Talk:Perfect fifth

message: 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)
thread_title: Sound files?

message: 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)
thread_title: Ratio

message: 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)
replies: text: Eb to B in C harmonic minor? Hyacinth (talk) 00:13, 10 January 2008 (UTC)
thread_title:  Diatonic Fifths 

message: 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)
replies: text: 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)
thread_title:  OK, no knowlegdeable person is working on this... 

message: Perfect!
A perfect fifth is an exact (math relation) harmony, of 2 frequencies (pitches), where the 2nd pitch is exactly 3x the first, and divided by 2 (an octave). The frequency difference between any pair of frequencies is called an musical interval and that pair of pitches has a frequency ratio of 3/2 (meaning multiply by 3, & divided by 2). "Perfect" means "no error" (of harmonic (multiples)), thus exact math (=without tolerance).
 (Wrongly stated below as, "or very nearly so".
 A fifth is either perfect, or it is not.)
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.
(That statement above is (almost) correct, if we delete
 ", or very near so",
 The colon ":" also does not explain the math well enough
 (for most people).
Using concert pitch at A 440 Hz
440 Hz x 3= 1320 Hz)/2=660 Hz Perfect fifth.
As can be seen
440 Hz x 3= 1320 Hz):(440 Hz x 2=880 Hz) is in the next octave above, unnecessarily so.
660 Hz/3=220 Hz):(440 Hz/2=220 Hz) refers to the octave below concert pitch 440 Hz.)
An equal tempered fifth is not harmonic, at 659.26 Hz, thus "beats" with 0.74 Hz (error)!
A good ear can hear that.
That error is a form of modulation.
Such a small error (1.955 cent) is tolerable, 
but if it gets large enough, like a Pythagorean comma (~24 cent=1.955 cent x 12)
it becomes very noticeable, & that (large error) is called a wolf
(because it sounds so terrible, it growls).
We use the word fifth to say, the first and "fifth" finger are used to play this interval ("pair" of notes) on the keyboard. 
Meaning we (ignore &) don't bother mentioning the 1st note, which is there (being played).
Peter Sheedy
Email PS20100401@gmx.de
"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)
replies: text: 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)

text: An interesting theory, but how does this account for the designation of "perfect" consonances (and their differentiation from "imperfect" ones) as far back as the 13th century?—Jerome Kohl (talk) 19:59, 16 February 2011 (UTC)
replies: text: As I take it, "perfect" relates to those intervals on a chromatic scale that cannot be discriminated in a "minor" or "major" version and thus appear only once. The attribute is hence redundant, as the term "fifth" inherently bears this property. Compare the German language, where both "Quinte" and "reine Quinte" exist -- the latter is mostly used to emphasize the fact that a fifth is a perfect interval (meaning there is only one such interval to a given base tone), but otherwise left out. I can only quote German sources though, so I will not edit the article. --Doubaer (talk) 13:10, 29 April 2013 (UTC)
replies: text: When the terms "fifth", "fourth", or "octave" are used alone (in English or in German), the assumption is that the "perfect" form is meant. However, both languages have qualifiers other than "perfect"/"reine", so that, in German, one may also speak of a "verminderte Quinte" or  "übermäßige Quinte". For this reason, the terms "perfect fifth" ("reine Quinte"), "perfect fourth" ("reine Quarte"), etc. are redundant only in casual usage. Still, perhaps this informal practice should be made more explicit in this article (it is presently hinted at in the first sentence).—Jerome Kohl (talk) 16:27, 29 April 2013 (UTC)
replies: text:  I agree, and there is a further discrimination between major/minor (e.g. große Terz, kleine Terz) and augmented/diminished (e.g. übermäßige/verminderte Terz), the latter of which are enharmonics of major second and perfect fourth, respectively. I personally regard all augmented/diminished intervals as modifications of diatonic intervals through use sharp or flat signs, so as you state, I take it that "perfect" relates to the non-modified (not aug./dim) interval, that also cannot be discriminated in major or minor. Is that correct? --Doubaer (talk) 14:11, 12 June 2013 (UTC)
replies: text: That is the way I understand the terminology as well, yes, with just one small caveat: while the characterizations "augmented" and "diminished" really only make sense in a diatonic context, so that distinction between the diminished fifth and augmented fourth depend upon notation based on a diatonic scale, naming the interval of a tritone remains a bit of a conundrum unless, in an undifferentiated twelve-tone context, an alternative notation is employed (such as the numeric measurement of interval size in semitones). In such a case, however, the notion of "third", "fourth", "fifth", etc. also becomes meaningless.—Jerome Kohl (talk) 16:13, 12 June 2013 (UTC)
thread_title:  "perfect"? 

