Why do we start counting beats in a measure with "one" and not "zero"?

[Sesquitone]

Why is "first" position not "zeroth" position?

Same reason as the "first" fence-post is not the "zeroth" fence-post.

By the way, what about birthdays?

[Sesquitone]

In general, when you are counting things (beats, measures, the number of posts to this discussion), you start at one. When you are measuring something (how many miles from your home to your next gig, how much your horn weighs), you start at zero.

When I am slicing up half a banana onto my morning cereal, I can estimate the necessary slice thickness so that I can count off exactly one dozen (things) as I slice: "1, 2, 3, . . . , 12". However, I invariably end up with thirteen slices of banana in the bowl. Is this just a matter of "bad luck"?

[JohnL]

When I am slicing up half a banana onto my morning cereal, I can estimate the necessary slice thickness so that I can count off exactly one dozen (things) as I slice: "1, 2, 3, . . . , 12". However, I invariably end up with thirteen slices of banana in the bowl. Is this just a matter of "bad luck"?

If it happens every time? You've developed a process that consistently yields thirteen slices (i.e., twelve cuts). You can either modify the process to yield 12 slices or you can leave the process as is and adjust you desired result.

In my kitchen, the dog would get the thirteenth slice. He would also get several others. He's demanding.

[imsevimse]

To provide an easily confusing example, consider a half-note. One naturally assumes that because a half-note is 2 beats long, that it ends when I count to "two". If I start counting at zero, this is true:

"zero" (note starts)
"one"
"two" (note ends)

However, the standard convention I've always seen to start counting at one means that the half-note actually ends at "three". It's the common "fencepost" problem in counting. I think that a lot of people find this to be pretty confusing.

The problem is exacerbated by the standard terminology to refer to subunits of beats: when someone says "the 'and' of one" what they mean is the 2nd eighth note in the measure, not the 4nd eighth note in the measure.

"Why do we start counting beats in a measure with "one" and not "zero"?"

Because we are only counting beats. Every bar starts on the first beat, ONE and if we play before that first beat then we also play before the start of the bar. Think of the bass drum on first beat. That's a loud strong beat ONE. It's over and done after less than a split second. Everything after is > 1. When you hear the sound of an apple hit the ground after falling from a tree you note the sound and count ONE apple. You wait and when next apple falls you count TWO. Between the two apples there are no beats but the space can still be imagined and must be somewhere in between 1 and 2. That's the length if ONE. If apples do fall regularly you can expect when next apple falls and we get a steady beat. If you play an halfnote and start when the first apple hits the ground you should hold it until just before the third apple hits the ground. You could try that analogy with your students

/Tom

[AndrewMeronek]

I have the same problem with musical intervals. A "second" is at a distance of one note.

You're right!

I guess it amounts to our musical language and maybe at least in some cases it's become archaic and not the best way to describe what we're doing, but we continue to use that language anyway . . .

Speaking of intervals, here's another case where zero-based counting shouldn't be used:

Our "first" partial is pedal B-flat, after which the "second" is this b

This language makes perfect sense because it can be used as a direct translation to the math: fundamental pitch (frequency, in Hz) multiplied by the partial "number" gets the frequency of the desired partial.

However, to calculate the frequency of an interval the way that we actually use pitch in 12ET, we start at zero for n:

F*2^(n/12)

where F is the starting frequency and n is the interval distance. N=0 means you get back your starting frequency. For example, for A=440Hz, C# is:

440*2^(4/12)=554.365 Hz

and of course noting that multiplying by one is VERY different from having one in an exponent. Here, literally a "second" is setting n=1 . . .

[AtomicClock]

Here, literally a "second" is setting n=1 . . .

Well, that gives a minor second. A major second uses n=2 (which almost makes sense).

[AndrewMeronek]

Here, literally a "second" is setting n=1 . . .

Well, that gives a minor second. A major second uses n=2 (which almost makes sense).

I stand clarified!

[andym]

In English it is convenient that one through six are all single syllables. Start at zero and you’ve screwed it up.

