Talk:Circle of fifths

Umbilic torus gif

File:The circle of fifths on umbilic torus surface.gif

The image

This image recently showed up in the "Modulation and chord progression" section, without accompanying text to explain it or motivate its inclusion. What encyclopedic value does it add? Just plain Bill (talk) 12:32, 24 May 2024 (UTC)

Hi,

The already existed text fits perfectly to the gif file. I do not think it needs any addition. Text says

"The circle of fifths is used to organize and describe the harmonic or tonal function of chords. Chords can progress in a pattern of ascending perfect fourths (alternately viewed as descending perfect fifths) in "functional succession".

The image does exactly that. Watch out a fixed CEBG rectangular. It is a C major seventh. Or anyone can imagine it as just CEG, a major chord. This chord moves by ``ascending perfect fourth" to F major. Next by another ``ascending perfect fourth" to Bb major. And so on until, by three visual turns, cover the whole circle of fifths and comes to where it started (because circle of fifths is a circle). It is self-evident that the single path C-F-Bb-Eb-etc is the circle of fifths. Compare the notes with the above image counterclockwise.

If the fact was not so self-evident, I would not dare to edit wikipedia. All sources that came to my attention recognize that there should exist a torus, like figure 5.9 on page 81 of pages's further reading or torus in Neo-Riemannian theory but can not clearly support the text ``Chords can progress in a pattern of ascending perfect fourths'' . The already existed text, however, can be supported perfectly, in a self-evident matter, by the C-F-Bb-Eb-etc curved path on the surface of an Umbilic torus.

If anyone follows the details of my image can see, in another image, that in the gif contains the twelve tones, twelve minor and twelve major chords in a pattern of ascending perfect fourths but that would indeed need accompanying text and common agreement on the correspondences.

The encyclopedic value of it is that the already existed text can be supported by a three-dimensional object and, in that knowledge, everyone would like to literally play the harmony of the 12 tone equal temperament system on their fingers.

I am at your disposal for any further clarification Jimishol (talk) 15:00, 24 May 2024 (UTC)

Thanks for these explanations. I nevertheless fail to see how this drawing can show a circle of fifths, nor how it can "organize and describe the harmonic or tonal function of chords." The text itself is not clear: it is not the chords themselves that "progress in a pattern of ascending perfect fourths," but their roots. What a "functional succession" is seems to me totally unclear (a succession of functions? But roots ain't functions!). The image shows a succession of identical chords (e.g. major sevenths), but no "functional succession" could be a succession of identical chords!!! Hucbald.SaintAmand (talk) 21:40, 25 May 2024 (UTC)

From the definition in the article "The circle of fifths organizes pitches in a sequence of perfect fifths, generally shown as a circle..." it follows that it is a sequence of notes. They are usually shown as a closed curve of a circle in two-dimensional space. The definition is not violated if they are shown as a closed curve in three-dimensional space, as in the gif. On the contrary, the gif reinforces the definition that it is a sequence of notes, since, in the same article, there is a mapping of the sequence to some other curve than a circle.

The title of our paragraph "Modulation and chord progression" and the explanatory text "Chord progressions also often move between chords whose roots are related by perfect fifth,...." already maps the notes of the sequence to chord roots. It is not the gif's responsibility to do so.

Therefore the movement in the gif ...G-C-F... is, in the spirit of the paragraph, a major chord progression.

The use of the phrase `Chords can progress ... in "functional succession"` implicitly assumes that a scale has been defined, otherwise "function" cannot be defined, in my opinion. Again, the gif doesn't need to clarify anything in favour of this.

So I think it would be fair for the gif to have the same fate as the text it seems to support. To me, the gif is less ambiguous than the text it supports. In fact, I think the image better expresses what the text wants to communicate. The following explanation of functional succession, then, applies first to the text, then to the gif.

By defining the C major as tonic then the movement of the example can be seen as...G-C-F...=...V-I-IV... In the figure a seventh major is moved to make it clearer that a scale can be visualized, in some way, as a surface.  In the gif, the C major scale seems to create at least the "half cylinder" outlined by the movement of the BG edge to EC and finally to AF. As is natural, the repetition of the same perfect fourth movement changes scale (in the figure, surface) and therefore it takes three cycles to repeat the C major of the initial position, because we pass through all the scales. I am totally against considering chords as surfaces of triangles but in this case if you fold the tonnetz diagram over the surface of the gif you will see the V-iii-I-vi-IV motion. To stay in tonic we must return to tonic in only one rotation, not three as in the gif. The only way to use D while staying in scale is to use it as the vertex of the minor triangle DFA of the "top" surface and, from there to "slide" to the vertex D of the GBD major of the "bottom" surface. Thus the above functional succession becomes I-vi-IV-ii-V-iii-I and thus return to tonic with a single rotation.