message: I removed this audio file, which was meant to show the beat in a perfect fifth tuned in equal temperament:
The idea of inserting an audio file was great, but in this example the "beat" was actually a slight tremolo which was clearly present in each separate note, and was not not due to their interference. This was highly misleading. The beat in a 700 cent interval is not so easy to hear. We should find a better example, similar to these (from just intonation):
: An A-major scale, followed by three major triads, and then a progression of fifths in just intonation.
: An A-major scale, followed by three major triads, and then a progression of fifths in equal temperament. If you listen to the above file, and then listen to this one, you might be able to hear a  slight buzzing in this file.
Unfortunately, I was not able to locate or produce an audio file containing only a perfect fifth. Some of you might be able to cut from the above two examples the A-E fifth that you can hear for a moment when the A scale is played together with a continuous A. Some very interesting examples of beat are given in the page beat (acoustics), but they are not limited to the perfect fifth. Paolo.dL (talk) 20:19, 26 June 2010 (UTC)
thread_title: Misleading audio file

message: the intro in the starwars theme is a perfect 4th not a 5th!  —Preceding unsigned comment added by 80.216.26.171 (talk) 19:10, 8 March 2011 (UTC)
thread_title:  Starwars 

message: According to the New Harvard Dictionary of Music, the pitch ration 3:2 is known as a hemiola. I put this fact in the article yesterday and it has been removed. Why?Dr clave (talk) 14:46, 3 February 2012 (UTC)
replies: text: According to the edit summary by User:Justlettersandnumbers, "where & when is it referred to as hemiola? please add reference to sources". The link to the Wikipedia article Hemiola is insufficient, since Wikipedia cannot be a reference for itself. Of course, if all readers were fluent in Ancient Greek, this would be superfluous. Sadly, today's education system has let us down badly.—Jerome Kohl (talk) 17:06, 3 February 2012 (UTC)
replies: text: Thanks, JK, sorry, Dr. C.! If it's in that dictionary, we should probably put it in the article somewhere. It is, however, a most unusual application of the term, and I'd be interested to know, out of personal curiosity, where and when it was so used. Julian Rushton mentions the usage in Grove, but doesn't apparently give date, place or indeed any reference (or have I misread?). It doesn't appear to be a common enough usage to deserve much prominence, though I'm very open to correction. Sesquialtera also appears to have been used for pitch ratios, btw. Justlettersandnumbers (talk) 18:34, 3 February 2012 (UTC)
replies: text: Yes, the Harvard Dictionary citation would probably be sufficient. The reason both terms are used is that they are mutual translations of one another (Greek and Latin). Latin music theory treatises often sought to upgrade their status by using Greek terms, or simply didn't bother to translate well-established Greek forms. Later, when educated people were no longer expected to communicate exclusively in Latin, vernacular treatises often did the same thing: peppering English, French, German, etc. prose with learned Latin and Greek terms. I have added a note in the Hemiola article about an apparent OR claim regarding which of these two terms is "obviously" the more frequent. Personally, I find "hemiola" unfamiliar in pitch-interval naming (but "sesquialtera" fairly common), but both words quite familiar in rhythmic theory. However, the Greek word (hemiola) I associate more with modern music theory (17th century to the present), while the Latin (sesquialtera) I think is more common in good old-fashioned, traditional theory (16th century and before).—Jerome Kohl (talk) 19:30, 3 February 2012 (UTC)