[Sesquitone]

Why is "first" position not "zeroth" position?

Why is there no calendar year "zero" between 1 BCE and 1 CE?
.

[WGWTR180]

Why is "first" position not "zeroth" position?

Same reason as the "first" fence-post is not the "zeroth" fence-post.

By the way, what about birthdays?

Birthdays are simple too-just like a bar. I full bar is bar 1. A full year is year 1. LOL
This thread cracks me up.

[AndrewMeronek]

In English it is convenient that one through six are all single syllables. Start at zero and you’ve screwed it up.

There is the not-often-used but convenient "nil".

[AtomicClock]

Birthdays are simple too-just like a bar. I full bar is bar 1. A full year is year 1. LOL

Only for some cultures.

https://en.wikipedia.org/wiki/East_Asian_age_reckoning

it starts at 1 at birth and increases at each New Year

I believe South Korea only transitioned to the Western system a few years ago.

[WGWTR180]

Birthdays are simple too-just like a bar. I full bar is bar 1. A full year is year 1. LOL

Only for some cultures.

Well for the purpose of this thread I’ll go with what I said. Always exceptions, right?

[Nomsis]

Not having read the entire thread I just want to make a short comment. This question seems very made up to me. There is no sense in talking about the zeroth beat, there is just the first beat in a bar. If you count apples there is no zeroth apple either. Some things in life get counted when they start, like beats in a bar: you say one when beat one starts. Some things are counted when they are finished, eg. years in life or hours in a day because you want to signal that it is now fully completed. But when counting beats you rather want to mark the start of it. So everything makes sense to me.

[BGuttman]

Actually hours in the day (clock time) starts at zero, or midnight (12:00 AM for those on 12 hour clocks). More like measuring things than counting things.

[Nomsis]

But measuring is just counting with floating point precision So it doesn't matter if we see it as assigning that number 'at start' or 'end' of an unit if the unit is 'infinitesimal' (whatever precision that might mean in a given context). But I still would say measuring is more like counting "afterwards", because we want to know what we have already achieved.

For time, at least in Germany, we can say something like "the third hour has struck" so it means already three hours are 'full', have passed.

[WGWTR180]

But measuring is just counting with floating point precision So it doesn't matter if we see it as assigning that number 'at start' or 'end' of an unit if the unit is 'infinitesimal' (whatever precision that might mean in a given context). But I still would say measuring is more like counting "afterwards", because we want to know what we have already achieved.

For time, at least in Germany, we can say something like "the third hour has struck" so it means already three hours are 'full', have passed.

Agreed with everything you've said. There will be a day when one of the "zero" folks will start teaching band kids to start at zero. That should be fun too.

[robcat2075]

Why is there no calendar year "zero" between 1 BCE and 1 CE?

A part of the answer is that Roman math didn't use or need a zero to represent anything. Roman numerals didn't use "places" to denote powers of ten and so didn't need a zero to hold an unused place in a number.

I... X... C... M... all powers of 10 but no zero needed.

They also probably had few occasions to have a zero in any calculation they did. And so, counting with a zero was not a custom.

[harrisonreed]

Why is "first" position not "zeroth" position?

Why is there no calendar year "zero" between 1 BCE and 1 CE?
.

(I know that you're not arguing for a year zero and that you've posed a rhetorical question. But to answer it, because it answers the OP)

Because, like in music, you are counting the entire period of time as "one". And the start of that period of time as "one".

1CE is the entire first year of the common era.

1 BCE is the entire first year before the common era starts.

Beat 1 is the start of and the entire first beat that starts a measure. Not the completion of a beat starting at zero.

There was no entire year zero that separated the two, because the start of the common era was similar to the start of the first beat -- you tap your foot and you're inside that first period of time. Tap your foot again and you're inside the second period of time. Throw your calendar away and you're in the third period of time. You don't get that whole period only once it ends. You experience it while you're inside of it.

[tbdana]

I blows my mind that this has so many replies.

