Talk:Semitone


 * Talk:Semitone/Archive 1 - 20 December 2005 - 16 August 2006
 * Talk:Semitone/Archive 2 - 19 August 2006 - 20 September 2006 (major revisions after merge with minor second)

Rational semitones
I wrote a program to compile a list of all practical rational semitones. That is, all denominators were tested from 1 to 50000, and a new possibility was added to the list only if it was better than the best so far having a smaller denominator. Here they are, with their cents:


 * 1/1 = 0.0
 * 10/9 = 182.40371213406007
 * 11/10 = 165.00422849992202
 * 12/11 = 150.6370585006306
 * 13/12 = 138.57266090392307
 * 14/13 = 128.29824469981426
 * 15/14 = 119.44280826109726
 * 16/15 = 111.73128526977776
 * 17/16 = 104.95540950040728
 * 18/17 = 98.95459223036757
 * 53/50 = 100.87711774616947
 * 71/67 = 100.38951485629148
 * 89/84 = 100.09920982516498
 * 107/101 = 99.90660437922274
 * 196/185 = 99.9940603186754
 * 873/824 = 100.00477973546587
 * 1069/1009 = 100.00281433695989
 * 1265/1194 = 100.0014579802408
 * 1461/1379 = 100.00046554742165
 * 1657/1564 = 99.99970789691965
 * 3118/2943 = 100.00006290886779
 * 4775/4507 = 99.9999397141372
 * 7893/7450 = 99.99998838019101
 * 11011/10393 = 100.0000094845786
 * 18904/17843 = 100.00000067284903

With a denominator smaller than 50000 there is nothing better than 18904/17843, apparently. I'm not sure when the next best one is. Anyhow, the list is smaller than I expected it to be. It might be worth including? I dunno. - Rainwarrior 05:44, 20 September 2006 (UTC)


 * Obviously, you are a computer whiz! I personally find it intruiging. But I think it might be "pushing the point" a little too far...the article is about the semitone...this is "pure math". If the average reader has even one reasonable approximation, the idea is conveyed. No offense, but I'd rather not see it in the article. (In fact, doing so could lead to similar lists for all the intervals!)
 * Anyway, what do you think of just removing the present 196/185, along with it's reference to the Hammond organ? Prof.rick 06:03, 20 September 2006 (UTC)


 * Hold on! Your 89/84 rings a bell! I feel sure I've come across it as a practised semitone, somewhere. I will start checking some resources now. Prof.rick 06:07, 20 September 2006 (UTC)


 * Sorry, no luck...can't find a reference to 89/84. I guess I imagined it. Prof.rick 06:24, 20 September 2006 (UTC)


 * I went ahead and removed 196/185, and the Hammond reference. (If you disagree, it's easy enough to put back.) Personally, I think this short list of "approximations" is just the right length to be proportional to the article as a whole. Let me know what you think. Prof.rick 06:33, 20 September 2006 (UTC)


 * I also create a script to calculate an fraction approximation of $\sqrt{2|12}$: https://codepen.io/yukulele/details/XpOwJy/?preview_height=650 Cpartiot (talk) 13:16, 15 February 2017 (UTC)

A nice article!
Looking over the article in it's entirety, I am quite happy with it. Of course, future improvements can be made, but I think, as it stands, it is complete but not excessive, intelligently presented, and attractive in it's layout...well worth the time we have invested.Prof.rick 06:54, 20 September 2006 (UTC)


 * I've taken this opportunity to archive the talk page. - Rainwarrior 21:07, 20 September 2006 (UTC)

Great! I'm sure we'll meet again on another article. Cheers, Prof.rick 00:31, 21 September 2006 (UTC)


 * Yes - a great article. Well done to both of you. Thanks, Prof for your kind words on my modest contribution, and I look forward to further collaborative efforts in future. (Mark - 21 September 2006)

Thank you, Mark! Please, don't underestimate your contributions! They were absolutely vital to the final product.

Re article, "Augmented Unison": changed "regardless of harmonic underpinning" to "independent of harmonic underpinning", since chromatic passages often appear unaccompanied by chords, especially in the Classical period. ("Regardless" might suggest some harmonic back-up is present, while "independent" leaves the matter wide open.)

And to you, Mark, I am sure we will meet again on another article!Prof.rick 04:25, 22 September 2006 (UTC)


 * I changed independant to "regardless" for that very reason. Chromatic scales very (very) frequently cut right across chord progressions in classical music and are not part of the harmony. - Rainwarrior 07:25, 22 September 2006 (UTC)

No problem. (It's really a matter of semantics rather than musical concepts.) I changed it back to "regardless". Prof.rick Sept. 22 2006

Rain, I noticed on your list of approximations, the denominators are 9 17 inclusive...then a large gap to 50! I think this is a very valid reason for your inclusion of 18/17, and a reference to it's use. (Funny, these ratios behave with the same unpredictability as prime numbers!) Prof.rick 05:33, 22 September 2006 (UTC)

Rain and Mark, I have been questioning the description of the Chopin "wrong note" Etude. This is such a subjective matter, as we try to pinpoint the "character" of the music in words. As well as humorous, I find it rather sardonic, even sinister! (Whenever I perform it, I am well aware of that "touch of evil"!) However, before changing the article, I would like your views. Prof.rick 02:34, 24 September 2006 (UTC)


 * Sorry, Prof. I'm not familiar with that etude (shameful, I know). However, it's mentioned elsewhere in Wiki at Chopin etudes where the effect is described as piquant rather than humorous. As you say, it's subjective. Maybe you could find a word that no-one can disagree with, such as 'striking'. (Mark - 24 September 2006)


 * I figured that the nickname itself is grounds enough to call this "humour". Of course your personal reaction to the sound is subjective, but I think this fits its general perception, and probably the composer's intent. This kind of dissonance, unprovoked, and unprolonged, is by no means typical of the style; it's meant to stick out, it's clumsy (especially for the player).


