Talk:List of pitch intervals/Archive 1

Archive 1

Archive 2

Too many redlinks

Generally, something should only be linked if it makes sense to write an article about it. What material could be used in an article on the septimal minor third? It's a good interval, even one of my favorites, but that doesn't mean it's worthy of its own article. —Keenan Pepper 05:06, 8 December 2005 (UTC)

Distance in semitones

I think it might be much more usefull if at least the musical intervals in the equal temperament would also include their width in semitones. —The preceding unsigned comment was added by 86.121.142.63 (talk) 13:29, 20 March 2007 (UTC).

It's already there. The first column states the interval in cents. One hundred cent is a semitone. So where it says 500 cents, you can read 5 semitones. −Woodstone 15:02, 20 March 2007 (UTC)

Unreferenced material

Intervals such as "ragisma" and "breedsma" need to referenced (dictionaries, texts, peer-reviewed journals). Frank Zamjatin (talk) 12:40, 15 April 2008 (UTC)

Intervals

I noticed that one of the Pythagorean intervals is missing from this list. Specifically, the interval(s) near 600 cents from the table found in Pythagorean tuning. However, there are two values listed there: 588.27 cents and 611.73 cents. Which of the two should we use? SharkD (talk) 21:34, 12 August 2008 (UTC) Also, half of the values for the Pythagorean tuning correspond to frequencies that have been tuned down from unison as opposed to tuned up, resulting in discrepancies equal to the Pythagorean comma. Is this OK, or should we only tune up or only tune down? SharkD (talk) 21:39, 12 August 2008 (UTC)

I've been reading Just Intonation Explained, and it says, "The smaller the numbers in an interval's ratio, the more consonant (sweet-sounding) it is, and the more useful it is for purposes of musical intelligibility." Does this imply that sticking unison smack-dab in the middle is the optimal solution? SharkD (talk) 00:53, 13 August 2008 (UTC)

I looked through the article Minor second and couldn't find any references to the ratio, 27:25 or "Maximus". Is this maybe an error in the table? SharkD (talk) 23:30, 12 August 2008 (UTC)

Frequency ratio

Is there an article or article section that specifically defines the term, "frequency/pitch ratio"? I couldn't find it in Frequency or Pitch (music). I would like to link to it in the column header like "Cents" is. SharkD (talk) 22:13, 14 August 2008 (UTC)

That term doesn't currently appear in the article. A "frequency ratio" is a ratio ("a comparison of two numbers by division") where the two numbers are the frequencies of musical sounds or pitches. Hyacinth (talk) 08:18, 16 August 2008 (UTC)

Yeah, I know what it is. I just thought it weird that it's not defined in an article. SharkD (talk) 08:21, 16 August 2008 (UTC)

"Frequency" and "ratio" are both defined in articles. Hyacinth (talk) 08:36, 16 August 2008 (UTC)

24-equal temperment

Should the equal tempered quarter tone, neutral second, neutral third, neutral sixth and neutral seventh be re-labeled as belonging to 24-TET? We could label the column "Q", for "quarter tone". SharkD (talk) 22:13, 14 August 2008 (UTC)

Sure, don't see why not. Hyacinth (talk) 08:19, 16 August 2008 (UTC)

Done. SharkD (talk) 10:18, 16 August 2008 (UTC)

Color coding

I suggest color-coding the table items depending on whether they are even tempered, just, pythagorean, etc. SharkD (talk) 22:57, 9 August 2008 (UTC)

Would these provide more information, such as revealing a pattern? Hyacinth (talk) 10:48, 10 August 2008 (UTC)

It would at least allow readers to sort the table items into groups in external software. No, I don't expect readers to see patterns at a simple glance. I would personally like to know which items belong to the same tuning systems (it's not obvious to me, a novice), and adding this sort of information here would eliminate the need to dredge through all the connected articles. Adding another column to the table is a possible alternative to color-coding. There is a "sortable" class of tables which would allow readers to sort the table based on these factors. The disadvantage of adding another column, of course, is that it takes up more space. SharkD (talk) 00:42, 11 August 2008 (UTC)

Wouldn't this be redundant? For example, fourteen of the intervals are already labeled as just. Seven are already labeled Pythagorean. Hyacinth (talk) 03:24, 11 August 2008 (UTC)

One problem is that some pythagorean intervals are also (5-limit) just intervals. The unison and octave are in every tuning. So they would have to have multiple colors. Also in just tuning, for some notes there are multiple choices, so picking out a matching set would not be easily achieved. We could experiment somewhat to see how it turns out. −Woodstone (talk) 07:11, 11 August 2008 (UTC)

I have been thinking about this and have an idea. How about adding a column with the factorisations of all the just intervals. So for example 10:9 = 2*5/3*3. Then the color could indicate the highest prime factor occurring. To complete this, there would be colors as follows:

• color1: 12-tone equal tempered (including unison and octave)
• color2: other non-fractional tones
• color3: pythagorean (3-limit, but not unison, octave)
• color4: 5-limit intervals (but not 3-limit)
• color5: 7-limit intervals (but not 5-limit)
• etc

I can work on it when I have time. What do you think? −Woodstone (talk) 09:26, 11 August 2008 (UTC)

I have completed the color coding as proposed above. If I may say so: it looks good. It actually brings out more pattern than I expected. −Woodstone (talk) 18:44, 11 August 2008 (UTC)

A couple of comments: the color-coding could be limited to the "Name(s)" column. I think that would be less distracting. The "Ratio" and "Ratio factors" columns could possibly be merged, or the factors could be turned into <ref>s and displayed in a "Notes" section at the bottom of the article. Turning the table into a sortable one as I described earlier, might be a good idea, but I'm not 100% sure.

Also, as I understand the table, the 13-limit just intonation includes the 11, 7, 5 and 3 limit intonations as well but aren't necessarily marked as such? I have to admit I'm a bit of a novice, so I'm not quite sure. SharkD (talk) 22:20, 11 August 2008 (UTC)

The labels for the equal tempered and Pythagorean (pink and yellow) tunings are clear, but I suspect the labels for the remaining tunings are a bit terse. Do these tunings have full, long names? SharkD (talk) 02:43, 12 August 2008 (UTC)

The factors play a role in judging the nature of the interval and are as such informational to the reader. The total fraction is less important, but easier to recognise for many people. Converting either to footnotes would create a very long list and would make it difficult to relate numbers to the tones. So I think both columns have a place in the table.

Choice of color and columns to be colored is a matter of taste. I experimented and to me this one looks best.

Yes, all intervals in "limit" tuning of course include the ones with a lower limit. To express that in the table would require 5 (or 6 for 2-limit or 7 including equal temperament) columns with different coloring. I'm afraid that would make it too messy.