[WGWTR180]

I blows my mind that this has so many replies.

Well you have to admit this thread is much more entertaining than "what mouthpiece helps me hit low notes."

[GabrielRice]

Well you have to admit this thread is much more entertaining than "what mouthpiece helps me hit low notes."

Seriously, Bill, what mouthpiece helps me hit low notes?

Screenshot_20251002_102153_Dropbox.jpg

[Sesquitone]

Why is there no calendar year "zero" between 1 BCE and 1 CE?
.

(I know that you're not arguing for a year zero and that you've posed a rhetorical question. But to answer it, because it answers the OP)

Yes, thank you! Going back to counting slide positions starting at "one" at an extension of "zero", Jeffrey Clymer has a handy algorithm for Calculation of Trombone Slide Positions, which depend on the (average) temperature inside the instrument. Some harmonics (e.g. the fifth and tenth)—in theory—require a slide contraction relative to the reference positions based on the fundamental. So, for example, on a trombone in Bb, the fifth harmonic D4 requires a contraction of 12 mm. If position 1 is at an extension of 0 mm, the nominal position is then "0.86", according to Jeff's algorithm. [Note the (very slight) extension for the sixth harmonic and the (significant) contraction for the seventh.]


.

[WGWTR180]

Well you have to admit this thread is much more entertaining than "what mouthpiece helps me hit low notes."

Seriously, Bill, what mouthpiece helps me hit low notes?

Screenshot_20251002_102153_Dropbox.jpg

Hah!! I have some ideas but no one will agree with me. LOL

[AndrewMeronek]

It turns out, for the vast masses on this forum who love the number zero, there is a Wikipedia entry that is not insignificant:

https://en.wikipedia.org/wiki/0

For the European tradition, Fibonacci as a big reason why zero got adopted in Europe, and the Arabic numerals in general. It's probably had a much bigger impact than his more famous Fibonacci Sequence.

[robcat2075]

"The arguments in academics are so intense precisely because the stakes are so small," said Henry Kissinger.

[AndrewMeronek]

1CE is the entire first year of the common era.

1 BCE is the entire first year before the common era starts.

I suspect it's because the Gregorian Calendar was designed by the Catholic Church, and for whatever reason (I don't know) really didn't like zero despite Fibonacci's influence on that subject three and a half centuries earlier.

However, there is this modern calendar that does include year zero:

https://en.wikipedia.org/wiki/ISO_8601

[AtomicClock]

I'm sure Gregory and his monks were trying to keep their calendar as close to the Julian as possible. And that one definitely predates Fibonacci.

[robcat2075]

The Gregorian calendar doesn't happen until the 1500s. It was instituted to correct the drift of the calendar year vs. the solar year, but is not the reform that gave us AD and BC.

In principle, the Romans counted years from the founding of Rome but in practice they had a confusing manner of counting years by when some official had been in office. None of this seems to have been standardized across the empire.

This continued into Christian times and somehow it became popular in some regions to count years from the reign of Diocletian who had martyred many Christians. It was this odd custom that Dionysius Exiguus sought to replace with his Anno Domini scheme that retains the Julian calendar's system of months, days and leap years, but defines an end to Diocletian Era years and begins counting further years with a reckoning that 525 years had already passed since the birth of Jesus.

Apparently Exiguus never really specified a Year 1, he was only interested in numbering years yet to come. The placement of AD 1 was inferred by later writers and chroniclers.

Anno Domini seems to have never been officially imposed by the Church or any regime, it just slowly became customary over several centuries.

[harrisonreed]

1CE is the entire first year of the common era.

1 BCE is the entire first year before the common era starts.

I suspect it's because the Gregorian Calendar was designed by the Catholic Church, and for whatever reason (I don't know) really didn't like zero despite Fibonacci's influence on that subject three and a half centuries earlier.

However, there is this modern calendar that does include year zero:

https://en.wikipedia.org/wiki/ISO_8601

No. It really is because when you're in the first year of a new time period, you call that first year ... the first year. You don't call the first year the zeroth year. That doesn't make sense.