I don't think the paragraph should be inflated so as to lead the reader to specific mappings. These should be left to the opinions and perspective of each theorist or reader. But it seems that, for these mappings, I cannot avoid mentioning my own personal viewpoints, which are recorded in the link existed in the details of the image. I therefore prefer the mapping of each note to the vertices. The mapping of major scales or chords to a curved section starting from the homonymous vertex, e.g. C major to the CF curve. The mapping of minor scales or chords to a section of a straight line starting from the homonymous vertex, e.g. c minor to the CAb edge.

Then, personally at least, I can even "see" the progress of the Neapolitan sixth through the path C-f-Db=CF-Fdb-DbF# From this perspective, the Fdb edge is the f minor, intermediate scale that does not need to be established, so with reference to it I have V-(i)-VI=V-VI of the f minor. By the same visualized logic, D major is Neapolitan of Db major, but because we must not use F# (leading tone of G) we compose and advance by a perfect fourth from D to G major. Visually at least, I can "see" the I-bII-V sequence, easily rather, somewhat like a "sequence" of two Neapolitans.

The gif shows the sequence of perfect fourths on a three-dimensional closed curve, as an alternative way of representing the circle of fifths. It is not his responsibility to suggest the best possible mappings of the functional succession. But it does exist and, as the beginning of the paragraph states, can be "...used to organize and describe the harmonic or tonal function of chords..."

Translated with DeepL.com (free version)

I am at your disposal for any further clarification Jimishol (talk) 10:09, 26 May 2024 (UTC)

Long story short. For each note, class [X], a local map is constructed containing the note [X] and its two basic connections to its "neighboring" notes [X*3/2] and [Y*5/4]. The set of twelve local maps, one for each note, defines a manifold as an abstract structure.  But this structure can be viewed in three-dimensional space and visualized as in the gif. The four paths created by the branches [Y*5/4] are circles of sixths or the augmented triads. The unique path created by the branches [X*3/2] is the circle of fifths. So this is a mathematical-musical tool that can be used by any music theory (school), whether it wants to describe chord progressions or anything else. Jimishol (talk) 04:58, 28 May 2024 (UTC)

I refer to manifold terminology because that's what I was familiar with. But I am puzzled by the fact that, when searching wikipedia, even in topological manifolds, their definition includes that they locally resemble real n-dimensional Euclidean space. To the question "is a tree graph a manifold with local maps the branches from each node?" the copilot answered "a tree graph exhibits manifold-like properties, especially when we focus on local regions around each node. It's a fascinating way to connect graph theory and geometry!". So a graph theory approach to gif might be more appropriate. Jimishol (talk) 08:38, 30 May 2024 (UTC)

Circle or cycle?

A recent modification by user 71.17.203.128 (what a strange name!), already reverted, raised once again the question of "circle" vs "cycle," already discussed on several occasions in this talk page. There are reasons to prefer "circle" which may be more common in English – the situation would be the opposite, say, in French. But I do believe that adding a word about this in the article could prevent further discussions. "Cycle" is used at least three times in the article, but not all three cases may be justifiable. Something should be done about this. Whaddya think? — Hucbald.SaintAmand (talk) 08:17, 22 June 2024 (UTC)

Cycle might make more sense, as IP user suggested, but lots of things in music don't make sense, e.g. a third is twice as big as a second. I've never heard any musician say "cycle of fifths." Is there a source which does? —Wahoofive (talk) 15:27, 22 June 2024 (UTC)

@Wahoofive, I don't mean that we should replace "circle" by "cycle", merely that we should say that "cycle" is a possible variant. This should close the discussion. Sources are not lacking:

