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Instead of trying to memorize every interval out of context, a more useful ear training goal is the "memorization" of each scale degree in relation to the tonic (Movable-do solfege). Each degree will eventually produce a certain sensation. [The context of a C major scale is used in this post when examples are given]

Some degrees are more stable than others (1, 3 and 5; 1 being the most stable) and some degrees are more unstable (2, 4, 6 and 7; 7 being the most unstable). The unstable tones produce a certain desire to step into another close stable degree. It's like 7 wants to be followed by 1; 2 wants to be followed by 1 or 3; etc...

My question is: How does that work if there is an underlying harmony?

If we play some melody on our solo instrument alone, the feeling of tendency tones and stable tones is easily heard. However, the degrees of the same melody will produce a different sensation over a different set of chords. A "C" would become less stable when played over an F chord and a "B" would be more stable if played over an Em chord.

It seems that solfege books don't introduce the "problem" of existing background chords. It seems to me that there is a "main center of gravity" (the tonality) and "movable satellite centers of gravity" (the chords). So, when you finish exercises of internalizing degrees and you are able to audiate simple melodies, you are an expert of doing so over a C chord, but when the harmony changes to an F chord, everything becomes much more difficult (the unstable "F" doesn't have such a strong desire to be followed by an "E", for example).

Would the recommendation still be to hear everything in relation to the tonic? It's not very natural to keep the tonic in mind while the harmony changes and it somewhat ruins the experience of hearing the music.

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    When you write stable and unstable degrees, you do mean strong and weak degrees, don't you? – user45784 Nov 30 '17 at 21:58
  • I'm not sure about the nomenclature. I'm talking about this as a solfege learning technique: What are Active Tones and Restive Tones? or this Why Do Chord Progressions Progress? (around 20:40) – Allan Felipe Nov 30 '17 at 23:11
  • Just found something like what I had in mind: Tonal Gravity – Allan Felipe Dec 27 '17 at 1:13
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    the same way you are hearing tendencies in the melodic notes the chords have tendencies as well, and this is why we have functional harmony to analyse these types of problems. en.wikipedia.org/wiki/… – b3ko Apr 30 '18 at 19:23
  • @user45784 I don’t believe the OP knows what scale degrees are. From the directions they assign to the notes I believe they hear the notes of the scale in context of a tonic chord (otherwise the directions make no sense, the chord on the third degree is certainly not more stable than the chord on the fourth degree, whereas the 1st, 3rd and 5th note are clearly the three most stable notes of the scale in context of a tonic chord) so when they talk about degrees they talk about single notes of the scale and not harmonies. – 11684 Jul 31 '18 at 0:11
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Your fifth paragraph seems correct to me. The principle behind solfege singing is that all the local stabilities—the stability of fa over the IV chord or ti over the V7 chord—are bracketed in a larger tonality rooted on do, the most stable pitch.

You are hinting at the idea of an "even more" movable do—if the goal is to have do be the most stable note, why not rename fa to do when you sing it over the IV chord?

The reason is that this obscures the relationship between the chords and their parent key. While the note fa is stable over the IV, the IV chord itself is unstable relative to the tonic (I). Using the same solfege syllables even as the accompanying harmony moves around is a way of acknowledging this larger tonal schema.

(If the piece is actually switching keys, e.g. by modulating to the IV, then you may switch your solfege syllables if the modulation persists for a long time.)

Another way to think about this is to recognize that the solfege system privileges melody over harmony. All of the tension and release in music, as far as solfege is concerned, is determined by what scale degree the melody is on. We know, of course, that this picture is incomplete and that harmony matters a great deal, which is why theory courses incorporate harmonic analysis as well. But the purpose of solfege is to help you, as a singer dealing with one pitch at a time, feel the gravity of the key center and know intuitively how far you are from the tonic at any given moment.

You seem unsatisfied by this, and I don't blame you, so here's a thought experiment: Could we come up with a solfege system that acknowledges both the global key center and local harmonic shifts? To do this, we'd probably need multiple names for each scale degree. E.g. do could be called do when it appears over the tonic, but (let's say) sa when it appears over a IV chord (as the fifth degree thereof). That way, even if you were just singing the melody in isolation, you could encode information about the background harmony.

In practice, such a detailed system isn't necessary; once you've practiced the song a few times with an accompanist, you'll easily remember which dos went with I chords and which ones went with IV chords and so on. But playing around with this sort of augmented solfege might give you some insight into why musicians have settled on the dual system of seven-syllable solfege and separate harmonic analysis.

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    "Could we come up with a solfege system that acknowledges both the global key center and local harmonic shifts?" this is exactly how it worked in past systems books.google.com/books?id=yyJnDAAAQBAJ&pg=PA36 – Michael Curtis Apr 22 at 16:16
  • Awesome, that is exactly what was in my mind. There could be a Do, Re, ... for notes over I; Do', Re', ... for notes over ii; Do'', Re'', ... for notes over iii, ... which is insane. So, it seems that our system throws away some information, but its idea is to privilege the relation to the parent key. – Allan Felipe Apr 22 at 22:16
  • @MichaelCurtis Thanks for the reference, it was already on my list of books to read for some time. – Allan Felipe Apr 22 at 22:17
  • The part about solfege and hexachords was probably the hardest part to read - for me - because the ideas were new to me. But, IMO, it's one of the most important parts of the book! – Michael Curtis Apr 23 at 13:26
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...Some degrees are more stable than others (1, 3 and 5; 1 being the most stable) and some degrees are more unstable (2, 4, 6 and 7; 7 being the most unstable).