Perhaps we could bring up the notes at the bottom, because they explain the terminology.

−Woodstone (talk) 07:29, 12 August 2008 (UTC)

I've been thinking about it further, and placing the factorized ratios in parentheses next to the simplified versions might be an option. For instance, 2401 : 2400 (74 : 25·3·52). SharkD (talk) 00:53, 13 August 2008 (UTC)

I notice that there are several "lines of symmetry" in the table surrounding the equal-tempered intervals. What I mean is that an equal-tempered interval may be surrounded by two 5-limit intervals, which are surrounded by two 3-limit intervals, which are surrounded by two 7-limit intervals, and so on. The undecimal neutral third is a good example of this, as it lies in the middle of several other major and minor thirds. Do you think we can draw attention to this pattern in any way? Maybe, instead of different hues we can have gradations of the same hue, from light to dark. On the other hand, it might be better to leave the table as it is and highlight this phenomenon in the diagram image instead. SharkD (talk) 21:47, 12 August 2008 (UTC)

I merged two of the columns into two others in order to reduce the width of the table and leave room for the possible future addition of more columns. SharkD (talk) 01:09, 16 August 2008 (UTC)

Merging the two ratio columns into one is not an improvement. It makes it difficult to see either of them in relation to their companions in the column. Also I kind of liked the narrowness of the "limit" columns, because there are so many of them. −Woodstone (talk) 11:58, 16 August 2008 (UTC)

I agree merging the column makes it harder to compare values. However, in essence both columns are the same (but on another scale), and I therefore felt the information to be not different enough to warrant being separated and taking up additional space. As for the narrowness of the columns, this will reoccur once more columns/tunings are added. SharkD (talk) 00:17, 17 August 2008 (UTC)

Adding more equal temperaments

I've been looking at other equal temperaments, such as 19-TET. Should they also be listed here, or should they be restricted to List of meantone intervals? I don't want to duplicate content, but I also want the list to be comprehensive. SharkD (talk) 00:28, 17 August 2008 (UTC)

Midi microtuning

The "audio files" being added are actually ".mid" files, or "midi" files. In that case, in order to have any intervals other than equal temperament these files need to employ microtuning. How certain are you that most computer's midi player support this not too common feature? −Woodstone (talk) 22:05, 8 August 2008 (UTC)

Wikipedia:Media help. Hyacinth (talk) 00:48, 9 August 2008 (UTC)

That really didn't answer the question. Not all PC MIDI synths support the MIDI microtonal tuning standard. The TiMIDIty softsynth does, but consumer-grade PC soundcards are anyone's guess. — Gwalla | Talk 01:04, 9 August 2008 (UTC)

Test your midi pitchbend range. Hyacinth (talk) 01:32, 9 August 2008 (UTC)

So everybody who wants to use your MIDI samples needs to test their software first? I'm not sure I get your point. A response with your own words in actual sentences might help, because right now it looks like you're trying to dodge. Plus, are you using pitchbend or the microtuning standard? They're different things! — Gwalla | Talk 05:36, 9 August 2008 (UTC)

I went ahead and did the test and it worked. I have one of the most generic Realtek integrated soundboards. SharkD (talk) 01:09, 17 August 2008 (UTC)

Okay, Woodstone: What would you prefer we label the midi files, if not audio? How certain are you that most computers do not use this supposedly "not too common" feature?

Gwalla: Apparently everyone who uses audio samples on Wikipedia may need to test their software first, as you would see if you checked Wikipedia's media help, as all media directs one to do if one has trouble. I assume that this is a feature of Wikipedia's media help because it is a standard feature of technical assistance, and not unreasonable. Hyacinth (talk) 06:31, 9 August 2008 (UTC)

Lastly, I'm using pitchbend controls. Why? Hyacinth (talk) 06:31, 9 August 2008 (UTC)

It's not a question of what to label the MIDI files. It's a question of whether MIDI files are appropriate for this use, or if Ogg should be used instead. But if you're using pitch bend messages, those should be supported by pretty much everything, so there shouldn't be a problem, I think. — Gwalla | Talk 03:19, 10 August 2008 (UTC)

Image

I was hoping to update the graph of intervals to include a few more limits, but am encountering issues with the software used to create the image. Namely, the text labels overlap in their current orientation and can't be rotated to be vertical. I can rotate the graph itself in order to accomadate the labels, but I don't find that to be a desirable solution. SharkD (talk) 00:32, 15 August 2008 (UTC)

As some other editors have pointed out earlier, the current table is rather non-informational. In essence both axes are the same (but on another scale). A better graph could be obtained by setting out the 12 tones horizontally and the relative frequency on a log scale vertically. Tones in the various tuning will stack up vertically for each note. The line connecting the equal temperament tones will be straight. The lines connecting pythagorean and 5-limit just tunings will snake around it. A few points on the curves wil coincide. −Woodstone (talk) 12:09, 16 August 2008 (UTC)

I can see how a logarithmic scale would be beneficial, as one would be able to fit many more intervals (especially beyond the first octave). However, I find the logarithmic scale a bit harder for general readers to comprehend (and therefore chartjunk), and intervals beyond the octave are rare. SharkD (talk) 00:13, 17 August 2008 (UTC)

• Chartjunk means unnecessary or distracting visual elements of a chart. Inappropriate choice of axis scale may be misleading or deceptive, or it may make the chart not very useful as a graphic presentation of information, but is not, strictly speaking, chartjunk.
• I don't see how a log scale would be of any use here. Cents for both, but let the horizontal axis run from zero to 1200, say, Let the vertical axis run from -50 cents to 50 cents or some such scale, with zero at the center. The horizontal axis could simply be "pitch numbers" from zero to 12, with the vertical stacks showing differences between similarly named pitches, with equal tempered frequencies at zero, and the other tunings snaking around it. Big job figuring it all out so it's clean and informative, certainly not a task I want to undertake.
• Intervals beyond an octave are commonly referred to in describing (or spelling) chords. __Just plain Bill (talk) 09:55, 22 August 2008 (UTC)

As discussed in Pitch (music), using a logarithmic scale is inappropriate for general readers. How are readers not going to be distracted by something that is not appropriate for their level? SharkD (talk) 11:06, 22 August 2008 (UTC)

Stupid question

Is "List of musical intervals" really the proper title for this page? I mean, is there something particularly "musical" about the intervals (do they carry a tune?) Wouldn't it be better to rename the article to "List of music intervals" or "List of intervals in music"? SharkD (talk) 07:56, 18 August 2008 (UTC)

