## Consonant effects on F0 are multiplicative

[Warning: an unusually nerdy follow-up to an unusually nerdy post…] In the comments on yesterday's post "Consonant effects on F0 of following vowels", the question came up whether the effect of consonant voicing on vowel pitch is additive (e.g. plus or minus N Hz) or multiplicative (up or down by M percent). The fact that I calculated the effects in proportional terms indicates that I assumed, without checking, that the effects are multiplicative.

One easy way to check this assumption is to redo the calculations for female vs. male speakers independently, since we expect the overall F0 patterns of female speakers to be about 65-70% higher on average. So for this morning's Breakfast Experiment™ I did just that — it required changing just two characters in the scripts I wrote yesterday, so this was the easiest experiment ever…

The two plots are in fact amazingly similar in proportional terms:

In fact, at first I thought I had made a mistake and calculated the same thing twice. FWIW, here are the female proportions:

"b" 1.0259 1.0141 1.0088 1.0040 1.0001 0.9962 0.9933 0.9897 0.9874 0.9856
"d" 1.0289 1.0154 1.0083 1.0038 0.9997 0.9966 0.9932 0.9895 0.9872 0.9861
"g" 1.0293 1.0178 1.0118 1.0063 0.9997 0.9955 0.9912 0.9879 0.9856 0.9844
"p" 1.0524 1.0324 1.0185 1.0081 0.9990 0.9911 0.9850 0.9784 0.9747 0.9713
"t" 1.0584 1.0383 1.0229 1.0110 1.0001 0.9898 0.9818 0.9756 0.9699 0.9662
"k" 1.0654 1.0416 1.0231 1.0094 0.9975 0.9884 0.9810 0.9737 0.9693 0.9647
"m" 1.0151 1.0061 1.0033 1.0017 0.9997 0.9978 0.9960 0.9944 0.9932 0.9924
"n" 1.0175 1.0080 1.0045 1.0026 0.9996 0.9974 0.9954 0.9936 0.9911 0.9896


And the male proportions:

"b" 1.0233 1.0135 1.0043 1.0014 0.9984 0.9955 0.9929 0.9913 0.9909 0.9900
"d" 1.0223 1.0123 1.0048 1.0019 0.9977 0.9955 0.9935 0.9924 0.9913 0.9919
"g" 1.0211 1.0140 1.0083 1.0026 0.9989 0.9949 0.9928 0.9906 0.9905 0.9906
"p" 1.0537 1.0322 1.0131 1.0043 0.9977 0.9911 0.9854 0.9808 0.9777 0.9748
"t" 1.0585 1.0340 1.0178 1.0073 0.9983 0.9909 0.9846 0.9794 0.9756 0.9715
"k" 1.0638 1.0377 1.0177 1.0060 0.9978 0.9904 0.9839 0.9791 0.9753 0.9715
"m" 1.0153 1.0066 1.0018 1.0000 0.9988 0.9978 0.9960 0.9954 0.9945 0.9935
"n" 1.0142 1.0061 1.0005 0.9986 0.9979 0.9975 0.9971 0.9962 0.9956 0.9960


On an additive rather than ratio scale (i.e. plotted in Hz.), the patterns have the expected large difference:

The overall F/M ratio for this sample is 1.683.