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Thread: How are melodic intervals measured in terms of frequency ratio?

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    Default How are melodic intervals measured in terms of frequency ratio?

    In general, I’m curious about any implications around measuring intervals when they move melodically. For example, does the direction an interval moves effect the perceived frequency ratio in any way? In other words, if you were to move in a major 3rd upwards is the frequency ratio different than if you were to move in a major 3rd downwards?

    Also, when we move melodically, does our brain ‘remember’ the pitch of the notes that came before and then compare the frequencies? I ask this because it seems whenever I play a chord arpeggiated, the melody always reflects the sound of the chord it’s arpeggiating. For example, if I only play the notes within a minor triad as a melody, it always has that dark, ‘minor’ sound no matter what order I play them in…

    Any insight into this is appreciated, even if it doesn’t answer my questions completely. Thanks!

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    The frequency of each semitone is equal to the frequency of the next lower semitone times the 12th root of 2. Any two intervals spanning the same number of semitones will sound identical except for overall pitch and, of course, whatever character is imparted by other surrounding music.

    This is true for equal temperament only.


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    Quote Originally Posted by youngcapone View Post
    In general, I’m curious about any implications around measuring intervals when they move melodically. For example, does the direction an interval moves effect the perceived frequency ratio in any way? In other words, if you were to move in a major 3rd upwards is the frequency ratio different than if you were to move in a major 3rd downwards?

    Also, when we move melodically, does our brain ‘remember’ the pitch of the notes that came before and then compare the frequencies? I ask this because it seems whenever I play a chord arpeggiated, the melody always reflects the sound of the chord it’s arpeggiating. For example, if I only play the notes within a minor triad as a melody, it always has that dark, ‘minor’ sound no matter what order I play them in…

    Any insight into this is appreciated, even if it doesn’t answer my questions completely. Thanks!
    There is no difference strictly in terms of ratios, because a ratio is a ratio, and represents a relationship.

    However, in tonality, if the notes are members of a scale (which is in a key), the direction in which they move does make a perceivable difference in terms of tonal gravity.

    In the case of a fourth (3:4), C "up" to F (going clockwise on a chromatic circle: C-D-E-F) or a fourth, C "down" to G (going counterclockwise C-B-A-G) we hear fourths (C>F or G>C) as being "root on top."

    A fifth (2:3) (C<G) is heard as being "root on bottom" (C as root).

    However, this is only true in tonal situations.

    The notion of "directionality" around a circle can get confusing in this sense, since C "down" to G is a fourth, expressed as C<G (C down to G) or G>C (G up to C).
    By contrast, C>G (C "up" to G) is a fifth (2:3).

    You can see how this notion of "directionality" can complicate things. Your opening question, "I’m curious about any implications around measuring intervals when they move melodically" is part of this complication.
    I think you should think of intervals in terms of their vertical nature first, as root movement, and as members of vertical chords, rather than as melodic entities spread out over time.
    Last edited by millionrainbows; Jul-03-2020 at 00:12.

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    Ok, so it seems my issue is I don't know enough about tonality in general. Do you have any suggestions for topics, concepts, resources etc. to better understand tonality? Or is it just a subject you understand through learning about other things?

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    Quote Originally Posted by youngcapone View Post
    Ok, so it seems my issue is I don't know enough about tonality in general. Do you have any suggestions for topics, concepts, resources etc. to better understand tonality? Or is it just a subject you understand through learning about other things?
    Nobody wants to "know" about tonality; they just want to use it.

    I learned about tonality as an accumulation of different 'models' and ideas, and by questioning and probing basic ideas that are presented as 'given.' It took a long time.

    Understand ratios, and how ratios relate to "1" which is the key note. Understand ratios as members of scales.

    Understand some math, especially number theory. I read three books on "zero." Understand the difference between cardinal numbers and ordinal numbers. Find out why calendars don't have a "zero" month.

    You can read books, but unless you ponder & apply that knowledge, it won't clarify things. Read slowly.

    Read Harry Partch's "Genesis of a Music."
    Read books about tunings & temperaments, because here you will be thinking about octaves, divisions of the octave, and ratios.










    Last edited by millionrainbows; Jul-03-2020 at 13:17.

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    In way too brief: Tonality refers to keys, which are simply customary orderings of eight whole- and half-steps among the twelve half-steps that extend from any note to its octave. Major keys (like the Sound of Music's "Do-Re-Mi") all sound the same (sort of). Minor keys are the same as each other (sort of) but darker sounding. Various other "antique" modes (Lydian, Mixolydian, . . . ) each have a characteristic, slightly odd to our ears, flavor. The point is that a key has a "home" base. Within a key, the ear is led up or down to the home note ("Do" in the song) where it wants to settle. On a more global level, you can begin a piece of music in a given home key, then move away from it ("modulate") to other keys or key areas that have the very real psychological effect of seeming to carry you away from "home" -- and then when the music takes you back to the original key, there is a palpable sense of arriving "home." The way tonality works expanded throughout the 19th c. and by WWI you could do just about anything, but much music remains tonally based. That's tonality for beginners. Cheers --

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    Quote Originally Posted by youngcapone View Post
    Ok, so it seems my issue is I don't know enough about tonality in general. Do you have any suggestions for topics, concepts, resources etc. to better understand tonality? Or is it just a subject you understand through learning about other things?
    I would use the term "harmony." You keep referring to harmonic questions in terms of counterpoint and melodic lines, and this flummoxes me.

    Harmony can be understood vertically, which is "static" and doesn't move through time.

    This is what you need to know more about; vertical relationships (such as chords) which DO NOT move through time, but are considered as vertical entities.

    You also need to view scales this way (vertically), NOT as an ordered set of notes which ascends. You need to understand the vertical cross-relations between each scale note and the tonic, like this:

    C major scale

    C-D
    C-E
    C-F
    C-G
    C-A
    C-B
    Then
    D-C (already done)
    D-E
    D-F
    D-G
    D-A
    D-B
    Then
    E-C (already done)
    E-D (already done)
    E-F
    E-G
    E-A
    E-B
    Then
    F-C (already done)
    F-D (already done)
    F-E (already done)
    F-G
    F-A
    F-B
    Then
    G-C (already done)
    G-D (already done)
    G-E (already done)
    G-F (already done)
    G-A
    G-B
    Then
    A-C (already done)
    A-D (already done)
    A-E (already done)
    A-F (already done)
    A-G (already done)
    A-B
    Then
    B-C (already done)
    B-D (already done)
    B-E (already done)
    B-F (already done)
    B-G (already done)
    B-A (already done)

    You need to do this procedure for every scale, and play the intervals on the keyboard and name them.
    Last edited by millionrainbows; Jul-08-2020 at 14:32.

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    young capone: Millionrainbows has laid out some good advice and great reading, but it will be dense. The Harry Partch book could change your life if you have a few months to spare--as millionrainbows says you gotta go real slow.

    If you are just getting into thinking about functional harmony you could try some more basic texts first, like the Berklee harmony book, or Walter Piston's book. These won't take you into ratios though--that's where Patch will blow your mind. With all of this stuff you have to read critically and don't necessarily swallow it whole. Another way of say that is: If you are reading closely enough, some contradictions will pop up in your mind.

    If you let Partch deep into your psyche you may find yourself seeing the whole world in musical terms. Like you'll meet a couple of friends on the street and you'll think to yourself "he's about 6 feet and she's about 5 feet tall, they're a minor third". Or a cashere will give you a quarter back from a dollar and you'll think "Two octaves". Stuff like that. Everything can turn into a big, all encompassing symphony. You gotta be careful with this stuff...

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