"Used in music" is a perfectly valid meaning of the term "musical". And since a tune is made out of them, I suppose you could say that they can carry a tune. — Gwalla | Talk 18:14, 18 August 2008 (UTC)

It still sounds odd to me. I think "List of intervals in music" would be better. SharkD (talk) 17:08, 20 August 2008 (UTC)

By any chance are you thinking of "musical intervals" in the sense of "musically pleasing intervals" or consonant intervals? I'd have a hard time calling a musical instrument an "instrument used in music," for example. By the way, carrying a tune is just one part of music; Aside from melody, there's also articulation, ornamentation, rhythm, harmony, sheets of sound, and who knows what else. __Just plain Bill (talk) 17:47, 20 August 2008 (UTC)

Yes, that's the ambiguity I was hoping to clear up. Note that I can recall periodic renamings of categories for similar reasons, for example Wikipedia:Categories for discussion/Log/2008 July 31#Category:Bridges and tunnels that are Registered Historic Places, Wikipedia:Categories for discussion/Log/2008 February 17#Category:Cycle races in... and Wikipedia:Categories for discussion/Log/2008 February 17#Category:US Maoist or Maoist sympathizing parties. SharkD (talk) 01:00, 22 August 2008 (UTC)

Intervals are basic musical items, pretty close to the foundation of music.

The OED's topmost definition of "musical" is "of or belonging to music" which is how it's used here. If someone doesn't get that right away, looking at the list itself may clear things up for them. I see no reason to use more awkward language to cater to some subset of readers who just might be unfamiliar with standard English usage; exposure to standard usage is an effective way for them to get familiar with it.

Who is going to say which intervals are more euphonious or pleasing or beautiful than others? For just one example, a minor second may give a sense of completion, when used as a step from leading tone to tonic. The same interval may not be so pleasant when a kitten steps on two adjacent piano keys, but it's still a musical interval, not a spacing or timing interval. __Just plain Bill (talk) 03:52, 22 August 2008 (UTC)

Yet, there are multiple definitions[1], and changing the adjective to a noun is meant to clear up this confusion, just as changing "Spanish" to "in Spain"[2] is. As for standard usage, maybe usage is incorrect in this case. Also, you can take Pitch (music) as another example of this. It isn't named Pitch (musical), it is named Pitch (music). SharkD (talk) 10:58, 22 August 2008 (UTC)

Usage is usage, it's how folks say what they mean to say so others will understand. Saying things like "maybe usage is incorrect" tells me that you might be interested in inventing your own brand of English. I don't have a problem with that at all, it happens all the time, but you need to know that it is ineffective unless others go along with it, understand it and adopt it. I don't see that happening here. Sorry if that seems harsh, but its the way I've got to call this one. __Just plain Bill (talk) 11:22, 22 August 2008 (UTC)

I assume this is not an aesthetic argument but a question regarding grammar.

This page consists of a list of intervals in isolation, none of which are actually being used in music in the immediate context of the list, they are simply being listed. Thus one may assume that "List of intervals potentially used in music and music theory" may be the most clear.

"Music" is a noun and thus "music intervals" would be inappropriate. "Musical" is an adjective which means "of or relating to music" [3], making it clear and accurate and making "in music" unnecessary. Hyacinth (talk) 05:04, 22 August 2008 (UTC)

Actually, English lets nouns modify other nouns, e.g. "cheese sandwich." Nobody says "cheesy sandwich" (unless they're talking about different degrees of cheesiness, I suppose.) Still, "musical intervals" strikes me as what cognizant English speakers would call the items on this list. __Just plain Bill (talk) 09:36, 22 August 2008 (UTC)

Please what? End of original comment by User:Hyacinth Thank you. Comment added by Just plain Bill

Yes, we could have "a list of cheese intervals". Hyacinth (talk) 02:25, 23 August 2008 (UTC)

I'll accept you arguing over nothing, but you may not add comments to my own. Hyacinth (talk) 02:54, 23 August 2008 (UTC)

I was asking for an end to pointless argument there, couldn't you tell? Too late to forbid, you saw your answer. You did ask... __Just plain Bill (talk) 03:42, 23 August 2008 (UTC)

I could not tell as I still haven't seen my answer, but I'll agree that I overreacted. Why can't we have a "list of musicy intervals"? Hyacinth (talk) 15:14, 23 August 2008 (UTC)

Umm, because it would conflict with the "list of musically intervals?" The original "oh please" had to to with a different line of this discussion, and was not pointed at you. The answer is still, "thank you!" __Just plain Bill (talk) 15:34, 23 August 2008 (UTC)

Adding audio files?

I'm trying to add links to audio files on list of meantone intervals just like this page. Am I doing it correctly? I need help to add the others.--206.248.172.247 (talk) 22:20, 10 November 2008 (UTC)

Uh, no. What you did doesn't really make sense. You added links to some audio files of intervals in equal temperament, but the whole point of that article is that these interval names can refer to different exact intervals in different temperaments. For example, the phrase "minor second" can refer to a 100-cent interval in 12-EDO, or a 126-cent interval in 19-EDO. So should the audio example be a 100-cent interval or a 126-cent interval? It's not really clear which one you should use. —Keenan Pepper 02:24, 11 November 2008 (UTC)

Flip the ratios

As suggested, indeed we should flip all ratios. See for example in the article Interval (music). The ratios should have values over 1. For example a fifth is 3:2. It is more common to think in frequencies than in string or tube length. −Woodstone 21:34, 20 February 2007 (UTC)

Makes sense to me, especially for the sake of consistency with the other article. Rigadoun (talk) 16:16, 21 February 2007 (UTC)

Yes this is all backwards, if I am not mistaken. An octave being "twice" the pitch should be 2:1, and intervals between unison and octave should be between 1:1 and 2:1, no? Also, the interval 4:7 (apparently 7:4) is listed as the "seventh harmonic" -- but strictly speaking, isn't the seventh harmonic 7:1? I'm also wondering if 7:4 is also called the "harmonic seventh" (perhaps the words got reversed?), the "blues seventh", and/or the "barbershop seventh"? Pfly 06:51, 9 March 2007 (UTC)

Well, it wasn't exactly wrong, as getting the intervals backwards just makes them descending instead of ascending, or in terms of string lengths and so forth, but having them greater than one is more common. Anyway, I've flipped them all for the sake of famiiliarity and consistency with most description. Yes, strictly speaking I suppose the seventh harmonic is 7:1, but it's more often thought of as being in the same octave as the nearby minor seventh (dividing by four just moves the pitch down two octaves). I'm not really sure abut the nomenclature, though. Rigadoun (talk) 18:07, 9 March 2007 (UTC)

