Talk:Interval (music)/Archive 1

message: This article, as it stands, I feel, is not only unclear about the various "diatonic intervals" discussed, because it does not reference them to other ways of labelling intervals, and is thus heavily biased towards tonal music. This is part of what led to the confusing, "in minor scales the minor intervals are introduced." I have recently added a few sentences to the beginning (about measuring intervals in post-tonal theory) that changed the article from being entirely non-NPOV, but I hope to do more.Hyacinth 23:35, 27 Dec 2003 (UTC)
thread_title: Rewrite

message: The following seems to belong in its own article describing whatever theory it is:
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The intervals can be divided into five "generations", which correspond to negative powers of two: 
Zeroth generation (1+2−0): P1, P8. 
First generation (1+2−1): P4, P5. 
Second generation (1+2−2): M3, m3, M6, m6. 
Third generation (1+2−3): M2, m7. 
Fourth generation (1+2−4): m2, M7, π. 
Each successive generation is more dissonant than the previous one.
Here is the derivation of each generation from the previous one:
Start with the octave's ratio, 2:1.  Multiply each of its two numbers by two, yielding 4:2.  Then stick the missing number in the middle, which gives 4:3:2.  This breaks up into a pair of ratios — 4:3 and 3:2.  The minor one is 4:3 and the major one is 3:2.  These are the perfect fourth and the perfect fifth, respectively, and they are the first generation.
Now take the perfect fifth's ratio, 3:2.  Multiply each of its two numbers by two to obtain 6:4.  Then stick the missing number in the middle, yielding 6:5:4.  This breaks up into a pair of ratios — 6:5 and 5:4.  The minor one is 6:5 and the major one is 5:4.  These are the minor third and major third, respectively.  Their inversions are 5:3 and 8:5, which are the major sixth and the minor sixth, respectively.  So these are the second generation: M3, m3, M6, m6.
Now take the major third's ratio, 5:4.  Multiply each of its two numbers by two, which yields 10:8.  Then stick the missing number in the middle, giving 10:9:8.  This breaks up into a pair of ratios — 10:9 and 9:8.  The minor one is 10:9 and the major one is 9:8.  Both of these are whole-tones, i.e. major seconds.  The inversion of 9:8 is 16:9, a minor seventh.  So these are the third generation: M2, m7.
Now take the whole-tone's ratio, 9:8.  Multiply each of its two numbers by two, giving 18:16.  Then stick the missing number in the middle to obtain 18:17:16.  This breaks up into a pair of ratios — 18:17 and 17:16.  The minor one is 18:17 and the major one is 17:16.  Both of these are semitones, i.e. minor seconds.  The inversion of 18:17 is 17:9, a major seventh.  The last interval is the tritone.  The tritone is ideally equal to the square root of two, which is irrational, but can be approximated by adding a semitone to a perfect fourth:
: {4 \over 3} \times {17 \over 16} = {1 \times 17 \over 3 \times 4} = {17 \over 12} 
or
: {4 \over 3} \times {18 \over 17} = {4 \times 6 \over 1 \times 17} = {24 \over 17}, 
which is the inversion of 17:12.  24:17 has the same denominator as 18:17, and 17:12 has the same numerator as 17:16.  So these are the intervals of the fourth generation: m2, M7, π.
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Agree. No clue what theory that is, though. --Wahoofive 04:05, 14 Mar 2005 (UTC)
thread_title: Generations of intervals

message: I do not see how "nomenclature" is less abstract than theory, it certainly is less readily understandable. "Diatonic theory" is also terminology actually used, as in: Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. . Hyacinth 23:30, 21 Mar 2005 (UTC)
thread_title: Diatonic

message: I think that anything which is applied to equal tempered intervals only when those are considered as the just intervals they approximate should go in a just section where there is one. Hyacinth 23:32, 21 Mar 2005 (UTC)
replies: text: The article in its current state is organized with naming conventions first, then analytical tools. That's why I moved interval root and strength to other places on the page.  --Wahoofive 00:46, 22 Mar 2005 (UTC)
thread_title: Just vs Equal