 * But, if you were going to change "humourous" to "striking" or "piquant" on the grounds that "humour" is too subjective, we're losing a lot of description. "Striking" says nothing about the character of the gesture, it would make the whole paragraph seem more or less useless to me. - Rainwarrior 16:15, 24 September 2006 (UTC)

I have to agree with Rain...the term "striking", for example, says little about the "character" of the music. I certainly agree with "humorous", but believe there is inherently more in this musical instance. (Consider how Liszt, for example, used the semitone, with a brief non-chord tone [semitone] in the opening of the "Mephisto Waltz" to convey an evil essence! It can certainly express a sinister element. "Mischievous" strikes me as an apt descriptive term. What about "humourous, yet rather mischievous"?" ("Wrong note" even suggests that somebody is "doing something wrong"...i.e. is "up to no good"! (Literally, dissonance can suggest "wrong", whether we interpret the word to mean funny [clumsy] or sinister.)

I am considering two other factors. First, this theme appears in a minor key, possibly lending a flavour of "darkness" or "spookiness". Second, compare it to the contrasting middle section...it may offer a clue. (Does the melodious mid-section offer a contrast primarily to humour or to "mischief"? I can't help but feel that it does both, but is a wonderful specimen of typically Chopinesque "soul-cleansing".) "Humourous, but naughty" or "humorously naughty", also occurred to me.

It might seem we are dwelling on a relatively minor point, but in the interest of doing our very best with this article, I think it's worth that extra bit of effort. (Mark...could you arrange to LISTEN to this Etude, then let us know here how it strikes you? This might help us reach a final decision on the description.) Prof.rick 19:48, 24 September 2006 (UTC)

Does anyone also find a sarcastic element in this Etude? (It remind me a bit of a little kid, sticking out his tongue...a rejection of "authority" or "expected behaviour". (Sassy!) Prof.rick 19:58, 24 September 2006 (UTC)


 * Well, in the Mussorgsky it's an obvious reference to chirping. In some of the music for the video game Super Mario 3, it gets used for a similarly "cute" effect. In Liszt's Mazeppa etude, it always strikes me as a very clumsy ride. In this Chopin Etude, it sounds to me deliberately annoying, like a joke (and not unlike laughter). It's also kind of weird how little time is actually spent in E minor in this piece. I dunno, what do you want to call this effect? - Rainwarrior 20:43, 24 September 2006 (UTC)


 * I only suggested 'striking' as an example of a less subjective term, not necessarily descriptive of that piece, which, as I said, I don't know. There's no need for me to listen to it as we can't allow my subjective appraisal to influence the description. Find another more appropriate term - or use "humorous" if the piece is known for its humorous effect. But be careful. Chopin may have used the semitone to humorous effect in that piece, but I'm sure he could have used a whole range of intervals to equally humorous effect. Don't dwell on this or you'll be in danger of giving the false impression that semitones are intrinsically funny - and then someone will come along quoting the 'Jaws' theme in protest. (Mark - 24 September 2006)

I agree, Rain, in the Moussorgsky, it is a reference to chirping, rather than humourous. Regarding the Liszt Mazeppa, I find it clumsy,and deliberately annoying, to say the least, and add "rude" and at times almost brutal, domineering, and even sadistic...definitely evil! Regarding the Chopin Etude, I have also thought of "mocking" or "teasing". A pianist-friend also added "frolicking", agrees with both "humorous" and "sinister" but added the valuable term, "unsettled". (By the way, I wonder who named this the "wrong note" Etude? Surely we can't simply acccept one text-book definition. Without success, I consulted five different books on the works of Chopin, and found no descriptions of this Etude!  (Maybe if we look at the broader meaning of the word "wrong"...I dunno.) If you think of music as "a living thing", and is therefore subject to "character change" as it progresses, then the fact that this exerpt has much material in the major key is not very signicant. Chopin often makes the major-minor change freely. However, It is the FIRST instance which sets the tone for the piece. (Consider, for e.g., the Fantaisie-Impromptu, "A" section. It begins in the minor, giving it a very serious nature, but also has substantial sections in the relative major. The tonality of the opening is the most critical is "setting the stage", I think. (Rain, on the other hand, I have also used acciaccatura semitones in my own compositions to convey a carefree escape from the harsh realities of life, the sublime, the heavenly.)

Mark, why can't we let your subjective appraisal influence the description? You've made a very important point, particular with reference to "Jaws"...the minor second can serve a wide variety of expressive possibilities. You have raised a VERY important point...we do NOT want to give the impression that semitones are inherently funny!

