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Author Topic: What are half notes in music?  (Read 3279 times)

thedoc

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What are half notes in music?
« on: 04/10/2013 20:30:01 »
Jeff Kotowski asked the Naked Scientists:
I have just started learning to play the guitar and there are some oddities in music that I have not been able to figure out. The biggest unknown (to me) is: Why are there sometimes half notes, as in B-to-C or E-to-F, but most whole notes?

Here is what I have found:
1) an octive is actually a doubling of the frequency. It is called an octive because the 8th note is an octive above the original. Oddly enough, the use of octive flows over into other fields like engineering.

2) If the sharps (flats) are considered, there are actually 12 notes equally spaced logrithmically from the base note. This makes more sense to me!

So far, the explanations for the half note are unacceptale: It sounds right. Or the answers are incomplete or silly. Please help! I'd like a rational (preferably scientific) explanation for the half notes.

Thanks,

Jeff Kotowski

_________________________________________________________________
Great minds discuss ideas,
Average minds discuss events,
Small minds discuss people

Eleanor Roosevelt

What do you think?
« Last Edit: 05/10/2013 19:25:40 by chris »

webplodder

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Re: What are half notes in music?
« Reply #1 on: 05/10/2013 10:23:15 »
Jeff Kotowski asked the Naked Scientists:
I have just started learning to play the guitar and there are some oddities in music that I have not been able to figure out. The biggest unknown (to me) is: Why are there sometimes half notes, as in B-to-C or E-to-F, but most whole notes?

Here is what I have found:
1) an octive is actually a doubling of the frequency. It is called an octive because the 8th note is an octive above the original. Oddly enough, the use of octive flows over into other fields like engineering.

2) If the sharps (flats) are considered, there are actually 12 notes equally spaced logrithmically from the base note. This makes more sense to me!

So far, the explanations for the half note are unacceptale: It sounds right. Or the answers are incomplete or silly. Please help! I'd like a rational (preferably scientific) explanation for the half notes.

Thanks,

Jeff Kotowski
530-277-6822

_________________________________________________________________
Great minds discuss ideas,
Average minds discuss events,
Small minds discuss people

Eleanor Roosevelt

What do you think?

Essentially, yes, the value of frequencies represented by the musical scale is arranged because they form a smooth transition that resonates with our brain. You could have any number of different frequencies in a scale but they would not seem musical to human beings. What the physiological basis of all this is is beyond my knowledge so you will have to research further if you want a deeper insight.

chiralSPO

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Re: What are half notes in music?
« Reply #2 on: 05/10/2013 20:08:41 »
Your math is right (each half step has about 6% increase in frequency over the last, though a "tempered" scale is not quite evenly space logarithmically). The issue with the scale is purely music theory. There are many types of scales (even when just limited notes in the 12-tone scale). Just a few:

major scale: C, D, E, F, G, A, B, C (1, 1, 0.5, 1, 1, 1, 0.5)
harmonic minor scale: C, D, Eb, F, G, Ab, B, C (1, 0.5, 1, 1, 0.5, 1.5, 0.5)
natural minor scale: C, D, Eb, F, G, Ab, Bb, C (1, 0.5, 1, 1, 0.5, 1, 1)
Freygish scale: C, Db, E, F, G, Ab, Bb, C (0.5, 1.5, 0.5, 1, 0.5, 1, 1)
whole tone scale: C, D, E, F#, G#, A#, C (1, 1, 1, 1, 1)
pentatonic scale: C, D, E, G, A, C (1, 1, 1.5, 1, 1.5)
blues scale: C, D#, E#, F#, G, A#, C (1.5, 1, 0.5, 0.5, 1.5 1)

Each of these has a distinctive sound, and sounds "right" or "familiar" to the experienced ear.

Bored chemist

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Re: What are half notes in music?
« Reply #3 on: 05/10/2013 20:59:54 »
Other scales are available
I like the second song best- it starts at about 3:15

CliffordK

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Re: What are half notes in music?
« Reply #4 on: 05/10/2013 21:16:06 »
Jeff Kotowski asked the Naked Scientists:

So far, the explanations for the half note are unacceptale: It sounds right. Or the answers are incomplete or silly. Please help! I'd like a rational (preferably scientific) explanation for the half notes.
I thought half notes and quarter notes just denoted the duration of the note.

A full note has a certain duration.
A half note takes half the duration of a full note.
A quarter note takes a quarter the duration of the full note.

I'm not sure how it affects different instruments.  Most horns have a finite length to each note after which either air flow is stopped, or a new note is started.  A stringed instrument can mix sounds, so does the note truly stop?

chiralSPO

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Re: What are half notes in music?
« Reply #5 on: 05/10/2013 21:54:00 »
whole note, half note, quarter note, eighth note etc. are terms that refer to duration.
whole tone, half tone refers to the interval between notes.

David Cooper

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Re: What are half notes in music?
« Reply #6 on: 05/10/2013 23:16:15 »
If you go up the harmonic sequence there might be a clue there. It starts by jumping an octave; then a fifth, then a fourth (which takes us to two octaves up from the start); then a major third, then a minor third, then another minor third, then a tone (which takes us to three octaves up from the start); and then we get a series of jumps starting with three more tones followed by a semitone. It gets messy after that, but these harmonics also become increasingly hard to hear and so they become less relevant as they go on higher. The pattern has been set though for all the standard intervals which we normally use in music.

evan_au

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Re: What are half notes in music?
« Reply #7 on: 06/10/2013 08:10:19 »
It has been known as early as the Greek philosopher/mathematician Pythagoras that notes played on stringed instruments sound most harmonious if the length of the strings is in the ratio of small integers such as 1:2 or 2:3*.

