How much difference is 30Hz from 29Hz?

[sfogg]

Ray,

"and bump one of them in a two or three octave range in the midrange where the ear is most sensitive, most folks can pick up a 0.1dB difference in blind testing."

Do you have a source for that?

Most everything I've seen suggests 0.1dB is inaudible/not perceivable... even on pink noise with the SPL difference being full range. Easy enough for a person to test their own hearing on this with the ABX program I linked to above though.

Shawn

[IndyKlipschFan]

Ray I second your feelings, too, on this matter.

In general it is like buying a 30 watt amp vs a 40 watt one. You may not "hear" the difference at all. You need 30 watts vs a 60 watt one to feel like it is louder or 2x as loud. Besides, as we have said in here a zillion times, it is the first 5 watts that matter on horn loaded efficient Klipsch speakers too. Now headroom on a SS amp../ 100 WPC or (there about) for headroom is the home run! Anyone that is using say a 200 WPC amp or higher is spending his/ her money foolishly. (assuming features are the same) Furthermore, those crucial 0- 5 watts may not sound very good too depending on the gain going to your speakers.

The low end on a Belle or La Scala vs say a Cornwall or K horn... while I love the La scalas... The Corns and K horns play the lower notes on a stand up bass with authority. Think really good jazz, or percussion drums and todays electronic synthesized music too. In some music you hear feel it, and are captivated by the richness. On other styles, it may not be as important. (Especially if you play it loud.) Your question in a round about way always seems to come up about La Scalas.. I will say this over the years if you have an outstanding tube amp....or really good SS you will be very happy with them too. If you ever want to go to a HT system with a La Scala or Belle... Your going to want a sub for sure.. They just were NOT made for the center or low end thump you need and want!

Lots to consider... I have learned a lot on this board thanks to all of you.

[formica]

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On 8/2/2004 10:54:51 AM D-MAN wrote:

Electrically speaking the change is logarythmic; amplifier has to increase wattage by a factor of 10 to achieve a 3db change, for instance 1 watt +3db = 10 watts. 10 watts +3db change = 100watts. 100watts +3db = 1000 watts, etc.

----------------

The relationship is logarithmic... but each 3db change requires the doubling of power... ie: 1W + 3db = 2W all the way up to 100W + 3db = 200W.

You were probably thinking of the 10db = 10 X power = double perceived loudness... ie: 100db appears twice as loud as 90db and requires 100W if 90db only required 10W.

Rob...

[artto]

Those kinds of specs are virtually meaningless in home environments. The room size/boundaries and listening position relative to the speakers and your position in the room will have far more influence on the speaker's actual "in-use" frequency response. I wouldn't worry about. Don't give it too much thought.

[IndyKlipschFan]

Very good point Artto too.. What you experience at home may make the specs meaningless. Bottom line over any spec too.. Are you happy with it too? YOUR the one that has to live with it too!

[WMcD]

I must say I'm a bit sheepish in that I've forgotten some of my musical theory regarding what is considered a whole note and a half note and can't be quite as accurate as I should be.

Let me set out what I recall. Larry C. will be able to elucidate. He REALLY knows what is going on.

The frequencies on the notes of the piano shown state what is called modern tuning. A4 = 440 Hz. It was not always that way and sometimes you hear recreations of older tuning putting A4 down at 420 or so. Larry will know.

In getting from a given tone, to its octave (C1 to C2), you double frequency (A4 is 440, A5 is 880, and A3 is 220 Hz). That has always been the standard. The octave is 8 white keys up. Hence "octave" or 8.

What we're looking at in the diagram is called "equal temperment." This answers the question of (in numbers) how to increase the frequency of the notes going up the musical scale within the doubling frequecies of octaves.

If you count the black keys (sharps and flats), we see that it takes 12 piano keys to get to a doubling at the next "octave" which is doubling in frequency.

In equal temperment, we want the relative change of frequency in each of the 12 shifts to be equal - - - so we arrive at a doubling in frequency after 12 increments.

What to do?

We're looking for a way of getting a number which multiplied by itself 12 times equals 2.

For example, if we wanted a number which when multiplied by itself once would result in 2, we'd take the square root of two on a calculator. That would be 1.414.

If we needed three multiplications,we'd ask for the cube root of 2.