1. Our article itself uses "cycle" three times:
   1. "It was known in [A]ntiquity that a cycle of twelve fifths was almost exactly seven octaves" – cycle is preferred here because the idea is to stress the origin of the (Pythagorean) comma, i.e. that the series does not close on itself as a circle.
   2. "Cycle' appears in a quotation from A. Whitall in The Oxford Companion to Music (see note 17), which I was unable to check.
   3. It also appears about a quotation from R. Scruton, The Ring of Truth: The Wisdom of Wagner's Ring of the Nibelung (see note 20), but the truth is that Scruton never writes "cycle or fifths" and only once "circle of fifths" (p. 174, about circles of third progressions replacing it in Schubert).
2. In my own electronic library, I find "cycle of fifths" many times, among others in
   1. E. Amiot (2016), Music Through Fourier Space.
   2. W. Apel (1950), Harvard Dictionary of Music (s.v. "Chinese Music").
   3. Th. Christensen (2019), Stories of Tonality in the Age of François-Joseph Fétis.
   4. S. Clark (2011), "On the Imagination of Tone in Schubert's Liedesend [etc.]", in The Oxford Handbook of Neo-Riemannian Music Theories.
   5. D. Conklin & S. Weisser, "Pattern and Antipattern Discovery in Ethiopian Bagana Song", in Computational Analysis.
   6. E. Kurth (1991), Selected Writings.
   7. L. Meyer (1973), Explaining Music.
   8. N. Newton (2019), "Chromatic Linear Progressions in Popular Music", in The Routledge Companion to Popular Music Analysis.
   9. C. Sachs (1943), The Rise of Music in the Ancient World.
   10. N. Waltham-Smith (2019), "Sequence", The Oxford Handbook of Critical Concepts in Music Theory.
       Etc.
3. Scholar Google gives about 1990 replies for "cycle of fifths", as against about 9130 for "circle of fifths" (i.e. a relation of about 20% for the first). In French, about 414 results for "cycle des quintes", as against 60 only for "cercle des quintes" (80% for the first – the situation is the reverse from that in English).

Hucbald.SaintAmand (talk) 11:40, 23 June 2024 (UTC)

I should have noted, in addition, that the French article corresponding to this one on FR.WP is "Cycle des quintes"; this may be a typically French usage, other European languages prefer "circle" or its equivalent. — Hucbald.SaintAmand (talk) 16:05, 24 June 2024 (UTC)

Comment: The normal name is "circle of fifths"; no problem in also using the word "cycle" appropriately as well in the article. But I do not think it is an improvement to start one of those ridiculous WPrambles, listing all sorts of "alternative names" in other languages, scripts, obscure/deprecated/wrong Unicode characters that might have something to do with it etc etc etc... Meanwhile this comment strikes me as bizarre: "cycle is preferred here because the idea is to stress the origin of the (Pythagorean) comma, i.e. that the series does not close on itself as a circle." But the meaning of "cycle" is (at least in its mathematical sense) precisely that of a closed cycle, otherwise it would not be a cycle. The CoF is isomorphic to the cyclic group of order 12, whose multiplication table can be used to convert semitones to CoF positions, for example. So arguably "cycle of fifths" might have been a better term, just as "cheap at twice the price" would have been better than the usual expression. Imaginatorium (talk) 07:03, 2 July 2024 (UTC)

We are not "starting" a ridiculous ramble (it started long ago), we are trying to close it. Could we agree that while the main term is "circle", "cycle" is a possible variant, and say so somewhere in the article? – Hucbald.SaintAmand (talk) 11:38, 2 July 2024 (UTC)

I'm fine with this. —Wahoofive (talk) 15:25, 2 July 2024 (UTC)

I added five words at the beginning of the article, which (I hope) should close the discussion. But feel free to formulate this otherwise. I don't think references are needed, the list of sources above will remain available. — Hucbald.SaintAmand (talk) 21:16, 2 July 2024 (UTC)

Circle of major and minor 7th chords?

I tried to add a section called Circle of major and minor 7th chords to this page, but someone removed it because they felt it should be its own page. I don't think I discovered anything groundbreaking other than I have never seen the note sequence DFACEGB mentioned before anywhere in music theory discussions. Anyway, I created a separate wikipedia page named "Circle of major and minor 7th chords" with a graphic that represents this 24 note sequence. If anyone knows if this synthetic scale or note sequence already has a name, please let me know in the "Talk" on that page.