The unstable tones are called tendency tones.

...How does that [solfege/tendency tones] work if there is an underlying harmony?

I think the way to think about this is: solfege/tendency tones and functional harmony are just "two sides of the same coin." Solfege tones don't happen over a harmonic background, the solfege tones are the harmony! I don't mean to be glib. We don't fit solfege to pre-existing functional harmony. It's the other way around. When tones move according to characteristic patterns of solfege/tendency then functional chord identities emerge.

The easiest way to think about it is to consider the tendency tones ^2, ^4, and ^7. Together they make a viio6 chord which has a strong resolution to the tonic chord.

The next question that comes up is: "how to consider the dominant tone ^5?" The dominant can be a chord tone in both the tonic I and the dominant seventh V7. The V7 chord has a strong resolution to the tonic I. This seems to case ^5 in an ambiguous role of both stable and unstable. Let's try to clarify this.

Tonic ^1 and dominant ^5 are both stable degrees. The are the pillars of stability in tonal music! When a plain triad is built on ^5 the V is a stable chord! This stability can be clearly head in the half cadence. The leading tone ^7 is in the V chord so it does resolve to I but V should be considered stable as the music can cadence on it.

When the seventh is added to V to make V7 the chord becomes unstable. FA has the tendency to move to MI and that is the source of the unstability. My understanding (mostly from William Caplin's writing) is that the unstable V7 would not be the goal of a half cadence.

So, the level stability of dominant harmony is the interplay of stability from ^5 and the instability of ^2, ^7, and ^4. Especially important is which tone is the bass! While V is stable, V6 is not.

A similar interplay of tone stability happens with the IV chord and I. Obviously the ^1 degree in both chords is stable, but the ^6 and ^4 in the IV chord are unstable and resolve down to ^5 and ^3 respectively. It is interesting to examine bass tones and inversions with these chords. With IV64 to I the inverted subdominant is obviously the unstable chord. With that specific voice leading we clearly hear LA and FA resolve down to SOL and MI respectively. But, what if we use difference inversions and voice leading? With I6 to IV the tonic chord is unstable and IV becomes relatively stable. This movement can be interpreted as a tonicization of IV in which case the movement of MI to FA becomes TI to DO.

However, if we don't have a tonicization and instead it's a move to a half cadence with I6 IV V we get to another important concept: tendency tones do not always move according to tendency! Again, the harmonic context is critical. In this half cadence progression FA is the stable root of IV. Compare this to another harmonic context: V42 to I6 where FA is in the bass, but as a chord tone it is the dissonant seventh of the dominant chord.

The examples above may be confusing, because the context keeps changing: tonicization changes the tonic, inversion makes stable chords unstable. But that gives us the background information for a generalization: tendency tones exhibit their tendencies when they are used in dominant harmony. In other words V7 to I is where we see tendency tones in action.

This leave LA as the tone with probably the least tendency, or perhaps the most ambiguity. LA's tendency to move to SOL is best understood by IV64 to I a contrapuntal movement to resolve the unstable 64 chord, or in cases like ii6 to V and IV6 to V the move LA to SOL is about doubling the V root instead of the chord 3rd/leading tone. The falling thirds sequence is a case where LA doesn't follow the tendency to SOL - I V6 vi iii6 - in this case LA moves to FA notice how that non-tendency movement doesn't involve V nor I.

  • tendency tones are most clearly observed in dominant harmony
  • tonicization redefines solfege members and effects tendency
  • chord inversion and counterpoint effect tendency
  • tendency tones do not always move according to the baic definition
  • Nice discussion and examples. So, it seems that you did a job similar to what I had in mind, but there is importance just on the V degree. Solfège notes are heard just over I and V, and the tendency comes just from considering these 2 chords! I just can't see how V can be considered stable under any definition. It can be present in the half-cadence, but this cadence is itself unstable. – Allan Felipe Apr 22 at 22:06
  • There is a variable degree of stability with cadences: like an imperfect cadence V to I6, the tonic is inverted and therefore unstable. A half cadence would be stable in the sense that it's a root position V, and SOL as the root of that stable triad is surely a stable tone - notice that SOL doesn't move in the resolution to tonic I - but the chord is relatively unstable due to the presence of the leading tone. – Michael Curtis Apr 23 at 13:23
  • After re-reading... the importance is not about V being a stable chord, but about SOL being a stable tone. V is surely unstable to the degree the leading tone moves to the tonic. But, again, notice that SOL doesn't move in resolving V to I. – Michael Curtis Apr 23 at 13:29
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Not exactly sure where you're coming from - as differing intervals will mean different things to different listeners. You mention 1,3,5 as stable. But when you're in C, but on F, the C note is a 5, so could be construed as stable, it now being a 5. Just like your B example over an Em - another 5. The concept seems a little confused with these examples.

