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Thread: Enharmonic intervals in a harmonic context

  1. #1
    afra91
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    Enharmonic intervals in a harmonic context

    There's something I don't understand about enharmonic intervals. I'm reading Harmony by Walter Piston and he says enharmonic intervals are difficult to distinguish if we only hear them because they have an equal tone. However, then he says that, on the other hand, enharmonic intervals are easily distinguished by ear (that's what I understand) when they are in a harmonic context and he shows an example. If someone could explain this it would be great. Here's the example.
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  2. #2
    Registered User JonR's Avatar
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    IMO he's being a little confusing.
    I don't agree the intervals themselves are "easily" distinguished in a harmonic context. In ex 13, we are hearing them buried in a chord.
    However, I think you could tell if the chord was played, then the individual notes in question were highlighted. Eg, in the first one, you should hear that the G# would go up to A and the F down to E. So we make the assumption that the notes are indeed F and G# (and not F and Ab).
    Likewise in the 2nd one, we should hear the top note as the 7th of the chord (Ab), and thus expect it to descend to a G on the next chord. So we conclude we are hearing F and Ab, not F and G#.

    IMO, that's not the same as clearly hearing the difference between the enharmonics themselves.

    So while I know what he is getting at, he's not really explaining it properly. He's skating over the details. Hearing the difference depends on quite a lot of previous listening experience (which admittedly we all have) as well as the support of all those other intervals.

    This also ignores the way tritone subs are used in jazz, which exploits the very fact that enharmonic intervals DO sound identical. Eg, we can play a Bb7 chord (with F and Ab in it), but resolve it to an A major or minor tonic - so the Ab moves up to A; IOW, is equivalent to a G#.
    IOW, even if we can distinguish enharmonic identities in chords, it's quite useful if we can still accept their ambiguity.

    This is only the case in equal temperament of course (and is in fact one of the big advantages of ET). In pure or just intonations, Ab would be a different frequency (very slightly) from G#. That would restrict the enharmonic games we can play with substitutions and modulation in ET.

  3. #3
    bitter old fool Jed's Avatar
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    Example 12.a shows an augmented 2nd between F and G#.
    Example 12.b shows a minor 3rd between F and Ab.
    Example 12.b shows a minor 3rd between E# and G#.

    In equal temperament tuning, the three intervals above sound exactly the same. On a guitar they are played using the exact same string & fret locations. On a piano they are played using the exact same keys. So why if they sound the same do they have different names?

    The names are different because the intervallic naming convention "counts" intervals relative to the lowest note (more specifically relative to the major scale of the lowest note), not based on just the mathematical "distance" from one note to another. The mathematic "distance" is covered by the intervallic naming conventions but the requirement to name an interval according to the major scale of it's lower note leads to these kinds of "same size / different names" occurrences.

    Example 13 - shows these three intervals in their harmonic context:

    Example 13.a shows a G# diminished 7 chord (1st inversion which includes an augmented 2nd from F to G#) resolving to an A minor triad. This resolution to A minor "identifies" the intervals from example 12 as the F to G# because you can hear the G# resolve to A while the F resolved down to the E. In this case it's the final resolution to A minor that provides the information about how the notes should be named.

    Example 13.b shows a B diminished 7 chord (root position which includes an minor 3rd from F to Ab) resolving to an C minor triad. This resolution to C minor "identifies" the intervals from example 12 as the F to Ab because you can hear the Ab resolve to G while the F resolved down to the Eb. In this case it's the final resolution to C minor that provides the information about how the notes should be named.

    Example 13.c shows a C# major triad (root position which includes an minor 3rd from E# to G#) resolving to an F# minor triad. This resolution to F# minor "identifies" the intervals from example 12 as the E# to G# because you can hear the G# resolve to F# while the E# resolved up to the F#. In this case it's the final resolution to F# minor that provides the information about how the notes should be named.

    The "take away" from this lesson is that when there are two or more enharmonic spelling available for an interval, the correct spelling is determined in accordance with the harmonic function of those notes as opposed to an arbitrary choice. In other words, enharmonic namings are specific and important. The ramifications of these facts are that it is important to know and understand the major and minor keys for all possible keys (12 common > 15 possible).

    cheers,

  4. #4
    Registered User JonR's Avatar
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    Jed's absoultely right (of course ) on the theoretical basis of enharmonic distinction. That's why it matters, and that's how we determine the differences.

    It doesn't address the issue of hearing them, however - which is where I think Piston is being misleading (perhaps even disingenuous). IOW, whether or not we can hear the difference doesn't really matter. We hear harmonic function - interactions between scale notes - in context, of course (due to familiarity with convention).
    And we name notes (choose enharmonics) according to key - or if they are chromatic, according to function (voice-leading).
    IMO, it's a waste of time to worry about whether (or when) we can hear the difference between a minor 3rd and an augmented 2nd - in absolute terms we can't. We just have to know the difference. (And then enjoy the ambiguity of sound.)

    btw, Merry Xmas to all (both??) my readers!
    "May your chords be major and bright
    and may all your intervals be right" hehe

  5. #5
    bitter old fool Jed's Avatar
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    Quote Originally Posted by JonR View Post
    It doesn't address the issue of hearing them, however - which is where I think Piston is being misleading (perhaps even disingenuous). IOW, whether or not we can hear the difference doesn't really matter. We hear harmonic function - interactions between scale notes - in context, of course (due to familiarity with convention).
    And we name notes (choose enharmonics) according to key - or if they are chromatic, according to function (voice-leading).
    IMO, it's a waste of time to worry about whether (or when) we can hear the difference between a minor 3rd and an augmented 2nd - in absolute terms we can't. We just have to know the difference.
    Agreed. If we read the passage to mean that Piston thinks we should be able to hear the difference between enharmonic intervals in context. That's not really the case. What we are hearing is the harmonic function or rather individual note functionality relative to the tonal center - but certainly not some special sound of the various enharmonic intervals themselves.

    Quote Originally Posted by JonR View Post
    btw, Merry Xmas to all (both??) my readers!
    "May your chords be major and bright
    and may all your intervals be right" hehe
    Merry Christmas to all.

    cheers,

  6. #6
    Registered User
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    "btw, Merry Xmas to all (both??) my readers!
    "May your chords be major and bright
    and may all your intervals be right" hehe "

    Lol....
    Merry Xmas to you and every one on this planet.

    It's only 18.40 hrs here Snow all around and -20C.

    Drink fresh and stay cool Or drink cool and stay fresh

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