BTW, if everyone agrees that the "Circle of major and minor 7th chords" is a useful addition to the topic of the circle of fifths, I would like to add a link to it in the "Circle of fifths" page. --Bsenim (talk) 23:56, 20 December 2024 (UTC)

As far as I can tell, this is simply saying "stacking four 5ths yields two octaves plus a third". Those pitch classes will, of course, start outlining a chord. And the idea that was presented isn't even sticking to perfect fifths. So I don't think it's a notable music theory phenomenon, and it's not really accurate. - Special-T (talk) 18:02, 19 December 2024 (UTC)

It seems to me that what is shown really is a circle of 3ds, which has been termed the tonal omnibus. It is a succession of neo-Riemannian R relations (from major to relative minor) and L relations (from minor to major by a "leading tone change", e.g. raising E to F in A–C–E to A–C–F). It only indirectly concern the circle of fifths. — Hucbald.SaintAmand (talk) 09:50, 20 December 2024 (UTC)

The 3-4-3-4-3-4... semitone step sequence (F#/G♭, B♭, D♭, F, A♭, C, E♭, G, B♭, D, F, A, C, E, G, B, D, F#, A, C#, E, G#, B, D#, F#/G♭) actually exists in most circle of fifths charts that include the associated minor keys in an inner circle. Not sure if it's correct to say "it only indirectly concern the circle of fifths." This is why I don't claim to have discovered anything groundbreaking. I just feel it's useful to mention that the 3-4-3-4... semitone step sequence (F#/G♭, B♭, D♭, F, A♭, C, E♭, G, B♭, D, F, A, C, E, G, B, D, F#, A, C#, E, G#, B, D#, F#/G♭) embeds all major and minor 7th chords and includes the circle of fifths. Bsenim (talk) 00:17, 21 December 2024 (UTC)

But the 3–4–3–4... sequence is not inherent in the circle of fifths (you write yourself "most circle of fifth charts"), and what you added to the article, F#/G♭–b♭–D♭–f–A♭–c–E♭–g–B♭–d–F–a–C–e–G–b–D–f#–A–c#–E–g#–B–d#–F#/G♭ obviously is a circle of thirds. It might be interesting to describe the link between these two circles, but to pass for that by a succession of 7ths seems somewhat farfetched. — Hucbald.SaintAmand (talk) 09:42, 21 December 2024 (UTC)

Isn't the circle of fifths technically a circle of 7 semitones? Bsenim (talk) 11:39, 21 December 2024 (UTC)

Maybe the answer lies in the origins of the name diatonic scale. Maybe "di" is tied to the relationship with the 3-4 step sequence. I'm not a music theory expert, so hopefully someone that has a deeper understanding of the theory behind a diatonic scale can add to this discussion. I don't think it's a chance coincidence that the components of a diatonic scale are logically mapped to the 3-4-3-4... sequence. It's actually really cool that the number 7 is deeply tied to the diatonic scale which is built on top of the number 12. Mannheim Steamroller's Fresh Aire 7 is one of my favorite albums. Bsenim (talk) 11:54, 21 December 2024 (UTC)

For what I know of ancient Greek, dia (δια) means "through." So, "diatonic" means "through tones," which won't help us here. Diatonic scales were described and discussed in Mesopotamia about 2500 years BC. The reason probably is that these scales permit maximizing the number of consonances of 4ths and 5ths, so that it might be argued that the circle of 5ths is at the origin of the diatonic scale. 3ds probably had not the same role because they are less consonant (particularly the minor one). But all this is speculation: I'd gladly discuss it further, but it obviously is not for WP. — Hucbald.SaintAmand (talk) 18:28, 21 December 2024 (UTC)

OK, I didn't get what you meant by circle of thirds at first, but I think you're correct in saying the name of the 3-4-3-4 step sequence is the circle of thirds, but nobody has added a graphic to that page yet, or mentioned the mnemonic DFACEGB yet, or talked about the fact that 7 sequential steps around the circle of thirds are components to a diatonic scale, or spelled out the repeating pattern of notes I have been describing here. Thanks for pointing out the circle of thirds page! Bsenim (talk) 12:39, 21 December 2024 (UTC)

I didn't even realize that there was a circle of thirds page on Wikipedia. As shown there (or here above), an alternation of major and minor thirds (4–3–4–3...) produces a chromatic scale and continues with enharmonies. The "tonal omnibus" is slightly different: in order to limit the circle to the diatonic scale, it has to involve two successive minor thirds. I found only one paper discussing it, "Tonal and "Modal" Harmony," which means that after all the concept might not be very common (nor very useful). — Hucbald.SaintAmand (talk) 18:49, 21 December 2024 (UTC)

The circle of thirds is useful for jazz musicians. This one sequence of 24 notes that repeats is an excellent pattern to memorize and get under your fingers for improvisation. Bsenim (talk) 19:13, 21 December 2024 (UTC)

Cycle of 48 notes of the first four notes of major scales in fifths order

File:First four notes of major scales in fifths order.jpg

This cycle of 48 notes represents the first four notes of each major scale, following the order of keys around the circle of fifths.

