Three types of progressive BPM speed-ups are stated as follows. They are arithmetic progression, geometric progression, harmonic progression.
Arithmetic BPM progression is defined as a change in tempo by a specific amount at intervals of a specific number of beats (does not need to be an integer). For example, deltaMAX by DM Ashura has arithmetic BPM progression. The tempo increases by 1 BPM per beat from 100 BPM to 573 BPM (WOW!). Also, WILD RUSH by FACTOR-X has arithmetic BPM progression because that song has tempo increasing by 20 BPM per 32 beats from 80 BPM to 180 BPM.
Geometric BPM progression is where the tempo multiplies by a specific multiplier (not necessarily a rational number) after a specific number of beats (not necessarily an integer). I currently do not know any songs with geometric progression, but I have an idea for a song with this type of progression. This song's tempo would double from 112.5 to 225 BPM after 12 bars (48 beats) and double again to 450 BPM (deltaMAX is still faster scrollwise) after another 12 bars. However, I would set the tempo to multiply by the 48th root of 2 (about 1.014545) each beat in the progression so that the tempo quadruples from 112.5 to 450 BPM in the 96 beats of the progression.
Harmonic BPM progression is easier to understand when considering the amount of time between beats. A 200 BPM song has 300 milliseconds between beats, and a 250 BPM song has 240 milliseconds between beats. The product of BPM and milliseconds is always 60,000. Therefore, dividing 60,000 by the BPM will result in milliseconds of the beat, and dividing 60,000 by milliseconds of beat equals the BPM. Harmonic progression is where the number of milliseconds between beats changes by a constant amount at intervals of a specific number of beats. For example, millisecond count decreasing from 300 to 100 by 25 milliseconds at 16-beat intervals is harmonic progression, and corresponds to BPM values of 200, 218.182, 240, 266.667, 300, 342.857, 400, 480, and 600.
If anyone finds a simfile with one of the above types of BPM progression, then post below.
Arithmetic BPM progression is defined as a change in tempo by a specific amount at intervals of a specific number of beats (does not need to be an integer). For example, deltaMAX by DM Ashura has arithmetic BPM progression. The tempo increases by 1 BPM per beat from 100 BPM to 573 BPM (WOW!). Also, WILD RUSH by FACTOR-X has arithmetic BPM progression because that song has tempo increasing by 20 BPM per 32 beats from 80 BPM to 180 BPM.
Geometric BPM progression is where the tempo multiplies by a specific multiplier (not necessarily a rational number) after a specific number of beats (not necessarily an integer). I currently do not know any songs with geometric progression, but I have an idea for a song with this type of progression. This song's tempo would double from 112.5 to 225 BPM after 12 bars (48 beats) and double again to 450 BPM (deltaMAX is still faster scrollwise) after another 12 bars. However, I would set the tempo to multiply by the 48th root of 2 (about 1.014545) each beat in the progression so that the tempo quadruples from 112.5 to 450 BPM in the 96 beats of the progression.
Harmonic BPM progression is easier to understand when considering the amount of time between beats. A 200 BPM song has 300 milliseconds between beats, and a 250 BPM song has 240 milliseconds between beats. The product of BPM and milliseconds is always 60,000. Therefore, dividing 60,000 by the BPM will result in milliseconds of the beat, and dividing 60,000 by milliseconds of beat equals the BPM. Harmonic progression is where the number of milliseconds between beats changes by a constant amount at intervals of a specific number of beats. For example, millisecond count decreasing from 300 to 100 by 25 milliseconds at 16-beat intervals is harmonic progression, and corresponds to BPM values of 200, 218.182, 240, 266.667, 300, 342.857, 400, 480, and 600.
If anyone finds a simfile with one of the above types of BPM progression, then post below.
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