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interval

Posted By: Jitin

interval - 08/15/19 01:27 PM

How is it decided when certain intervals are flat or sharp...

For instance, a flat five could be a sharp 4, or flat 6 could be a sharp 5 etc...
Posted By: Sam S

Re: interval - 08/15/19 02:29 PM

In general, you spell chords with thirds, which is why you use 3,5,7,9,11...

Sam
Posted By: keystring

Re: interval - 08/15/19 07:01 PM

Originally Posted by Jitin
How is it decided when certain intervals are flat or sharp...

For instance, a flat five could be a sharp 4, or flat 6 could be a sharp 5 etc...

It goes together with notation (letters) and the original way that majors and perfects were determined. Everything goes out from there on the naming side. As a quick review:

1. The names of intervals are based on the major scale, and the distance from the Tonic. This is easiest seen in C major, and the white keys on the piano give you an actual map:
CD - M2 (major 2)
CE - M3
CF - P4 (perfect 4)
CG - P5
CA - M6
CB - M7

Whether it is 2, 3, 4, 5, 6, 7 (2nd, 3rd, 4th etc.) comes from the number of notes involved. C to D = 2 notes. C to E (C,D,E) involves 3 notes, etc.

2 a) If the top note is one semitone lower (flatted) for a major interval, it becomes minor. So if CE = M3, then CEb = m3 (minor 3). etc. If the top note of a perfect interval is one semitone lower, it becomes diminished. So if CG = P5, then CGb = b5. There's your "flat 5".

2 b) If the top note of a major interval is two semitones lower, (or if the top note of a minor interval is one semitone lower - same thing), you get a diminished interval. If CA = M6, then CAb = m6, and CAbb (same as CG on piano) is dim6. You don't usually lower a Perfect interval by two semitones.

2 c) If the top note of a major interval is one semitone higher ("sharped") then it is an augmented interval. Thus if CA = M6, then CA# = aug6.

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To work in this manner with an interval starting on any other note, you imagine the major scale starting on that note. There are also other ways to get there.

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All this has to do with how things are named letter-wise, when the music is written. If you play CEb on the piano, and then play CD# on the piano, you will hear the same sound and press down the same keys. That actual distance between the the piano keys will be exactly the same.

So your sharp 4 ........ that's an augmented 4, or a P4 that has been "sharped" or made bigger by one semitone. If P4 is CF, then "sharp 4" is CF#.
Your flat 5 .... that's a diminished 5, or a P5 that has been lowered by a semitone. If P5 is CG, then "flat 5" is CGb. If you play CF# and then CGb you get the same sound and play the same piano keys. This gives you the famous "tritone.

Your "flat 6" is what you get when you "flat" an M6 ..... CA becomes CAb (also an m6).
Your "sharp 5" is what you get when you "sharp" a P5 .... CG becomes CG# (also an aug5).
Again, if you play CAb and then CG#, you hear the same sound, and press the same piano keys.

The reason for using different choices such as CAb vs. CG#, or CD# vs. CEb has to do with "grammar rules" in music.
Posted By: BruceD

Re: interval - 08/15/19 07:43 PM

Originally Posted by keystring
[...] As a quick review:

[...]


Thanks to Jitin for asking the question; thanks to Keystring for the response; that was very helpful!

Regards,
Posted By: Fouyaut

Re: interval - 08/16/19 12:30 PM

Originally Posted by keystring

The reason for using different choices such as CAb vs. CG#, or CD# vs. CEb has to do with "grammar rules" in music.


To go further, in tonal music there is a big difference between an augmented fourth and a diminished fifth.

C F# appears only in the key of G. F# is the leading tone. C is the seventh of the dominant chord D F# A C. This interval usually resolves to a sixth B(b) - G

C Gb appears only in the key of Db. C is the leading tone. Gb is the seventh of the dominant chord Ab C Eb Gb. This interval usually goes to the third Db - F(b).

So the spelling of an interval is a strong hint of what key the music is written in.


Another example : you only find C - G# in A minor (or sometimes in E major with the C borrowing to the minor mode).
And C - Ab can in no way belong to A minor (in the key of A there is no Ab). It appears in F minor, in C minor, Ab major, etc.
Posted By: Jitin

Re: interval - 08/16/19 02:39 PM

I definitely understand how the two namings sound the same, but when you say grammer rules, how do you know what rules are applicable, is it having to do with major scale?