I found the link between the circle of fifths and the circle of thirds. If you take the cycle of 24 notes from the circle of thirds (the 3-4-3-4... minor/major thirds step interval)

F#/G♭, B♭, D♭, F, A♭, C, E♭, G, B♭, D, F, A, C, E, G, B, D, F#, A, C#, E, G#, B, D#, F#/G♭

And you use the jump pattern 15263748... repeating around the circle of thirds. You have a 48 note cycle of modular arithmetic (modulo 12) that groups common tones together.

C, D, E, F, G, A, B, C, D, E, F#, G, A, B, C#, D, E, F#, G#, A, B, C#, D#, E, G♭, A♭, B♭, B, D♭, E♭, F, G♭, A♭, B♭, C, D♭, E♭, F, G, A♭, B♭, C, D, E♭, F, G, A, B♭

The most succinct way to describe this cycle without coining any new term is to say that this 48 note cycle is:

A cycle of 48 notes representing the first four notes of each major scale, following the order of keys around the circle of fifths.

or

Cycle of 48 notes of the first four notes of major scales in fifths order

This cycle of 48 notes is all the major scales in succession in the order of the circle of fifths.Bsenim (talk) 10:36, 23 December 2024 (UTC)

I feel this is worthy of a new page because it is not original research and only facts about the circle of fifths and the circle of thirds. Bsenim (talk) 10:44, 23 December 2024 (UTC)

I'd like to talk here about what the appropriate name should be for the new page. Bsenim (talk) 10:45, 23 December 2024 (UTC)

This cycle of 48 notes also contains 4 modes. For example starting with C Major, the next mode is D Dorian, followed by E Phrygian, followed by F Lydian and then the mode cycle repeats with G Major. Bsenim (talk) 13:43, 23 December 2024 (UTC)

Oh yeah, I forgot to mention that it's probably not a coincidence that the Ionian mode maps to the 3-4-3-4... minor/major thirds step sequence because the Ionian mode half steps are also a 3-4-3-4... step sequence. Hopefully an expert on modular arithmetic can tie these two 3/4 ratios together. Bsenim (talk) 15:59, 23 December 2024 (UTC)

You need to read the section on Wikipedia:No original research again. —Wahoofive (talk) 21:35, 23 December 2024 (UTC)

Thanks, I thought the rule was against invented/coined/discovered ideas. I didn't know that there was a policy against mathematical facts that can be easily proved. Bsenim (talk) 21:47, 23 December 2024 (UTC)

Have you ever wondered why there isn't a page about why 1 + 1 = 2? -- Jack of Oz ^{[pleasantries]} 22:12, 23 December 2024 (UTC)

valid point Bsenim (talk) 22:13, 23 December 2024 (UTC)

• "I found the link..." means that this is transparently OR. But there is almost nothing here; you have simply taken the circle of fifths and filled in the notes of the major scale from one to five; obviously this automatically includes major and (natural) minors scales of all keys, most of the modes etc etc. Imaginatorium (talk) 04:21, 24 December 2024 (UTC)

Quinticircles and quarticircles

Quinticircles (quintine circles) use 12 clavisignatures between the fourflat (F minor/A-flat major [#0000CC/DHB]) and the sevensharp (A-sharp minor/C-sharp major [#CC6600/DHO]).

Quarticircles (quartine circles) use 12 clavisignatures between the foursharp (C-sharp minor/E major [#33FF33/LHG]) and the sevenflat (A-flat minor/C-flat major [#CC0066/DHP]).

The 12 Visibone melochromies (musical colors) are DHB (#0000CC), DHV (#6600CC), DHM (#CC00CC), DHP (#CC0066), DHR (#CC0000), DHO (#CC6600), LHY (#FFFF33), LHS (#99FF33), LHG (#33FF33), LHT (#33FF99), LHC (#33FFFF) and LHA (#3399FF).