message: Do we need the mathematical notation in the set-theory stuff? It seems kind of pretentious to say you subtract two numbers, then use a formula to show 
 DIFFERENCE = MINUEND - SUBTRAHEND
 INVERSE = SUBTRAHEND - MINUEND
 ABSOLUTE DIFFERENCE = | MINUEND - SUBTRAHEND |
The distinction between <> brackets and () parentheses is difficult to see, too. It's much more clearly explained on the musical set theory page. I think we could just summarize it in text only. --Wahoofive 05:08, 28 Mar 2005 (UTC)
replies: text: But its not mentioned on musical set theory. Hyacinth 05:52, 29 Mar 2005 (UTC)
thread_title:  Pitch class notation 

message: (by Wahoofive)
*It is important to note that while intervals may be named by their harmonic functions, for instance, a major second, may be described by a ratio, cent, or integer, not every interval described by these more general terms may be described with the harmonic function name. For instance, all major seconds (in twelve tone equal temperament) are 200 cents, but not every interval of 200 cents is a major second. See: enharmonic.
*simple and compound
Hyacinth 06:13, 11 Apr 2005 (UTC)
thread_title: Removed

message: Please forgive my ignorance on this topic, but is everyone sure that a unison is actually called an interval, when there is clearly no interval at all?--Light current 22:49, 5 November 2005 (UTC)
replies: text: Is zero a number? By the way, Light current, don't forget to sign your talk-page posts with ~~~~ —Wahoofive (talk) 19:52, 5 November 2005 (UTC)

text: I guess I was being too subtle. Unison is an interval in exactly the same sense that zero is a number: you wouldn't use it to count anything, but it's essential as a starting point and an indicator of no change. —Wahoofive (talk) 04:01, 6 November 2005 (UTC)

text: In fact, I can pursue the analogy further. An interval is a difference between notes. A difference between two numbers can certainly be zero. —Wahoofive (talk) 04:05, 6 November 2005 (UTC)
thread_title:  Unison 

message: In the section on intervals using equal temperament, maybe there could be a table with the name of the interval, its abbrevation, and a few examples of well-known songs that start with that interval?  That would be helpful for people learning to recognize intervals. Skybrian 21:02, 19 February 2006 (UTC)
replies: text: The names of the intervals are already in the table. So I am confused what you ask. The list of well known songs is a good idea, but is a project on its own, deserving a separate page. −Woodstone 21:28, 19 February 2006 (UTC)
replies: text: Yes, the examples are what I'm most interested in.  A separate page is fine, but I'm not sure what to call it or how it relates to the main article.  There's already a List of Musical Intervals which is mostly unusual intervals, and separate pages for each equal temperament interval. - Skybrian 18:47, 20 February 2006 (UTC)

text: You may want to have a look at songs by interval. I have no idea about the copyright status of this site, so be careful in converting it to wikipedia. −Woodstone 19:24, 20 February 2006 (UTC)
thread_title:  Examples of intervals 

message: Is the interval produced by two notes with frequencies with the golden ratio musically significant?--Lkjhgfdsa 19:26, 7 June 2006 (UTC)
replies: text: Interesting question. The golden ratio is (1+sqrt(5))/2=1.618034, which corresponds to 833.09 cents. This is the interval from c to about a third of a semitone between g# and a. Checking the extensive list at List of musical intervals this does not appear to have any musical significance. Viewed from another angle, musical relations are usually ratios between small numbers, whereas φ is not a rational number. −Woodstone 20:34, 7 June 2006 (UTC)
replies: text: It does have a special property though: in a certain sense it is the most dissonant interval because its continued fraction expansion 1+1/(1+1/(1+1/... converges the most slowly. Isn't it weird how paintings and architecture that use the golden ratio look beautiful, but the golden ratio sounds ugly as a musical interval? —Keenan Pepper 21:58, 7 June 2006 (UTC)
thread_title: Golden ratio

