RichJ - Posted - 08/20/2023:  07:21:19

Have always thought a GDAE standard tuned fiddle has strings separated by perfect 5ths (5 tone intervals). Last night it suddenly dawned on me that tone intervals for B-C and E-F are only half tones. So, since each of the three intervals separating G, D, A, and E strings on a standard tuned fiddle have a half tone note interval separating the strings wouldn't it seem the actual tone interval between strings is 41/2 rather than 5?

What am I missing or not understanding here?

DougD - Posted - 08/20/2023:  08:06:33

Intervals are named after the scale degree, not the actual tones or half tones within them. Looking at the two inner strings, the D scale is D, E, F#, G, A. B, C#. A is the fifth degree of the scale, so D to A is a fifth.
A diatonic scale has 7 notes, but if you want to look at it chromatically, in half steps, there are twelve tones - five are just not part of the diatonic scale. An interval of a fifth actually contains 7 half steps, a fourth 5 half steps, and the octave twelve.
Look at a mandolin fretboard and you'll see 7 frets between strings, even though its tuned in fifths like a violin.

DougD - Posted - 08/20/2023:  08:33:37

PS - If you look at a guitar fretboard, which is tuned in fourths (except between the 3rd and 2nd strings, just to confuse the unwary) you'll find 5 frets between strings, except 4 between the 3rd and 2nd strings - a major third.

RichJ - Posted - 08/20/2023:  09:10:31

quote:

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Originally posted by DougD

Intervals are named after the scale degree, not the actual tones or half tones within them. Looking at the two inner strings, the D scale is D, E, F#, G, A. B, C#. A is the fifth degree of the scale, so D to A is a fifth.

A diatonic scale has 7 notes, but if you want to look at it chromatically, in half steps, there are twelve tones - five are just not part of the diatonic scale. An interval of a fifth actually contains 7 half steps, a fourth 5 half steps, and the octave twelve.

Look at a mandolin fretboard and you'll see 7 frets between strings, even though its tuned in fifths like a violin.

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OK, so it's "diatonic scale degrees" rather than "diatonic tone intervals" that define "string tone" separation. Guess it depends on how you slice up the sausage.  I find music theory is fascinating but try not to spend too much time thinking about it. lol

Thanks anyway Doug for helping me understand all this a tiny bit better.   

Lonesome Fiddler - Posted - 08/20/2023:  12:58:41

1. Sing (or otherwise intone) Do Re Mi Fa So. It doesn't matter what particular pitch your voice wants to do it in. Just do it several times.
2. Sing Do and then So. Do it four times in succession. Or five if you want to be poetic about it.
Do-So, Do-So, Do-So, Do-So.

Chances are more than decent that you'll begin to hear the pitch interval known as the Fifth.

And oh yeah, you can call So "Sol" if ya' gotta...

RichJ - Posted - 08/21/2023:  04:43:14

quote:

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Originally posted by Lonesome Fiddler

1. Sing (or otherwise intone) Do Re Mi Fa So. It doesn't matter what particular pitch your voice wants to do it in. Just do it several times.

2. Sing Do and then So. Do it four times in succession. Or five if you want to be poetic about it.

Do-So, Do-So, Do-So, Do-So.



Chances are more than decent that you'll begin to hear the pitch interval known as the Fifth.



And oh yeah, you can call So "Sol" if ya' gotta...

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Thanks Ed - I usually use "Twinkle-Twinkle Little Star" for 5ths and "Hear Comes the Bride" for 4ths. lol

