absolute properties of notes

Let's start with a relatively short answer and see how much that clears the problem up.

Each tone relates to the next tone by a factor of 1.05946309436. So an A, with a frequency of 440Hz (you hear the result of a string or whatever vibrating 400 times per second) is related to A# (or Bb) by multiplying the frequency by 1.05946309436 (440 * 1.05946309436 = ca 466Hz) and to G# (Ab) by dividing : 440 / 1.05946309436 = ca 415Hz.

If you calculate all the notes in an octave, you arrive at the result that A one octave higher than 440Hz is actually vibrating at 880Hz. The octave below is vibrating at 220Hz.

How many times does one tone occur in the range of human hearing?

The nearest note to 20Hz - the absolute lowest frequency heard by a normal human in the prime of life is (by my reckoning) an E at 20.6HZ. If you allow that we have a very special person who can hear beyond the normal 20000Hz, you could hear that tone 11 times (the last at 21094.4Hz)

Does that help at all? :shock:

Yeah, that helped quite a bit. :)

I'm a bit surprised there aren't more hearable tones, though. Maximum 11, you say?

So tones are measured in Herz, and there is nothing more to a tone than how many vibrations per second it represents?

On my electronic tuner, there's a button labeled "pitch", and pressing it cycles through a number on the screen, ranging from 435 Hz to 455 Hz. What's the deal with that?

There are only 11 notes (as against "tones") in Western music. Everything else is just a repetition of those notes, although the tones (pitches, cycles per second) never repeat.

Hertz is just a name for "cycles (or vibrations) per second"

The pitch button determines the pitch (= frequency) of Concert A. There is an American standard of 440Hz and an international standard of 435Hz. You can determine what pitch concert A and, therefore, every other tone should be based on.

If you'd like to read a bit more about this, although it's cloaked in bizarre humor, click on my signature link and read "Gin and Diatonic"

Here's a table you may find interesting:

Note Hertz
E2 41.20 E-string on bass
F2 43.65
Gb2 46.25
G2 49.00
Ab2 51.91
A2 55.00 A-string on bass
Bb2 58.27
B2 61.74
C3 65.41
Db3 69.30
D3 73.42 D-string on bass
Eb3 77.78
E3 82.41 E-string on guitar
F3 87.31
Gb3 92.50
G3 98.00 G-string on bass
Ab3 103.83
A3 110.00 A-string on guitar
Bb3 116.54
B3 123.47
C4 130.81
Db4 138.59
D4 146.83 D-string on guitar
Eb4 155.56
E4 164.81
F4 174.61
Gb4 185.00
G4 196.00 G-string on guitar (octave on bass G)
Ab4 207.65
A4 220.00
Bb4 233.08
B4 246.94 B-string on guitar
C5 261.63
Db5 277.18
D5 293.66
Eb5 311.13
E5 329.63 Highest note of bass, high E-string of guitar
F5 349.23
Gb5 369.99
G5 392.00
Ab5 415.30
A5 440.00
Bb5 466.16
B5 493.88
C6 523.25
Db 554.37
D 587.33
Eb 622.25
E 659.26 12th fret of guitar high E-string
F 698.46
Gb 739.99
G 783.99
Ab 830.61
A 880.00
Bb 932.33
B 987.77
C 1046.50
Db 1108.73
D 1174.66
Eb 1244.51
E 1318.51 24th fret of guitar, high E-string


Thanks, that's an interesting read :)

Edit: One thing, you said there is an "american standard" and an "international standard". Does that mean a piece of music sounds different if it is played by an european musican as opposed to an american musican? :?

It wouldn't be noticeably different. 5 Hertz up from 435 is a very small difference. If one musician in an ensemble was considering 440 to be their reference point and everyone else was using 435, you would be able to tell they were out of tune, but if everyone is together, no one will notice.

You say "considering 440 to be their reference point", does that mean that all the other tones sound different too?

Jarle,
as I said in my first post, all the tones are related by the factor of 1.05946309436. So basing Concert A on 435HZ would change all other tones, in relation.

A# above Concert A would become 460.9Hz

Yes. All octaves are doubles/halves of the original note, so if A=440 there are also A notes at 110, 220, 880, 1760, etc; if A=435, the other A notes will fall at 108.25, 217.5, 870, 1740, etc.

The relationship between the other notes is more complex. In 'perfect' or 'just' intonation there are relationships between vibrations - a perfect fifth is a ratio of 3:2, so if A=440, E=(440x3/2)=660; if A=435, E=652.5. You'll notice this is a bit different from Helgi's chart... iff you just tempering around the circle of fifths, you'll have all the notes sounding very nice... but you'll find there is a difference between F# and Gb, as well as any of the other 'in between' notes! Early keyboard makers actually included two black keys between each pair of white keys to be able to play the notes properly.

This was solved by the creation of the 'even tempered' tuning method. Essentially, the differences between these notes was split, resulting in a fixed space between each note. Every note except the reference note and its octaves is slightly out of tune, but by so little you don't notice it. Since the octaves are still in perfect relation, the space between any two chromatic notes will be the 12th root of 2 times the first note's frequency - roughly 1.059.... so A=440 leads to Bb=465.96, B=493.45, etc. (I'm rounding to the 1.059, so it's a hair off from Helgi's chart)

Certain instruments, like keyboards and guitars, MUST play in even temperment because of their construction. Other instruments, like violins, can handle either even or just temperment. It's quite common for ensembles that have only classical strings, or choruses, to perform in just temperment, and they adjust when even tempered instruments are added to the mix.

Wow, this was a great thread! I learned lots of stuff I never knew. Especially Greybeard who made it so simple.

Thanks to all.

Wes

:oops: :oops: :oops:

Wow, this was a great thread! I learned lots of stuff I never knew. Especially Greybeard who made it so simple.

Thanks to all.

Wes

Hear! Hear!

I'm an electronics tech as a day job and those are some of the better explanations of audio frequency tonal relationships I've seen. Much clearer than the engineering texts on the subject.

Now can you explain harmonics with the same clarity?

On a guitar it is easy, as you have just three octaves (I think) to chose from. But on for example a piano, where there are many octaves, how would you know which octave to play a certain song in?

I think this got skipped over...

In standard notation, middle C is used as a standard reference. On the grand staff, middle C will occur one line below the lowest line of the treble clef.

If a composer wants to indicate that the notes should be played relative to a different C, they use the notation "8va--------" above the section to indicate that. Now who knows what "8va" actually means in technical terms?