True, it wasn't wrong, although the cents would be negative :) ...thanks for flipping. As for 7:4, the Scala's list of pitches (which seems to be a widely used standard) calls it "harmonic seventh",[4], as does Mathieu's book "Harmonic Experience", as I read last night. So I think I'll flip the words. It appears that Harmonic seventh was once a page here, or at least there are some redlinks to it. A quick google seems to imply that there is some mild controversy about 7:4, but the sources I am most familiar with seem comfortable enough calling it "blue seventh" as well as "harmonic seventh". But perhaps "blue notes" are inherently not well defined. Thanks for the response! Pfly 18:50, 9 March 2007 (UTC)

The reciprocal ratios are essentially the same in concert practice. If you hit two notes that are a fifth apart, then one of them is ten, and the other is fifteen. Making the ratio higher than one is nothing but a tradition. That is why colons are used instead of slashes, because the division is not done. So, do not edit war over this one. 216.234.170.74 (talk) 19:36, 3 September 2009 (UTC)

Factorization column

In the table of intervals may be column named Factorization to indicate intervals of Just Intonations and its limit for them. If somebody have another opinion, please discuss. Commator (talk) 18:31, 13 December 2007 (UTC)

When writing tunes into synthesizers written for this stuff, factoring is very useful. If that is your work, then thanks. 216.234.170.74 (talk) —Preceding undated comment added 19:39, 3 September 2009 (UTC).

Prime vs odd limit

You use prime limit and ignore odd limit, yet you say "The lower the number, the more consonant the interval is considered to be". This is not correct for prime limit. See http://organicdesign.org/peterson/tuning/consonance.html for example. 243:128 has a prime limit of 3, but is not consonant at all. (243:128 = 3^5:2^7) It has an odd limit of 243, though, which indicates its dissonance. —Preceding unsigned comment added by 96.224.65.203 (talk) 22:09, 25 November 2008 (UTC)

I agree with the rebuttal, and in a different vein. For example, 3:2 is sometimes called the dominant harmony. I liked it in my own voice the first time I heard it, for entire songs. Other people did not like it that much. So, I will delete the statement in favour of what people might glean, and this is that perfect ratios *tend* to be more consonant than major ratios, which are usually more consonant than minor ratios. For that matter, I do not like using "consonant" in this context, because the first book I read on the subject favoured "assonant". Too much dominant harmony makes you sound assonant. 216.234.170.74 (talk) 19:58, 3 September 2009 (UTC)

Audio examples

I think MIDI is better because it's a "mathematical" format, just like vector images are better than Raster images. SharkD (talk) 01:04, 17 August 2008 (UTC)

On the linux box here, I find .ogg more convenient to play, followed by .mp3. I don't even bother trying to play MIDI files. Only use I have for them is converting to standard score notation.

Vector images have advantages over raster images for many uses, but they are not "better" in all cases. Using MIDI for showing intervals as played on real instruments (whose timbre comes from partials that may be more or less harmonically related to the fundamental note, and so will affect the sound of the interval when both notes are played together) makes about as much sense as using a vocoder to show what any individual person's voice sounds like. Add uncertainty about accuracy of decoding at the receiving end, and most usefulness disappears. __Just plain Bill (talk) 02:44, 19 August 2008 (UTC)

Must instruments be used at all? Why not play back pure tones? SharkD (talk) 04:54, 19 August 2008 (UTC)

Unfortunately Wikipedia:Manual of Style (music) gives us no guidance as to general priorities in audio examples, though they are often requested on talk pages with {{Audio requested}}, and neither does Wikipedia:WikiProject Music/MUSTARD/Sounds and multimedia.

Just plain Bill has implied some general priorities for audio examples for this article. I would suggest using the same sound for all intervals, so that one is not distracted by novel timbres. We could also try using two different instruments/sounds in each example, to distinguish each note of the dyad. An instrument/sound with sustain seems like a must. I would also suggest having them all based on the same note, though this would not keep them in the average register it would keep the bottom note always in the same. Hyacinth (talk) 06:48, 19 August 2008 (UTC)

Pure tones will be a good start for simple examples. Can bump into some oddities without going to novel timbres: the partials of a piano string are slightly inharmonic, leading to the need for stretch tuning. Played on different instruments, perhaps in different registers, the same interval may have a slightly different flavor. Going a bit further, I believe dense multi-voice harmonies will be poorly represented by pure tones. __Just plain Bill (talk) 11:33, 19 August 2008 (UTC)

The audio example for Just Perfect Fourth is incorrect. It sounds like some sort of major third.--Mark Pfannschmidt (talk) 15:06, 17 September 2009 (UTC)

Secor

I found the ratio for the Secor, (18/5)^(1/19), at http://tonalsoft.com/enc/s/secor.aspx. --Glenn L (talk) 00:41, 21 October 2009 (UTC)

Mean tone

Some information on meantone temperament was added. I have some doubts about how that fits in this table. The values in the column "ratio" so far have all been exact values. The ones now added for meantone are approximations. The definition of the equal and "limit" tunings are very clear and so can easily be marked in their own trailing columns, but there are many meantone systems and the correponding marking column gives a very hazy and incomplete view on that collection. −Woodstone (talk) 08:56, 21 March 2010 (UTC)

The values for meantone intervals in the ratio column may simply be removed if they bother you, but I'm not sure why they do. They definitions may be clear, though that may depend on one's level of knowledge. I assume you mean that since you find the definitions clear you find just and 12-TET intervals easy to mark (rather than definitions). Did you notice that there are many systems of equal temperament, besides 12, and that we include those in the table? We simple don't mark them. Hyacinth (talk) 11:30, 21 March 2010 (UTC)

I did notice the other equal temperaments and agree that they should not be marked in a separate column, since they are not prevalent enough to merit that. I understand that each of the meantone systems has well determined intervals, but it goes above my knowledge to calculate these exact values. If you are able to work out the exact value of the meantone intervals that would be great. Having approximate values sort of negates the underlying exact nature of the definitions. −Woodstone (talk) 11:48, 21 March 2010 (UTC)

Definition and "exact" values added. Hyacinth (talk) 13:38, 21 March 2010 (UTC)

I think where you "add" fractions like (81:80)^(1/4), you actually mean multiplying the ratio by that amount. I checked some with the given cents and it matches. −Woodstone (talk) 14:53, 21 March 2010 (UTC)

Color codes

I propose the color coding below. Right now the colors are unobtrusive, but indistinguishable. Hyacinth (talk) 08:56, 13 May 2014 (UTC)

New Code	Compliant?	Legend (simplified)	Old Code
E	sort of	12TET.	E
Q	sort of	24TET.	Q
2	NO	2-limit.	2
3	NO	3-limit/Pythagorean.	3
5	sort of	5-limit/just.	5
7	YES	7-limit/ septimal.	7
11	sort of	11-limit.	11
13	NO	13-limit.	13
17	NO	17-limit.	17
19	NO	19-limit.	19
23	NO	23-limit.
29	NO	29-limit.
M	sort of	Meantone temperament.	M
U	YES	Measure/higher ET.	U
S	NA	Superparticular (no code).	S
H	YES	Higher harmonics.	H

As one climbs the limits one progresses through the rainbow.

