# Time Frequency Function

03 Feb 2016When considering how the frequency changes in a given time domain

we often judge by looking at (or hopefully calculating) the

frequency change but there are times that utterances are being

prolonged (mostly duration is a function of tone i.e. our tone

will alter duration; With that being said most of my calculations

do not consider duration or time as an independent variable);

This increase in producing the utterance does have a pragmatic

effect and thus it is worthwhile to consider it in transcribing

prosody.

`ToBI`

is a system of transcribing prosodic features of speech.

ToBI is easy to learn, easy to share, and easy to use. these 3

features have made ToBI a widely used system for transcribing

prosody. But ToBI has some downfalls too. Since it is based on

the **phonological level** of the speech it does not contain

phonetic features of speech. I have some ideas to implement

phonetic features of prosody in ToBI and on the top of that

adding frequency change in the ToBI system.

I, therefore, decided to design a formula based on frequency time

change. The formula is:

Z is the `time frequency function`

on the scale from
`1.0 to 4.0`

where Z from `1.0 to 2.0`

is flagged as low
`2.0 to 3.0`

flagged as medium and lastly `3.0 to 4.0`

flagged as
high. F is the frequency in Hertz and it is scaled from
`75 to 300`

. T is short for Time on FFT frequency display. Both F and
T are indicators of the change in the pitch track and hence they
are calculated as: `F2 - F1`

and `T2 - T1`

. T is always
positive bud F can sometimes be negative so I used Absolute value
in the formula to avoid F being zero.

I have written a Python code that plots the distribution of the

outputs across Z axis. X axis is T and Y axis is F.

The Python code is:

The proposed symbols for transcribing this scale in ToBI is using

commas, semicolons, and colons.

** a)** because it’s more intuitive

**b)** because it is easily read.

`[comma]`

for low change, `[semicolon]`

for medium change,

and `[colon]`

for high change. examples are:

**(a)** L+H:% (Indicaating high frequency change in the given

time domain)

**(b)** L+H;* (Indicating medium frequency change in the given

time domain)

**(c)** H,* (Indicating low frequency change in the given time

domain)

Consider the following example:

This is a recording from Kurmanji Kurdish.

The values for F and T are:

Calculating the above data we will get:

`2.80`

in our Time Frequency Function (TFF) is considered

`Medium`

change so we transcribe it as: `H+L;%`

Edit `Feb 16`

: On the second thought I observed that there are numerous problems with the ToBI and the AM so I’m thinking of changing the framework. I’ll post later if I had another idea.