Why don't we all re-read this section of the talk page, and make a list of the possible adjectives...then narrow it down. I would begin by removing "jocular", and "whimsical" which were used in the article (Of course, the question arises: are we trying to describe one musical specimen, or the "musical disposition" of the semitone?) I also like the word "striking", but feel we should be more specific. Maybe we should make a list on this page, then vote on it. Prof.rick 02:54, 25 September 2006 (UTC)

"Itchy?" Prof.rick 03:17, 25 September 2006 (UTC)

Whatever description we arrive at, I think we should use a term such as "might be described as", rather than stating a subjective matter as though it were unquestionable fact (e.g is humourous). Also, the use of two or three adjectives might help, but not the existing three, which are too much alike to convey this musical paradox. Prof.rick 03:23, 25 September 2006 (UTC)

Rain, referring to the major/minor element, I would also like to point to the first Chopin Waltz (Op. 18). The B-flat minor section also makes use of acciaccatura semitones, (as well as some other intervals) (bars 133 - 148)for a specific purpose in the overall structure. All along, the piece has been so jubilant, and in major keys. So often in every art, a "conflict" somewhere along the line is employed, to "play up" the sublime, serene, or joyous sections (or vice versa!). The fact that this passage is written in a minor key seems to suggest that it is IS the "conflict" section. (Which of course, suggests that Chopin was well aware of the element of conflict which the semitone can convey.)

Also, I had previously given you examples of Chopin's use of the harmonic augmented unison in one Ballade, and the Berceuse. You can also find it in the 8th Nocturne, Op. 27, No. 2 (bar 13). (And it each of the 3 Chopin instances I have quoted, the effect is hauntingly beautiful and ethereal.) The point is: I am wondering if the Liszt Etude is the best example of a harmonic augmented second, since it's use there is defiant and very dark, even ugly...yet in the Chopin examples, it is literally "a breath of heaven". What do you think? (We know that sounds which are displeasing in the bass might be quite delicious in the high treble, corresponding approximately to the "spacing" of the harmonic series.) Prof.rick 04:53, 25 September 2006 (UTC)

Mark, although you have far less to say that either Rain or I, your comments are always well-thought, and have been indispensible. Often, a one-on-one difference of views seems insoluble...the voice of a knowledgeable third party (especially one with your particularly astute and unique insight) can help bring about a final "answer". We NEED you!!! Following is a list of some of the adjectives so far mentioned, to describe the semitones in that Chopin Etude (and I DO hope you can find an opportunity to listen to it...playing it is one matter, but to interpret it's musical statement requires only open-minded listening). Here is the list:

humorous, whimsical, jocular, sardonic, sinister, naughty, mischievous, striking, piquant, defiant, sassy, itchy, clumsy, rude, mocking, teasing, frolicking, unsettled. (Add more, if you wish.) If we can narrow it down to 2 or 3 agreed adjectives, we've won!

I won't express my own proposal yet, but wait to hear what you, Rain and Mark, have to say. However, we must keep in mind that music is a language unto itself; therefore, our verbal descriptions are inherently both subjective and inadequate...it's something like trying to teach the Russian language, using only French. (Just one musical phrase can "say" many different things, hinging on the listener, and his mood/disposition at the time of listening.) But ultimately, we must ask, what, to the best of our knowledge, was the composer's intention.

Chopin is SUCH a complex character, full of wit, and even a "mimic" of others. (Apparently, he could he even contort his facial muscles to "look like" the person he was impersonating!)

PS: Judging by spelling and grammar, are we all Canadians? Prof.rick 06:08, 25 September 2006 (UTC)
 * I thought we were all Brits.
 * Prof - "If it aint broke, don't fix it". I just had another read of that paragraph and it's FINE. "Eccentric dissonance" is a great phrase. Let anyone argue with that if they dare. "Humorous" and "whimsical" are fine too, (Maybe "jocular" is pushing it a bit). As Rain said, its nickname suggests that it's known for its humorous effect, so I don't think you're being subjective in using that term. For style purposes, two phrases I would suggest changing are "...used for a humorous effect" to "...used to humorous effect" and "...which contrasts with a more lyrical middle section" to "...which contrasts with its more lyrical middle section".
 * The first change makes it sound a little more encyclopedic and the second change reminds us the main topic is the semitone, not the Chopin piece. Somehow using "a lyrical middle section" sounds like we've shifted the main focus from semitone to the etude's lyrical section. (Mark - 25 September 2006)


 * I like Mark's suggestions. Make whatever amendations you think are appropriate. I like the idea of making the opening sentence more general. Maybe start with something more like: "In unusual situtations, the minor second can add a great deal of character to the music. For instance, in Chopin's..." and then discuss this specific one? As for the nickname, I don't know who came up with it (a lot of 19th century critics liked to give nicknames to pieces... if I had to point a finger, I'd probably point at Eduard Hanslick), but I've seen it in a few places. - Rainwarrior 01:48, 26 September 2006 (UTC)


 * And BTW, I am a Canadian, yes. It says so on my user page. - Rainwarrior 01:50, 26 September 2006 (UTC)

Actually, I though we were all French Poles. Re:"if it ain't broke...": In a sense it was broke, possibly implying that all semitones are humorous, a point previously made by Mark. I admit, I've been thinking about this matter all day. Semitones can also be very sensuous (e.g. their use as grace notes in jazz and blues). Obviously, we cannot list all the expressive possibilities of the semitone. I also like Mark's idea, and yours, of starting with an opening sentence which "leaves the door open", and I like the "for instance", as the reader will understand that "humorous" does not necessarily apply to all semitones. I'm satisfied. I'll leave the edit to your discretion. (Man, this is a great article!!!) Prof.rick 03:29, 26 September 2006 (UTC)

And I LIKE the phrase, "eccentric dissonance". HA! Prof.rick 03:34, 26 September 2006 (UTC)

Rain, I've used your introductory sentence (re character of the minor second), and moved "humourous" to replace jocular. (Of course, you can change it back if you like!)

