*2After a jury trial, the defendant, Cirilo Garcia, was convicted of dissemination of matter harmful to a minor, G. L. c. 272, § 28 ; rape of a child aggravated by age difference, G. L. c. 265, § 23A (a ) ;1 incest, G. L. c. 272, § 17 ; and witness intimidation, G. L. c. 268, § 13B, all arising from a series of assaults against his biological daughter when she was between the ages *344of seven and eleven.2 On appeal he contends that (1) the conviction of dissemination of matter harmful to a minor must be vacated, because of a statutory exception applicable to parents and legal guardians, (2) his conviction on one indictment for rape must be vacated, because the indictment was improperly amended at trial, (3) the conviction of incest must be vacated because the jury instructions prejudicially enlarged the indictment for that charge, and (4) the evidence of witness intimidation was insufficient to support his conviction, because the threats supporting the conviction occurred before any criminal investigation began. We discern no merit in the defendant's challenges to his convictions of incest and witness intimidation, but we conclude that we are constrained to reverse the challenged counts of rape and dissemination of matter harmful to a minor.
Background. The defendant is the victim's father. The defendant moved to the United States from Guatemala around the time *3of the victim's birth in 2000. His wife, the victim's mother, followed him to the United States in 2003, leaving their two children with their maternal grandmother in Guatemala. In 2006, when the victim was five or six years old, she moved to New Bedford to live with her parents and siblings3 and met the defendant for the first time. The defendant and his wife worked different shifts, such that the defendant was home alone with the children in the morning and sent them off to school. However, the victim missed "a lot" of school because her father kept her home. When the victim was seven years old, the defendant began raping her.
In all, from the time the victim was seven until she was eleven, the defendant raped her forty or more times. As the defendant raped the victim, he would talk about the victim's aunt's recent marriage and sex life despite the victim's protests that she was "too little to hear about it." The defendant also showed the victim naked men "putting their private stuff on each other" on the Playboy television channel as he raped her. The defendant threatened to kill the victim, her mother, and her family if she ever told anyone about the abuse. He told the victim that even if he went to jail and got deported he would pay someone to kill her and her family.
On July 8, 2012, the defendant raped the victim vaginally, orally, and anally. This was the last time the defendant raped her; she disclosed the abuse to her mother on that date. She disclosed the abuse because her parents were fighting, the children had to intervene, and the victim thought her "dad was actually going to kill" her mother. The victim went into her mother's bedroom, locked the door, and hid in the closet with her mother as she described the abuse. After the disclosure, the victim spoke to the police and went to the hospital. A nurse there took vaginal and anal-rectal swabs. The defendant's deoxyribonucleic acid (DNA) matched the major profile of the sperm found on both swabs. A supervisor in the State police forensics laboratory testified that the defendant's DNA profile is "very rare."4
*345Discussion. 1. Dissemination of matter harmful to a minor. The defendant contends, and the Commonwealth concedes, that his *4conviction of dissemination of matter harmful to a minor cannot stand because the statute provides a defense where "the defendant was in a parental or guardianship relationship with the minor." G. L. c. 272, § 28. See Commonwealth v. Poitras, 55 Mass. App. Ct. 691, 692 n.1, 774 N.E.2d 647 (2002). Our independent review of the record, see Commonwealth v. McClary, 33 Mass. App. Ct. 678, 686 n.6, 604 N.E.2d 706 (1992), cert. denied, 510 U.S. 975, 114 S.Ct. 466, 126 L.Ed.2d 418 (1993), demonstrates that the defendant was in a parental relationship with the victim,5 and he is entitled to the parental defense provided by the statute. Accordingly, his conviction of dissemination of matter harmful to a minor under G. L. c. 272, § 28, must be reversed.
2. Rape of a child aggravated by age difference. The defendant contends that his conviction of rape of a child aggravated by age difference on indictment no. 2012-742-1 (indictment no. 1) must be reversed because the Commonwealth's proof, the judge's instructions, and the verdict slip constructively amended the indictment. The defendant argues that the judge's instructions "enlarge[d]" the indictment, "replaced" its allegation, and "impermissibly permit[ted] a material change" in the grand jury's work, thereby violating his due process rights by "adding an additional ground of criminal liability for which the defendant could be found guilty."