12TET is made the same color (reddish) as 2-limit, since 2-limit only includes octaves.

24-TET is made a pinkish red.

Meantone is made an orange to match the color Pythagorean happens to be according to the rainbow pattern.

Units of measurement or equal temperament is made pink (12 is red, 24 is red/pink, > is pink).

Higher harmonics are gray.

Hyacinth (talk) 09:43, 13 May 2014 (UTC)

The highly saturated colors will make it difficult to read the text in the cells. Much fainter colours are required for legibility.

Why not use white or grey for equal temperament, which is the least colourful tuning system.

I do not understand why the legend has entries like " 2 3 5 7 11 13 17 19 = 19-limit (not 17-limit)". Would it not be simpler to have "7 = 7-limit". There are many rows that do not occur in the current legend list, such as "7 11 13 17 19". Any n-limit entry is also m-limit for m>n.

−Woodstone (talk) 12:02, 13 May 2014 (UTC)

There is a policy/guideline on legibility, specifically with colored backgrounds: Wikipedia:Manual of Style/Accessibility#Color points towards WCAG and provides a link to a test of contrast.

Hyacinth (talk) 01:45, 14 May 2014 (UTC)

D3D3D3 and 9ACD32 (yellow and light green) pass the contrast test as backgrounds for black text. Perhaps we should add more bright colors. Hyacinth (talk) 02:04, 14 May 2014 (UTC)

Inversion

How should this list treat inversions? Should the inversion of any interval present be included, or should only integer classes be included? In the second case there would be no intervals above 600 cents, in the latter case there may be many unnamed intervals. For example, should both 3/2 and 4/3 be included, and would that require that both 531441/524288 and 1048576/531441? Should we have only 4/3 and 531441/524288? Hyacinth (talk) 10:10, 13 May 2014 (UTC)

Musically, inversions are just as important. There are not really non-inverted ratios. Intervals come in pairs. In my opinion they should all be included. Limiting to one octave would be fine. −Woodstone (talk) 07:50, 14 May 2014 (UTC)

Redesign

The reason that there were separate columns for each of the "limit" tunings was the ability to sort by them. Sorting on the 5 column would bring all 5-limit tones together in the list, still sorted by frequency. With the current single column this is no longer the case. I think we should go back on this. −Woodstone (talk) 07:46, 14 May 2014 (UTC)

For the original version: 21:29, 13 May 2014‎

For the version with TET merged: 23:35, 13 May 2014‎

For the version with TET & Limits merged: 03:19, 14 May 2014‎

Hyacinth (talk) 20:00, 14 May 2014 (UTC)

Title: pitch interval

See also: Talk:List of pitch intervals § Stupid question

Why is this list at "List of pitch intervals"? According to the edit summary when it was moved: "In ordinary terminology (e.g., in Grove), these are pitch intervals; 'musical intervals' are 'Major third' and the like". Major third is included in this list. According to its article, a pitch interval is, "the number of semitones that separates one pitch from another, upward or downward". This doesn't seem to describe this list. Hyacinth (talk) 00:52, 14 May 2014 (UTC)

Pitch interval is not the right name, since pitch is a physio-psychological measure. The entries in the table are frequency ratios. What is intended to be described here are intervals relevant in music theory. Musical intervals would be a suitable name. −Woodstone (talk) 07:55, 14 May 2014 (UTC)

I don't agree; the vast majority of these intervals have no relevance at all in music theory, except insofar as theory of tuning is considered part of theory of music. The functional musical intervals that are fundamental to music theory are listed at List of musical intervals. Justlettersandnumbers (talk) 09:50, 14 May 2014 (UTC)

That still means the article title should not contain "pitch intervals". Hyacinth (talk) 00:48, 17 May 2014 (UTC)

All these intervals, the harmonics excepted, are only relevant in musical context. The terminology is never used in any other field. Therefore I still propose to include the word music in the title. Perhaps "Intervals in music" is better than the old "Musical intervals" to which objections exist. −Woodstone (talk) 04:59, 17 May 2014 (UTC)

Non-rational intervals

For the non-rational intervals, it does not make much sense to express them as an explicit ratio. I propose to remove all the superfluous ": 1" tails in expressions like "2^7/12 : 1". The ratio is just an irrational number. I have already removed the copies in the column "factors" as that is a meaningless breakdown for irrationals. −Woodstone (talk) 15:25, 22 July 2014 (UTC)

[copied from personal talk page]

You have removed prime factorization of non-rational numbers, but also rational powers of rational numbers can be factorized in an unique way as product of rational powers of different prime numbers. I have asked on Mathematics Stack Exchange. I don't have source, but two people have agreed that it is obvious. Can I put the factorizations back? And if you find most of my calculations too trivial, I think that quarter-comma meantone simplifications are useful, even if you do not want to call them factorization. BartekChom (talk) 16:53, 27 July 2014 (UTC)

In most of the cases the removed data in the "factors" column was exactly the same as in the "frequency ratio" column. So I think the table is in better shape without the redundancy. Compare several possible arrangements:

cents	ratio	factors	comment
386.31	5 : 4	5 : 22	current rational
400.00	24/12 : 1	21/3 : 1	before the contested edits
400.00	24/12 : 1		current irrational
400.00	24/12		(my preference)
400.00	21/3	(21/12)4	possible compromise
400.00	24/12	21/3	another compromise
400.00	21/3	24/12	still other compromise

But personally, I think it is better to reserve the factors column for harmonic relationships only. And as said, I propose to remove the meaningless ":1" after irrationals.

−Woodstone (talk) 08:50, 28 July 2014 (UTC)

The one before last does not make much sense for me as (2^1/12)⁴ is not unique - not very good as factorization. And I think that they are called ratios for some reason, so 2^4/12 : 1 is not worse than 2 : 1. But maybe (3 : 2)^1/9 without ":1" would be logical - I really think that Alpha scale and family are made of "parts" (roots) of ratios (if they are really so defined - {{Citation needed}} suggest that this interpretation is dubious). (2 : 1)^4/12 is analogical, but makes notation longer by "()".