Mark, I'm also following your suggestion: change "used to humourous effect" and "which contrasts with a lyrical middle section". Prof.rick 22:14, 28 September 2006 (UTC)

Sorry, Mark! I re-read your comments, and replaced a with its. Hope your find these minor edits OK. Prof.rick 22:45, 29 September 2006 (UTC)

The Minor Second is back!
I was quite surprised that vandalism had corrupted this article on Nov. 28/06. An attempt was made to recover the page, but somehow the Minor Second (item 1 of the Contents) had vanished! I have tried to restore it, using "copy and paste" from the History. I hope this has not caused any unnecessary problems. (Future edits were preserved).

Please, when ANYONE (especially those anonymous IP editors) want to make edits to any article, it would be appreciated if you'd leave a note on the Discussion Page, mentioning your reasons for change. Some of us invest a great deal of time, effort, research, discussion, and scrutiny...to arrive at the most complete and accurate articles possible. Prof.rick 10:36, 16 January 2007 (UTC)


 * Hi Prof Rick. I completely missed the vandalism, probably because it was an accident. It looks like was reverting other vandalism which replaced the section with jibberish and forgot to replace the original material there, so I guess I thought the vandalism had been taken care of, but it hadn't. Anyhow, it looks fine now. Thanks for correcting that. - Rainwarrior 05:17, 17 January 2007 (UTC)

Editing augmented unisons
Hi Rain, Hope you don't mind...I have edited out your use of diatonic semitones to notate a chromatic passage: e.g. C, Db, Ebb, Fbb, Gbbb, etc. I feel this particular point is irrelevant...it may suggest that the chromatic semitone is a "necessary compromise". (How often have you come across a triple-flat?) Obviously, both composers and readers prefer the most direct route, e.g. C, C#, D, D#, E, and think in such terms. I don't believe the use of chromatic semitones needs to be justified. (Of course, if you disagree, you can restore your example.) Best, Prof.rick 07:41, 21 January 2007 (UTC)

i thought the tritone was the most dissonant interval
i'm no harmonic scholar, but it seems that the tritone is always dissonant, whereas the semitone is only sometimes dissonant. to my ears the tritone always sounds far more difficult.67.172.61.222 22:52, 9 March 2007 (UTC)
 * Taken out of context (a musical context) it seems hard to say what is more dissonant. In any case, the article's opening statement of the semitone being "the smallest interval commonly used in Western music, and is considered the most dissonant" -- it would be nice to have a reference (ie, who says it is the most dissonant?), and/or some kind of note about what method of measuring dissonance results in the semitone being the most.  The dissonance pages makes it clear that the term is used variously, with differing ways of measuring. Pfly 02:52, 13 March 2007 (UTC)


 * The tritone appears in every dominant seventh chord; it is extremely common. The minor second on the other hand is used quite sparingly, harmonically. This speaks to its relative dissonance in a way. The simplest just ratio for a tritone is 7/4 whereas it is 16/15 for the semitone, which is a more complicated ratio, which is one way to quantify dissonance. There are other arguments though, you could make the argument that the tritone has a greater implication for resolution than the minor second (because of its place in the dominant seventh chord), and if your definition of dissonance is a tension that leads to resolution (which is a different way of qualifying dissonance), it's could be reasonable to say that the tritone is more dissonant. All in all, I'd say statements like "most dissonant" aren't terribly useful anyway, given how various the definitions of dissonance are, but by most usages, the minor second is the more dissonant. - Rainwarrior 05:43, 13 March 2007 (UTC)
 * a dominant seventh chord sounds, without any surrounding context, fairly dissonant to my ears, at least quite tense. i think the best measure of dissonance, as a totally subjective concept, is the ability of an interval to sound "natural", which the tritone, quite simply, never does. listen to "From the Morning" by Nick Drake if you want a good example of a semitone used as an interval. if you try to write a piece on any instrument that includes a tritone, good luck making it sound that melodic. by a more meaningful measure of dissonance, a tritone divides the octave exactly in half, creating a lack of a tonal center in just two notes. lastly, just play a semitone as two individual notes, and then do the same for a tritone. you'll find that going from E to F sounds much different than E to A#. 67.172.61.222 00:47, 16 March 2007 (UTC)
 * Dissonance is subjective, dependent on harmonic context, context of the individual piece of music, and cultural music experience of the listener. And to give a global perspective, if you open up other tunings, such as non-Western tunings, or microtonal equally tempered scales, there are numerous intervals that are considered more dissonant in some settings. Cazort (talk) 15:42, 12 October 2012 (UTC)

Diatonic and chromatic
The article uses the terms "diatonic" and "chromatic" without adequate explanation. These terms cause serious uncertainties at several other Wikipedia articles, and in the broader literature. This is amply demonstrated in discussion above, and in the archived discussion. For example, some take the term "diatonic scale" to include all of the minor scales, and they have justification for this usage in published sources. One example will suffice. User Prof.rick writes, in Talk:Semitone/Archive_2: "The problem with referring to 'diatonic steps' could present a possible source of confusion to first-level theory students. (What does 'diatonic' mean? Which kind of diatonic scale? Major? Natural minor? Harmonic minor? Melodic minor?) This seems to be an easier way to define a minor interval, in terms the average first-level theory student can readily grasp." This is not an aberrant or isolated understanding of the term "diatonic" by any means, but it is inconsistent with the article Diatonic scale; and that article itself comes close to being internally inconsistent. It certainly would be misleading to the reader seeking clear and current definitions. Some of us thought that both "diatonic" and "chromatic" needed special coverage, so we started up a new article: Diatonic and chromatic. Why not have a look, and join the discussion? Be ready to have comfortable assumptions challenged!