Crimes must be "proved as charged," so as to "protect[ ] the grand jury's role in the criminal process and ensure[ ] that the defendant has proper notice of the charges against him." Commonwealth v. Hobbs, 385 Mass. 863, 869, 434 N.E.2d 633 (1982). See art. 12 of the Massachusetts Declaration of Rights. "A constructive amendment to an indictment occurs when either the government (usually during its presentation of evidence and/or its argument), the court (usually through its instructions to the jury), or both, broadens the possible bases for conviction beyond those presented by the grand jury" (citation omitted). Commonwealth v. Bynoe, 49 Mass. App. Ct. 687, 691-692, 732 N.E.2d 340 (2000). "[A]n amendment may not broaden the charges against a defendant." Commonwealth v. Ruidiaz, 65 Mass. App. Ct. 462, 464, 841 N.E.2d 720 (2006). Indictments may be amended as to form but not as to substance. See Mass. R. Crim. P. 4 (d), 378 Mass. 849 (1979). An amendment is substantive where "an acquittal on the original charge would not bar prosecution *5on the amended charge." Bynoe, 49 Mass. App. Ct. at 691, 732 N.E.2d 340.
Here, indictment no. 1 charged the defendant with rape of a child aggravated by age difference under G. L. c. 265, § 23A (a ).6 The text of the indictment alleged that the defendant "did have sexual intercourse" with the victim, a "child under sixteen years of age when there existed more than a five-year age difference" between them. At the commencement of trial, the Commonwealth made clear that it *346intended to rely at trial on the oral or anal rape of the victim, and the Commonwealth consistently did so during the course of the trial. Consistent with that approach, the judge's instructions and the verdict slip for that indictment referenced "unnatural" or "oral" sexual intercourse.
"Sexual intercourse," as used in the statute, means "the traditional common law notion of rape, the penetration of the female sex organ by the male sex organ, with or without emission." Commonwealth v. Gallant, 373 Mass. 577, 584, 369 N.E.2d 707 (1977). "Similarly, the definition of 'unnatural sexual intercourse' must be taken to include oral and anal intercourse, including fellatio, cunnilingus, and other intrusions of a part of a person's body or other object into the genital or anal opening of another person's body." Id.7 General Laws c. 265, § 23A (a ), clearly prohibits both sexual intercourse (natural) and unnatural sexual intercourse with children.8 However, the Commonwealth chose to charge the defendant, in indictment no. 1, with the former, and the indictment made *6no mention of the latter.9 At trial, the evidence, the jury instructions, and the verdict slip on that indictment all concerned the alleged oral rape of the victim, an act of unnatural sexual intercourse.
"Although the trial court did not permit a formal amendment of the indictment, the effect of what it did was the same." Stirone v. United States, 361 U.S. 212, 217, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960). This constructive amendment was one of substance.10 Accordingly, the defendant's conviction of rape of a child aggravated by age difference on indictment no. 1 must be reversed. See Commonwealth v. Mayotte, 475 Mass. 254, 265-266, 56 N.E.3d 756 (2016) (vacating conviction where indictment charged one statutory theory of crime while testimony and jury instructions expanded indictment by introducing different theory); Commonwealth v. Barbosa, 421 Mass. 547, 554, 658 N.E.2d 966 (1995) ("Where there is a substantial risk that the defendant was convicted of a crime for which he was not indicted by a *347grand jury, we cannot apply a harmless error standard.... Instead, we must reverse the convictions").
3. Incest. The defendant similarly contends that his conviction of incest must be reversed based on the trial judge's instructions allegedly enlarging the indictment. The indictment charged the defendant with "[i]ncest" and alleged that the defendant, "being father of" the victim, had "carnal knowledge of the body" of the victim. The "carnal knowledge" language from the indictment directly tracks the statutory form language set out in G. L. c. 277, § 79.11 See Commonwealth v. Canty, 466 Mass. 535, 547-548, 998 N.E.2d 322 (2013) ("Indeed, the various statutory forms of indictment in G. L. c. 277, § 79, do not set forth all of the required elements for many crimes, such as larceny, but these forms contain sufficient descriptions of the crimes listed therein" [quotation omitted] );
*7Commonwealth v. Lopes, 455 Mass. 147, 168-169, 914 N.E.2d 78 (2009) (finding "no merit" to defendant's claim that trial judge erred by permitting Commonwealth to seek conviction on joint venture theory that did not appear on face of indictment and was not presented to grand jury, where indictment for murder tracked statutory form and, further, defense counsel was aware of testimony before grand jury that provided evidence supporting joint venture theory).