1. Most important for me is that quarter-comma meantone simplifications are included somewhere in corresponding rows.
2. Besides I find my version ("before the contested edits") most useful, but current notation looks probably more serious (does no contain trivial calculations like 2^1/3=(2^1/12)⁴) and contains less original research, so I'm not going to quarrel.
3. I'm for removing ":1" in Alpha scale and family but mildly against removing it from edo intervals and for example savart. BartekChom (talk) 11:21, 28 July 2014 (UTC)

They are called ratio because they are a ratio of frequencies: the highest divided by the lowest of the two notes forming the interval. This ratio is a plain real number, most of them between 1 and 2. The uniqueness for non-rationals is questionable. The expression (2^1/12)⁴ shows the underlying structure of the interval: four identical factors. The structure of the quarter-comma mean tone intervals can also be expressed this way, using as few as possible different non-rational factors. −Woodstone (talk) 14:22, 28 July 2014 (UTC)

If you think so, I'm not going to quarrel, but why 2^4/12 : 1 is worse than 2 : 1? (2^1/12)⁴ shows that this interval equals four semitones, and this is its construction in practice, but it is also (2^1/6)² - makes sense in hexatonic scale, (2^1/9)³, (2^1/12)⁴, (2^1/15)⁵ and for example (2^1/306)¹⁰² - makes sense in theoretically good 306edo. So I prefer as exponent an irreducible fraction 1/3, but these are trivial calculations anyway. In case of quarter-comma mean tone intervals there are probably many interpretation that make sense (including currently usedone ) and I only think it is necessary to write one that is more easily transformable to the simplest.

I've written a lot, but final answer is shorter: I can agree on removal ":1" from irrational numbers. If you are still willing to agree on what you called "another compromise", we can use it and it will be the end of our discussion. BartekChom (talk) 14:01, 29 July 2014 (UTC)

I agree the ":1" is just as unnecessary in 2:1, but let's not touch the rational intervals. I removed the tail from the irrationals. For the "factors" column the question is how to distinguish it from the ratio column. I added another row to the table above. What reason is there to choose which of 2^(4/12) and 2^(1/3) is in which column? −Woodstone (talk) 07:25, 31 July 2014 (UTC)

"Ratio" is something like definition in case of non-natural intervals. So I think that prime factorization should be simplest notation. Besides factorization should be unique. That's why I prefer "another compromise" over "still other compromise". BartekChom (talk) 12:23, 31 July 2014 (UTC)

Requested move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

No consensus to move, despite extended discussion. I would encourage further discussion to reach a conclusion as to what is the best possible title for this page, and what should be done with respect to various other related titles, but no conclusion seems to be forthcoming in the time frame for this proposal. bd2412 T 13:39, 21 August 2014 (UTC)

List of pitch intervals → List of musical intervals – Pitch refers to absolute frequencies, intervals are frequency ratios. — Relisted. Jenks24 (talk) 14:17, 7 August 2014 (UTC) Omegatron (talk) 23:50, 30 July 2014 (UTC)

• Support as described above. Also fine with "List of intervals in music". — Omegatron (talk) 00:24, 8 August 2014 (UTC)
• Support. Pitch interval is not the right name, since pitch is a physio-psychological measure. The entries in the table are frequency ratios. What is intended to be described here are intervals relevant in music theory. Musical intervals would be a suitable name. −Woodstone (talk) 06:49, 31 July 2014 (UTC)

• Oppose. There's already a list of functional musical intervals at List of musical intervals, though someone had misguidedly redirected it here a few days ago. The intervals in this list have, contrary to what Woodstone writes, no relevance whatsoever in music theory: the function of a musical interval is not dependent on the way it is tuned - a major ninth, say, has the the same musical functions and requirements whether the voices or instruments playing it are using a Renaissance mean-tone tuning, a Baroque temperament such as Werckmeister IV or a modern 3-cents wide equal temperament. This is a list of intervals encountered in tuning or intonation, not in music or music theory. I'd have no objection to a move to List of tuning intervals. Justlettersandnumbers (talk) 07:32, 31 July 2014 (UTC)
  • That they aren't used in your particular music theory tradition doesn't make them non-musical, or mean that the people who use them aren't engaged in making music. — Omegatron (talk) 00:24, 8 August 2014 (UTC)

• Oppose. That "Pitch interval" requires renaming is obvious, as this name is meaningless. (Musical) intervals cannot be reduced to frequency ratios. In addition, many of the intervals described here are totally irrelevant to music and exist only in unbridled fantasies. Many of the sytems implied by many of the 'intervals' in this incredible list have never had any musical use – at least as intervals. Among the many inconsistencies of this article, let me quote a few:

• To describe "Pythagorean" (Pythagorean what, by the way: philosophy? intonation? tuning? consonance? interval?) as "3-limit just intonation" is a derision: "just intonation", which is a historical term dating from the 18th century, never meant Pythagorean intonation, it denoted systems producing 'just' triads. And the definition in the article Just intonation again is pure fantasy with respect to the historical meaning of the term.
• To state that "the prime limit is a number measuring the harmony of an interval" merely evidences a total misunderstanding of what "harmony" means ("the harmony of an interval" is properly meaningless).
• And to say that "The lower the number [of the prime limit], the more consonant the interval is considered to be" not only doesn't say by whom this is considered so, but is unbelievable in any conception of consonance: we would be made to admit that 9:10 (the minor tone) is as consonant as 4:5 (the major third), merely because both can be factorized down to 5.
• A cent, or a savart (or an eptameride which, by the way, is not identical with a savart) are not 'musical intervals', they are measure units without any direct function in music.
• Etc., etc.

The article not only is in need of a change in its name, but also of a thorough revision in its content.

The List of musical intervals, on the other hand, needs to be restored as soon as possible, because it is a useful list, doing exactly what its title says.

