Talk:Perfect fifth

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[edit] Sound files?

Aren't there some sound files someone can upload so that we can hear what each diatonic interval sounds like? Artichoke84 10:57, 13 March 2007 (UTC)

[edit] Ratio

In this article a just fifth "corresponds to a pitch ratio of 2:3".

From what I know pitch ratio, or interval is the ratio of higher frequency over lower frequency. Hence it should be 3:2 instead. What do you think?

I agree and I've changed it. (24 October '05)
I've added to the ratios conversation, by reordering the wording of a sentence. I also stated that the P5 is harmonically significant because it is the half-point of the octave (E.g., 2^7/12 = appr. 1.5) See Normalizing the Musical Scale for info to back up that claim. (GaulArmstrong)

It's true that normalising the frequency scale enables the 3/2 ratio of the perfect fifth to appear as 1.5 and therefore the halfway point of the octave. But that's not why it's harmonically significant. Its harmonic significance lies in the fact that it corresponds (in just intonation) with the very important 3rd harmonic generated by the fundamental. I think the more traditional view of having the midpoint of the octave represented by the note that corresponds with the ratio equal to the square root of 2 (1.414) i.e., the 6 semitone augmented 4th/ diminished 5th tritone identifies that interval's harmonic significance nicely and accurately. (Mark 10 February 2007)

I still contend the point, although your generally correct. I agree that the 3rd harmonic is the important subject, and not the 7th step of whetever-tet system we're using. No contest. But, what is central to my point is that the 3rd harmonic is the half-point of the octave. Take the 2nd harmonic and the 4th one (both U1's). They span exactly one octave. Now the 3rd harmonic (P5), you might guess is the midpoint of this octave because (2+4)/2=3. And surprisingly, it is this simple. But because frequency is an exponential scale based on 2x, the midpoint is right-skewed to log2(1.5). It doesn't seem to be the midpoint of the octave, because it falls on the 1.582...-point of the linear frequency scale. In linear terms-- no, the half-point is not the P5, but the tritone. So, if I pick up my guitar and play the note half-way between E and E, I'm going to play A#. But in terms of 'the way your and my ears work', the P5 is the half-point of the octave -- because we hear a linear pitch scale and not the exponential frequency scale. The question is which takes precedence, our ears or our tablature? I say our ears, and that's why the P5 is the half-point. (GaulArmstrong Feb 11 2007)
Well, no. Our ears say that the intervals E-A# and A#-E are identical. Then, A# is the midpoint between E and E, at least if we are going to accept the usual meaning of "midpoint". Musicians recognize a tritone whenever they hear it, even if they don't have a perfect pitch (relative pitch is of course necessary). And our ears say clearly that the intervals E-B and B-E are different. That's how we can tell the difference between a 5th and a 4th by ear. No need of playing, not to say looking at any instrument. Also, I am unable to see how a P5 could be considered the midpoint of the octave in any other way. Old Palimpsest 21:27, 23 February 2007 (UTC)

[edit] Merge with dominant

It has been suggested that this article be merged with Dominant. I strongly disagree. They are significantly different concepts.

What the article does now need is some repair work regarding the following points:

"It is the most important interval for chord structure, song development, and western tuning systems."

No - the 'third' is the most important interval in western (tonal) harmony - That's why it's called tertian harmony. As for tuning systems, the musical tuning article lists only Pythagorean tuning as being based on perfect fifths.

"Gregorian chant was the first formal composition"

Perhaps in Europe, but Indian, Persian and Arabic formal composition all predate Gregorian chant. And maybe not even in Europe, if we include music based on Greek modal systems.

(Heading) "Use in ....tonal systems" - This term needs needs explaining or a link to a relevant article.