message: As a global encyclopedia, a NPOV for Wikipedia means a global point of view. The discription of intervals here concentrates on European or western scales. There are many totaly different scales in othere cultres. For example, in the classical courtly music of Buganda, played on instruments like amadinda and akadinda xylophones and on the enanga harp the scale used is a roughly equidistant pentatonic scale which means that the octave is divided into five equal intervals of about 240 cents (2.4 semitones). Moreover, some musical cultures have a higher tollerance for variation in their scales, so an emic and etic distinction seems appropriate here (similar to the distinction of phonetics and phonology). So the article needs to be structured into a general part definig general concepts applicable in all cultures (like "interval", "cent" etc.) and a section or sections describing specific intervals or interval systems occurring in certain musical cultures (like classical european music or classical buganda music). Nannus 22:21, 5 August 2006 (UTC)
replies: text: I couldn't agree more. This article needs some major work to avoid systemic bias. It should start out with the universals: the terminology, the mathematics, the octave (the only interval with a good claim to universality), and then it should have equal sections for all the musical traditions of the world. A lot of the material should probably be broken off into its own article, Intervals of common practice music or Intervals of the diatonic scale or whatever. —Keenan Pepper 03:18, 6 August 2006 (UTC)
replies: text: I agree also, though some of my comments early in 2005 (see above) might seem to show that I disagree. I do think there needs to be a clearly marked and well-managed "core" of theory, which can then be applied in treatments of several different traditions. As things stand, the coverage of Western common practice is pretty thorough; but it tends to blend too seamlessly and therefore confusingly with talk of Pythagorean commas, schismata, and the like. One problem might be that few have the expertise to undertake the non-Western coverage. Myself, I know the common-practice side of things well, but for the rest I could only assist with the task of integration and copyediting for consistency. So how about you, Nannus and Keenan Pepper? (By the way, KP: did you mean "systematic bias"? That's the more usual expression, and seems to refer to POV bias. By the way, I'm not sure that NPOV is precisely what is lacking here: would anything that falls short of full global coverage be aptly called a lapse from NPOV? Nannus: do you mean "the distinction of phonetics and phonemics", which is the usual way of glossing the etic–emic distinction?) Noetica 04:23, 6 August 2006 (UTC)
replies: text: Good assessment. I have access to a good music theory library (Allen library at FSU) and enough knowledge to use it. I thought it was systematic too, but Wikipedia:WikiProject Countering systemic bias uses the other word. —Keenan Pepper 04:56, 6 August 2006 (UTC)
thread_title: NPOV

message: I reformatted the explanations of perfect intervals to match the list style of major/minor intervals which is easier to read. I didn't change any content. --64.175.42.169 20:14, 23 November 2006 (UTC)
thread_title:  Minor reformatting 

message: Should this article contain information on common compound intervals and their enharmonic equivalents?
maybe we could say that these intervals are part of the western chromatic scale, cuz i doubt we can find any experts on the 22-tone or parche scales. Blueaster 03:00, 28 November 2006 (UTC)
thread_title:  Compound intervals 

message: We seriously need a RCM (royal conservatory of music) official to rewrite the faulty parts of the article..... that way, there won't be half as much arguing over the topic....
however, I don't think that they would respect a free online version of conservatory theory.... therefore.... Ex-Conservatory members?
User: 17:39, 2 December 2006 (UTC)
thread_title: Topic Rewrite

message: In an article about musical intervals? What the galluking plick is up with that??151.202.111.202 02:09, 26 December 2006 (UTC)
replies: text: Anonymous, I do not have dialogue with Roivas, who (I note) continues to attribute feelings, opinions, and actions to me inaccurately and without evidence. Because it has been impossible to work through things coolly, with tolerance of the unfortunate uncertainties in some core terminology, and with respect and intellectual detachment on all sides, I do not now edit at this page. See recent additions at Talk:Diminished seventh for more. The rather ill-focused citations added there earlier by Roivas to support a single doctrinare interpretation of the term diatonic are mostly irrelevant, since no one disputes that the term is used in the way claimed; what is disputed is whether it is also used in other senses as well. In general, in the absence of further supporting argument, evidence for A is not automatically evidence against B. (Should be obvious, but apparently it isn't.) – Noetica 02:26, 27 December 2006 (UTC)
thread_title: Neutrality disputed???