–&thinsp; Noetica ♬♩&thinsp;Talk 22:14, 3 April 2007 (UTC)

Phi Semitone
To Dicklyon:

No, you will not find the Phi semitone described directly at the references I provided. However, at the "Elliott Sharp" page, check the discography. Find "String Quartets 1986-1996 (2003)". Read the CD insert. Would you like it mentioned in the article? If you're not satisfied, feel free to remove the Phi semitone, by all means.

Your aggressive approach could certainly be used at "Mathematical Coincidence", which still has a ton of garbage. I corrected the expression of 1/81. Rather than removing it, I've called for discussion. Also, "Golden Ratio" still has a lot of it, too. Prof.rick (talk) 01:46, 15 January 2008 (UTC)


 * OK, I'll take it out then. I agree the 1/81 should go, but I saw you were headed that way, so didn't see a need to get involved.  As for golden ratio, I do keep after junk there; feel free to point out any you notice that I missed, or fix it yourself. Dicklyon (talk) 03:59, 15 January 2008 (UTC)

Dick:

Reverted to the Phi semitone version, pending your reading of my comments regarding source, and possible discussion by other editors. Prof.rick (talk) 07:06, 15 January 2008 (UTC)


 * No problem. While we're waiting, why not go ahead and add a citation to that CD insert, with a quote, so we'll know what it says. Dicklyon (talk) 07:19, 15 January 2008 (UTC)

Reference to Elliott Sharp's String Quartets removed. Prof.rick (talk) 00:06, 16 January 2008 (UTC)

As one of the two principal writers of the Semitone article (which required many weeks of exhaustive research, organization, etc.) I admit we had agreed to keep the section on "approximations of the tempered semitone" brief and relevant. I have therefore removed any mention of the Phi semitone. The information is trivial, and simply doesn't warrant extended quotes from CD inserts. Prof.rick (talk) 01:50, 16 January 2008 (UTC)

use of "half tone"
"Half tone" is used in several sources, including ones by Aaron Copland and Leonard Bernstein:
 * "Subdivision of the half-tone: All these investigations were based on our system of twelve half-tones, the product of the subdivision of the perfect octave into twelve tolerably equal tone-spaces." Toch, 1948, repr. 1977.
 * "... the twelve chromatic ones, arranged in the following order: two whole tones followed by a half tone, plus three whole tones followed by a half tone." Copland & Schuman, 1957, repr. 2002.
 * "Now, if you remember that the step from any note on the piano to the note just next to it, whether it's black or white, is a step of a half tone, you can see that the entire piano keyboard is made up of only half tones, one after another." Bernstein, speaking in 1961, repr. 2005.
 * "The larger pitch distance is called whole tone, the smaller half tone." Zuckerkandl, 1971.
 * '"All right, now," he said in a clear, crisp voise. "Everyone transpose a half tone up."' André Previn By Martin Bookspan, Ross Yockey, 1981.
 * "Intervals as small as the Western half tone are rarely encountered in African scales." Encyclopaedia Britannica, 1987.
 * "... almost a half-tone sharp." Flegler, 1990
 * "Tones and Half Tones: ... This is easy on the guitar, since from one fret to the next is a half tone (also called half step or semitone)." Noad, 2001.

--Jtir (talk) 13:54, 24 August 2008 (UTC)
 * Will someone who knows how fold this topic up since it's already resolved (added to the article), so it only appears here as a clickable title to expand the old conversation?

Mathematical equation?
I came to this page hoping to understand how the musical notes are assigned to various frequencies. For instance, if A = 440 Hz, and every octave represents a doubling in frequency, then there must be some way to calculate the exact frequencies for each note in the diatonic scale. I did not find that information on this page but I eventually worked out on my own that with twelve semitones per octave, a semitone must represent an increase in pitch of $$2^{\frac{1}{12}}-1=5.95%$$. Is there some reason not to include this information on this page? Ronnotel (talk) 01:31, 21 May 2009 (UTC)

The size of the semitone in twelve-tone equal temperament is covered in the equal temperament section. It's not expressed as a percentage because percentages are rarely used in tuning. &mdash; Gwalla | Talk 16:55, 21 May 2009 (UTC)
 * OK, thanks, I see it now. Ronnotel (talk) 18:04, 21 May 2009 (UTC)

Comments on Diminished unison would be appreciated
Seems to be a questionable term. Reply at talk:Diminished unison for now. Thanks --Jubilee♫ clipman 23:32, 20 December 2009 (UTC)