I can understand that with chords, but if you are studying intervals for ear training or if studying interval of a melody line, I feel like the naming is trivial since it sounds the same?
Originally Posted by keystring
[quote=Jitin



The reason for using different choices such as CAb vs. CG#, or CD# vs. CEb has to do with "grammar rules" in music.
Posted By: zrtf90

Re: interval - 08/17/19 03:03 PM

Originally Posted by Jitin
...if you are studying intervals for ear training or if studying interval of a melody line, I feel like the naming is trivial since it sounds the same...
Naming an interval for ear training is indeed flexible. C-F# is an augmented fourth because C-F is written as a fourth in staff notation, whether the sharp appears in the key signature or as an accidental. C-Gb is a diminished fifth because C-G is written as a fifth. The intervals are the same in sound and use the same keys on the piano but their spelling is context sensitive. Either can be used for ear training and naming intervals but one may be more practical when writing a score.

The grammatical 'rules' are not complex but they're not applied the same way all the time so they seem more complicated until you learn your way around.

In Chopin's Prelude in E Minor, Op. 28 No. 4, for example, the E in the second measure drops to Eb halfway through. That's how Chopin wrote it. Some editors, e.g. Paderewski, have obligingly 'corrected' Chopin's score and rewritten the Eb as D# to reflect the underlying harmony (B7 sus 4 resolving to B7). B7 is spelled B-D#-F#-A not B-Eb-F#-A. Chopin was a pragmatist in his scoring.
Posted By: keystring

Re: interval - 08/17/19 04:22 PM

Originally Posted by Jitin
I can understand that with chords, but if you are studying intervals for ear training or if studying interval of a melody line, I feel like the naming is trivial since it sounds the same?[quote=keystring]
Do you mean that you are doing some kind of ear training where you are given an interval to listen to, and you are asked to name the interval you hear? In that case, it would be important for you to be able to recognize say an M2, a P5, since they sound different. Hearing develops, so at first somebody might only be able to hear "smooth sounding intervals" (thirds, fourth, fifths, sixths, maybe) and "rough sounding intervals (seconds, sevenths, maybe tritones) without being able to distinguish between them. At some point you'll want to be able to distinguish between the sound of an m3 and M3, and recognize the unique sound quality of each. Whether at that point you name that m3 an m3 or an aug2 should be immaterial. But if you are using some kind of app where you have to click on an answer, then the weakness lies on the app if it only accepts one of the two. Designing any kind of test is a tricky process and imperfect. If, however, that app actually shows notation as it sounds out the interval, then indeed, if you see CD# in notation, your only choice is aug2; and if you see CEb in notation, your only choice is m3.

The problem is that if, in order to communicate with each other, we want to refer to an interval we hear, then we have to give it a name. And those names are hopelessly tied up in the whole grammar conventions. We're stuck with it.

[quote=zrtf90]The grammatical 'rules' are not complex but they're not applied the same way all the time so they seem more complicated until you learn your way around.

In Chopin's Prelude in E Minor, Op. 28 No. 4, for example, the E in the second measure drops to Eb halfway through. That's how Chopin wrote it. Some editors, e.g. Paderewski, have obligingly 'corrected' Chopin's score and rewritten the Eb as D# to reflect the underlying harmony (B7 sus 4 resolving to B7). B7 is spelled B-D#-F#-A not B-Eb-F#-A. Chopin was a pragmatist in his scoring.


Richard, I'm so glad you wrote this. thumb That is such an important point. In fact, that is why I was as vague as I was in simply referring to grammar.
Posted By: keystring

Re: interval - 08/17/19 04:36 PM

The above post is a mess which I can't edit.

Rewriting:
Originally Posted by Jitlin
I can understand that with chords, but if you are studying intervals for ear training or if studying interval of a melody line, I feel like the naming is trivial since it sounds the same?


Do you mean that you are doing some kind of ear training where you are given an interval to listen to, and you are asked to name the interval you hear? In that case, it would be important for you to be able to recognize say an M2, a P5, since they sound different. Hearing develops, so at first somebody might only be able to hear "smooth sounding intervals" (thirds, fourth, fifths, sixths, maybe) and "rough sounding intervals (seconds, sevenths, maybe tritones) without being able to distinguish between them. At some point you'll want to be able to distinguish between the sound of an m3 and M3, and recognize the unique sound quality of each. Whether at that point you name that m3 an m3 or an aug2 should be immaterial. But if you are using some kind of app where you have to click on an answer, then the weakness lies on the app if it only accepts one of the two. Designing any kind of test is a tricky process and imperfect. If, however, that app actually shows notation as it sounds out the interval, then indeed, if you see CD# in notation, your only choice is aug2; and if you see CEb in notation, your only choice is m3.

The problem is that if, in order to communicate with each other, we want to refer to an interval we hear, then we have to give it a name. And those names are hopelessly tied up in the whole grammar conventions. We're stuck with it.

Originally Posted by zrtf90
The grammatical 'rules' are not complex but they're not applied the same way all the time so they seem more complicated until you learn your way around.


Richard, I'm so glad you wrote this. thumb That is such an important point. In fact, that is why I was as vague as I was in simply referring to grammar.
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