You asked why we count music the way we do, and it's been answered. Now this thread has turned into "wouldn't it be good if". No, it wouldn't be good if we can't the first beat the zeroth beat. It doesn't make sense to do it that way or change it at this point.

[AndrewMeronek]

You asked why we count music the way we do, and it's been answered. Now this thread has turned into "wouldn't it be good if". No, it wouldn't be good if we can't the first beat the zeroth beat. It doesn't make sense to do it that way or change it at this point.

My point is NOT to change to start counting at zero. My point is that our language makes it harder than it needs to be, and all the ways people here have noted different ways we count things proves it. My point is to not dismiss weird things like this because it's "too pedantic" and that we sometimes need to have tools to clarify what we're talking about.

Examples:

When I say "start on beat 3" I mean the beginning of beat 3.
When I say "end on beat 3" I mean end on the beginning of beat 3, which also means the end of beat 2.

et cetera.

[harrisonreed]

I think the language can get in the way, especially with measures and rehearsal letters. Beats should be a little less muddy though.

The beat is always counted on an infinitely small starting point. The metronome beat/click doesn't take up the entire space of "the beat", but it's what you count. So when you "take the note all the way to three", you take it all the way until the met clicks "three". "The end of two" is not as clear, and not as defined.

[timothy42b]

The beat is always counted on an infinitely small starting point. The metronome beat/click doesn't take up the entire space of "the beat",

The beat is infinitely small, right?

But the metronome click has a duration; while short, it is finite and hearable.

So now we have an additional problem: is it the start of the click, or the end?

(we are perilously close to Zeno's paradox)

[WGWTR180]

And when one has to think this hard about HOW to count it ceases to be music and more about math.

[harrisonreed]

The beat is always counted on an infinitely small starting point. The metronome beat/click doesn't take up the entire space of "the beat",

The beat is infinitely small, right?

But the metronome click has a duration; while short, it is finite and hearable.

So now we have an additional problem: is it the start of the click, or the end?

(we are perilously close to Zeno's paradox)

giphy (1).gif

[WGWTR180]

Last night rehearsing Tchaikovsky Symphony #4 the principal trumpet player requested that the brass section cut a certain chord off on beat 2. Somehow a major debate did not ensue as to whether he meant beat 2 or the end of beat 1.

[elmsandr]

Last night rehearsing Tchaikovsky Symphony #4 the principal trumpet player requested that the brass section cut a certain chord off on beat 2. Somehow a major debate did not ensue as to whether he meant beat 2 or the end of beat 1.

And all that matters is that the entire low brass was behind in the finale; regardless of where they were in relation to the actual beat and tempo. (According to every conductor… I think this is actually printed in the score)

Cheers,
Andy

[Nomsis]

If you want to be precise you should note that when you start at beat/click one and want to hold a half note for full value you should not end it on beat/click three but right before. So on click three you should already have ended the note. So not quite sure if "ending on beat three" is even correct language. It is like open and closed intervals in maths. Although it is just one infinitesimal difference and thus strictly speaking the exact same length it's more of a conceptual importance.
Considering that we do not play with infinite mathematical precision anyways, it maybe doesn't matter to much. I would still not really use the language of "ending on beat three", because that would mean on exactly click three there is still some note. And we should definitely be prepared for the next note starting on click three instead to start it in time.

I think rhythm is more about when a note starts and feeling the "pulse" and though not completely unimportant I think we should worry less about when the note stops compared to when the note starts. Percussion instruments which are undoubtedly the most rhythmic instruments of all have usually a very defined start to a note but a much more undefined end. Many instruments are like that and although wind instruments can certainly end a note pretty precisely the start is still much more defined and of greater importance to the rhythm in my opinion.

Saying all this just to say that I think a language centered around the start of the beat is quite right in my opinion

In certain contexts surely it can be helpful to use language considering the end of a beat/bar. Eg given you might say to your student: The accidentals are valid until the end of the bar.