We now know that this translates into frequencies that are in the ratio of small integers. Frequencies which can't be expressed this way sound dissonant, and are used sparingly (at least in Western music).
• Instruments like a piano distinguish the "white" notes from the "black" notes. Most of the white notes are a tone apart (T), with two semitone intervals (S). A black-to-white interval is a semitone. It is possible to almost ignore the black notes and play many simple tunes on just the white notes, as this covers most of the harmonic ratios. This key (C Major) has the pattern TTSTTTS.
• Instruments like guitars have a fretboard, which allows you to make the string an accurate length by pressing down in approximately the right location. But it makes no distinctions between white and black notes; all intervals are a semitone. When playing chords, the fingers select a combination of strings which sounds harmonious.
• Violins are more difficult as the musician must manually define the length of the string by accurately positioning their fingers on the string (but this also makes the instrument much more flexible). The violin does not dictate any concept of tones or semitones. When playing a composition, the fingers select lengths of the string which sound harmonious. (A similar effect can be achieved by some fretted instruments with adjustable frets.)
If you tune your instrument to only make use of these simple ratios, you end up with compositions which should only be played in a certain musical key (like some orchestral compositions). But probably people who aren't musical purists could not tell the difference unless it were pointed out.

There is a problem if you have a singer accompanying the music; their vocal range may be a bit high or low for the key in which the music is written. You would like to move the frequencies up or down a little. In practice, modern instruments have an "equal-tempered" scale, with frequency ratios of the "twelfth root of 2", or 1.05946..., in which the frequencies are not exactly simple ratios, but it does have the advantage that you can move the tuning up and down at will. This is achieved fairly easily by using a capo on a guitar, or even easier on an electronic keyboard. It is a bit trickier on a traditional piano, as you now need to play a mixture of black and white notes if you are to keep that same pattern of TTSTTTS.

For "ideal" tuning (and how it is sometimes tweaked), see: http://en.wikipedia.org/wiki/Just_intonation
For modern tuning, see: http://en.wikipedia.org/wiki/Equal_temperament

* Don't try this on a standard guitar or violin. As well as varying the frequency by varying the length of the string, these instruments extend their frequency range by varying the mass/unit length of the string. You could try restringing the guitar with two identical strings (eg use two "G" strings).
« Last Edit: 06/10/2013 08:13:09 by evan_au »

evan_au

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Re: What are half notes in music?
« Reply #8 on: 06/10/2013 18:28:59 »
The "white" notes on a piano keyboard translate directly to the graphical frequency representation of a musical staff, when used without a key signature. This is easiest for a beginner to read.

Another, more sombre tone can be achieved just with the piano's white notes by playing the "A minor" key, which has the intervals TSTTSTT.

Major and minor keys sound rather monotonous after a while, and more "interest" can be added by throwing in the occasional "accidental" black note which has a frequency ratio which constructed from larger integers (eg10:9).

Even in Western musical traditions, Jazz/Blues scales must be written with many sharps and flats on a musical staff, as they don't limit themselves to the restricted tonal combinations available on the piano's white keys.

The musical frequencies which sound most natural and normal to you will depend on what type of music you listened to when growing up. In different musical cultures, different musical scales are considered normal.

Stringed instruments naturally generate harmonics with integer 2:1 and 3:1 frequency ratios (best described by sine waves). In some cultures, music is dominated by drums and gongs. I vaguely recall from university that the oscillation patterns of a drum skin are better described by Bessel functions. The resonances of a gong are a complex function of its shape.
« Last Edit: 06/10/2013 22:37:55 by evan_au »

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Re: What are half notes in music?
« Reply #9 on: 24/03/2014 09:58:23 »
I totally agree. The explanation for the half notes are really unreasonable. I too would love to hear some satisfactory explanation. I have even asked this question to many newbielink:https://plus.google.com/101635215738395229687/ [nonactive] guy, but he too seems indecisive.

jeff_kotowski

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Re: What are half notes in music?
« Reply #10 on: 18/05/2014 06:35:30 »
First of all, thanks to everyone who replied, your inputs have been very helpful. Second, I guess the question was really about half tones.

I have been doing some research, and the tone/half-tone oddity does indeed go back to the ancient greeks and the perfect fifth. Evidently the greeks liked fractions and disliked irrational numbers. The frequency of oscillation of the fifth is 1.5 times the oscillation of the root. All the notes in the greek system are obtained by going up and down from the root by ratios of 1.5.

The only way I can explain this is by example. If we start at C (261.6Hz) and go up one fifth by multiplying by 1.5 we get G (392.4Hz). If we then go up from G by another fifth we get D (588.6Hz) although this is 2x the D in in fundamental range (which would be 294.3) . Continue up and down and the result are the familiar C-D-E-F-G-A-B notes with half steps at the familiar places. My terminology is likely off, but I hope the point is clear.

Using the 1.5 ratios the note frequencies came out slightly different from the logarithmic ratios we use today, although very close. Another oddity of the greek system is the sharps and flats. In today's system the shrp of one note falls exactly on the flat of the next note. However using the 1.5 ratio this was not the case. Perhaps this is why we have flats and sharps when we really only need one or the other.

The one thing I haven't figured out is why the odd half steps "sound right". Is it learned? Is it natural? Is it that we like a little bit of dissonance?

Anyway, thanks for all your help!
« Last Edit: 18/05/2014 06:40:01 by jeff_kotowski »

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Re: What are half notes in music?
« Reply #10 on: 18/05/2014 06:35:30 »