In a catalogue of 46,656 songs 23,328 are quinticircular and 23,328 quarticircular. It starts in the "ZZW" (quarticircular baritonal fourflat) and ends in the "ZZV" (quinticircular mesosopranine onesharp).

200.155.118.244 (talk) 11:20, 25 January 2025 (UTC)

??? — Hucbald.SaintAmand (talk) 20:30, 29 May 2025 (UTC)

Commentary: 46,656 divided different songs by 12 different tonalities (0000CC/DHB, 6600CC/DHV, CC00CC/DHM, CC0066/DHP, CC0000/DHR, CC6600/DHO, FFFF33/LHY, 99FF33/LHS, 33FF33/LHG, 33FF99/LHT, 33FFFF/LHC and 3399FF/LHA) (Eolians or Jonians) are 3,888 different artists (bands, choirs, orchestras or singers). The ZZW (46,652) is a quarticircular tetrabemollic baritonal song and the ZZV (46,651) a quinticircular monodiesic mesosopranine.

Observation: Baritone (E♭♭2-B♯4), tenor (B♭♭2-F♯♯5), contralto (F♭3-C♯♯6) and mesosoprano (C♭4-G♯♯6).

2804:18:1079:5D62:1408:7EFF:FE3C:526B (talk) 21:59, 29 May 2025 (UTC)

Is this AI ??? To me, "a quarticircular tetrabemollic baritonal song" and "a quinticircular monodiesic mesosopranine" sound like jokes. — Hucbald.SaintAmand (talk) 06:25, 30 May 2025 (UTC)

Examples of quarticircular* clavisignatural* cantional* codes:

Baritone: ZX8, ZX9, ZXA, ZXB (sevenflat), ZXC, ZXD (fiveflat), ZXE, ZXF, ZXG, ZXH, ZXI (sixflat) and ZXJ; ZZW, ZZX, ZZY, ZZZ*, 0, 1*, 2, 3, 4, 5, 6* and 7;

Tenor: ZXK, ZXL, ZXM, ZXN*, ZXO, ZXP*, ZXQ, ZXR, ZXS, ZXT, ZXU* and ZXV; 8, 9, A, B*, C, D*, E, F, G, H, I* and J;

Contralto: ZXW, ZXX, ZXY, ZXZ*, ZY0, ZY1*, ZY2, ZY3, ZY4, ZY5, ZY6* and ZY7; K, L, M, N*, O, P*, P, Q, R, S, T, U* and V;

Mesosoprano: ZY8, ZY9, ZYA, ZYB*, ZYC, ZYD*, ZYE, ZYF, ZYG, ZYH, ZYI* and ZYJ; W, X, Y, Z*, 10, 11*, 12, 13, 14, 15, 16* and 17.

Examples of quinticircular* clavisignatural cantional codes:

Baritone: ZYK, ZYL, ZYM, ZYN (fivesharp), ZYO, ZYP (sevensharp), ZYQ, ZYR, ZYS, ZYT, ZYU (sixsharp) and ZYV; 18, 19, 1A, 1B*, 1C, 1D*, 1E, 1F, 1G, 1H, 1I* and 1J;

Tenor: ZYW, ZYX, ZYY, ZYZ*, ZZO, ZZ1*, ZZ2, ZZ3, ZZ4, ZZ5, ZZ6* and ZZ7; 1K, 1L, 1M, 1N*, 1O, 1P*, 1Q, 1R, 1S, 1T, 1U* and 1V;

Contralto: ZZ8, ZZ9, ZZA, ZZB*, ZZC, ZZD*, ZZE, ZZF, ZZG, ZZH, ZZI* and ZZJ; 1W, 1X, 1Y, 1Z*, 20, 21*, 22, 23, 24, 25, 26* and 27;

Mesosoprano: ZZK, ZZL, ZZM, ZZN*, ZZO, ZZP*, ZZQ, ZZR, ZZS, ZZT, ZZU* and ZZV; 28, 29, 2A, 2B*, 2C, 2D*, 2E, 2F, 2G, 2H, 2I* and 2J.