So what we're looking for is the 12th root of 2. However, checking out the keys on our calculator . . . it is nowhere to be found, and we didn't find a cube root either. But most scientic calculators and spread sheets will raise an X to the power of Y, or X^Y.

We must now recall some high school math. Finding a root is the same thing as taking the exponent of the inverse of the root. That means we can punch in 2^(1/2) to get a square root of 2. If we punch in 2^(1/3) we get the cube root of 2.

And, if we punch in 2^(1/12) we get the 12th root of 2. That number is 1.059463.

Now, look at the frequencies of the black and white keys on the diagram. Each adjacent one increases by a multiple of 1.058463. If you have to go down from one, you divide by that same number. A4 = 440 Hz is the standard and all others fit in by the math.

So, Gil, what is the point?

As Larry C pointed out the step from 40 to 39 is less than that 1/1.0584 to make it a step down. And I implied it was about a half note. However, I'm disagreeing that a half note is the fraction he reported. I'm just not clear in what is considered a half note. I can only talk to frequency and notes on the piano and math.

In any event 40 to 39 Hz is not worth anything in frequency response if our speakers are like a piano.

= = = =

I diverge here. Equal temperment is somewhat of a cludge from more ancient standards. In classical temperments, the third whole note note up from the fundamental is 1.25 of the frequency. The fifth whole note up is 1.5 of the fundamental. If you take a very close look at the equal temperment scale, they're off by a few percent.

Some of this comes to mind because of the movie "Close Encounters of the Third Kind". There the scientist were attempting to communicate with the aliens with music. You hear comments of "up a third" or "down a fifth" or the like. I wonder which temperments were being used (equal or otherwise) and whether the aliens were using one or the other.

The truth is out there. Perhaps someone can explain music and temperments better.

Gil

[LarryC]

----------------

On 8/3/2004 9:37:58 PM William F. Gil McDermott wrote:

...So what we're looking for is the 12th root of 2...if we punch in 2^(1/12) we get the 12th root of 2. That number is 1.059463.

Now, look at the frequencies of the black and white keys on the diagram. Each adjacent one increases by a multiple of 1.058463. If you have to go down from one, you divide by that same number. A4 = 440 Hz is the standard and all others fit in by the math.

As Larry C pointed out the step from 40 to 39 is less than that 1/1.0584 to make it a step down. And I implied it was about a half note. However, I'm disagreeing that a half note is the fraction he reported. I'm just not clear in what is considered a half note. I can only talk to frequency and notes on the piano and math.

Gil

----------------

As usual, Gil, you take these things to a whole new level. You're surely absolutely right in calculating the 12th root of 2 as the basic means of determining each half step. I had not fully realized that until I read your post....

Gil's ratio can be verified by calculating the multipliers to go from, say B to C and E to F, the only white key half-steps. Multiplying the frequencies for B and E by Gil's magic multiplier produces extremely close figures to the ones given in the figure for C and F, respectively. Great work!

My 15/16 was a very close approximation for half-steps in the natural harmonic, rather than tempered, scale. Not applicable to these figures. Sorry --

Half-steps are those between immediately adjoining keys, whether black or white. Except for B-C and E-F, all the white keys are "whole steps" apart because there are (half-step) black keys in between.

Larry

[Coytee]

Lordy, did I create this post?

Been interesting reading, although it has in part, digressed from the intent of my question. (I guess I asked it poorly, or the answer was above my head... "if it sounds good and you like it, dont' worry about it")

[3dzapper]

Here is a little something to consider. As has been stated the ear is more sensitive to the mid range than the bass.

When the Ao key is struck the primary freq is 27.5 but the string also produces 55,110,220,440 and 880, etc. harmonics.When the Bo string is struck (rounded) the primary is very close but the harmonics are at 62,124,248,496,992, etc these fundamentals and harmonics continue until the key or the sustain pedal is released. You would be able to hear differences because of the harmonics produced.

A speaker fed a single 39Hz tone or burst followed by a 40Hz tone (burst) would go thump, thump with no real discernable difference IMHO.

????????

[WS65711]

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On 8/1/2004 4:50:36 PM jdm56 wrote:

A doubling of power will yield a 3db loudness increase, while 1db is considered to be about the least detectible change, if I am not mistaken.