Hucbald.SaintAmand (talk) 19:47, 31 July 2014 (UTC)

Prime limit description corrected. Measure units should be included at least for comparison. You can add explanation, if you think that now it is misleading. If you want to correct definitions of just etc., add explanations from sources, but probably current definitions are also used by somebody. BartekChom (talk) 11:51, 3 August 2014 (UTC)

I don't intend to change anything to this article, because if I began, I'd change everything. And I won't "add explanations from sources", while the article as it is doesn't provide a single source to justify its "explanations" (the ones I question below). I don't see the purpose of such an article. My problems remain:

• I don't understand the meaning of the expression "pitch interval".
• While your corrected definition of the prime limit indeed is somewhat clearer, it fails to indicate the nature of the "frequency ratio" concerned. (You seem to believe that an interval always can be expressed as a frequency ratio, but that merely is not true: a tempered fifth in ET, for instance, 700 cents, cannot be expressed as a ratio, and therefore cannot be factorized).
• The idea that "Intervals with lower prime limit are used more often" is wishful thinking. More often than what? In what kind of music? Piano music?
• The claims that "Pythagorean means 3-limit just intonation" and that "Just means 5-limit just intonation" appear to contradict each other, unless the meaning of "just intonation" is not "an intonation that is said to be just".
• I don't understand the statement "every tone in a 3-limit unit can also be part of a 5-limit tuning". Don't you mean "every interval..."? As to "every tone", it can of course be one of the two tones of any interval.
• The article states "In general, a meantone is constructed the same way as Pythagorean tuning"... A meantone tuning, strictly speaking, is one in which the tone is the mean between the major and the minor tones; such tunings are also called "regular", because they use only one size of fifth. The Pythagorean tuning, or ET, are meantone tunings. ET is a 1/12 comma meantone, but the comma is here the Pythagorean one, not the syntonic one.
• The definition of "Equal-tempered" as ET "with intervals corresponding to X multiples per octave" is totally obscure to me. Would it not be simpler to say "with the octave divided in X equal intervals", if that is what is meant?

As to the list itself, most of these intervals do not seem "musical" to me, despite the article's initial claim. I really wonder what kind of music would make use of a ragisma, a breedsma, a septimal kleisma, an Orwell comma or the like.

Hucbald.SaintAmand (talk) 16:51, 5 August 2014 (UTC)

Yes, this is a beautiful modern-day example of the age-old division between the teorici such as Gioseffo Zarlino, who spent their lives calculating the values of theoretical musical intervals and attempting to demonstrate their connection with celestial mathematics, the nature of god and the like, and the prattici such as Lodovico Zacconi, who talk about how people actually play music. This page is a sort of musical numerology, verging on WP:FRINGE. Justlettersandnumbers (talk) 19:24, 5 August 2014 (UTC)

I'd be more severe: this article, as I read it, really is an example of what WP defines as a Fringe, a domain that justifies itself merely by autoreference. I think that neither Zarlino nor Zacconi should get involved: after all, they both were theorici and prattici, even if they had a different sensibility about that. Even Huyghens, often cited, probably wouldn't have endorsed the claims made here. I am by nature indulgent, and I don't want to intefere with what others may be trying here. WP is a free project, where everybody is free to do as (s)he feels, as long as (s)he leaves the same freedom to others. I find it quite aggressive that the article List of musical intervals should be reduced to a redirection to this article, the purpose of which obviously is different, or even more that this one should be renamed to the name of the other: I won't do anything against the existence of this "pitch intervals" article; its authors similarly should not prevent the "musical intervals" article to exist. I presume that, if this were to become a matter of real conflict, WP authorities have procedures to resolve it. – Hucbald.SaintAmand (talk) 20:34, 5 August 2014 (UTC)

Generally I know the topic only from internet, so my answers are only guessing. So:

Explanations are more or less sourced in other articles.

• I understand pitch interval as interval between pitches, i.e. ratio of frequencies, as opposed to a view in which equal tempered major third and equal tempered diminished fourth are different intervals.
• I understand that ratio can be any number, not necessary ratio of two integer numbers. And some irrational numbers can be factorized (rational powers of rational numbers). Anyway, prime limit is only applicable to just intervals (rational ratios). Ok. I understand that it sounds strange, but in Polish "rational ratios" is wymierne stosunki, so I find it a coincidence, although rational numbers are ratios of integer numbers.
• If you do not agree, this can be removed. But I think that this is true: taking into account only 7-limit intervals are less standard, 11-limit ones (and so one) even more so. Of course in practice 12edo is most common.
• I understand that just intonation denotes ratios of (usually small) integer numbers, but in practice most often are used 5-limit ratios, so this is another meaning.
• Every interval. Unless we assume that we have common base tone.
• "They use only one size of fifth", so are "constructed the same way as Pythagorean tuning" - by adding fifths. Two perfect fifths (minus octave) give major second, three - major sixth and so one.
• It probably really would be more correct. I understood "multiples" as "steps" and didn't notice this problem.

For example ragisma can be encountered in 7-limit tuning if we make analogue of comma pump like just major sixths and lesser just major second up, and septimal major third and two just minor third down:

${\frac {5}{3}}\cdot {\frac {10}{9}}\cdot {\frac {7}{9}}\cdot \left({\frac {5}{6}}\right)^{2}\cdot {5}{9}={\frac {5^{4}\cdot 7}{2\cdot 3^{7}}}$

Hucbald.SaintAmand, now do you like organisation of this topic on Wikipedia? BartekChom (talk) 20:20, 6 August 2014 (UTC)

BartekChom, I won't comment on this anymore, I am merely not interested and I think to have said all I had to say on Talk:List_of_musical_intervals. I have first-hand knowledge of Benedetti's 16th-century comments on pitch drift in just intonation. I also studied schismatic exchange in 13th-century Arabic theory – and in 14th-century Western tunings. My own interest is in understanding these ancient theories – and these early musics – in their own terms, not through the lenses of modern fantasies. I don't think WP talk pages are the right places to further discuss such matters. – Hucbald.SaintAmand (talk) 21:02, 6 August 2014 (UTC)

• Oppose – the article is more about pitch intervals (pitch ratios), as anyone can see and as the discussion above clarifies. Dicklyon (talk) 05:12, 10 August 2014 (UTC)

• Oppose Comment - I think, let me see if I have this straight. The proposal is to move this to List of musical intervals? Someone above wrote "There's already a list of functional musical intervals at List of musical intervals, though someone had misguidedly redirected it here a few days ago." But currently List of musical intervals is a not a redirect or a list page, but a disambig page, linking here and to Interval (music)#Main intervals. So that's all a bit confusing.

That aside, the main complaint here seems to be that "pitch interval" isn't the right term, although I'm not clear on why. One person wrote that the term "pitch interval" is "meaningless", yet I have no trouble understanding it. Perhaps it is technically wrong and should be "pitch frequency ratios" or something, but that seems more likely to be confusing, even if pedantically more accurate. So I think I agree with Dicklyon, who seems to be saying that "pitch interval" means "pitch ratio", "as anyone can see". Still, a change to an alternate term that isn't too unwieldly would be okay with me.

Also in this thread some seem to argue that some of the intervals on this page are not "musical", or are even "totally irrelevant to music and exist only in unbridled fantasies". I disagree there. "What kind of music would make use of a ragisma, a breedsma, a septimal kleisma, an Orwell comma or the like?" A music that moves between tuning systems, for one. I myself have made music that shifts around by very small commas and the like. Not a lot of people make music like that, but that doesn't make the intervals "unmusical". Very small intervals are not melodic, mostly, but they are certainly important harmonically when making music like this. Very very small intervals like a ragisma or breedsma are not likely to be distinguished by ear, but their effect can be very noticeable in transforming harmonic spaces. As for the septimal kleisma, it is what is tempered out in Septimal meantone temperament, similar to how the Pythagorean comma is tempered out in 12 tone equal temperament. Is the Pythagorean comma "musical"? Not in a melodic sense, usually. Is it musically important? Without a doubt. And the septimal kleisma is used and important in other ways too.