General Laws c. 272, § 17, punishes "[p]ersons within degrees of consanguinity within which marriages are prohibited or declared by law to be incestuous and void, who ... have sexual intercourse with each other, or who engage in sexual activities with each other, including but not limited to, oral or anal intercourse, [or] fellatio ...."12 The trial judge's instructions regarding this indictment quoted the statute and defined "sexual intercourse" for purposes of the incest statute as "natural or unnatural." The indictment sufficiently alleged incest by following the statutory form; the incest statute prohibits natural and unnatural sexual intercourse between people within specified degrees of consanguinity, and the trial judge's instructions therefore did not vary from, constructively amend, or enlarge the indictment. See Canty, 466 Mass. at 547-548, 998 N.E.2d 322 ; Lopes, 455 Mass. at 168-169, 914 N.E.2d 78.13 Accordingly, we discern no error in the defendant's conviction of incest.
4. Witness intimidation. The defendant contends that the trial judge should have allowed his motion for a required finding of not guilty on the indictment for witness intimidation, because the intimidation occurred before "any stage of a criminal investigation." G. L. c. 268, § 13B (1) (c ) (i), as appearing in St. 2006, c. 48, § 3.14 However, the evidence was *348sufficient to support the defendant's conviction on this charge. We consider "the evidence *8in the light most favorable" to the Commonwealth and determine whether "any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Commonwealth v. Bin, 480 Mass. 665, 674, 107 N.E.3d 1146 (2018), quoting Commonwealth v. Latimore, 378 Mass. 671, 677-678, 393 N.E.2d 370 (1979).
Under this familiar standard, there was sufficient evidence that the defendant's witness intimidation occurred during a stage of a criminal investigation. "[T]o convict a defendant of witness intimidation ... the Commonwealth must prove that ... a possible criminal violation occurred that would trigger a criminal investigation or proceeding ...." Commonwealth v. Fragata, 480 Mass. 121, 122, 101 N.E.3d 297 (2018). "[T]he statute's reference to a 'potential witness at any stage of a criminal investigation' indicates that the investigation need not have already begun when the intimidation occurred." Id. at 125, 101 N.E.3d 297. Therefore, a "potential witness at any stage of a criminal investigation" encompasses those "who are likely to participate in a future investigation that has not yet begun." Id. at 126, 101 N.E.3d 297.
The evidence introduced at trial demonstrated that the defendant had raped the victim, his minor daughter, forty or more times over a period of four years. Even from the first time the defendant raped the victim, when she was seven years old, he told her that if she disclosed the abuse, he would "kill me or mom and everyone, my family." The last time the defendant raped the victim -- vaginally, orally, and anally -- he said he would kill her if she told anyone; if he went to jail, he would get deported and "send people to kill [the victim and her family]. He's going to pay someone." When the victim disclosed the abuse to her mother, the victim went into her mother's bedroom, locked the door, and insisted on hiding in the closet. A rational jury could have found that the defendant's conduct of raping his daughter was more than the "possible criminal violation" Fragata requires the Commonwealth to demonstrate, and that the victim was clearly a "potential witness" who was "likely to participate in a future investigation." Fragata, 480 Mass. at 122, 125-126, 101 N.E.3d 297. Accordingly, there was sufficient evidence to convict the defendant of witness intimidation under G. L. c. 268, § 13B.
Conclusion. On the indictment charging dissemination of matter harmful to a minor, and indictment no. 2012-742-1, charging rape of a child aggravated by age difference, the judgments are reversed, the verdicts are set aside, and judgments shall enter for *9the defendant. The remaining judgments are affirmed.15
So ordered.