text: I find diapente to be the common name for the interval of a fifth, at least from Zarlino to Bach or so. Hmm, I'm about to climb on to a hobby-horse. Can you cite any written source that mentions hemiola in its modern sense before about 1934? (I ask because I'd really like to know). The ratio of 2:3 described in the hemiola article is subsesquialtera, not sesquialtera. But maybe we should move this there? Justlettersandnumbers (talk) 19:43, 3 February 2012 (UTC)
replies: text: The word diapente (Greek for "through five [strings]") refers to the interval of a fifth, but not specifically to the one tuned in a ratio of 3:2 (I hadn't noticed that the article got the numbers of the ratio backward but I shouldn't be surprised, considering the many other lapses). As far as I am aware, the earliest use in English music-theory sources of the word "hemiola" to describe rhythm is Thomas Morley's Plaine & Easie Introduction to Practicall Musicke (1597). It is found in Latin treatises as early as 1517 to describe rhythmic proportions, in Andreas Ornithoparchus's Musice active micrologus, liber secundus of 1517 (hardly surprising to discover this, since Morley relied heavily on Ornithoparchus), as well as in, e.g., Nicolaus Listenius (Musica , 1549), Adrian Petit Coclico (Compendium musices, 1552), Lampadius (Compendium musices, 1554), Hermann Finck (Practica musica, 1556), and in Luca Lossio's tantalizingly named Erotemata musicae practica (1563). In reference to pitch ratios, the sources go back much earlier, as far as the anonymous, late-9th or early 10th-century Alia musica ("et hoc est quod ait: musicos esse numeros, qui per ter et quater dividuntur, comparati eidem duodenario. Nam VIII. qui per quater, et VIIII. qui per ter dividuntur, ad eundem sub epitrita vel hemiola proportione comparantur …").—Jerome Kohl (talk) 20:24, 3 February 2012 (UTC)
replies: text: Does an English encyclopedia article on pitch need to use a sesquipedalian term that may have been tossed into an early treatise as a fancy foreign-sounding way of saying "one and a half?" I will leave it to more learned heads than mine, but this is the first time I've ever seen "hemiola" refer to a pitch ratio. Rhythmic hemiola is another matter, and a lot of fun. __ Just plain Bill (talk) 21:02, 3 February 2012 (UTC)

text: To be perfectly honest, when I said I found the use of hemiola "unfamiliar in pitch-interval naming", what I really meant was that I had never before today encountered this usage in English. Perhaps readers in other parts of the anglophone (to use a terser word than "English-speaking") world have different experiences. If so, I hope they will come forward and set the record straight. Until then, I could not possibly disagree with you less.—Jerome Kohl (talk) 21:32, 3 February 2012 (UTC)

text: No probs. The fuss kicked up was disproportionate, but nevertheless raised some productive issues. I have again changed the word "idealized", since all theoretical interval constructions are "ideals", not merely the ones defined by whole-number ratios.—Jerome Kohl (talk) 03:54, 4 February 2012 (UTC)
thread_title: hemiola

message: After all, they're the same thing. Power chords are just what some poncy guitarists call open fifths. Is this serious enough for you, Bill? Or still too frivolous? SquidSix (talk) 21:57, 16 July 2021 (UTC)
replies: text: They may involve bare fifths, but IMO they inhabit a different context than this more thoretical article about a musical interval. I am content to keep them as separate articles with links to each other. "Poncy" is a value judgement that has no place in the article, not without massive support from reliable sources, which I doubt you will find. Just plain Bill (talk) 22:32, 16 July 2021 (UTC)
thread_title:  Power Chord Article Should Merge With This 

message: The article says 
"Perfect intervals are also defined as those natural intervals whose inversions are also perfect, ...".
But this is a circular definition since it uses the concept of perfect to define perfect. Should it be rewritten like this: 
"Perfect intervals are also defined as those natural intervals whose inversions are also natural, ..."? 81.175.221.202 (talk) 14:33, 7 January 2024 (UTC)
thread_title:  Self-referential definition