Merge Diminished unison
I suggest that Diminished unison is not a viable article as it stands. The content should be merged into Semitone. Augmented unison, which would be an alternative, redirects to Semitone anyway (as does Minor second). Perhaps Diminished third should also be merged here, too? (I fully recognise the fact that equal temperament "irons" all these out, it just seems better to get them all under one wing for now to help citations and style etc.)--Jubilee♫ clipman 02:21, 22 December 2009 (UTC)


 * Why isn't the current "diminished unison" article viable? Hyacinth (talk) 06:48, 22 December 2009 (UTC)


 * There's nothing more to say about the interval than what's already there, without duplicating the content of semitone. I agree with clipman, although I don't know about diminished third.  Powers T 15:14, 22 December 2009 (UTC)


 * It was proposed on the article talk page that the concept was inconceivable and the term didn't even exist. This was then shown not to be true. Hyacinth (talk) 15:32, 22 December 2009 (UTC)
 * I read the talk page but couldn't see where any of that was contradicted per se. Regardless, my point stands even so.  Powers T 15:41, 22 December 2009 (UTC)


 * Talk page proves that Augmented unison is a widely used term and makes sense. OTOH, Deskford calls the term Diminished unison a paradox and a joke; Opus33 asks for confirmation that the term is taken seriously and suggests explaining the rare usage (and actually recommends deletion if none of this can be done); Melodia simply points out that Augmented unison is a redirect (and implies that diminished unison should also be a redirect); I was trying to make sense of it all; no one there actually questions the existence of the term nor attempts to prove that it exists.  The main problem I can see with the article is that it basically says: This interval is smaller than the smallest [pseudo-]interval. Most theorists reject the term though some use it when referring to the inversion of the augmented 8va. It then quotes an indecipherable statement about flat being augmented and sharp being diminished - or should that be the other way around?  The only fact that actually makes sense here is that augmented inverts to diminished therefore logically aug 8va inverts to dim unison (while dim 8va inverts to aug unison).  All of this could just as easily be in the main article on semitone or in an article on the augmented unison.  If we created articles on Augmented unison and Minor second then this article could either stay and be expanded, or be merged to aug unison and expanded (given that the article suggests these are in effect the same interval; expand explaining why aug -> dim and vice versa, pointing out that the term is often used in jest, and that it is rare to find the term being used seriously).  (BTW, the interval is not actually a second, so it cannot be called a minor second. I have removed the following stricken through words etc from the article: it might perhaps be better called an augmented unison or minor second : C to C♭ is the same as C♭ /B to C<)  Diminished third is actually a tone so scrub that: I got confused there! I actually meant the theoretical double diminished third: C ♯-e𝄫.  --Jubilee♫ clipman  17:52, 22 December 2009 (UTC)

I've added my latest thoughts on the paradox over at Talk:Diminished unison. I think however that the augmented unison perhaps should have its own article rather than redirecting to semitone. Just about every other conceivable interval seems to have its own article &mdash; see List of musical intervals for a fascinating article that I've only just discovered. --Deskford (talk) 22:46, 22 December 2009 (UTC)


 * I've just expanded Template:intervals. Originally, I only meant to add the wolf interval but then found several others...  I found List of musical intervals today, too, while doing this work!  So, yes perhaps keep this article.  Perversely, though, many of the more common intervals lack their own articles:  Minor second (redirect), Augmented unison (redirect), Augmented third (red link), Augmented fourth (redirect), Diminished fifth (redirect), and Diminished sixth (red link) and even augmented octave (red link).  These should all be created.  (Note: aug4 and dim5 are not necessarily the same!) Augmented seventh redirected to Augmented seventh chord but I corrected that by creating an article for it.  --Jubilee♫ clipman  02:10, 23 December 2009 (UTC)

Additional citations
Why, how, and where does this article need additional citations for verification? Hyacinth (talk) 15:03, 1 March 2010 (UTC)


 * Tag removed. Hyacinth (talk) 04:47, 10 May 2012 (UTC)

Semitone by tuning system
The current version singles out 15:14 (119 cents) and 17:16 (105) as primary examples of semitone. This is odd, since they are part of a 7 and 17-limit tuning, whereas a 5-limit tuning is more noteworthy. The logic in the article suffers. A standard 5-limit 12 tone scale contains semitones of 25:24 (71 cents), 135:128 (92 cents) and 16:15 (112 cents). &minus;Woodstone (talk) 03:42, 6 May 2010 (UTC) (not my edit)


 * How does the current version do so? Hyacinth (talk) 12:42, 16 January 2011 (UTC)


 * What about http://en.wikipedia.org/w/index.php?title=Talk%3ASemitone&action=historysubmit&diff=360446036&oldid=347099039 ? Hyacinth (talk) 09:10, 17 January 2011 (UTC)


 * Of course I saw that also. That's why it's a mystery. I have seen it happening occasionally real time as well. Sometimes (by great exception) an edit is attributed to the wrong editor. &minus;Woodstone (talk) 15:10, 17 January 2011 (UTC)