[robcat2075]

A true instant of sound is impossible since any sound wave form must have a beginning and end... a departure from zero pressure and a final return to zero.

However, our mind can understand it to point to an instant.

[AndrewMeronek]

If you want to be precise you should note that when you start at beat/click one and want to hold a half note for full value you should not end it on beat/click three but right before. So on click three you should already have ended the note. So not quite sure if "ending on beat three" is even correct language. It is like open and closed intervals in maths. Although it is just one infinitesimal difference and thus strictly speaking the exact same length it's more of a conceptual importance.

I think there is performance practice to consider here, and adjusting to the acoustics of specific performing environments. For example, if I'm in a reverberant church performing Gabrieli, yes it can definitely be appropriate to kind of "pre-shape" the ends of notes before the next beat arrives. But if I'm playing funk in a jazz club, absolutely the better decision is to be crisp and clear and end notes right where the next beat starts.

Thus: there also appears to be historical and practical drift on what all this means, which also reinforces how it is important to know when to clarify things.

[WGWTR180]

Last night rehearsing Tchaikovsky Symphony #4 the principal trumpet player requested that the brass section cut a certain chord off on beat 2. Somehow a major debate did not ensue as to whether he meant beat 2 or the end of beat 1.

And all that matters is that the entire low brass was behind in the finale; regardless of where they were in relation to the actual beat and tempo. (According to every conductor… I think this is actually printed in the score)

Cheers,
Andy

Not this low brass section.

[BGuttman]

Note that as brass players (and especially trombone players) we can't really play a full length note up to the next beat. We have to allow time to adjust the slide and set the embouchure for the next note. This can be a remarkably short time for really good players, but many of us need more time. Is is usually important to start the note exactly on the beat (some Big Bands used to start a little early or a little late, but the whole band did this).

[tbdana]

I kind of think we should look at the number of measures in a piece and count backwards. Like, if a piece has 430 measures, you start counting the first bar as -430, then go to -429, etc., and when we reach 0 the piece ends.

This is The Way.

[timothy42b]

I kind of think we should look at the number of measures in a piece and count backwards. Like, if a piece has 430 measures, you start counting the first bar as -430, then go to -429, etc., and when we reach 0 the piece ends.

This is The Way.

What if the first measure, last measure, either or both, is only a partial measure? Start at 429.75?

[AndrewMeronek]

I kind of think we should look at the number of measures in a piece and count backwards. Like, if a piece has 430 measures, you start counting the first bar as -430, then go to -429, etc., and when we reach 0 the piece ends.

This is The Way.

Got an arrangement of Countdown that does this?

[VJOFan]

I had a music history prof who during a lecture one day mused about how music was the only art form that deliberately marks off time. He was sadly battling a terminal illness at the time so was perhaps more focussed than most on the finite nature of things.

I don’t think I could stomach always being reminded by a counting system that at the end of a piece there is just nothing….

[ed. Note. I know the above discussion is lighthearted. I just forgot the wink emoji]

[BGuttman]

I had a music history prof who during a lecture one day mused about how music was the only art form that deliberately marks off time. He was sadly battling a terminal illness at the time so was perhaps more focussed than most on the finite nature of things.

...

I guess he didn't consider Dance an art form...

[Posaunus]

Isn't it interesting that in many (most?) countries outside the United States, multi-story buildings have a "zero" level (ground floor); you have to climb up to the "first" floor. Counting from zero is alive and well!

[tbdana]

I had a music history prof who during a lecture one day mused about how music was the only art form that deliberately marks off time. He was sadly battling a terminal illness at the time so was perhaps more focussed than most on the finite nature of things.

...

I guess he didn't consider Dance an art form...

Or plays. Or movies.

[tbdana]

Isn't it interesting that in many (most?) countries outside the United States, multi-story buildings have a "zero" level (ground floor); you have to climb up to the "first" floor. Counting from zero is alive and well!

Well, ya know, those backward countries don't even use the imperial measuring system, so...