I've made a couple of minor fixes for now, mainly rewording, and removed an irrelevant sentence concerning thirds, but would appreciate some comments on the above points before making any further changes - Thanks (Mark - 28 March 06)

  • hello mark, glad for a speedy response. i made some changes to reflect your points.
"tonal systems" could be a better term, i agree, something that includes keys and scales and whatever.
"most important interval" - changed, silly to argue this point. with the impact on tuning systems, i was thinking of like gamelan music tuning, which sounds funny mostly because of its sharp 5th.
gregorian has been softened to "a very early formal music composition" or something
merge, lets keep the tag for now, to get other opinions maybe

thanks Spencerk 20:54, 28 March 2006 (UTC)

Hi Spencer. That's much better now. My only remaining concern is about it being merged with 'dominant'. Do you feel they should share an article? I can't see that they have that much in common, except that the dominant is a perfect fifth above the tonic. Anyway, thanks for your positive response to my comments (Mark 28March 06)

Which title would be kept? In other words, which article should be merged into which? Hyacinth 08:56, 29 March 2006 (UTC)

I'm a professed mergist, yet I don't think "Perfect fifth" and "Dominant" should be merged. They're totally different concepts. The interval of a perfect fifth is used in music that totally lacks the concept of tonic and dominant. —Keenan Pepper 15:30, 29 March 2006 (UTC)
I second Keenan's view that they should not be merged as they are completely different concepts. I can see no advantage in merging them. Fretsource (29-03-06)
Don't merge with dominant. The perfect fifth an interval. The dominant refers to a change of harmonic centre (which happens to be at the interval of a fifth). They're really very different. Rainwarrior 21:16, 4 April 2006 (UTC)
  • i removed the merge suggestion and put dominant (music) in a 'see also'. There is a section called "popular wang ba dans", i dont know what this means and have found nothing on in google or wikipedia. Am beginning to think that it is vandalism because "wang ba dan" is a chinese swear word. Also, i'd like to see "music with a perfect fifth" clarified too, like does that mean contains a perfect fifth harmony? cause that would be crazy. Would be awesome to have this clarified on the page. any thoughts?Spencerk 21:53, 5 April 2006 (UTC)
I don't know where this "wang ba dan" thing is you're talking about, but it sounds like vandalism. It probably doesn't mean anything. Rainwarrior 22:37, 5 April 2006 (UTC)
I think the whole contribution of 70.24.220.81 should be reverted. Apart from the mysterious 'wang ba dans' the content is far from encyclopedic, and seems to be more about military marches (with inappropriate and unsuccessful attempts at humour), and the list of music containing perfect fifths is obviously nonsense - especially the 'obscure' Chopin concerto. Yet, I'm not sure it's vandalism as he (or she) seems to have gone to a lot of effort. I vote revert, but let's leave it for a bit to let others have a look or for the author to respond. (Mark 6 April 06)
I was right - He's not a vandal, he's a nut, as confirmed by another (now reverted) contribution to Chopin, which reported that 'wall-mines' were put in place to deter Chopin from damaging the walls by kicking them while playing... (wait for it)... perfect fifths. (Mark)

[edit] Diatonic Fifths

About diatonic fifths, it is said that the perfect fifth is

"one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one chromatic semitone smaller, and the augmented fifth, which is one chromatic semitone larger."

As far as I know, there is no augmented fifth in a diatonic scale; there are six perfect fifths and one diminished fifth. I think there is a confusion here with the diatonic minor sixths (E-C, A-F and B-G in the diatonic natural scale). Although they are indeed enharmonic to augmented fifths, they span six diatonic degrees, not five.

If you all agree, I suggest a correction here. Old Palimpsest 18:26, 23 February 2007 (UTC)

Eb to B in C harmonic minor? Hyacinth (talk) 00:13, 10 January 2008 (UTC)

[edit] Contradiction?

Isn't it contradictory to speak of a fifth as being "perfect" when equal temperament is used? Equality of temperament necessarily means that the fifth is not quite perfect and will have a slightly dissonant sound. I hoped to hear an actually perfect and fully consonant fifth with a 3-to-2 frequency ratio. Where's the sound file for that? Michael Hardy (talk) 05:07, 12 March 2008 (UTC)

This article begins as follows:

The perfect fifth or diapente (sometimes abbreviated P5) is a musical interval which is responsible for the most consonant, or stable, of the unison and octave.