DougD - Posted - 08/21/2023:  15:08:35

Richj - The half steps between E and F and B and C do play a part in the sound of various scales, especially the "modes." If you have a keyboard available (and if you don't you can download handy apps for PCs and phones) you can see how this works.
If you use just the white keys, but start on successive notes starting with C, you will create the scales of the various modes. You can see how the half steps fall in different places in the scales, and give them their distinctive sounds, like this:
C. Ionian WWHW
D. Dorian WHWW
E. Phrygian HWWW
F. Lydian WWWH
G. Mixolydian WWHW
A. Aeolian WHWW
B. Locrian HWWH
This list shows where the whole and half steps fall between the tonic and the fifth.
In all cases, there are 7 semitones in the interval, EXCEPT ONE. The Locrian scale, beginning on B, has TWO half steps in that interval, so there are just 6 semitones. This means that the fifth is diminished, not perfect. This lack of a perfect fifth means that scale is not very useful, and some even condider it only "theoretical."
There are also 5 semitones in the fourth (the first three intervals) EXCEPT LYDIAN, which has three whole steps, which means the fourth is augmented, which gives this mode an unusual sound too.
You can see that Ionian and Mixolydian, and Dorian and Aeolian share the same arrangement of steps, which is why they sound similar. The difference between Ionian and Mixolydian (both "major" modes) is in the seventh, and between Dorion and Aeolian (both "minor" modes) is in the sixth.
Hope you might find this mildly interesting.

alaskafiddler - Posted - 08/21/2023:  16:28:30

Some of the hurdle folks have is dealing with the semantics, terminology that can be a bit clunky or somewhat confusing. 

The term "tone" is good example; takes on slightly different meanings. As Doug brought up, folks often refer to we have a "12 tone" system, (or pentatonic, hexatonic, to 17, 19, 31...) it's how many individual tones/pitches in octave .  But as well (in different context) refer to older meaning of a "tone" as meaning "whole tone", and a "semitone"; or as linear whole step, half-step.

The terms like fifth, or perfect fifth in different context; to refer to the 3/2 interval relationship; and regardless of if actual fifth note in scale. 

Related to that, when folks use something like "Hear Comes the Bride" for 4ths;  can be a bit confusing as well... if as ascending scale step, vs as in terms of key/scale... where first 2 notes are going from a fifth below (Here) to the tonic (comes), IOW "here" is the perfect fifth to "comes". So can be a bit confusing. 

RichJ - Posted - 08/22/2023:  03:18:43

Thanks for the extra comment there Doug and Geo. I guess the physics of precise frequencies and string tunings in music can get pretty complicated. Having no formal training in music I became fascinated by many facts picked up after staring to fool around with a fiddle 12 years ago. Stuff like Western music being a derivation of only 12 tones and the octaves. But for me the most amazing thing is the phycological effects those string vibrations have on our brains. Every so often some new tonal combinations will draw my interest. Most recently, the magic of that 4 chord in many OT tunes.

alaskafiddler - Posted - 08/22/2023:  14:53:47

A lot of music theory concepts themselves aren't quite as complicated to understand; it's often the explanation in words that gets complicated.

ChickenMan - Posted - 08/22/2023:  16:03:58

I used to use "Taps" as my 4th interval (guitar tuning quickie). And for fun, the third note is a 6th from the first.

DougD - Posted - 08/22/2023:  16:52:44

George is right that the ratio of the fifth is 3/2, but every time I look at it that way I run afoul of equal temperament vs. just tuning, etc.
In the really old days this was referred to the relative length of a vibrating string. If you look at your banjo, the scale length from nut to 12th fret, divided by 3 should be very close to the distance from the nut to the 7th fret, divided by 2.
For my very old banjo I measured this common denominator as 4.41 for the octave, and 4.40 for the fifth. Close enough for banjo playing.

alaskafiddler - Posted - 08/23/2023:  10:07:33

3/2 I was referring to the relative pitch of a fifth; has a relation of one and half times frequency; as in Hz. Wasn't so much trying to delve much into describe math for precision, calculating out distance, frets or temperament. 

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But as mention distance, you can use distance correlation on a string; a fifth is 2/3 the length compared to whole length of open string; so the 7th fret of fretted instrument; or on fiddle where the 4th finger/pinky in first position; thus tuning in fifths will be unison to the adjacent open string.

There is another aspect that can be useful, it's the harmonics. Divide the entire string length (bridge to nut) in thirds; the harmonic chime played at those node points will sound a perfect fifth to the open string;  albeit one octave higher. So on the D string, sounds an A note. Similarly, divide the entire string length in halfway point makes an octave harmonic to open string.  This can be useful way to use unison harmonics to tune to adjacent strings as perfect fifths.

pete_fiddle - Posted - 08/23/2023:  11:43:02

Interval "quality" is important i think, Major, Minor, Perfect, Diminished, and Augmented.
Also whether an interval is Diatonic or Chromatic.
Being able to identify these by ear must be a massive advantage imo.