----------------

I always thought that a 3db increase was perceived as twice as loud,

and required 4 times the power output from the amp.

Does anyone here know the real answer to this?

[LarryC]

----------------

On 8/5/2004 10:05:36 AM WS65711 wrote:

----------------

On 8/1/2004 4:50:36 PM jdm56 wrote:

A doubling of power will yield a 3db loudness increase, while 1db is considered to be about the least detectible change, if I am not mistaken.

----------------

I always thought that a 3db increase was perceived as twice as loud,

and required 4 times the power output from the amp.

Does anyone here know the real answer to this?

----------------

See Formica's post of 8/2/04 at 1:28:07 p.m., above -- the human ear is logarithmic, not linear, in how it hears sound level changes. This is probably because sound levels in nature can vary by hundreds ir thousands of times, and could blow out our hearing if we actually heard even just a doubling in its true 2X relationship. Therefore, a mere doubling of sound power is perceived by our hearing system as rather minimal, though perceptible. Expert posts above describe how as little as 1 db is usually audible, but the minute 0.1 db usually is not.

Three (3) decibels IS that minimally audible doubling of power; 6 db is 2 times 2, or 4 times the power, and 10 db is 10 times. Because 3 db is so minimal to our ears, there has been a wish to express a doubling of subjective loudness in a db number. While 10 db does sound like it could be twice as loud, I suspect that there is no objective basis for saying that it is, and I myself do not sense that 10 db is "right" while other differences are not.

Larry

[richinlr]

Very interesting discussion.

Only two points to add:

1) Most pianos are NOT tuned in 'equal temperment' because, if so they sound great if all the music played on the piano is in the key of 'C'. They don't sound right if other musical keys are played.

My brother in law has been tuning pianos for almost all his life and he starts with equal temperament and tuning forks. After getting his baseline, he then plays chords in several different musical keys and adjusts some of the notes so that the piano sounds correct in all musical keys. There is a name for this tuning scale but it eludes me right now.

2) Many modern orchestras are using A = 445 Hz. nowdays. I am sort of glad I don't play any more because I would probably have to have the head joint on my flute cut off a bit just to get up to 445.

[skonopa]

----------------

On 8/3/2004 9:37:58 PM William F. Gil McDermott wrote:

So what we're looking for is the 12th root of 2. However, checking out the keys on our calculator . . . it is nowhere to be found, and we didn't find a cube root either. But most scientic calculators and spread sheets will raise an X to the power of Y, or X^Y.

We must now recall some high school math. Finding a root is the same thing as taking the exponent of the inverse of the root. That means we can punch in 2^(1/2) to get a square root of 2. If we punch in 2^(1/3) we get the cube root of 2.

And, if we punch in 2^(1/12) we get the 12th root of 2. That number is 1.059463.

----------------

Oh boy, some of that music theory I took in college coming back to haunt me! . Anyway, very interesting none-the-less.

FYI, I checked your math, as my fancy-dancy calculator does have a key that can take the 12th root of a number (actually, any "nth" root), and indeed, it came back with 1.059463094 when taking the 12th root of 2.

[WMcD]

My recall is that "natural temperment" is when the instrument is set up so the 3rd is at 1.25 and the 5th is a 1.5 of the fundamental, which has to be some note. But natural temperment does work to make it possible to play music in any "key". But a real piano tuner may know best.

On the other hand, in a piano where where are multiple strings (usually three) for a note (usually in the treble only) the tuner will detune one or two to give something other than a pure tone.

I did a little more fooling with the math and Sunny Sal's diagram. The point was to calculate the frequency of B0 starting with A4.

I used 440 * (2^(1/12)) ^-46 and the result was 30.86771 Hz, which is correct.

The 440 is the reference. The 2^(1/12) is the step change per key. On the diagram A4 is key number 49 and B0 is key number 3, so we're making 46 steps.

Raising the step change to the -46th power is just to say we're going down 46 steps, dividing on every step.

Gil

[v3spitfire]

What I've done is stick funnels in my ear, sort of an inverted cone directly into the ear, and angled these directly at the speakers. I pick up 3-6 decibals, though I can't move my head.