And, the stable/unstable is questionable - 1, 4 and 5 could easily be seen as very stable, as it's the staple diet of most sequences - take any '3 chord trick' and there's 1,4 and 5.

  • Ok, some clarification: in my first paragraph, I mean the idea of memorizing the 12 intervals (ascending and descending) and sometimes even associating some song with each interval. When I write numbers, I mean the scale degree in relation to the tonic, which is the idea of solfege (So, in C major, 5 will always be "G"). – Allan Felipe Nov 30 '17 at 22:42
  • I understand, but have the feeling that some will feel that G in a C chord may take on a different mantle when it's in a G chord, if that makes sense. – Tim Dec 1 '17 at 8:37
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    Yes, that's my point. So, you would say that we should get used to hear "5" played over a C, over a Dm, over an Em, ... ? (By the way, I added some links in a comment in the original post) – Allan Felipe Dec 1 '17 at 20:04
  • I think that's the way to go, as the harmony will keep changing during a piece, and while we may recognise a B in Em as the 5th, it becomes a maj7 in Cmaj7, which effectively gives it a different job, even though it's the same note - but it can't be called a 5th anywhere else except in an E something. – Tim Dec 1 '17 at 20:23
  • So, you would disagree with the practice and teaching of solfege as aural skill? Because calling 5 everywhere is the definition of solfege (..., 3 = mi, 4 = fa, 5 = sol, ...). A "sol" is a "sol" over any chord. – Allan Felipe Dec 1 '17 at 21:29
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I'd still recommend hearing everything in relation to the tonic. Movable-do solfege and Roman numeral notation are analogous in that regard.

As an extreme example, secondary dominants like #4 and borrowed notes like b6 should stay that way to denote how foreign they are in the context of the greater tonic (yet we're able to get away with using them at all because of the underlying harmony).

Only switch solfege note labels once you modulate and switch tonics.

  • That makes sense, but don't you think that the feeling of the "1 = do", for example, changes over each chord of a progression like: I-III7-vi-IV-ii-V7-iv-I ? For every chord, the feeling of "do" is a little bit different from the one acquired when practicing while singing alone without varied backgrounds in aural skills classes. – Allan Felipe Dec 4 '17 at 7:18
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    It does, but according to what I've read, solfege generally isn't fine-grained enough to pick up on the contrast in roles that "1 = do" has between implied I and implied vi (for example). For an exercise in getting used to that lack of devotion, try notating Schubert's "Die Forelle" in movable do solfege. – Dekkadeci Dec 4 '17 at 15:53
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I was taught that solfege meant that the symbols are always the same in any key, and therefore there is no distinction between whether underlying harmony is present or not. In C, Re is always D, and solfege doesn't show how the notes wish to resolve, even if that D feels stable over a Dm chord. In a more classical analysis, yes, certain scale degrees do tend to resolve in certain directions, but these are separate ideas from solfege, as solfege doesn't reflect resolution patterns by itself.

  • This is not true. Tendency and resolution are a critical part of solfege. FA to MI and TI to DO - the half step movements - are critical in the history of counterpoint and harmony. books.google.com/books?id=yyJnDAAAQBAJ&pg=PA34 – Michael Curtis Apr 22 at 16:28
  • @MichaelCurtis Very true. My argument is that those resolution tendencies are unrelated to the actual syllables used to describe, say, Fa and Mi. – user45266 Apr 22 at 18:27
  • I think that meaning might not be clear from your wording – Michael Curtis Apr 22 at 18:43
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you should be able to do both. Hear what the intervals are over each chord, and also in relation to the main key of the song.

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If your question is "How does that work if there is an underlying harmony?", we could say that note perception in general depends on underlying harmony. Chord under note (real or under-heard, suggested) and tone under-heard decide the perception.

Let's take the C prelude by Bach (we can see it as a monodic music — in a cathedrale with reverberation).

in: C E G C E, C is very stable, 1 is 1

then in: C D A D F, C isn't so stable. Even more when you know this piece. Perception changes when you know the piece, when you know where go the notes.

When you don't know the piece, you can hear a pedal. C is not very stable, on this II, but stable anyway (due to the "pedal" function maybe).

But when you know this piece well, I feel this C very instable here, it can be heard as a "sus 4" of the dominant. It desires to "resolve" on the B of the G7 after.

1 is not 1 anymore. Not 7th (of the II). But 4th of the V.

1, 2, 3 etc. is just a conventional way to talk about notes outside a particular tone. But that's not decide the functions nor the stability of the notes nor how we hear them. Chord does. Harmony (heard or suggested) does. Concerning perception, we change it every time we change chord.

  • Thanks. So, would you recommend the practice of solfège over every set of chords? For example, sing the major scale over the I chord, but also, ii, iii, IV, etc... ? – Allan Felipe Apr 21 at 21:54
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    Yes, it can be a good practice. More over, I recommend to listen carefully at every note of each chord. It's not so easy to hear the notes. And maybe you could use harmonic progressions more interesting than I ii iii, IV etc. – user59242 Apr 22 at 3:56

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