Thread by @silvpscl793s

Thread Remastered I: Taylor Swift's vocal mini analysis from Physics (Waves & Oscillations) and Music (General Vocal) perspective, Extended Version (an educational thread) #TaylorSwift Part 1

For anyone who's looking at the original thread of this version, the link below will provide you, with the original thread, which's the very first thread I created on Twitter and always intended to keep it around. Therefore, enjoy both versions!

https://twitter.com/silvpscl793s/status/1347522523198492675?s=20

What's new for this version?
- Additional on Theoretical Physics materials on Waves & Oscillations, Taylor's Vocal, her method to combined her vocals, accolades for her
- Polished & restructured sentences in the thread
- More Pictures & GIFs
- Sources Quoted Extended

Disclaimer: For this remastered version of my first thread here, there will be more additional "scientific" on both perspectives here, therefore, please reminds me if there's a lacking that I should add in the future. Sources always quoted on the last page. Enjoy!

I. Introductory
Taylor has been in the music industry for 15 years, and music has a close connection to Physics. The study of this is known as Musical acoustics. Physics material that has a relation with music is Waves & Oscillations. Here's a brief explanation of them:

II. Theoretical Physics Explanation:
In Physics, Sound is represented in the Waves diagram. Inside the Diagram below, there are some legends that are notable in Waves, such as Amplitude, Wavelength, & more. In scientific disciplinary, it has notations for each legend below:

- Wavelength (λ) [distance between crests/troughs],
- Amplitude (A) [displacement of peak wave & flat wave],
- Frequency (Hz) [how many occurrences], and period (sec.) [time to take to happen]
- One complete cycle: Wavelength goes both crests & troughs

One complete cycle in waves can be defined when the waves go through two points, at the same position phase. This is the exact diagram with Sine Waves in Trigonometry
The basic equation of Waves in Physics: "v = λ x f", can be inversed
*Additional: y = sin [f x 360 x t]

Because it represented a sine wave for the transversal wave, it will have its own advanced equation for it (called: Sinusoidal Wave), noted as:
V(t) = Vmax sin (wt + q)
Vmax = Maximum of Amplitude Tension
W = Angular velocity/sec.
Wt = Sinusodial Wave Argumen
q = angle phase

For the breakdown of each component equation:
Frequency: f = 1/T (f= frequency, Hz | T = period, sec.) Lambda: λ = c/f (λ = length of waves in meter, c = constant of speed of light at 3000 km/s, f = frequency, Hz)
As well: vλ = c
The reason why Light is both Wave & Particle

A logic in Physics and Music, the sound depends on frequency and amplitude that resounds during its performance. It's inversely proportional
Higher freq. = higher pitcher, lower freq. = lower pitcher | Higher amps. = louder, lower amps. = quieter

And brief for the longitudinal waves, where the medium of waves displacement stays the same in the vibration mode, unlike transverse one. It has the equation of:
y (x,t) = y0 cos (w (t - x/c)
In longitudinal, it has compression and rarefaction.

Breakdown of each element in the equation:
y = traveling soundwave point displacement
x = traveled from wave source distance in the point it has move
y0 = oscillations amplitude
w = wave angular frequency
t = time elapsed
c = wave speed

The simple way to understand waves as well oscillations, where defined as "regular variation in magnitude or position around a central point.", this pendulum gif could give you a picture of how it does:

III. Taylor Swift Vocal Analysis:
Taylor Swift's voice type is Light-Lyric Soprano, though she could hit Mezzo Tessitura), with vocal types of 2 Octaves & 4 notes (C#3 - E5 - G/G#5), with the longest notes she registered at 17 seconds. A great thing for a non-vocalist like her.

In the frequency range of general Soprano (units in Hertz/Hz), Soprano sits between 261 Hz to 880 Hz in Choral, which Taylor and most female singers range sits. Meanwhile, Operatic Music could be clocked higher, 1046 Hz and beyond. In the Physics Music view, that's very high.

This is because, in a Female's anatomy of the vocal cord, it has a larger gap and a female has a higher estrogen hormone (C18H24O2) to produce, resulting in bigger vocal cords than a male one, hence it has a higher voice. I have a Biology thread on Taylor, stay tuned!

IV. Extended Analysis:
To note, however, Taylor isn't a vocalist, as her singing is decent but not great. This's the reason sometimes why Taylor dragged by haters. In scientific notations, let's assume the standard is A4 = 440 Hz, & Taylor's set at E4 for benchmarks (Piano).

The calculation of the Taylor's vocal range gap results:
Q1 (low.) = 138.591 Hz, Q3 (high.) = 830.609 Hz, Q2 (avg) = 329.628 Hz [All in SI unit]
Q3-Q2 = (830.609 - 329.628) Hz = 500.981 Hz
Q2-Q1 = (329.628 - 138.591) Hz = 191.037 Hz
Q3-Q1 = (830.609 - 138.591) Hz = 692.018 Hz

From what we gathered above, that Taylor's vocal range results in Piano conversion, which has a gap from the high. to low. approximately 692.018 Hz, which's decent, but for some people, it's less than expected. Let's see the gap for The Diva, Mariah's Carey.

The calculation for Mariah's vocal range gap:
Mariah highest (B7 as Q3) = 3.951,07 Hz
Mariah lowest (F2 as Q1) = 87,3071 Hz
Average (D5 as Q2) = 587.330 Hz [All in SI Unit]
Q3-Q2 = (3.951,07 - 587.330) Hz = 3.363,74 Hz
Q2-Q1 = (587,330 - 87,3071) Hz = 500,0229 Hz
[cont. below]

Q3-Q1 = (3.951,07 - 87,3071) Hz = 3.863,7629 Hz
That's an enormous number of Hertz math.

Difference between Taylor & Mariah
3.863,7629 - 692,018 Hz = 3.171,7449 Hz different!

No wonder some haters sometimes like to tease Taylor in her singing ability, just look at the numbers!

Though on some occasions, Taylor could sing with quite high notes, as seen in IDWLF with Zayn, IKWYT-OOTW live version, DWOHT, State of Grace, Don't Blame Me, RFI? etc. You name it. Mostly on reputation era, but also another album or live tour, like 2019 AMAs w/ Blank Space.

Taylor Swift's vocal range is decent as we pointed out. However, it's lower compared to Mariah, Ariana, or diva peers, which could score 5 octaves [Mariah] or 4 [Ariana, Beyoncé]. Here you can see the chart below, the note of singers could hit, and Taylor is one of the lowest.