Merge: Minor second
I suggest that Minor second be merged into this article as it is a stub with 1) duplicate or 2) overlapping content (WP:Merging). Hyacinth (talk) 08:09, 28 May 2012 (UTC)
 * "Minor second" seems like a strange term to me, since no minor scale has a semitone interval between the first note and the second. So it seems like a misnomer.  But how about instead merging Minor second into Augmented unison?  I think of semitone as an atomic concept used in the descriptions of all intervals that are integer numbers of semitones, "minor second" (aka "augmented unison") being an interval whose size happens to be one semitone.CountMacula (talk) 05:20, 22 July 2012 (UTC)
 * The fact that a scale doesn't start with this interval isn't relevant to the concept as described in the article. But how about merge both into here?  Both articles are tiny.  Actually, we already have sections on them, longer than the articles, so a merge should be pretty trivial.  Dicklyon (talk) 05:35, 22 July 2012 (UTC)
 * "The fact that a scale doesn't start with this interval isn't relevant to the concept as described in the article." The concept of semitone doesn't depend on any of the concepts of named intervals (augmented unison, major second, perfect fourth, etc.).  It is the other way around.  Concepts of named intervals depend on the concept of semitone, and are more complex than the concept of semitone.  IMO there should be at least thirteen articles for named intervals, at least one for each of the integer lengths 0-12, I guess exactly thirteen, plus the present article for the independent atomic concept of semitone.CountMacula (talk) 16:58, 22 July 2012 (UTC)

I agree with Dicklyon. See also Tritone, in which both the diminished fifth and the augmented fourth are defined, and to which both of them are redirected. Paolo.dL (talk) 12:17, 25 July 2012 (UTC)


 * Yes, Dicklyon is absolutely correct. If the interval between scale-degrees 1 and 2 were the determining factor, there would be no difference between what we call major and minor scales. Furthermore, major and minor scales are just a couple of jumped-up, johnny-come-latelies, by comparison to the semitone or minor second, both concepts which had been around for nearly two millennia before those scales reared their ugly heads. Also, where does all this stuff about there being only thirteen "integer-lengths" come from? If you are going to go that route, you will need separate articles for a minimum of 72 "integer lengths", before even getting out of the octave, and probably a lot more than that, once you have cast off equal temperament and understood how tuning actually works when not confined to the mechanical workings of a piano (even more of a johnny-come-lately than the major-minor scale system).—Jerome Kohl (talk) 16:40, 25 July 2012 (UTC)


 * I discovered a previous discussion above in this talk page about merging Augmented unison into here. I read it and I changed my mind. I think we should keep separate articles for minor second and Augmented unison. Even though there is certainly a lot of overlapping with this article, they may be useful. Paolo.dL (talk) 10:36, 27 May 2013 (UTC)

I think that the scope of this discussion is too small. We see here only a part of the problem, as a very similar merging problem is found for Whole tone and Tritone as well, and it is quite desirable to find a consistent approach to deal with it. We should open a discussion with broader scope, probably not in this page. See below for my proposal. Paolo.dL (talk) 19:33, 27 May 2013 (UTC)

Requested move

 * The following discussion is an archived discussion of the proposal. 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. 

The result of the proposal was not moved. No positive rationale provided for the move; per consensus appears to be the common name everywhere, and WP:ENGVAR would apply if the common name only in some geographic regions.--Fuhghettaboutit (talk) 13:36, 20 December 2012 (UTC)

Semitone → Half tone – No reason for naming the article "semitone". Hyacinth (talk) 01:25, 13 December 2012 (UTC)


 * I would have supposed this was a joke, if I did not know about the recent discussion at Talk:Tritone. Are we also going to consider changing Hemisphere to "Half ball", Demimonde to "Half world", and Semiconductor to "Half material allowing flow of electrical charge"? OK, jokes aside, it is agreed that no reason has ever been offered for naming the article "semitone"; is there a reason for naming it anything else?—Jerome Kohl (talk) 02:07, 13 December 2012 (UTC)


 * Oppose – it's a semitone. No need for this joke move.  Dicklyon (talk) 04:53, 13 December 2012 (UTC)
 * Oppose. I always call it a semitone here in England. Anthony Appleyard (talk) 23:29, 13 December 2012 (UTC)
 * Oppose. I always call it a semitone too (in NZ). Tayste (edits) 01:39, 14 December 2012 (UTC)
 * Oppose. No reason has ever been given explicitly for naming this article "Semitone" because the reason was obvious to most editors. It is the most commonly used name for A1 and m2. Similarly, nobody ever provided the reason for using the title Chair. Paolo.dL (talk) 19:42, 14 December 2012 (UTC)
 * Oppose. While my understanding is that in the US, half-tone is more frequently used, there is no rationale for changing this international standard. Tiggerjay (talk) 03:20, 16 December 2012 (UTC)
 * Oppose. The reason for naming the article "semitone" is that's what it's commonly called. Possibly not in the USA, but if so WP:ENGVAR applies. -- Necrothesp (talk) 17:00, 18 December 2012 (UTC)
 * Comment. Since two editors have raised the question, the word "semitone" is the common term in the US and Canada as well as in Britain. I believe this is also the case in Australia, New Zealand, Ireland, and South Africa. As indicated in the discussion on the Tritone "talk" page linked above, the term "half tone" is given preference mainly in publications with "Complete Idiot" or "Dummies" in the title. I think it is about time that Hyacinth voiced his reasons for proposing this change of title.—Jerome Kohl (talk) 17:08, 18 December 2012 (UTC)

"Because" is an especially weak reason to title an article something (as is "I like it"). If you all think this move request is a joke, the reasons given to oppose it are even funnier. Hyacinth (talk) 18:13, 18 December 2012 (UTC)
 * Then you need to give a reason why you think it should be moved. "No reason for naming the article "semitone"" is hardly a reason for moving it away from a perfectly good title. You can't expect others to give your proposal serious consideration if you can't be bothered to give a good reason for it (at the moment, your reason seems to be WP:IDONTLIKEIT). You seem to have been under the misapprehension that everyone would consider "half tone" to be a better title than "semitone" without further explanation. -- Necrothesp (talk) 18:22, 18 December 2012 (UTC)
 * The above discussion is preserved as an archive of the proposal. 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.