I don't quite understand that. Could it have been intended to say that it is more consonant than any interval except the unison and the octave?

Later in the same paragraph it says the article says:
The prefix perfect identifies it as belonging to the group of perfect intervals (perfect fourth, perfect octave) so called because of their extremely simple pitch relationships resulting in a high degree of consonance.

With all this talk of "high degree of consonance", it seems very (pardon the pun) unjust to use as an example, for the reader to listen to, the approximation that occurs in the equally tempered scale. That interval is obviously NOT so highly consonant. If I had suitable software and knew how to create these sound files, I'd replace the one that's here. Michael Hardy (talk) 23:47, 12 March 2008 (UTC)

Michael, are you telling us that you can not only hear the difference between a just perfect fifth and an equal tempered one, but can also hear that the equally tempered one is less consonant? The difference is only 2 cents!! As far as I'm aware the limit of human pitch discrimination is around 5 cents, 3 or 4 if you're super sensitive - but 2 cents? Isn't that superhuman? (Mark - 28/3/08) —Preceding unsigned comment added by 84.68.179.71 (talk) 22:13, 28 March 2008 (UTC)

I don't know whether I can hear the difference between the two notes, the "G" and the slightly sharp "G", if you play then in succession, but I believe I can hear the difference between the two intervals---the C with the justly tuned G, and the C with the equally tempered G. I think the fact that it's played with another note at the same time may make it perceptible where it otherwise would not be. And I ask you: have you tried it, to see whether you can hear the difference? I can certainly hear the slight dissonance when that pair of notes is played on a piano. In about 2001 I encountered a musician who had an electronic instrument with a keyboard and with the ability to change from equal temperament to a scale on which the ratio of G to C was 3:2. I could hear the dissonance on the equally tempered scale and not on the one with the 3:2 ratio. Michael Hardy (talk) 23:19, 28 March 2008 (UTC)

I've just done as you suggested. I mixed a 5 second, 440Hz sine wave with a 660Hz one to get a "just" perfect fifth and then mixed the 440Hz one with one 700 cents sharper to get the equally tempered fifth. The only difference I could hear is what you'd expect - beats. There are about 8 noticeable pulses within the 5 second duration of the tempered mix. Obviously that beat frequency is too low to cause dissonance. Dissonance only occurs when the beats are too rapid to be perceived individually but are perceived instead as a roughness of sound. Remember, I'm using sine waves though. Complex wave mixes such as from certain musical instrument (especially synthesizers) may introduce dissonances via their various overtones, which are absent from pure sine waves. That's irrelevent to this article though, which should focus purely on the fifth, regardless of the harmonic series of the constituent tones. (Mark - 29 March 08) —Preceding unsigned comment added by 84.68.6.30 (talk) 20:28, 29 March 2008 (UTC)

Can you post those sound files hear so that I, and others discussion this, can hear them? Then the discussion might be able to advance beyond this impasse. Michael Hardy (talk) 17:09, 30 March 2008 (UTC)

There's an impasse? There's no need to post any files. The difference between a 'just' perfect fifth and an equally tempered perfect fifth is well known. The only difference is that the tempered one causes about 2 (faintly) audible beats per second. This is NOT dissonance.
Both are mathematically precise - one is precisely 3/2, the other is precisely 700 cents.
Both are equally consonant. There's nothing in the tempered one that can cause dissonance. A 2 beats per second variation in amplitude can't be perceived as dissonance by any stretch of the imagination. If you can hear dissonance in any properly tuned tempered perfect fifth, then it's probably caused by an interaction of the harmonics produced by the instrument, speaker cabinet, ear wax or whatever, not the perfect fifth itself.
Last but not least, the term perfect fifth is a musical term, describing a musical interval and its function within the music system that named it. It's not a physics or mathematical term describing frequency ratios. It's not concerned with the mathematics of any chosen tuning system. Whether its just or tempered, musically, it's still a perfect fifth. So I think you're missing the point in criticising the article's use of a tempered perfect fifth rather than a just perfect fifth. Musically, both are perfect fifths. (Mark - 30 March 2008) —Preceding unsigned comment added by 84.64.78.152 (talk) 19:20, 30 March 2008 (UTC)

OK, so you're UNWILLING to post those things here.