Clavisignatural semitonarchy* (legend above):

Fourflat (F minor/A-flat major): W, 8 and K;

Threesharp (F-sharp minor/A major): X, 9 and L;

Twoflat (G minor/B-flat major): Y, A and M;

Sevenflat (A-flat minor/C-flat major) [quarticircle] and fivesharp (G-sharp minor/B major) [quinticircle]: Z, B and N;

Zeroaccident or zeroalteration (A minor/C major): 0, C and O;

Fiveflat (B-flat minor/D-flat major) [quarticircle] and sevensharp (A-sharp minor/C-sharp major) [quinticircle]: 1, D and P;

Twosharp (B minor/D major): 2, E and Q;

Threeflat (C minor/E-flat major): 3, F and R;

Foursharp (C-sharp minor/E major): 4, G and S;

Oneflat (D minor/F major): 5, H and T;

Sixflat (E-flat minor/G-flat major) [quarticircle] and sixsharp (D-sharp minor/F-sharp major) [quinticircle]: 6, I and U;

Onesharp (E minor/G major): 7, J and V.

200.155.125.114 (talk) 10:26, 30 May 2025 (UTC)

I am confused. Is that nomenclature Lusitanian, or something else? I am familiar with sol-fa as used in many Romance languages, along with the letters (CGDAE and so on) used in my native English idiom. A link explaining the basis of your terminology would be useful here. cheers, Just plain Bill (talk) 16:46, 30 May 2025 (UTC)

The 15 mentioned names of the 15 clavisignatures (key signatures) above are organized semitonarchically (in semitonal order). The 36 mentioned unitarian alphanumeric digits (alphanumeric HTU system [hundred, ten and unit]) follow this mentioned tonal sequence above. I do not confounded the seven notes (C, D, E, F, G, A and B) with my commentary above. "Quarticircle" means "circle of fourths" and "quinticircle" "circle of fifths".

2804:18:107C:3F6F:DC18:ABFF:FE5B:A1BD (talk) 20:26, 30 May 2025 (UTC)

The whole "ZXK, ZXL, ZXM..." style is opaque to me. In what context is that a standard notation? Just plain Bill (talk) 20:56, 30 May 2025 (UTC)

What's the point of renaming "key signatures" as "clavisignatures", or "semitonal order" as "semitonachically", etc.? Are you trying to invent a new language? Ain't you satisfyed with English? – Hucbald.SaintAmand (talk) 21:13, 30 May 2025 (UTC)

Explication: I am a logatomatist (creator of words of the none) and a protologist (creator of first new words) because I am a verbophile (logophile). The mentioned alphanumeric tridigital codes I use for possibly appreciate until 3,888 different artists (1,944 quarticircular and 1,944 quinticircular [bands, choirs, orchestras or singers]) [46,656 divided different songs {23,328 quarticircular and 23,328 quinticircular} by 12 different tonalities]. "46,655" is "ZZZ" alphanumerically and "0" "0", exemplarly.

I am a passionated man about the 216 Visiosteic (Visibone Anglocentric Color Code - Visiosteum) colors, as 0000CC/DHB, 6600CC/DHV, CC00CC/DHM, CC0066/DHP, CC0000/DHR, CC6600/DHO, FFFF33/LHY, 99FF33/LHS, 33FF33/LHG, 33FF99/LHT, 33FFFF/LHC and 3399FF/LHA, exemplarly, who I consider they as melochromies (musical colors). These sequencial colors represent the notes geesharp/ayflat, geedoublesharp/ay/beedoubleflat, aysharp/beeflat, aydoublesharp/bee/ceeflat, beesharp/cee/deedoubleflat, ceesharp/deeflat, ceedoublesharp/dee/edoubleflat, deesharp/eflat, deedoublesharp/e/efflat, esharp/ef/geedoubleflat, efsharp/geeflat and efdoublesharp/gee/aydoubleflat. They also represent the 12 unitarian groups who are W-8-K, X-9-L, Y-A-M, Z-B-N, 0-C-O, 1-D-P, 2-E-Q, 3-F-R, 4-G-S, 5-H-T, 6-I-U and 7-J-V. The 36 digits are the 36 units in the HTU (hundred, ten and unit) system. Exemplarly, "ZZZ" is composite by the hundred "Z", by the ten "Z" and by the unit "Z". "Semitonarchy" means "semitonal order" in my second commentary.

Read my commentary carefully over my exemplar tridigital codes of each one of the four cited chorophonies (choral voices) in my second.

200.155.125.114 (talk) 01:13, 31 May 2025 (UTC)