message: I really think the diagram illustrating the intervals needs to include all the chromatic intervals to illustrate the exact use of each interval quality more clearly. Secondly, the following statement "There [sic! just noticed will fix] are called perfect because of their extremely simple pitch relationships resulting in a high degree of consonance..." is not enough, there needs to be some basic information about ratios, and it is no use describing these intervals in semi-tones, as 1) the interval of a semi-tone has not yet been defined, and as we know, varies between different systems of temperament/tuning. Matt.kaner 03:58, 27 February 2007 (UTC)
thread_title: Diagram poor

message: As a person who has been appealed to by both sides, let me make the following observations:
#Both of you seem to believe that using more words makes your argument more emphatic. Nothing could be further from the truth. Be concise.
#I'm going to try to summarize the basic confict here. Please confirm that my understanding is correct. Rovias argues that the overwhelming consensus of music theorists is that the harmonic minor scale (and perhaps the melodic as well) is not "diatonic", whereas Noetica thinks there is substantial doubt.
#Rovias acknowledges that chords (and intervals) derived from these minor-variant scales are often considered diatonic even by those who consider the underlying scales to be non-diatonic. I haven't looked at your references in detail, but this seems pretty hard to swallow. The term is almost always defined in terms of scales.
#Noetica observes, correctly, that the term "diatonic" is used pretty loosely in Wikipedia articles, a reflection of the confusion regarding this term among musicians in general. Feetonthedesk's editing, which introduced this term throughout this article, did nothing to make it more comprehensible. However, I'm not clear what Noetica's proposed solution is. There's no way to indicate that a term is ambiguous every time you use it. 
#Why is this discussion not taking place in the article Diatonic? I don't see that either of you has ever edited, or commented on, that article.
Do me a favor and keep your answers short. —Wahoofive (talk) 16:33, 23 March 2007 (UTC)
replies: text: Thanks Wahoofive. This talk page is so long and almost unreadable in places! And it is odd that the debate is here (and on a few other pages) rather than at Diatonic scale (Diatonic) -- a page which right off the bat defines "diatonic" quite clearly. Pfly 17:57, 23 March 2007 (UTC)
replies: text: Pfly, Diatonic scale at first presents "the" minor scale as if there were only one, and as if it were clearly diatonic. A reader might easily become confused, by the subsequent discussion of the harmonic minor, because by the basic definition in the article the harmonic minor is not diatonic. The article Minor scale, to which there is a link, is also ambivalent. If the harmonic minor is not to be considered diatonic, why is it glibly introduced at all in the article Diatonic scale? Because that article is itself in conflict: in a way it "unconsciously" wants to classify all those common scales that are not chromatic as diatonic ("The modern major and minor scales are diatonic..."), yet it also wants to preserve the strict pre-common-practice notion, involving only tones and semitones in a certain order. A recipe for confusion! It is perhaps hard to appreciate the difficulties that new-comers will find with such things, since we have been using these terms for years. But new-comers, especially, need everything logical and unambiguous. –Noetica 00:19, 24 March 2007 (UTC)
thread_title: Diatonic summarized

message: I'm going to continue this discussion at Talk:Diatonic scale, since it certainly doesn't belong at Interval. —Wahoofive (talk) 04:51, 24 March 2007 (UTC)
replies: text: Fine with me, Wahoofive. I will just note in passing that the discussion doesn't fit naturally at any existing article, though, because the terms in question are applied to all sorts of things: scales, intervals, chords, harmony, etc. But OK, no more here. –Noetica 05:42, 24 March 2007 (UTC)
thread_title: Discussion moved