 * You seem to be under the misapprehension that "semitone" is a "perfectly good title" for no reason whatsoever. Beside empty assertion, what makes "semitone" a perfectly good title? Hyacinth (talk) 00:49, 21 December 2012 (UTC)
 * WP:COMMONNAME and stats like this and this. "Half tone" is relatively rare, and the trend in recent years to dumb it down to "half step" is not something that we need to adopt, per WP:RECENTISM.  Dicklyon (talk) 06:49, 21 December 2012 (UTC)


 * While the Ngram initially looked decisive, I tried it with different terms and the results where fairly different with each run.
 * Entering "a semitone", etc., suggests that "a half step" only recently surpassed "semitone"'s greater popularity.
 * Entering "one semitone", etc., suggests that "half step" surpassed "semitone"'s popularity around 1960.
 * Entering "A semitone", etc., suggests that semitone recently became slightly more popular.
 * Entering "The semitone", etc., suggests that semitone recently became slightly more popular.
 * Hyacinth (talk) 04:52, 27 December 2012 (UTC)
 * Indeed, it's a bit complicated. I was trying to find a good search that would exclude most of the non-musical uses that you see as a moderate percentage of the hits for "a half step" and "the half step".  But compared to "a semitone", the rest are small potatoes.  In the case of "a half step", I find that in this book search, 26 of the first 100 hits are for non-semitone, non-musical uses of the phrase, so the "a semitone" stay always in the lead.   Dicklyon (talk) 05:12, 27 December 2012 (UTC)

User:Jerome Kohl also provided this list of 6 references at Talk:Tritone:

However, this article already contains 10 references: Semitone, half step, half tone, halftone, and half-tone are all variously used in sources. Aaron Copland, Leonard Bernstein, and others use "half tone". . Hyacinth (talk) 04:35, 27 December 2012 (UTC)

Whence the term "minor second"?
How is it that a semitone is called a "minor second"? It is not the interval from the tonic of a minor scale to the second scale degree. Then in what sense is it minor and in what sense is it a second? And what is the history of the term? The answer to these questions should go in the article near the first use of the term "minor second". Thank you if you can clear this up.CountMacula (talk) 20:13, 24 May 2013 (UTC)


 * We will explain ASAP. If you are curious, you can find everything about this weird (but widely used) terminology in Interval (music). Paolo.dL (talk) 19:09, 27 May 2013 (UTC)

Proposing "multi-article" discussion about Semitones, Whole tones, Tritones
Dicklyon proposed above to merge both Augmented unison (A1) and Minor second (m2)into this article (05:35, 22 July 2012). A discussion about this is useful. However, the discussion should have a broader scope, as a similar problem concerns the articles Whole tone, and Tritone. I believe we should open a "multi-article" discussion, somewhere, about: As you can see, we currently deal with these three similar problems with maximum inconsistency: for each of them we used a different approach (the most questionable one being the absence of a separate article about Whole tone!).
 * 1) merging A1 and m2 into Semitone
 * 2) merging M2 and d3 into Whole tone (which now redirects to M2!)
 * 3) keeping A4 and d5 merged into Tritone (currently, there are no separate articles about A4 and d5).

Where can we discuss about a consistent strategy to deal with these problems, so that we can obtain consensus by as many editors as possible? Perhaps in Talk:Interval (music)? Paolo.dL (talk) 10:26, 27 May 2013 (UTC)


 * We might also add to this list the separate article for Ditone, which (apart from the distinction occasionally made in specialized articles on tuning theory) is synonymous with Major third. I'm not sure I am advocating such a merger, but I think it at least ought to be discussed in this context. After all, Semiditone redirects to Minor third.—Jerome Kohl (talk) 20:19, 27 May 2013 (UTC)


 * Indeed, Ditone is nothing but a synonym for major third; I don't care much which title we choose, but I agree they should merge, and that we should do more or less as Paolo suggests with the others. Dicklyon (talk) 20:51, 27 May 2013 (UTC)


 * Ok, where is the best page to discuss this? Is there a way to attract contributions? Dicklyon, I did not mean to suggest a merge. I only meant to start a discussion about that. Paolo.dL (talk) 20:56, 27 May 2013 (UTC)


 * The Talk page for the Music Theory Project is the most logical place, I should think.—Jerome Kohl (talk) 20:58, 27 May 2013 (UTC)


 * Thank you. OK, I'll start a discussion there in a few days, as soon as I can. Dicklyon and Jerome, please feel free to start it yourself, if you wish. Paolo.dL (talk) 21:10, 27 May 2013 (UTC)

I'm pretty sure there's no such a thing as "S4 = 27/25" in 5-limit tuning
I'm too lazy to do a full calculation check, but the ratio between A and B♭ (5/3 and 16/9) is still 16/15.

Somebody'd better delete that "S4" stuff. 2001:B011:C000:3A70:56BC:1380:82BC:A552 (talk) 19:33, 17 September 2023 (UTC)