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This is a very beginner question as I am a complete beginner. How is change in speed during a song notated in standard notation? Is it done by changing the time signature for each measure that has a different speed? What if one measure has multiple different speeds? Do you have to write the tempo above each measure that has a different speed? Thank you in advance for your help. (If anyone knows a free site etc. where I can learn about writing standard notation, that would be greatly appreciated.)

When you're talking about speed, it's important to keep three concepts separated:

1. the underlying pulse of the music. I.e., how much time passes between each quarter note, or in layman's terms, when you're tapping your foot to the music, how fast are you tapping? Changes in the pulse are notated as "acc." for "accelerando" (get faster) and "rit." for "ritardando" (get slower) when it's a gradual change. For a sudden change, you write the new speed above the measure where the tempo changes (either in beats per minute, or in one of the vague tempo terms like "moderato" or "presto").


2. the values of the notes you're playing. If you're playing in 4/4, you can play one whole note per bar, or two half notes, or four quarters, or eight eighths... obviously, when you switch from a melody consisting of half and quarter notes to one of sixteenths, you have to play faster, even though the tempo doesn't change. You just have to write the appropriate note values. Likewise, unless you are in the realm of avantgarde music, you don't have more than one tempo simultaneously. You have one tempo, and if different instruments play shorter or longer notes, you just write the appropriate note values to match the tempo.


3. the time signature - roughly speaking, how many beats in your given tempo do you play before the rhythmic structure repeats. This is not really related to speed. You could have a 3/4 time signature at 120 bpm, or a 4/4 at 120 bpm, and you'd play at exactly the same speed as long as the note values are the same. (It is common to write very fast-paced music as 2/2 rather than 4/4, but that's more a matter of conveying the feel than a mathematical necessity.)

A great beginner's question!

Several ways, and not usually by a change of tempo (bpm). Generally, each bar (measure) is the same length timewise, so faster notes will make it feel quicker; slower (longer) notes make it feel like it's slowed down.

There are signs which indicate speed change - accelerando, ritardando, rallentando being some. It's possible to go from, say, 4/4 to 3/4 making the latter shorter, but that's not particularly to make the music speed up.

How is speed change notated?

Usually fairly imprecisely. The most precise way to notate it is with a metronome marking. If the change in speed is to be sudden, this is precise. However, if the speed is to change over a period of time, there is no way to be precise about it aside from using a word such as accelerando, rallentando, ritardando, or the like. These indications give no clue about the rate of change of the speed.

They are even ambiguous as to whether you reach the target speed smoothly, or just approach it or even bypass it and then adopt it suddenly. For example, consider the following:

X:1

K:C

M:4/4

L:1/4

Q:1/4=80

cBAG|cBAG|[Q:"accelerando"]cBAG|cBAG|[Q:1/4=120]cBAG|cBAG|

The eight notes in measures 1 and 2 should each last for 0.75 seconds. The last eight should each last for 0.5 seconds. But there's nothing that precisely specifies the duration of any note in measures 3 and 4. One can conclude that each note should have a shorter duration than the one preceding it, but even that is a matter of interpretation. For example, the last note in measure 4 could be shorter than the first note in measure 5, or it could be maybe 0.7 seconds long, so the tempo would increase over measures 3 and 4 but still jump up at the beginning of measure 5.

Sometimes composers do "write out" a rallentando explicitly, with varying degrees of complexity. It's hardly unusual to see something like this:

X:2

K:C

M:4/4

L:1/4

CCGG|AAG2|F2F2|E2E2|D4|D4|C8|]

A modern classical composer might do something like this:

X:3

K:C

M:4/4

L:1/8

Q:1/4=80

C2C2G2G2|A2A2G4|[M:7/8]F3F4|[M:5/8](E3E2)|[M:3/4]E6|[M:4/4]D8|[M:8/4]D16|(C16|C16)|]

Do you have to write the tempo above each measure that has a different speed?

Yes

What if one measure has multiple different speeds?

Divide the measure into two, each with different time signature and tempo. Example) if 4/4 measure has the first quarter note with tempo 112 and the remaining 3 quarter notes with tempo 70, then have the following two measures.

1. first measure with time signature 1/4 and tempo 112,


2. second measure with time signature 3/4 and tempo 70,

where I can learn about writing standard notation

try here and here