Also, I would agree that a lot of this tiny interval stuff would be fringe theory with little or no real application if we were still in the Renaissance, Baroque, or 13th-century Arabic theory, or even in most of the 20th century. But these days people can and do make music with computers, which have made many impossible things possible, theoretical things practical. Pfly (talk) 06:20, 11 August 2014 (UTC)

@Pfly. The several discussions that led to replacing List of musical intervals, first merely by a link to this page, then by the disambiguation page that it now became, are spread on the talk pages of both articles. In the history of List of musical intervals, you'll see that the existing list has been removed three times in less than a month (and restored twice). The whole could have happened in a less aggressive way.

I think that vulgarization is not about replacing difficult concepts by approximations, but about trying to explain them as simply as possible. "Pitch interval" is not a good expression because a pitch is a frequency (e.g. 440 Hz) associated with a note name (e.g. A4). The intervals discussed in this article are not between pitches properly speaking, if only because they are independent from any particular frequency. The expression can be understood, which is why it has not (yet) been changed, but I persist thinking that it is essentially wrong.

A "musical interval", to me, is an interval used in music, and not in the discourse about music – otherwise it should be renamed as something like "music theoretic interval", or "intervals used in tunings and temperaments". But neither of these are really satisfying. A cent, an eptameride, a savard are not intervals, they are merely units for measuring intervals. The 12-TET intervals (and most others listed in the column headed TET) cannot be expressed as fractions and cannot be factorized (they are irrational). These are but a few of the approximations of the article.

I agree that computers make everything possible (or so it seems). Yet, many of the intervals in this list result from excessive "digitalisation", i.e. express in numbers what in real music can neither be perceived, nor even conceived in this manner. You speak yourself of a music that "shifts between tuning systems". Many historical tunings similarly have been shifting between segments of simpler tunings. 'Just intonation' (of Zarlino's type) can be described as segments of Pythagorean tuning shifted by a syntonic comma; this does not mean that the syntonic comma was used as a musical interval. 18th-century irregular temperaments make use of all sorts of shifts, many of which cannot be expressed as ragisma or breedsma or anything of the kind, merely because they cannot be expressed as fractions.

All this considered, it appears to me that what the List of pitch intervals article does is digitalizing intervals, i.e. approximating them in whole numbers. But the article does not say so, is not even aware of doing so. These intervals may or may not have been used in music. Let's admit that they all could be used in music – it is not exactly the same... The article rests on implicit notions of what a note is, of what a pitch is, of what an interval is, and supposes that these notions are universal. This to me is both vulgarization and eurocentrism at their worst.

Hucbald.SaintAmand (talk) 08:54, 11 August 2014 (UTC)

To be clear, my 'oppose' was mainly to do with the fact that the proposed move is to a currently existing disambig page. I was not and am not up on whatever other discussions and moves are going on. I just saw the move proposal, then saw the disambig page and thought, given that, the proposed move wasn't a good idea. I'm not against the page being renamed. I agree that "pitch intervals" is non-ideal. I almost posted a "comment" rather than an "oppose". In fact I think I'll change it above.

The debating about whether some of the intervals listed here are musical, theoretical, or whatever, seems mostly tangential to the proposed move and associated issues of redirects, disambigs, and so on. I see now there is a larger issue involving several pages and various recent changes, and that some stuff needs to be worked out. What concerned me when I read this page move thread was the the comment "The article not only is in need of a change in its name, but also of a thorough revision in its content." That worried me because I personally find this page very useful. But reading more carefully I see you later wrote "I won't do anything against the existence of this "pitch intervals" article; its authors similarly should not prevent the "musical intervals" article to exist." Sounds good to me, and makes sense. I hope you all can work it out! I'm not active enough to dive too deep just now.

PS, just to continue the debate a little, I'm not sure I understand your comments about "digitalisation", fractions, irrational numbers, and so on. I understand that the intervals of 12-TET (and many other intervals) involve irrational numbers. But they are still "ratios" between two frequencies. A 12-TET semitone is often described as 2^1/12:1. Our semitone page says the 12-TET semitone "is a ratio of 2^1/12." I didn't realize we had a page on the Twelfth root of two! This page, "pitch intervals", in the "frequency ratio" column, says a 12-TET semitone is "2^1/12," just like the semitone page. My inner pedant complains that "2^1/12" is not a ratio—it should say 2^1/12:1! Would we say the frequency ratio of an octave is "2"? That only makes sense when ratios are confused with fractions, I think. People often write 2/1, and we know that fractions in the form x/1 can just be written as x. But intervals are ratios, not fractions! (okay, my inner pedant is done for now)

Anyway, maybe your main concern is with this page's lead text rather than the list itself so much. If that's the case I agree—the lead text could be much improved. It does seem to suggest that all intervals involve whole number "rational" ratios. Pfly (talk) 06:45, 12 August 2014 (UTC)

The question of the requested move appears settled. My concern indeed is mainly with the lead, which doesn't at all contextualize the contents of the article. What is exposed here is a modern, Western view of intervals of all kinds, many of which are there only as numerical (digital) descriptions of what more often is described as movable degrees, in Western culture in former times and even today, and certainly in non-Western cultures. I find it most revealing that Ján Haluška, who seems to be one of the main sources of this article, at one point in his book claims that Turkish music counts 53 degrees in the octave: this typically is the point of view of a mathematician believing he knows something of music theory (and possibly a confusion with Holder's comma of the 18th century, which in turn is an approximation of the Pythagorean comma). I strongly doubt that any Turkish musician would endorse such a claim. Even the 20th-century idea that Arabic music is based on 48 quarter tones in the octave tends to be rejected today. And I'd very much like to know the historical origin of the fancy names of many of these intervals. But enough about that, which does not deserve so lengthy comments. – Hucbald.SaintAmand (talk) 11:28, 12 August 2014 (UTC)

Even a mathematician without an ounce of musical training might tend to reject the idea of cramming 48 quarter tones into an octave.—Jerome Kohl (talk) 15:46, 12 August 2014 (UTC)

• Support List of musical intervals as per the current titling within the article. No opposition to variations on this, but the current sounds like Association_football_pitch#Other_markings. --SmokeyJoe (talk) 06:38, 15 August 2014 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.