[Woofers and Tweeters]

On 8/3/2004 at 5:37 PM, WMcD said:

I must say I'm a bit sheepish in that I've forgotten some of my musical theory regarding what is considered a whole note and a half note and can't be quite as accurate as I should be.

Let me set out what I recall. Larry C. will be able to elucidate. He REALLY knows what is going on.

The frequencies on the notes of the piano shown state what is called modern tuning. A4 = 440 Hz. It was not always that way and sometimes you hear recreations of older tuning putting A4 down at 420 or so. Larry will know.

In getting from a given tone, to its octave (C1 to C2), you double frequency (A4 is 440, A5 is 880, and A3 is 220 Hz). That has always been the standard. The octave is 8 white keys up. Hence "octave" or 8.

What we're looking at in the diagram is called "equal temperment." This answers the question of (in numbers) how to increase the frequency of the notes going up the musical scale within the doubling frequecies of octaves.

If you count the black keys (sharps and flats), we see that it takes 12 piano keys to get to a doubling at the next "octave" which is doubling in frequency.

In equal temperment, we want the relative change of frequency in each of the 12 shifts to be equal - - - so we arrive at a doubling in frequency after 12 increments.

What to do?

We're looking for a way of getting a number which multiplied by itself 12 times equals 2.

For example, if we wanted a number which when multiplied by itself once would result in 2, we'd take the square root of two on a calculator. That would be 1.414.

If we needed three multiplications,we'd ask for the cube root of 2.

So what we're looking for is the 12th root of 2. However, checking out the keys on our calculator . . . it is nowhere to be found, and we didn't find a cube root either. But most scientic calculators and spread sheets will raise an X to the power of Y, or X^Y.

We must now recall some high school math. Finding a root is the same thing as taking the exponent of the inverse of the root. That means we can punch in 2^(1/2) to get a square root of 2. If we punch in 2^(1/3) we get the cube root of 2.

And, if we punch in 2^(1/12) we get the 12th root of 2. That number is 1.059463.

Now, look at the frequencies of the black and white keys on the diagram. Each adjacent one increases by a multiple of 1.058463. If you have to go down from one, you divide by that same number. A4 = 440 Hz is the standard and all others fit in by the math.

So, Gil, what is the point?

As Larry C pointed out the step from 40 to 39 is less than that 1/1.0584 to make it a step down. And I implied it was about a half note. However, I'm disagreeing that a half note is the fraction he reported. I'm just not clear in what is considered a half note. I can only talk to frequency and notes on the piano and math.

In any event 40 to 39 Hz is not worth anything in frequency response if our speakers are like a piano.

= = = =

I diverge here. Equal temperment is somewhat of a cludge from more ancient standards. In classical temperments, the third whole note note up from the fundamental is 1.25 of the frequency. The fifth whole note up is 1.5 of the fundamental. If you take a very close look at the equal temperment scale, they're off by a few percent.

Some of this comes to mind because of the movie "Close Encounters of the Third Kind". There the scientist were attempting to communicate with the aliens with music. You hear comments of "up a third" or "down a fifth" or the like. I wonder which temperments were being used (equal or otherwise) and whether the aliens were using one or the other.

The truth is out there. Perhaps someone can explain music and temperments better.

Gil

I sure do miss you posting here Gil.

 

On 8/4/2004 at 11:44 AM, Coytee said:

Lordy, did I create this post? http://forums.klipsch.com/idealbb/images/smilies/10.gif

Been interesting reading, although it has in part, digressed from the intent of my question. (I guess I asked it poorly, or the answer was above my head... "if it sounds good and you like it, dont' worry about it") http://forums.klipsch.com/idealbb/images/smilies/9.gif

Yes you did. 

[JohnA]

On my guitar tuner, 30 Hz is a B0 (30.87} tuned 49 cents (a lot) flat.  29 Hz is Bb0 (29.14) tuned 8 cents flat.  8 cents is inaudible.  49 cents might sound a little "off" to some, but I don't hear it. There is 100 cents between notes. 

 

B0 is the open low string on a 5-string bass. 

[Deang]

I read through this entire thread, only to find that no one knows the answer, which is 1 Hz. 🙂

[The Dude]

There sure is a lot of older members in this thread.  Oh, the good Ole days.

[Schu]

1Hz of a 20Hz to 20,000Hz range is about .005%