not built on fifths (of the major scale). The pattern you cite, {{W, W, H}, W, {W, W, H}}, is a common explanation but I can't find its origin story. Do you know it? – Randy Zeitman Sep 26 at 10:55
  • They simply are NOT built on 5ths. I can't understand why you are saying this. There are relationships between keys but that is not a key ingredient for building one. – ggcg Sep 26 at 11:58
  • @RandyZeitman, You still seem to be misusing terms as you have realized. The Keys of C and G are similar and in a sense very close. This has nothing to do with the closeness of the starting note. – ggcg Sep 26 at 13:19

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