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What is a "whole tone duodecime"? Doesn't make sense at all in music theory, but I think you might mean something else?

[EDIT]: Oops, my fault, got it…



...but I seriously recommend that you change your definition. "The whole tone" is, and will remain, 1 full step = one half step = two semi-tones in all musically related discussion. It is well established, and not easily changed. Thus, there will not be such a thing as "a whole tone 5th" or "a whole tone 12th" in English. [/EDIT]

I've often seen the term "whole tone": listen at a note/interval as a whole tone, opposed to listen at specific or near coincident partials. When we voice we speak also of the "tone" of the piano as being the sum of all partials of a given note.

We are talking as tuners and I believe the term describes fine what it means.

What do you think about: F-A# P4th, G#-C M3, for example used by most of the E.T. piano tuners, instead of the correct F-Bb P4th and Ab-C M3?

Raphael,
What do you mean?

Musically speaking a fourth is an interval between a note and the 4th note away.

example: C-D-E-F so C-F is a fourth.

counter example: F-G-A-A# is not a fourth it is a 3rd (augmented)
A# count as an alteration of A.

example: F-G-A-Bb so here F-Bb is a fourth.

In E.T. sharps and flats are enharmonics. So A# is the same note (same frequence) than Bb.

In just intonation for example sharps and flats are totally different from each other. So A# has not the same frequence than Bb, and there is indeed a difference between an augmented third and a perfect 4th.

So musically speaking it is incorrect to name the F-A# interval as a fourth.

I have no problem with the latter, as long as we speak about the notes of the piano and do not move into harmony.

And I have no problem with "whole tone" in itself either, I just think that there could be a better expression. To say something like "a whole tone fifth" is to music theory what "a car with 4 1/2 wheels" would be to a mechanic. Impossible. Or then, if you really would go to lengths, it would be an augmented fifth, ie C-G#.

If piano tuning will have to deal with music and not become an abstract art, there shouldn't be vague terms. In fact, i think that might be the reason for the different terms harmonic, overtones and partials.

There is no full tone scale, so why not speak about "full tone" or "complete tone" or something like that? Just a thought.

... and in this context, in a sentence, there is no ambiguity. A "whole tone 5th" is another matter.

In Kees example, I would tune the 4ths and 5ths to sound right. The difference would probably be unnoticeable in the 3rds and 6ths. Intervals that are tempered 2 cents are 7 times more sensitive than those tempered 14 cents. After setting the temperament, I usually run through the chromatic major chords. If one stands out it is always because of a fourth or fifth, never a 3rd or 6th even if they are not quite progressive.

Kees: Love the graphs! Notice that the fifths are always narrower than the 3:1 twelfths (duh!). How tall is your Heintzmann?

Pat: Or "Entire Tone" or "Whole Sound" but we know what was meant.

Mr. Stopper: Thanks! I had thought about the 6:2 twelfths in the bass lately when I noticed that my tunings had produced octaves between 6:3 and 8:4. But I am including the note an octave above the lower note in addition to the 12th, so the “Entire Tone” that I am listening to is different.

Talking of "pure tone" Someone noticed that the beat of an octave, a third, etc, is always heard at the upper note level ?
One have to force the ear to discriminate beats at a partial match level

Yes, I have had a hard time because I've been listening to far too many things. Focusing on just what you're supposed to took me a lot of time.

Isaac, at least one exception would be the 4th that beats with the lower note, but then again that is pretty easily heard because it is so high in relation to the fundamental!

I'd say it depends on what kind of music you are talking about, and what theoretical framework you are working with. What you say is correct if you speak about the common practice period, and also correct for a lot of music from the 20th century onwards. But I'd not say *musically speaking*, because there are LOTS of different possibilities (both old, and recent).

You can have a perfectly good theoretical system saying F-A# and F-Bb are be the same interval. You can work just fine without considering "archaic" notational conventions. That difference between thirds and fourths made a lot of sense for non-fixed pitch instruments that were playing notes derived from exact ratios, and it made a lot of sense in a tonal system.

But we can write music and not have anything to do with those old ways. Most of that notational system is still used just because everybody knows it, and because it's kind of useful. But the grammar developed with that system is long gone, unless we are playing "retro" music, in which case F-A# is, indeed, a very nasty interval.

Isn't just intonation used anymore? Even among singers?

Is it the ONLY way to build a musical scale or construct intervals? Even in electronic music?

I mean, as long as just intonation will be used these are not "archaic" notations, but useful and precise ways of naming different notes.

Every time I read about tuning the "fourth" FA# I cringe.
But I know what they mean

Kees

When I played in a recorder consort the way to tune (say) E6 to C6 is to listen to the difference tone and make sure it is exactly C4.

Kees

My point exactly: it depends on what kind of music you are talking about, and what theoretical framework you work with.

For a keyboard instrument with 12 notes to the octave it is acceptable.

For other contexts it may be wrong.

It CAN be acceptable, but that is not always the case, for an instrument with 12 notes per octave.

The keyboard can be the same, and it can be tuned in the same way, but the logic behind the music could be completely different for two different works to be played on that very same keyboard instrument, one after the other. In such case, it is not about tuning, but about "spelling" and "grammar."

Therefore, it can be musically correct to say "F-A# and F-Bb are both fourths" for one work, and musically incorrect for another.

I guess you are right.

It is not a question of tuning, temperament, keyboard design, number of keys in an octave, instrument, voice intonation or whatever. It is a question of spelling and grammar. I mean musical rules.

Musically speaking, all of these intervals are thirds, even if they range from 2 to 6 semitones:

F-Ab, F-A, F-A#, Fb-Ab, Fb-A, Fb-A#, F#-Ab, F#-A, F#-A#

And all of these are fourths:

F-Bb, F-B, F-B#, Fb-Bb, Fb-B, Fb-B#, F#-Bb, F#-B, F#-B#

(Double flats and double sharps may be added to the above lists).


But then, in which case can it be musically correct to say "F-A# fourth"? It goes against rules.

Perhaps one could refer to Mr Stopper's "whole tone" as "complete tone envelope".

The interesting thing, for me, is that aiming for the best complete tone envelope is how I've always tried to tune intuitively - until the day I stumbled across PianoWorld and read about partials, inharmonicity, octaves types, stretch, etc. etc.

In a (rather unsettling!) way, I feel as though I've come full circle - or perhaps "full spiral".