There's also a question of more complicated things than sine waves. The Fourier series of a seemingly simple square wave has higher-frequency components---overtones. The thing in the sound file here doesn't sound like a simple sine wave. Your remarks may apply to sine waves, but that's not what we've got here. Michael Hardy (talk) 21:47, 30 March 2008 (UTC)

That's right. I'm UNWILLING to post them here as this article is about a musical term. I might have considered it if the article was relating to acoustics or physics. But it's not, and such discussions are irrelevant here. The article mentions the difference between both types of perfect fifth and that's fine. If the reader wants to delve deeper into the differences from a mathematical or any other non-musical perspective, they will go to articles on equal temperament, acoustics, wave theory, etc, where such concepts are presumably discussed in detail.
Whether or not dissonance is introduced by any particular tuning system, or by the complex waveform of a particular instrument, in no way affects the status of an interval's quality. An equally tempered major third is noticeably less consonant than a just one - yet it's no less a major third because of it. (Mark - 30 March 2008) —Preceding unsigned comment added by 62.136.27.173 (talk) 22:45, 30 March 2008 (UTC)

How can the question of whether they're dissonant or consonant be irrelevant to the article when the article begins with a statement that this interval is more consonant than any other except the unison and the octave? Besides, the definition of the term is not all that matters in an article about the term. There's also the question of whether, or why, the concept is important. That depends in part on these issues of dissonance or consonance.

Also, you seem to assume that any comments I could post after hearing the sound files you're talking about could be of interest only if YOU are able to anticipate, BEFORE posting them, what I would say that would be of interest. Michael Hardy (talk) 23:32, 30 March 2008 (UTC)

[edit] OK, no knowlegdeable person is working on this...

It's been more than two weeks since I pointed out problems here, and I don't see people knowledgeable in music coming forward to say anything about my concerns, either to tell me I've got it wrong or otherwise, or to edit the article. I'm going to alter the mangled opening sentence of the article so that it says what I'm guessing it meant. Then I'll see if I can find some musically knowledgeable Wikipedians to assist further. Michael Hardy (talk) 21:38, 28 March 2008 (UTC)

It seems you misunderstand the distinction between intervals and tuning. There are serval types of fifths, viz dimished fifth, perfect fifth, and augmented fifth. How these intervals are implemented is the tuning. Does that answer your question? Brettr (talk) 10:03, 30 March 2008 (UTC)

How would it either answer any question I had or address any other concern I had? Michael Hardy (talk) 17:06, 30 March 2008 (UTC)

[edit] "perfect"?

The article now says this:

The term perfect identifies it as belonging to the group of perfect intervals (perfect fourth, perfect octave) so called because of their simple pitch relationships and their high degree of consonance.

Several people who have posted on this page have told me that the fifth on an equally tempered scale should be included as one example of a "perfect fifth". If that is true, then the statement that it has this "simple pitch relationship" and "high degree of consonanace" is false. Michael Hardy (talk) 03:25, 8 April 2008 (UTC)

Hello MH, I took out your recent change, but wouldn't mind it going back in provided you can find a legitimate reference source to back it up. Along this lines, I looked at Piston's widely-used harmony text, and I found that it covers harmony without a single mention of tuning and temperaments; i.e. Piston evidently considered them to be separate matters. So if you really want to make the claim that an equally-tempered fifth doesn't count as perfect, I think you should find a published reference source that says this. Sincerely, Opus33 (talk) 16:01, 8 April 2008 (UTC)

Well, evidently this Wikipedia article fails to treat them as "separate matters" when it speaks of consonance between notes on a scale. Michael Hardy (talk) 16:19, 8 April 2008 (UTC)